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github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
setup_hover_configuration.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR Discret variable por gradiente/setup_hover_configuration.m
| 1,251 |
utf_8
|
64adcf1fe19761bf7637c5f4ced7cb21
|
% SETUP_HOVER_CONFIGURATION
%
% SETUP_HOVER_CONFIGURATION sets and returns the model model parameters
% of the Quanser 3 DOF Hover plant.
%
%
% Copyright (C) 2010 Quanser Consulting Inc.
% Quanser Consulting Inc.
%
%
function [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration( )
%
% Gravitational Constant (m/s^2)
g = 9.81;
% Motor Armature Resistance (Ohm)
Rm = 0.83;
% Motor Current-Torque Constant (N.m/A)
Kt_m = 0.0182;
% Motor Rotor Moment of Inertia (kg.m^2)
Jm = 1.91e-6;
% Moving Mass of the Hover system (kg)
m_hover = 2.85;
% Mass of each Propeller Section = motor + shield + propeller + body (kg)
m_prop = m_hover / 4;
% Distance between Pivot to each Motor (m)
l = 7.75*0.0254;
% Propeller Force-Thrust Constant found Experimentally (N/V)
Kf = 0.1188;
% Propeller Torque-Thrust Constant found Experimentally (N.m/V)
Kt_prop = 0.0036;
% Normal Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktn = Kt_prop;
% Counter Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktc = -Kt_prop;
% Equivalent Moment of Inertia of each Propeller Section (kg.m^2)
Jeq_prop = Jm + m_prop*l^2;
% Equivalent Moment of Inertia about each Axis (kg.m^2)
Jp = 2*Jeq_prop;
Jy = 4*Jeq_prop;
Jr = 2*Jeq_prop;
%
% end of setup_hover_configuration()
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoGradiente.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR Discret variable por gradiente/LQRDiscretoGradiente.m
| 3,665 |
utf_8
|
13e8e428d22e76f8e2b9eae5df76100f
|
function LQRDiscretoGradiente()
clc;
clear all
%%Comentarios de este metodo
% Se confia solo un parametro la accion de ponderacion entre la K calculada
% y el Gradiente obtenido de la prediccion d ela accion.
% El dejar solo un aprmetro de ponderacion seria MENOS efectivo usar los
% parametro Q y R en el LQR que son parametro de ponderacion. Lo ideal
% seria poder calcularlos en funcion de X_actual y r_requerida
[ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
HOVER_ABCD_eqns;
%% LQR suministrado por el fabricante
Q = diag([500 350 350 0 20 20] );
R = 0.01*diag([1 1 1 1]);
% Automatically calculate the LQR controller gain
K = lqr( A, B, Q, R )
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[psi,theta,phi,psi',theta',phi']
x_k= zeros(6,1); % Este valor puede estar dado o por la integracion o por los sensores
r_k=transpose( [0,0,0,0,0,0.1]); % Referencia dada en el paso anterior
r_k1= transpose( [0,0,0,0,0,0.5]); % Referencia a donde queremos ir
At=0.01;
beta=10;% Se confia a beta la accion de ponderar la importancia del gradiente
initial_K=K; % Cojemos por ahora la K del fabricante; La inicial deberia ser la del paso anterior
initial_K = reshape(initial_K,size(initial_K,1)*size(initial_K,2),1);
[J,Grad] = FuncionCoste(A,B,At,x_k,r_k,r_k1,initial_K);
Grad=reshape(Grad,size(K));
display(J)
display(Grad)
fprintf(' Coste inicial y gradiente\n');
fprintf(' Se procedera a encontrar la K optima\n');
% pause
K_optima=reshape(initial_K,size(K)) + beta*reshape(Grad,size(K)); % Se confia a beta la accion de ponderar la importancia del gradiente
fprintf(' K optima y evolucion del coste\n');
display(K_optima)
display(K)
close all
fprintf(' Pasaremos a hacer una simulacion\n');
pause
%% Simulacion
% Intentaremos integrar con un RK3 las ecuaciones usando ambas K's
x(:,1)= zeros(6,1); % Psicion inicial
r=transpose( [0,0,0.1,0,0,0.1]); % Referencia dada en el primer paso
r_obj= transpose( [0,0,0.5,0,0,0.5]);
% K del fabricante
for j=1:20
if j>1
r=r_obj;
end
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,1)
plot(x(6,:))
hold on
plot(x(2,:),'r')
plot(x(3,:),'g')
hold off
fprintf('K discreta optima\n');
% pause
% K Opt discreta
for j=1:20
if j>1
r=r_obj;
end
K = reshape(K,size(K,1)*size(K,2),1);
[Coste,Grad] = FuncionCoste(A,B,At,x(:,j),r,r_obj,K);
K = reshape(K,4,6) + beta*reshape(Grad,4,6)
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,2)
plot(x(6,:))
hold on
plot(x(2,:),'r')
plot(x(3,:),'g')
hold off
end
function [J,Grad]=FuncionCoste(A,B,At,x_k,r_k,r_k1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )* ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 );
% Grad=-2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )*At*B* [ (x_k-r_k)'; (x_k-r_k)' ; (x_k-r_k)' ; (x_k-r_k)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = -2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )' * At*B(:,i) * (x_k-r_k)';
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
setup_hover_configuration.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto 2 steps/setup_hover_configuration.m
| 1,251 |
utf_8
|
64adcf1fe19761bf7637c5f4ced7cb21
|
% SETUP_HOVER_CONFIGURATION
%
% SETUP_HOVER_CONFIGURATION sets and returns the model model parameters
% of the Quanser 3 DOF Hover plant.
%
%
% Copyright (C) 2010 Quanser Consulting Inc.
% Quanser Consulting Inc.
%
%
function [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration( )
%
% Gravitational Constant (m/s^2)
g = 9.81;
% Motor Armature Resistance (Ohm)
Rm = 0.83;
% Motor Current-Torque Constant (N.m/A)
Kt_m = 0.0182;
% Motor Rotor Moment of Inertia (kg.m^2)
Jm = 1.91e-6;
% Moving Mass of the Hover system (kg)
m_hover = 2.85;
% Mass of each Propeller Section = motor + shield + propeller + body (kg)
m_prop = m_hover / 4;
% Distance between Pivot to each Motor (m)
l = 7.75*0.0254;
% Propeller Force-Thrust Constant found Experimentally (N/V)
Kf = 0.1188;
% Propeller Torque-Thrust Constant found Experimentally (N.m/V)
Kt_prop = 0.0036;
% Normal Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktn = Kt_prop;
% Counter Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktc = -Kt_prop;
% Equivalent Moment of Inertia of each Propeller Section (kg.m^2)
Jeq_prop = Jm + m_prop*l^2;
% Equivalent Moment of Inertia about each Axis (kg.m^2)
Jp = 2*Jeq_prop;
Jy = 4*Jeq_prop;
Jr = 2*Jeq_prop;
%
% end of setup_hover_configuration()
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoControlador.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto 2 steps/LQRDiscretoControlador.m
| 4,329 |
utf_8
|
203f1bb38ac4878e5a89eeb58398e36a
|
function LQRDiscretoControlador()
clc;
clear all
global A B
% Set the model parameters of the 3DOF HOVER.
% These parameters are used for model representation and controller design.
[ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
%
% For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% Initialization the state-Space representation of the open-loop System
HOVER_ABCD_eqns;
%% LQR suministrado por el fabricante
Q = diag([500 350 350 0 20 20] );
R = 0.01*diag([1 1 1 1]);
% Automatically calculate the LQR controller gain
K = lqr( A, B, Q, R )
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[psi,theta,phi,psi',theta',phi']
x_k_1= transpose( [0.1,0,0,0,0,0]); % Este valor puede estar dado o por la integracion o por los sensores
x_k= transpose( [0.1,0,0,0,0,0]);
r_k_1=transpose( [0.5,0,0,0,0,0]); % Referencia dada
At=0.1;
initial_K=K; % Cojemos por ahora la K del fabricante; La inicial deberia ser la del paso anterior
initial_K = reshape(initial_K,size(initial_K,1)*size(initial_K,2),1) % Para usar fmingc hay que usar un ector como parametro a optimizar
[J,Grad] = FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,initial_K);
Grad=reshape(Grad,size(K));
display(J)
display(Grad)
fprintf(' Coste inicial y gradiente\n');
fprintf(' Se procedera a encontrar la K optima\n');
% pause
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,t);
options = optimset('MaxIter', 1);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
fprintf(' K optima y evolucion del coste\n');
K_optima=reshape(K_optima,size(K));
display(K_optima)
display(K)
fprintf(' Pasaremos a hacer una simulacion\n');
pause
%% Simulacion
% Intentaremos integrar con un RK3 las ecuaciones usando ambas K's
x(:,1)= transpose( [0.1,0,0,0,0,0]); % Posicion inicial
x(:,2)= transpose( [0.1,0,0,0,0,0]);
r= transpose( [0.5,0,0,0,0,0]);
% K del fabricante
for j=1:40
% r=j/100 +0.1;
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,1)
plot(x(1,:))
hold on
% plot(x(4,:),'g')
hold off
fprintf('K discreta optima\n');
% pause
% K Opt discreta
for j=2:40
% r=j/100 + 0.1;
initial_K=K; % La primera K la cogemos del LQR normal. Hacemos la optimizacion desde la K anterior
% Se podria evitar oscilaciones de la solucion optimizando siempre
% desde una misma K_opt por ejemplo la K del LQR normal
initial_K = reshape(initial_K,size(initial_K,1)*size(initial_K,2),1);
% % % FunciondeCoste = @(t) FuncionCoste(A,B,At,x(:,j-1),x(:,j),r,t);
% % % [K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima = LQRDiscretoFUNC(At,x(:,j-1),x(:,j),r,initial_K);
K=reshape(K_optima,size(K));
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,2)
plot(x(1,:))
hold on
% plot(x(4,:),'g')
hold off
end
function [J,Grad]=FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
% Se observa que puede tener un mejor comportamiento cuando el estado
% actual (K) se desprecia y se estima a partir del antrior x_k_1
% % % % % % % x_k=( eye(6)+At*A )*x_k_1 -At*B*K*( x_k_1 - r_k_1 ); %
% Cambiar esto cuando se queira!!!!
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 ) * ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 );
% % Grad=-2*( ( eye(6)+At*A )*x_k_1 -At*B*K*(x_k_1-r_k_1) - r_k_1 )*At*B* [ (x_k_1-r_k_1)'; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = 2*( ( eye(6)+At*A )*x_k - At*B*K*( x_k - r_k_1 ) - r_k_1 )' * ( -At*B(:,i)*( x_k -r_k_1 )' - ( ( eye(6)+At*A )-At*B*K ) * At*B(:,i)* (x_k_1 -r_k_1 )' );
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoFUNC.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto 2 steps/LQRDiscretoFUNC.m
| 10,697 |
utf_8
|
bc88d145dce1b4d9ca8aca19412ff81c
|
function K_optima = LQRDiscretoFUNC(At,x_k_1,x_k,r_k_1,initial_K)
% % %
% % % % Set the model parameters of the 3DOF HOVER.
% % % % These parameters are used for model representation and controller design.
% % % [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
% % % %
% % % % For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% % % % Initialization the state-Space representation of the open-loop System
% % % HOVER_ABCD_eqns;
% % % %% LQR suministrado por el fabricante
% % % Q = diag([500 350 350 0 20 20] );
% % % R = 0.01*diag([1 1 1 1]);
% % % % Automatically calculate the LQR controller gain
% % % K = lqr( A, B, Q, R )
global A B
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[theta,theta',phi,phi',psi,psi']
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,t);
options = optimset('MaxIter', 100);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima=reshape(K_optima, 4 , 6);
end
%% Funciones usadas
function [J,Grad]=FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
x_k=( eye(6)+At*A )*x_k_1 -At*B*K*( x_k_1 - r_k_1 );
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 ) * ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 );
% % Grad=-2*( ( eye(6)+At*A )*x_k_1 -At*B*K*(x_k_1-r_k_1) - r_k_1 )*At*B* [ (x_k_1-r_k_1)'; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = 2*( ( eye(6)+At*A )*x_k - At*B*K*( x_k - r_k_1 ) - r_k_1 )' * ( -At*B(:,i)*( x_k -r_k_1 )' - ( ( eye(6)+At*A )-At*B*K ) * At*B(:,i)* (x_k_1 -r_k_1 )' );
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
%
% See also: checkgrad
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
%
%
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
%
% Permission is granted for anyone to copy, use, or modify these
% programs and accompanying documents for purposes of research or
% education, provided this copyright notice is retained, and note is
% made of any changes that have been made.
%
% These programs and documents are distributed without any warranty,
% express or implied. As the programs were written for research
% purposes only, they have not been tested to the degree that would be
% advisable in any important application. All use of these programs is
% entirely at the user's own risk.
%
% [ml-class] Changes Made:
% 1) Function name and argument specifications
% 2) Output display
%
% Read options
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
length = options.MaxIter;
else
length = 100;
end
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = ['feval(f, X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
S=['Iteration '];
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
% % fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
% % fprintf('\n');
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
setup_hover_configuration.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto 2 steps/Simulacion en Simulink/setup_hover_configuration.m
| 1,251 |
utf_8
|
64adcf1fe19761bf7637c5f4ced7cb21
|
% SETUP_HOVER_CONFIGURATION
%
% SETUP_HOVER_CONFIGURATION sets and returns the model model parameters
% of the Quanser 3 DOF Hover plant.
%
%
% Copyright (C) 2010 Quanser Consulting Inc.
% Quanser Consulting Inc.
%
%
function [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration( )
%
% Gravitational Constant (m/s^2)
g = 9.81;
% Motor Armature Resistance (Ohm)
Rm = 0.83;
% Motor Current-Torque Constant (N.m/A)
Kt_m = 0.0182;
% Motor Rotor Moment of Inertia (kg.m^2)
Jm = 1.91e-6;
% Moving Mass of the Hover system (kg)
m_hover = 2.85;
% Mass of each Propeller Section = motor + shield + propeller + body (kg)
m_prop = m_hover / 4;
% Distance between Pivot to each Motor (m)
l = 7.75*0.0254;
% Propeller Force-Thrust Constant found Experimentally (N/V)
Kf = 0.1188;
% Propeller Torque-Thrust Constant found Experimentally (N.m/V)
Kt_prop = 0.0036;
% Normal Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktn = Kt_prop;
% Counter Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktc = -Kt_prop;
% Equivalent Moment of Inertia of each Propeller Section (kg.m^2)
Jeq_prop = Jm + m_prop*l^2;
% Equivalent Moment of Inertia about each Axis (kg.m^2)
Jp = 2*Jeq_prop;
Jy = 4*Jeq_prop;
Jr = 2*Jeq_prop;
%
% end of setup_hover_configuration()
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoFUNC.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto 2 steps/Simulacion en Simulink/LQRDiscretoFUNC.m
| 10,695 |
utf_8
|
a46dd8ac4bd18ae4baf7779ffc8dfc29
|
function K_optima = LQRDiscretoFUNC(At,x_k_1,x_k,r_k_1,initial_K)
% % %
% % % % Set the model parameters of the 3DOF HOVER.
% % % % These parameters are used for model representation and controller design.
% % % [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
% % % %
% % % % For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% % % % Initialization the state-Space representation of the open-loop System
% % % HOVER_ABCD_eqns;
% % % %% LQR suministrado por el fabricante
% % % Q = diag([500 350 350 0 20 20] );
% % % R = 0.01*diag([1 1 1 1]);
% % % % Automatically calculate the LQR controller gain
% % % K = lqr( A, B, Q, R )
global A B
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[theta,theta',phi,phi',psi,psi']
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,t);
options = optimset('MaxIter', 2);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima=reshape(K_optima, 4 , 6);
end
%% Funciones usadas
function [J,Grad]=FuncionCoste(A,B,At,x_k_1,x_k,r_k_1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
x_k=( eye(6)+At*A )*x_k_1 -At*B*K*( x_k_1 - r_k_1 );
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 ) * ( ( eye(6)+At*A )*x_k -At*B*K*( x_k - r_k_1 ) -r_k_1 );
% % Grad=-2*( ( eye(6)+At*A )*x_k_1 -At*B*K*(x_k_1-r_k_1) - r_k_1 )*At*B* [ (x_k_1-r_k_1)'; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ; (x_k_1-r_k_1)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = 2*( ( eye(6)+At*A )*x_k - At*B*K*( x_k - r_k_1 ) - r_k_1 )' * ( -At*B(:,i)*( x_k -r_k_1 )' - ( ( eye(6)+At*A )-At*B*K ) * At*B(:,i)* (x_k_1 -r_k_1 )' );
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
%
% See also: checkgrad
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
%
%
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
%
% Permission is granted for anyone to copy, use, or modify these
% programs and accompanying documents for purposes of research or
% education, provided this copyright notice is retained, and note is
% made of any changes that have been made.
%
% These programs and documents are distributed without any warranty,
% express or implied. As the programs were written for research
% purposes only, they have not been tested to the degree that would be
% advisable in any important application. All use of these programs is
% entirely at the user's own risk.
%
% [ml-class] Changes Made:
% 1) Function name and argument specifications
% 2) Output display
%
% Read options
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
length = options.MaxIter;
else
length = 100;
end
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = ['feval(f, X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
S=['Iteration '];
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
% % fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
% % fprintf('\n');
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
setup_hover_configuration.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto/setup_hover_configuration.m
| 1,251 |
utf_8
|
64adcf1fe19761bf7637c5f4ced7cb21
|
% SETUP_HOVER_CONFIGURATION
%
% SETUP_HOVER_CONFIGURATION sets and returns the model model parameters
% of the Quanser 3 DOF Hover plant.
%
%
% Copyright (C) 2010 Quanser Consulting Inc.
% Quanser Consulting Inc.
%
%
function [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration( )
%
% Gravitational Constant (m/s^2)
g = 9.81;
% Motor Armature Resistance (Ohm)
Rm = 0.83;
% Motor Current-Torque Constant (N.m/A)
Kt_m = 0.0182;
% Motor Rotor Moment of Inertia (kg.m^2)
Jm = 1.91e-6;
% Moving Mass of the Hover system (kg)
m_hover = 2.85;
% Mass of each Propeller Section = motor + shield + propeller + body (kg)
m_prop = m_hover / 4;
% Distance between Pivot to each Motor (m)
l = 7.75*0.0254;
% Propeller Force-Thrust Constant found Experimentally (N/V)
Kf = 0.1188;
% Propeller Torque-Thrust Constant found Experimentally (N.m/V)
Kt_prop = 0.0036;
% Normal Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktn = Kt_prop;
% Counter Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktc = -Kt_prop;
% Equivalent Moment of Inertia of each Propeller Section (kg.m^2)
Jeq_prop = Jm + m_prop*l^2;
% Equivalent Moment of Inertia about each Axis (kg.m^2)
Jp = 2*Jeq_prop;
Jy = 4*Jeq_prop;
Jr = 2*Jeq_prop;
%
% end of setup_hover_configuration()
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoControlador.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto/LQRDiscretoControlador.m
| 4,041 |
utf_8
|
49fa6e6fb5a7ffd6b252d4f1727b2792
|
function LQRDiscretoControlador()
clc;
clear all
global A B
% Set the model parameters of the 3DOF HOVER.
% These parameters are used for model representation and controller design.
[ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
%
% For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% Initialization the state-Space representation of the open-loop System
HOVER_ABCD_eqns;
%% LQR suministrado por el fabricante
Q = diag([500 350 350 0 20 20] );
R = 0.01*diag([1 1 1 1]);
% Automatically calculate the LQR controller gain
K = lqr( A, B, Q, R )
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[psi,theta,phi,psi',theta',phi']
x_k= zeros(6,1); % Este valor puede estar dado o por la integracion o por los sensores
r_k=transpose( [0,0,0,0.1,0,0]); % Referencia dada en el paso anterior
r_k1= transpose( [0,0,0,0.5,0,0]); % Referencia a donde queremos ir
At=0.01;
initial_K=K; % Cojemos por ahora la K del fabricante; La inicial deberia ser la del paso anterior
initial_K = reshape(initial_K,size(initial_K,1)*size(initial_K,2),1) % Para usar fmingc hay que usar un ector como parametro a optimizar
[J,Grad] = FuncionCoste(A,B,At,x_k,r_k,r_k1,initial_K);
Grad=reshape(Grad,size(K));
display(J)
display(Grad)
fprintf(' Coste inicial y gradiente\n');
fprintf(' Se procedera a encontrar la K optima\n');
% pause
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k,r_k,r_k1,t);
options = optimset('MaxIter', 100);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
fprintf(' K optima y evolucion del coste\n');
K_optima=reshape(K_optima,size(K));
display(K_optima)
display(K)
plot(Coste)
close all
fprintf(' Pasaremos a hacer una simulacion\n');
pause
%% Simulacion
% Intentaremos integrar con un RK3 las ecuaciones usando ambas K's
x(:,1)= transpose( [0,0,0,0,0.1,0]); % Posicion inicial
r=transpose( [0,0,0,0,0.1,0]); % Referencia dada en el primer paso
r_obj= transpose( [0,0,0,0,0.5,0]);
% K del fabricante
for j=1:20
if j>1
r=r_obj;
end
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,1)
plot(x(2,:))
hold on
plot(x(5,:),'g')
hold off
fprintf('K discreta optima\n');
% pause
% K Opt discreta
for j=1:20
if j>1
r=r_obj;
end
initial_K=K; % La primera K la cogemos del LQR normal. Hacemos la optimizacion desde la K anterior
% Se podria evitar oscilaciones de la solucion optimizando siempre
% desde una misma K_opt por ejemplo la K del LQR normal
initial_K = reshape(initial_K,size(initial_K,1)*size(initial_K,2),1);
% % % % % % FunciondeCoste = @(t) FuncionCoste(A,B,At,x(:,j),r,r_obj,t);
% % % % % % [K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima = LQRDiscretoFUNC(At,x(:,j),r,r_obj,initial_K);
K=reshape(K_optima,size(K));
k1=A*x(:,j) - B*K*(x(:,j)-r);
k2=A*( x(:,j) + At*k1/2) - B*K*( x(:,j) + At*k1/2 -r);
k3=A*( x(:,j) + At*(2*k1-k1) ) - B*K*( x(:,j) + At*(2*k1-k1) -r);
x(:,j+1) = x(:,j) +At/6*( k1+4*k2 + k3 );
end
subplot(2,1,2)
plot(x(2,:))
hold on
plot(x(5,:),'g')
hold off
end
function [J,Grad]=FuncionCoste(A,B,At,x_k,r_k,r_k1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )* ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 );
% Grad=-2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )*At*B* [ (x_k-r_k)'; (x_k-r_k)' ; (x_k-r_k)' ; (x_k-r_k)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = -2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )' * At*B(:,i) * (x_k-r_k)';
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoFUNC.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto/LQRDiscretoFUNC.m
| 10,486 |
utf_8
|
14e8eecb2067901be5d86b60fb4332e7
|
function K_optima = LQRDiscretoFUNC(At,x_k,r_k,r_k1,initial_K)
% % %
% % % % Set the model parameters of the 3DOF HOVER.
% % % % These parameters are used for model representation and controller design.
% % % [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
% % % %
% % % % For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% % % % Initialization the state-Space representation of the open-loop System
% % % HOVER_ABCD_eqns;
% % % %% LQR suministrado por el fabricante
% % % Q = diag([500 350 350 0 20 20] );
% % % R = 0.01*diag([1 1 1 1]);
% % % % Automatically calculate the LQR controller gain
% % % K = lqr( A, B, Q, R )
global A B
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[theta,theta',phi,phi',psi,psi']
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k,r_k,r_k1,t);
options = optimset('MaxIter', 100);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima=reshape(K_optima, 4 , 6);
end
%% Funciones usadas
function [J,Grad]=FuncionCoste(A,B,At,x_k,r_k,r_k1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )* ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 );
% Grad=-2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )*At*B* [ (x_k-r_k)'; (x_k-r_k)' ; (x_k-r_k)' ; (x_k-r_k)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = -2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )' * At*B(:,i) * (x_k-r_k)';
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
%
% See also: checkgrad
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
%
%
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
%
% Permission is granted for anyone to copy, use, or modify these
% programs and accompanying documents for purposes of research or
% education, provided this copyright notice is retained, and note is
% made of any changes that have been made.
%
% These programs and documents are distributed without any warranty,
% express or implied. As the programs were written for research
% purposes only, they have not been tested to the degree that would be
% advisable in any important application. All use of these programs is
% entirely at the user's own risk.
%
% [ml-class] Changes Made:
% 1) Function name and argument specifications
% 2) Output display
%
% Read options
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
length = options.MaxIter;
else
length = 100;
end
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = ['feval(f, X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
S=['Iteration '];
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
fprintf('\n');
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
setup_hover_configuration.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto/Simulacion en Simulink/setup_hover_configuration.m
| 1,251 |
utf_8
|
64adcf1fe19761bf7637c5f4ced7cb21
|
% SETUP_HOVER_CONFIGURATION
%
% SETUP_HOVER_CONFIGURATION sets and returns the model model parameters
% of the Quanser 3 DOF Hover plant.
%
%
% Copyright (C) 2010 Quanser Consulting Inc.
% Quanser Consulting Inc.
%
%
function [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration( )
%
% Gravitational Constant (m/s^2)
g = 9.81;
% Motor Armature Resistance (Ohm)
Rm = 0.83;
% Motor Current-Torque Constant (N.m/A)
Kt_m = 0.0182;
% Motor Rotor Moment of Inertia (kg.m^2)
Jm = 1.91e-6;
% Moving Mass of the Hover system (kg)
m_hover = 2.85;
% Mass of each Propeller Section = motor + shield + propeller + body (kg)
m_prop = m_hover / 4;
% Distance between Pivot to each Motor (m)
l = 7.75*0.0254;
% Propeller Force-Thrust Constant found Experimentally (N/V)
Kf = 0.1188;
% Propeller Torque-Thrust Constant found Experimentally (N.m/V)
Kt_prop = 0.0036;
% Normal Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktn = Kt_prop;
% Counter Rotation Propeller Torque-Thrust Constant (N.m/V)
Ktc = -Kt_prop;
% Equivalent Moment of Inertia of each Propeller Section (kg.m^2)
Jeq_prop = Jm + m_prop*l^2;
% Equivalent Moment of Inertia about each Axis (kg.m^2)
Jp = 2*Jeq_prop;
Jy = 4*Jeq_prop;
Jr = 2*Jeq_prop;
%
% end of setup_hover_configuration()
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
LQRDiscretoFUNC.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/docs/Control Theory/Proporcional (LQR) predictivo/LQR optimo Discreto/Simulacion en Simulink/LQRDiscretoFUNC.m
| 10,481 |
utf_8
|
eb775de51e9fce3be563ab62100dda8d
|
function K_optima = LQRDiscretoFUNC(At,x_k,r_k,r_k1,initial_K)
% % %
% % % % Set the model parameters of the 3DOF HOVER.
% % % % These parameters are used for model representation and controller design.
% % % [ Ktn, Ktc, Kf, l, Jy, Jp, Jr, g ] = setup_hover_configuration();
% % % %
% % % % For the following state vector: X = [ theta; psi; theta_dot; psi_dot]
% % % % Initialization the state-Space representation of the open-loop System
% % % HOVER_ABCD_eqns;
% % % %% LQR suministrado por el fabricante
% % % Q = diag([500 350 350 0 20 20] );
% % % R = 0.01*diag([1 1 1 1]);
% % % % Automatically calculate the LQR controller gain
% % % K = lqr( A, B, Q, R )
global A B
%% LQR calculado optimizando coste de forma discreta
% Definimos el vector de estado x =[theta,theta',phi,phi',psi,psi']
FunciondeCoste = @(t) FuncionCoste(A,B,At,x_k,r_k,r_k1,t);
options = optimset('MaxIter', 100);
[K_optima, Coste] = fmincg(FunciondeCoste, initial_K, options);
K_optima=reshape(K_optima, 4 , 6);
end
%% Funciones usadas
function [J,Grad]=FuncionCoste(A,B,At,x_k,r_k,r_k1,K)
K=reshape(K, 4 , 6); % CUIDADO CON ESTO!!!! Cuando se cambien las dimesiones de los vectores
J= transpose ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )* ( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 );
% Grad=-2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )*At*B* [ (x_k-r_k)'; (x_k-r_k)' ; (x_k-r_k)' ; (x_k-r_k)' ] ;
for i=1:size(B,2)
Grad ( i, : ) = -2*( ( eye(6)+At*A )*x_k -At*B*K*(x_k-r_k) - r_k1 )' * At*B(:,i) * (x_k-r_k)';
end
Grad = reshape(Grad,size(Grad,1)*size(Grad,2),1); % Para usar fmingc hay que usar un vector como gradiente tambien
end
function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5)
%
% See also: checkgrad
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
%
%
% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen
%
% Permission is granted for anyone to copy, use, or modify these
% programs and accompanying documents for purposes of research or
% education, provided this copyright notice is retained, and note is
% made of any changes that have been made.
%
% These programs and documents are distributed without any warranty,
% express or implied. As the programs were written for research
% purposes only, they have not been tested to the degree that would be
% advisable in any important application. All use of these programs is
% entirely at the user's own risk.
%
% [ml-class] Changes Made:
% 1) Function name and argument specifications
% 2) Output display
%
% Read options
if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter')
length = options.MaxIter;
else
length = 100;
end
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = ['feval(f, X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
S=['Iteration '];
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
% fprintf('%s %4i | Cost: %4.6e\r', S, i, f1);
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
% fprintf('\n');
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
vview.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/lib/qcat1_2_1/QCAT/qcat/vview.m
| 6,443 |
utf_8
|
b3958410b2ea29230fa8cc7d5831170e
|
function ratio = vview(B,plim,P)
% VVIEW - View the attainable virtual control set.
%
% 1) vview(B,plim)
%
% Shows the attainable virtual control set considering actuator
% position constraints, given by { v : v = B*u, umin < u < umax }.
%
% 2) ratio = vview(B,plim,P)
%
% Compares the set of feasible virtual control inputs when
%
% a) the actuator redundancy is fully utilized (as above) [blue]
% b) a linear allocation control law u = Pv is used (BP = I) [red]
%
% The second set is given by { v : umin < P*v < umax }.
%
% Inputs:
% -------
% B control effectiveness matrix (k x m)
% plim control position limits [min max] (m x 2)
% P virtual control law matrix (m x k)
%
% Outputs:
% --------
% ratio The ratio between the sizes (areas, volumes, ...)
% of the two sets
%
% The result is only graphically illustrated for k = 1, 2, or 3.
%
% See also: VVIEW_DEMO
% Model dimensions
[k,m] = size(B);
% ------------------------------------------------
% a) Find maximum attainable virtual control set
% considering constraints.
% ------------------------------------------------
% Generate matrix to index corners of feasible control set.
idx = zeros(2^m,m);
M = 1:m;
for i = 1:2^m;
cbin = dec2bin(i-1,m); % '001'
c = str2num(cbin')'; % [0 0 1]
c = c(end:-1:1); % [1 0 0]
idx(i,:) = 2*M - c;
end
% Generate corner points of the feasible control set.
plimT = plim';
U = plimT(idx)';
% Compute the corresponding points in the virtual control space
V = B*U;
if nargin > 2
% ---------------------------------------------
% b) Find attainable virtual control set when
% a linear control law u=Pv is used.
% ---------------------------------------------
% We want to determine where the k-dim. hyperplane Pv
% intersects the m-dim. hyperbox of feasible controls.
% To get the corner points of this set, solve
% Pv = x where x has k specified entries.
%
% Example: m=3, k=1 -> points will lie on surfaces
% m=3, k=2 -> points will lie on edges
% Generate index matrix for all combinations of min and max indeces
% in k dimensions.
sub_idx = idx(1:2^k,1:k);
Ulin = [];
% Loop over all combinations of dimensions
i_dim = nchoosek(1:m,k);
for i = 1:size(i_dim,1)
% For each combination, compute the intersections with all
% possible min/max combinations.
% k-dimensional min/max combinations
sub_plimT = plimT(:,i_dim(i,:));
sub_u_boundary = sub_plimT(sub_idx)';
% Determine which virtual control sub_u_boundary corresponds to
sub_P = P(i_dim(i,:),:);
if rank(sub_P) == k % Avoid "parallel" cases
% Solve sub_u_boundary = sub_P v for v
v = sub_P\sub_u_boundary;
% Determine the full countol vector (contains sub_u_boundary)
u_boundary = P*v;
% Store feasible points
i_feas = feasible(u_boundary,plim);
Ulin = [Ulin u_boundary(:,i_feas)];
end
end
% Compute the corresponing points in the virtual control space
Vlin = B*Ulin;
end
% Compute and visualize the convex hull of the set(s)
clf
switch k
case 1
K = [min(V) max(V)];
if nargin > 2
Klin = [min(Vlin) max(Vlin)];
ratio = diff(Klin)/diff(K);
% Illustrate
plot(K,[0 0],'b-o',Klin,-[0 0],'r-o')
else
plot(K,[0 0],'b-o')
end
xlabel('v')
case 2
[K,area1] = convhull(V(1,:),V(2,:));
if nargin > 2
[Klin,area2] = convhull(Vlin(1,:),Vlin(2,:));
ratio = area2/area1;
% Illustrate
fill(V(1,K),V(2,K),[.95 .95 1],...
Vlin(1,Klin),Vlin(2,Klin),[1 1 .9])
hold on;
plot(Vlin(1,Klin),Vlin(2,Klin),'r',V(1,K),V(2,K),'b')
hold off;
else
fill(V(1,K),V(2,K),[.95 .95 1]);
hold on;
plot(V(1,K),V(2,K),'b')
hold off;
end
axis equal;
xlabel('v_1')
ylabel('v_2')
otherwise
[K,vol1] = convhulln(V');
if nargin > 2
[Klin,vol2] = convhulln(Vlin');
ratio = vol2/vol1;
end
if k == 3
% Illustrate
if nargin > 2
% h = polyplot(Klin,Vlin',1);
% set(h,'EdgeColor','r','FaceColor',[1 1 .9]);
hold on;
% Fix: Make V wireframe enclose Vlin
V0 = repmat(mean(V')',1,size(V,2));
V = 1.0001*(V-V0)+V0;
h = polyplot(K,V',1);
set(h,'EdgeColor','b','FaceColor',[.95 .95 1]);
alpha(0.4)
hold off
else
h = polyplot(K,V',1);
set(h,'EdgeColor','b','FaceColor',[.95 .95 1]);
end
xlabel('v_1')
ylabel('v_2')
zlabel('v_3')
view(3);
axis equal;
axis vis3d;
grid on;
end
end
function f = feasible(x,plim)
% x m*n
% lb m
% ub m
m = size(x,1);
% Mean point
x0 = mean(plim,2);
% Make the mean point the origin
x = x - x0*ones(1,size(x,2));
lb = plim(:,1) - x0; % < 0
ub = plim(:,2) - x0; % > 0
% Check for feasibility
tol = 1e-5;
f = sum((diag(1./ub)*x <= 1+tol) & (diag(1./lb)*x <= 1+tol)) == m;
function h = polyplot(face,vert,merge)
if merge
% Merge adjacent, parallel triangles to get fewer lines that
% are not edges of the polyhedron.
face4 = [];
% Loop over all combinations of triangles
k = 1;
while k < size(face,1)
l = k+1;
while l <= size(face,1)
iv = intersect(face(k,:),face(l,:)); % Intersecting vertices
if length(iv) == 2 % Two common vertices
% Are the faces parallel?
niv = setxor(face(k,:),face(l,:)); % Non-intersecting vertices
% Vectors from first common vertex to remaining three vertices
A = [vert(iv(2),:) - vert(iv(1),:);
vert(niv(1),:) - vert(iv(1),:);
vert(niv(2),:) - vert(iv(1),:)];
if abs(det(A))<100*eps
% Vectors lie in same plane -> create patch with four vertices
face4 = [face4 ; iv(1) niv(1) iv(2) niv(2)];
% ... and remove the two triangles
face = face([1:k-1 k+1:l-1 l+1:end],:);
k = k-1;
break
end
end
l = l+1;
end % inner loop
k = k+1;
end % outer loop
h = [patch('Faces',face,'Vertices',vert)
patch('Faces',face4,'Vertices',vert)];
else
% Just plot the polyhedron made up by triangles
h = patch('Faces',face,'Vertices',vert);
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
ip_alloc.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/lib/qcat1_2_1/QCAT/qcat/ip_alloc.m
| 5,473 |
utf_8
|
ad58dd244a7a2785cbffb745e1ffba9b
|
function [u,iter] = ip_alloc(B,v,umin,umax,ud,gam,tol,imax)
% IP_ALLOC - Control allocation using interior point method.
%
% [u,iter] = ip_alloc(B,v,umin,umax,[ud,gamma,tol,imax])
%
% Solves the weighted, bounded least-squares problem
%
% min ||u-ud||^2 + gamma ||Bu-v||^2 (unit weighting matrices)
%
% subj. to umin <= u <= umax
%
% using a primal dual interior point method.
%
% Inputs:
% -------
% B control effectiveness matrix (k x m)
% v commanded virtual control (k x 1)
% umin lower position limits (m x 1)
% umax upper position limits (m x 1)
% ud desired control (m x 1) [0]
% gamma weight (scalar) [1e4]
% tol tolerance used in stopping criterion [1e-4]
% imax max no. of iterations [100]
%
% Outputs:
% -------
% u optimal control
% iter no. of iterations
%
% See also: WLS_ALLOC, WLSC_ALLOC, FXP_ALLOC, QP_SIM.
%
% Contributed by John Petersen.
% Set default values of optional arguments
if nargin < 8
imax = 100; % Heuristic value
[k,m] = size(B);
if nargin < 7, tol = 1e-4; end
if nargin < 6, gam = 1e4; end
if nargin < 5, ud = zeros(m,1); end
end
% Reformulate min ||u-ud||^2 + gamma ||Bu-v||^2
% s.t. umin <= u <= umax
%
% as min ||Ax-b||^2 + h ||x-xd||^2
% s.t. 0 <= x <= xmax
%
% where x=u-umin, h=1/gamma, A=B, b=v-B*umin, xd=ud-umin, xmax=umax-umin
h = 1/gam; A = B; b = v - B*umin; xd = ud - umin; xmax = umax - umin;
% ||Ax-b||^2 + h ||x-xd||^2 = 1/2x'Hx + c'x + f(xd)
c = -2*(b'*A + h*xd');
% Solve QP problem.
[x,iter] = pdq(A,b,c',xmax,h,tol,imax);
% Optimal control.
u = x + umin;
function [x,iter] = pdq(A,b,c,u,wc,tol,imax);
% Primal dual IP solver
[k,m] = size(A); % k = #constraints , m = #variables
As2=A*sqrt(2);
[s,w,x,z] = startpt(A,b,c,u,wc);
rho = .9995; sig = 0.1; m2 = 2*m;
xs = x.*s; wz = w.*z;
mu = sig*(sum(xs + wz))/m2; % eq. (7)
nxl=norm(x,1); iHd = 0;
ru = 0; rc = 0; rb = 0;
for iter = 1:imax+1
if (mu < tol)
% Close enough to optimum, bail out.
break;
end;
rxs = (xs - mu);
iw = 1./w; rwz = (wz - mu);
ix = 1./x; ixs = ix.*s;
iwz = iw.*z;
d = 2*wc + ixs + iwz;
[ds,dw,dx,dz] = direct(d,As2,rb,rc,ru,rxs,rwz,ix,iw,ixs,iwz,z);
alpha = stepsize(dx,ds,dw,dz,x,s,w,z);
ralpha = rho*alpha;
s = s + ralpha*ds;
w = w + ralpha*dw;
x = x + ralpha*dx;
z = z + ralpha*dz;
xs = x.*s; wz = w.*z;
gap = sum(xs + wz)/m2;
mu = min(.1,100*gap)*gap;
end
iter=iter-1; %True number of iterations is one less
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initial starting point
function [s,w,x,z] = startpt(A,b,c,u,wc);
m = size(A,2);
en = ones(m,1);
% Start at the center of the constraint box
x = u/2; w = u - x; z = en; s = en;
if 0
AA = csm(A'); % csm efficiently computes cb'*cb
for i=1:m
AA(i,i) = AA(i,i) + wc;
end % H = 2(A'A+wcI);
else
AA = A'*A + wc*eye(m);
end
ec = c + 2*AA*x; %initial residual error used to initialize z,s;
g = .1; sg = 1+g;
i = find(ec>0); s(i) = sg*ec(i); z(i) = g*ec(i); % Hx + c + z - s = 0;
i = find(ec<0); z(i) = -sg*ec(i); s(i) = -g*ec(i);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Compute step direction
function [ds,dw,dx,dz] = direct(d,As2,rb,rc,ru,rxs,rwz,ix,iw,ixs,iwz,z);
ixrxs = ix.*rxs; iwrwz = iw.*rwz;
rr = iwrwz - ixrxs;
if 0
iHd = smwf(d,As2); % smwf is a fast smw for the specific form used here
dx = iHd*rr;
else
% iHd = inv(diag(d)+As2'*As2);
dx = (diag(d)+As2'*As2)\rr;
end
ds = -ixs.*dx - ixrxs; dw = -dx;
dz = -iwz.*dw - iwrwz;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Compute stepsize
function alpha = stepsize(dx,ds,dw,dz,x,s,w,z);
i = find(ds<0); as = min(-s(i)./ds(i));
i = find(dw<0); aw = min(-w(i)./dw(i));
i = find(dx<0); ax = min(-x(i)./dx(i));
i = find(dz<0); az = min(-z(i)./dz(i));
alpha = min([aw ax as az 1]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% csm.m compute symmetric matrix from X = B*B'
function X = csm(B);
[m,n] = size(B);
for i=1:m-1
for j=i+1:m
X(i,j) = B(i,:)*B(j,:)';
X(j,i) = X(i,j);
end;
end;
for i = 1:m; X(i,i) = B(i,:)*B(i,:)'; end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% smwf.m computes the inverse of (A + B'B) using Sherman-Morrison-Woodbury formula
% Fast version for specific matrices.
% where A is a diagonal matrix, but designated only by a vector
% i.e. the input is the vector of the diagonal
% B is non-square matrices
% H = inv(A) - inv(A)B'*inv(B*inv(A)B' + I)*B*inv(A);
%
function H = smwf(A,B);
[k,m] = size(B);
iA = 1./A; iAB = zeros(m,k); BiA = zeros(k,m); BAB = zeros(k);
for i = 1:k iAB(:,i) = iA.*B(i,:)'; end;
for i = 1:k BiA(i,:) = B(i,:).*iA'; end;
for i=1:k-1
for j=i+1:k
BAB(i,j) = B(i,:)*iAB(:,j);
BAB(j,i) = BAB(i,j);
end;
end;
for i = 1:k; BAB(i,i) = B(i,:)*iAB(:,i); end;
Q = BAB;
for i = 1:k; Q(i,i) = Q(i,i) + 1; end
QBA = Q\iAB';
for i=1:m-1
for j=i+1:m
ABQBA(i,j) = iAB(i,:)*QBA(:,j);
ABQBA(j,i) = ABQBA(i,j);
end;
end;
for i = 1:m; ABQBA(i,i) = iAB(i,:)*QBA(:,i); end
H = -ABQBA;
for i = 1:m
H(i,i) = iA(i) + H(i,i);
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
Control_GUI.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design ACC/Control_GUI.m
| 37,417 |
utf_8
|
385e097e99302c6cc85b41c7f39c5a64
|
function Control_GUI
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('UI for faults and damages at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('Toolbar','none',...
'MenuBar','none',...
'IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('UI for faults and damages at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
global oversize_param
oversize_param=0;
Main = uipanel('Parent',hf,'Title','Main Panel','FontSize',20,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 -oversize_param 0.95 1+oversize_param]);
uicontrol('Style','Slider','Parent',hf,... % Slider
'Units','normalized','Position',[0.97 0 0.03 1],...
'Value',1,'Callback',{@slider_callback1,Main});
uicontrol('Parent',Main,...
'Style','text','FontSize',16,...
'Units','normalized',...
'Position',[0 1-0.06 0.95 0.05],...
'String','This GUI allows the user to inputs faults, changes in control surfaces and airframe, as well as, control the learning proces of ANNs',...
'Backgroundcolor',[1 1 1]);
%% Control surfaces
panel_control = uipanel('Parent',Main,'Title','Control surfaces','FontSize',12, 'Units','normalized','Position',[.02 .25 .45 .7]);
% Blockades
panel_control_blockades = uipanel('Parent',panel_control,'Title','Blockades','FontSize',10, 'Units','normalized','Position',[.05 .5 .9 .49]);
string={'Elev_L','Elev_R','Ail_L','Ail_R','Rudd','LEF_L','LEF_R'};
panel_control_blockades_at = uipanel('Parent',panel_control_blockades,'Title','Blockade at:','FontSize',10, 'Units','normalized','Position',[.01 .4 .98 .55]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_at,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_blockades_at,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7,0.3]);
uicontrol('Parent',panel_control_blockades_at,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Block','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Blockat_CurrentValue_Callback,Val_h{i},i}) ;
end
panel_control_blockades_now = uipanel('Parent',panel_control_blockades,'Title','Blockade NOW','FontSize',10,'Units','normalized','Position',[.01 .02 .98 .36]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_now,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_blockades_now,'Style','togglebutton','Tag',['Block_now',num2str(i)],'String','Block now','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Blocknow_CurrentValue_Callback,i}) ;
end
% Floating or loss
panel_control_Float = uipanel('Parent',panel_control,'Title','Floating or loss','FontSize',10,'Units','normalized','Position',[.05 .30 .9 .17]);
for i=1:7
uicontrol('Parent',panel_control_Float,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_Float,'Style','togglebutton','Tag',['Float',num2str(i)],'String','Lose or float','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Float_loss_Callback,i}) ;
end
% Lose effectivenes or surface
panel_control_Area = uipanel('Parent',panel_control,'Title','Loss effectiveness or Surface: Input % lost','FontSize',10,'Units','normalized','Position',[.05 .02 .9 .27]);
for i=1:7
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7-0.02,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_Area,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7-0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/7*(i)-0.03,0.4,0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Affect','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Loss_area_Callback,Val_h{i},i}) ;
end
%% Structural changes
panel_control2 = uipanel('Parent',Main,'Title','Airframe and global changes','FontSize',12,'Units','normalized','Position',[.5 .25 .48 .7]);
panel_control_massprop = uipanel('Parent',panel_control2,'Title','Mass properties changes','FontSize',10,...
'Units','normalized','Position',[.05 .57 .9 .4]);
Val_h={};
% mass and xcg
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta mass(%) of 9295.4kg','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{1}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','x_cg position in% of CMA(0.3%)','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{2}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0.3','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
% Moments of inertia
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_y(%) of 75673.6kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{3}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_xz(%) of 1331.4kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{4}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_z(%) of 85552.1kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{5}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=4;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_x(%) of 12874.8kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{6}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
panel_control_AeroAndArea = uipanel('Parent',panel_control2,'Title','Aerodynamics and surfaces changes','FontSize',10,...
'Units','normalized','Position',[.05 .17 .9 .4]);
% Surface changes
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Left wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{7}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Right wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{8}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Fin surface loss(%) of 6.56m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{9}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
% DElta coeffs
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Lift (additionally to ~0.2)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{10}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Drag (additionally to ~0.036)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{11}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_pitch_moment (additionally to ~ - 0.054)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{12}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control2,'String','Update Changes','FontSize',16,'Units','normalized',...
'Position',[0.65 0.02 0.3 0.13],'Callback',{@Surf_and_Mass_changes,Val_h});
%% ANN control
panel_controlANN = uipanel('Parent',Main,'Title','ANNs control','FontSize',12,'Units','normalized','Position',[.02 .02 .96 .22]);
% Roll
panel_control_Roll = uipanel('Parent',panel_controlANN,'Title','Roll chanel','FontSize',12,...
'Units','normalized','Position',[.01 .02 .98/4-0.01 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','down'}});
% Long chanel
panel_control_Long = uipanel('Parent',panel_controlANN,'Title','Long chanel','FontSize',12,...
'Units','normalized','Position',[0.98/4+0.005 .02 .98/4-0.005 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_learn','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_reg','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_reg','down'}});
% Yaw chanel
panel_control_Yaw = uipanel('Parent',panel_controlANN,'Title','Yaw chanel chanel','FontSize',12,...
'Units','normalized','Position',[2*.98/4+0.005 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','down'}});
% Complete ANN
panel_control_Com = uipanel('Parent',panel_controlANN,'Title','Complete ANN','FontSize',12,...
'Units','normalized','Position',[3*.98/4+0.01 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'C_learn','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'C_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'C_reg','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'C_reg','down'}});
function Change_params(hObject, eventdata,handles)
MDL = 'F16ASYM_Controlled';
Str_to_change= findall(get(hObject,'parent'),'Tag',handles{1});
switch handles{1}
% Roll
case {'Roll_learn'}
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Roll_reg'}
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Long
case {'Long_learn'}
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Long_reg'}
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Yaw
case {'Yaw_learn'}
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Yaw_reg'}
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Completed
case {'C_learn'}
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'C_reg'}
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
end
function Surf_and_Mass_changes(hObject, eventdata,handles)
% Data from mdl
MDL = 'F16ASYM_Controlled';
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch str{i}
case {'delta_mass'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
case {'xcg'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=3:6
NewStrVal = get(handles{i}, 'String');
Actual_val(i-2) = str2double(NewStrVal)/100;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% 'delta_S_L','delta_S_R','delta_S_fin'
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=10:12
NewStrVal = get(handles{i}, 'String');
Actual_val(i-9) = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Loss_area_Callback(hObject, eventdata,handles, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = 1-str2double(NewStrVal)/100;
set(hObject,'String','Affected');
set(Elem,'Visible','off')
else
Actual_val(1,num) = 1;
set(hObject,'String','Affect');
set(Elem,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Float_loss_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Block_at',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 0;
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 1;
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blockat_CurrentValue_Callback(hObject, eventdata, handles,num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = str2double(NewStrVal);
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = NaN;
set(hObject,'String','Block');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blocknow_CurrentValue_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_at',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 1;
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 0;
set(hObject,'String','Block now');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function slider_callback1(hObject, eventdata, handles)
global oversize_param
val = get(hObject,'Value');
set(handles,'Position',[0.02 -oversize_param*val 0.95 1+oversize_param])
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
MDL = 'F16ASYM_Controlled';
% Reseting effectiveness
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)),']']);
% Blockades at
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)*NaN),']']);
% Blockades now
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
set_param(char(Block_search),'Value',['[',num2str(zeros(1,7)),']']);
% Airframe parameters
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
Actual_val=[];
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
switch str{i}
case {'delta_mass'}
Actual_val = 0;
case {'xcg'}
Actual_val = 0.3;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% 'delta_S_L','delta_S_R','delta_S_fin'
Actual_val=[];
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = 0;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
for i=3:6
Actual_val(i-2) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
for i=10:12
Actual_val(i-9) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
delete(hObject)
% close all Force
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
FE_plot.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design ACC/FE_plot.m
| 2,767 |
utf_8
|
33f67ce7964a466b12f76d5a8029b6ce
|
function FE_plot
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
Main = uipanel('Parent',hf,'Title','Flight Envelope plot','FontSize',15,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 0.02 0.95 0.95]);
% Plots and axis
global hplot htext hlist
AX=axes('Parent',Main,'Units','normalized ','Position',[0.1 0.1 0.85 0.85]);
load('FlightEnvelope.mat')
plot(AX,F_envelope.M_1g ,F_envelope.H_1g ,'r')
xlabel(AX,'Mach')
ylabel(AX,'Alt (m)')
% PLot th epoint
hold(AX)
hplot=scatter(AX,0,0,'o','filled');
hChildren = get(hplot, 'Children');
set(hChildren, 'Markersize', 10)
htext = text(0,0,[' YOU ';'\downarrow'],'HorizontalAlignment','Center','VerticalAlignment','Bottom','FontSize',18,'Parent', AX);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add Listener
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Block_search = [MDL,'/Environment params Estimations/ALT_and_M_GAIN_LIST'];
hlist = add_exec_event_listener(Block_search, 'PostOutputs', @localEventListener);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
global hplot hlist
try
delete(hlist)
delete(hObject)
catch
close all Force
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
tgear.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design ACC/Used Functions/tgear.m
| 535 |
utf_8
|
f0c3d6ed53bf5e044ed13e3251d92c3b
|
%=====================================================
% tgear.m
%
% Author : Ying Huo
%
% power command vs. thtl. relationship used
% in F-16 model
%=====================================================
function tgear_value = tgear ( thtl )
if ( thtl <= 0.77 )
tgear_value = 64.94 * thtl;
else
tgear_value = 217.38 * thtl - 117.38;
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
trimfun.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design ACC/Used Functions/trimfun.m
| 4,041 |
utf_8
|
908902ca2678a4efb48b714eddeca553
|
%=====================================================
% F16 nonlinear model trim cost function
% for longitudinal motion, steady level flight
% (cost = sum of weighted squared state derivatives)
%
% Author: T. Keviczky
% Date: April 29, 2002
%
% Added addtional functionality.
% This trim function can now trim at three
% additional flight conditions
% - Steady Turning Flight given turn rate
% - Steady Pull-up flight - given pull-up rate
% - Steady Roll - given roll rate
%
% Coauthor: Richard S. Russell
% Date: November 7th, 2002
%
%
%=====================================================
%%**********************************************%%
% Altered to work as a trimming function %
% for the HIFI F_16 Model %
%%**********************************************%%
function [cost, Xdot, xu] = trimfun(UX0)
global phi psi p q r phi_weight theta_weight psi_weight pow
global altitude velocity fi_flag_Simulink
% UX0 = [throttle, elevator, beta, alpha, aileron, rudder]
% Implementing limits:
% Thrust limits
if UX0(1) > 1
UX0(1) = 1;
elseif UX0(1) < 0
UX0(1) = 0;
end;
% elevator limits
if UX0(2) > 25
UX0(2) = 25;
elseif UX0(2) < -25
UX0(2) = -25;
end;
% sideslip limits
if (fi_flag_Simulink == 0)
if UX0(3) > 45*pi/180
UX0(3) = 45*pi/180;
elseif UX0(3) < -10*pi/180
UX0(3) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(3) > 30*pi/180
UX0(3) = 30*pi/180;
elseif UX0(3) < -20*pi/180
UX0(3) = -20*pi/180;
end
end
% angle of attack limits
if (fi_flag_Simulink == 0)
if UX0(4) > 45*pi/180
UX0(4) = 45*pi/180;
elseif UX0(4) < -10*pi/180
UX0(4) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(4) > 90*pi/180
UX0(4) = 90*pi/180;
elseif UX0(4) < -20*pi/180
UX0(4) = -20*pi/180;
end
end
% Aileron limits
if UX0(5) > 21.5
UX0(5) = 21.5;
elseif UX0(5) < -21.5
UX0(5) = -21.5;
end;
% Rudder limits
if UX0(6) > 30
UX0(6) = 30;
elseif UX0(6) < -30
UX0(6) = -30;
end;
if (fi_flag_Simulink == 1)
% Calculating qbar, ps and steady state leading edge flap deflection:
% (see pg. 43 NASA report)
rho0 = 1.225; tfac = 1 - 6.5e-3/288.15*altitude;
temp = 288.15*tfac; if (altitude >= 11000) temp = 216.65; end;
rho = rho0*(tfac.^4.2586);
qbar = 0.5*rho*velocity^2;
ps = 287*rho*temp;
dLEF = 1.38*UX0(4)*180/pi - 9.05*qbar/ps + 1.45;
elseif (fi_flag_Simulink == 0)
dLEF = 0.0;
end
% Verify that the calculated leading edge flap
% have not been violated.
if (dLEF > 25)
dLEF = 25;
elseif (dLEF < 0)
dLEF = 0;
end;
xu = [ 0 ... %npos (m)
0 ... %epos (m)
altitude ... %altitude (m)
phi*(pi/180) ... %phi (rad)
UX0(4) ... %theta (rad)
psi*(pi/180) ... %psi (rad)
velocity ... %velocity (m/s)
UX0(4) ... %alpha (rad)
UX0(3) ... %beta (rad)
p*(pi/180) ... %p (rad/s)
q*(pi/180) ... %q (rad/s)
r*(pi/180) ... %r (rad/s)
tgear(UX0(1)) ... % pow
UX0(1) ... %throttle (0-1)
UX0(2) ... %ele (deg)
UX0(5) ... %ail (deg)
UX0(6) ... %rud (deg)
dLEF ... %dLEF (deg)
fi_flag_Simulink ...% fidelity flag
]';
OUT = feval('nlplant',xu);
Xdot = OUT(1:13,1);
% Create weight function
weight = [ 0 ...%npos_dot
0 ...%epos_dot
5 ...%alt_dot
phi_weight ...%phi_dot
theta_weight ...%theta_dot
psi_weight ...%psi_dot
2 ...%V_dot
10 ...%alpha_dpt
10 ...%beta_dot
10 ...%P_dot
10 ...%Q_dot
10 ...%R_dot
5 ...% pow_dot
];
cost = weight*(Xdot.*Xdot); % Mean Square to be minimized
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
Control_GUI.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design AoA/Control_GUI.m
| 37,417 |
utf_8
|
385e097e99302c6cc85b41c7f39c5a64
|
function Control_GUI
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('UI for faults and damages at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('Toolbar','none',...
'MenuBar','none',...
'IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('UI for faults and damages at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
global oversize_param
oversize_param=0;
Main = uipanel('Parent',hf,'Title','Main Panel','FontSize',20,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 -oversize_param 0.95 1+oversize_param]);
uicontrol('Style','Slider','Parent',hf,... % Slider
'Units','normalized','Position',[0.97 0 0.03 1],...
'Value',1,'Callback',{@slider_callback1,Main});
uicontrol('Parent',Main,...
'Style','text','FontSize',16,...
'Units','normalized',...
'Position',[0 1-0.06 0.95 0.05],...
'String','This GUI allows the user to inputs faults, changes in control surfaces and airframe, as well as, control the learning proces of ANNs',...
'Backgroundcolor',[1 1 1]);
%% Control surfaces
panel_control = uipanel('Parent',Main,'Title','Control surfaces','FontSize',12, 'Units','normalized','Position',[.02 .25 .45 .7]);
% Blockades
panel_control_blockades = uipanel('Parent',panel_control,'Title','Blockades','FontSize',10, 'Units','normalized','Position',[.05 .5 .9 .49]);
string={'Elev_L','Elev_R','Ail_L','Ail_R','Rudd','LEF_L','LEF_R'};
panel_control_blockades_at = uipanel('Parent',panel_control_blockades,'Title','Blockade at:','FontSize',10, 'Units','normalized','Position',[.01 .4 .98 .55]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_at,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_blockades_at,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7,0.3]);
uicontrol('Parent',panel_control_blockades_at,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Block','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Blockat_CurrentValue_Callback,Val_h{i},i}) ;
end
panel_control_blockades_now = uipanel('Parent',panel_control_blockades,'Title','Blockade NOW','FontSize',10,'Units','normalized','Position',[.01 .02 .98 .36]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_now,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_blockades_now,'Style','togglebutton','Tag',['Block_now',num2str(i)],'String','Block now','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Blocknow_CurrentValue_Callback,i}) ;
end
% Floating or loss
panel_control_Float = uipanel('Parent',panel_control,'Title','Floating or loss','FontSize',10,'Units','normalized','Position',[.05 .30 .9 .17]);
for i=1:7
uicontrol('Parent',panel_control_Float,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_Float,'Style','togglebutton','Tag',['Float',num2str(i)],'String','Lose or float','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Float_loss_Callback,i}) ;
end
% Lose effectivenes or surface
panel_control_Area = uipanel('Parent',panel_control,'Title','Loss effectiveness or Surface: Input % lost','FontSize',10,'Units','normalized','Position',[.05 .02 .9 .27]);
for i=1:7
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7-0.02,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_Area,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7-0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/7*(i)-0.03,0.4,0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Affect','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Loss_area_Callback,Val_h{i},i}) ;
end
%% Structural changes
panel_control2 = uipanel('Parent',Main,'Title','Airframe and global changes','FontSize',12,'Units','normalized','Position',[.5 .25 .48 .7]);
panel_control_massprop = uipanel('Parent',panel_control2,'Title','Mass properties changes','FontSize',10,...
'Units','normalized','Position',[.05 .57 .9 .4]);
Val_h={};
% mass and xcg
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta mass(%) of 9295.4kg','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{1}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','x_cg position in% of CMA(0.3%)','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{2}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0.3','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
% Moments of inertia
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_y(%) of 75673.6kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{3}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_xz(%) of 1331.4kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{4}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_z(%) of 85552.1kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{5}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=4;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_x(%) of 12874.8kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{6}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
panel_control_AeroAndArea = uipanel('Parent',panel_control2,'Title','Aerodynamics and surfaces changes','FontSize',10,...
'Units','normalized','Position',[.05 .17 .9 .4]);
% Surface changes
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Left wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{7}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Right wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{8}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Fin surface loss(%) of 6.56m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{9}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
% DElta coeffs
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Lift (additionally to ~0.2)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{10}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Drag (additionally to ~0.036)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{11}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_pitch_moment (additionally to ~ - 0.054)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{12}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control2,'String','Update Changes','FontSize',16,'Units','normalized',...
'Position',[0.65 0.02 0.3 0.13],'Callback',{@Surf_and_Mass_changes,Val_h});
%% ANN control
panel_controlANN = uipanel('Parent',Main,'Title','ANNs control','FontSize',12,'Units','normalized','Position',[.02 .02 .96 .22]);
% Roll
panel_control_Roll = uipanel('Parent',panel_controlANN,'Title','Roll chanel','FontSize',12,...
'Units','normalized','Position',[.01 .02 .98/4-0.01 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','down'}});
% Long chanel
panel_control_Long = uipanel('Parent',panel_controlANN,'Title','Long chanel','FontSize',12,...
'Units','normalized','Position',[0.98/4+0.005 .02 .98/4-0.005 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_learn','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_reg','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_reg','down'}});
% Yaw chanel
panel_control_Yaw = uipanel('Parent',panel_controlANN,'Title','Yaw chanel chanel','FontSize',12,...
'Units','normalized','Position',[2*.98/4+0.005 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','down'}});
% Complete ANN
panel_control_Com = uipanel('Parent',panel_controlANN,'Title','Complete ANN','FontSize',12,...
'Units','normalized','Position',[3*.98/4+0.01 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'C_learn','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'C_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'C_reg','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'C_reg','down'}});
function Change_params(hObject, eventdata,handles)
MDL = 'F16ASYM_Controlled';
Str_to_change= findall(get(hObject,'parent'),'Tag',handles{1});
switch handles{1}
% Roll
case {'Roll_learn'}
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Roll_reg'}
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Long
case {'Long_learn'}
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Long_reg'}
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Yaw
case {'Yaw_learn'}
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Yaw_reg'}
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Completed
case {'C_learn'}
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'C_reg'}
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
end
function Surf_and_Mass_changes(hObject, eventdata,handles)
% Data from mdl
MDL = 'F16ASYM_Controlled';
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch str{i}
case {'delta_mass'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
case {'xcg'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=3:6
NewStrVal = get(handles{i}, 'String');
Actual_val(i-2) = str2double(NewStrVal)/100;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% 'delta_S_L','delta_S_R','delta_S_fin'
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=10:12
NewStrVal = get(handles{i}, 'String');
Actual_val(i-9) = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Loss_area_Callback(hObject, eventdata,handles, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = 1-str2double(NewStrVal)/100;
set(hObject,'String','Affected');
set(Elem,'Visible','off')
else
Actual_val(1,num) = 1;
set(hObject,'String','Affect');
set(Elem,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Float_loss_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Block_at',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 0;
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 1;
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blockat_CurrentValue_Callback(hObject, eventdata, handles,num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = str2double(NewStrVal);
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = NaN;
set(hObject,'String','Block');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blocknow_CurrentValue_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_at',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 1;
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 0;
set(hObject,'String','Block now');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function slider_callback1(hObject, eventdata, handles)
global oversize_param
val = get(hObject,'Value');
set(handles,'Position',[0.02 -oversize_param*val 0.95 1+oversize_param])
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
MDL = 'F16ASYM_Controlled';
% Reseting effectiveness
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)),']']);
% Blockades at
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)*NaN),']']);
% Blockades now
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
set_param(char(Block_search),'Value',['[',num2str(zeros(1,7)),']']);
% Airframe parameters
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
Actual_val=[];
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
switch str{i}
case {'delta_mass'}
Actual_val = 0;
case {'xcg'}
Actual_val = 0.3;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% 'delta_S_L','delta_S_R','delta_S_fin'
Actual_val=[];
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = 0;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
for i=3:6
Actual_val(i-2) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
for i=10:12
Actual_val(i-9) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
delete(hObject)
% close all Force
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
FE_plot.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design AoA/FE_plot.m
| 2,767 |
utf_8
|
33f67ce7964a466b12f76d5a8029b6ce
|
function FE_plot
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
Main = uipanel('Parent',hf,'Title','Flight Envelope plot','FontSize',15,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 0.02 0.95 0.95]);
% Plots and axis
global hplot htext hlist
AX=axes('Parent',Main,'Units','normalized ','Position',[0.1 0.1 0.85 0.85]);
load('FlightEnvelope.mat')
plot(AX,F_envelope.M_1g ,F_envelope.H_1g ,'r')
xlabel(AX,'Mach')
ylabel(AX,'Alt (m)')
% PLot th epoint
hold(AX)
hplot=scatter(AX,0,0,'o','filled');
hChildren = get(hplot, 'Children');
set(hChildren, 'Markersize', 10)
htext = text(0,0,[' YOU ';'\downarrow'],'HorizontalAlignment','Center','VerticalAlignment','Bottom','FontSize',18,'Parent', AX);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add Listener
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Block_search = [MDL,'/Environment params Estimations/ALT_and_M_GAIN_LIST'];
hlist = add_exec_event_listener(Block_search, 'PostOutputs', @localEventListener);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
global hplot hlist
try
delete(hlist)
delete(hObject)
catch
close all Force
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
tgear.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design AoA/Used Functions/tgear.m
| 535 |
utf_8
|
f0c3d6ed53bf5e044ed13e3251d92c3b
|
%=====================================================
% tgear.m
%
% Author : Ying Huo
%
% power command vs. thtl. relationship used
% in F-16 model
%=====================================================
function tgear_value = tgear ( thtl )
if ( thtl <= 0.77 )
tgear_value = 64.94 * thtl;
else
tgear_value = 217.38 * thtl - 117.38;
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
trimfun.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/Scheduling design/Scheduling design AoA/Used Functions/trimfun.m
| 4,041 |
utf_8
|
908902ca2678a4efb48b714eddeca553
|
%=====================================================
% F16 nonlinear model trim cost function
% for longitudinal motion, steady level flight
% (cost = sum of weighted squared state derivatives)
%
% Author: T. Keviczky
% Date: April 29, 2002
%
% Added addtional functionality.
% This trim function can now trim at three
% additional flight conditions
% - Steady Turning Flight given turn rate
% - Steady Pull-up flight - given pull-up rate
% - Steady Roll - given roll rate
%
% Coauthor: Richard S. Russell
% Date: November 7th, 2002
%
%
%=====================================================
%%**********************************************%%
% Altered to work as a trimming function %
% for the HIFI F_16 Model %
%%**********************************************%%
function [cost, Xdot, xu] = trimfun(UX0)
global phi psi p q r phi_weight theta_weight psi_weight pow
global altitude velocity fi_flag_Simulink
% UX0 = [throttle, elevator, beta, alpha, aileron, rudder]
% Implementing limits:
% Thrust limits
if UX0(1) > 1
UX0(1) = 1;
elseif UX0(1) < 0
UX0(1) = 0;
end;
% elevator limits
if UX0(2) > 25
UX0(2) = 25;
elseif UX0(2) < -25
UX0(2) = -25;
end;
% sideslip limits
if (fi_flag_Simulink == 0)
if UX0(3) > 45*pi/180
UX0(3) = 45*pi/180;
elseif UX0(3) < -10*pi/180
UX0(3) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(3) > 30*pi/180
UX0(3) = 30*pi/180;
elseif UX0(3) < -20*pi/180
UX0(3) = -20*pi/180;
end
end
% angle of attack limits
if (fi_flag_Simulink == 0)
if UX0(4) > 45*pi/180
UX0(4) = 45*pi/180;
elseif UX0(4) < -10*pi/180
UX0(4) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(4) > 90*pi/180
UX0(4) = 90*pi/180;
elseif UX0(4) < -20*pi/180
UX0(4) = -20*pi/180;
end
end
% Aileron limits
if UX0(5) > 21.5
UX0(5) = 21.5;
elseif UX0(5) < -21.5
UX0(5) = -21.5;
end;
% Rudder limits
if UX0(6) > 30
UX0(6) = 30;
elseif UX0(6) < -30
UX0(6) = -30;
end;
if (fi_flag_Simulink == 1)
% Calculating qbar, ps and steady state leading edge flap deflection:
% (see pg. 43 NASA report)
rho0 = 1.225; tfac = 1 - 6.5e-3/288.15*altitude;
temp = 288.15*tfac; if (altitude >= 11000) temp = 216.65; end;
rho = rho0*(tfac.^4.2586);
qbar = 0.5*rho*velocity^2;
ps = 287*rho*temp;
dLEF = 1.38*UX0(4)*180/pi - 9.05*qbar/ps + 1.45;
elseif (fi_flag_Simulink == 0)
dLEF = 0.0;
end
% Verify that the calculated leading edge flap
% have not been violated.
if (dLEF > 25)
dLEF = 25;
elseif (dLEF < 0)
dLEF = 0;
end;
xu = [ 0 ... %npos (m)
0 ... %epos (m)
altitude ... %altitude (m)
phi*(pi/180) ... %phi (rad)
UX0(4) ... %theta (rad)
psi*(pi/180) ... %psi (rad)
velocity ... %velocity (m/s)
UX0(4) ... %alpha (rad)
UX0(3) ... %beta (rad)
p*(pi/180) ... %p (rad/s)
q*(pi/180) ... %q (rad/s)
r*(pi/180) ... %r (rad/s)
tgear(UX0(1)) ... % pow
UX0(1) ... %throttle (0-1)
UX0(2) ... %ele (deg)
UX0(5) ... %ail (deg)
UX0(6) ... %rud (deg)
dLEF ... %dLEF (deg)
fi_flag_Simulink ...% fidelity flag
]';
OUT = feval('nlplant',xu);
Xdot = OUT(1:13,1);
% Create weight function
weight = [ 0 ...%npos_dot
0 ...%epos_dot
5 ...%alt_dot
phi_weight ...%phi_dot
theta_weight ...%theta_dot
psi_weight ...%psi_dot
2 ...%V_dot
10 ...%alpha_dpt
10 ...%beta_dot
10 ...%P_dot
10 ...%Q_dot
10 ...%R_dot
5 ...% pow_dot
];
cost = weight*(Xdot.*Xdot); % Mean Square to be minimized
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
Control_GUI.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/7dof FCS Development/Control_GUI.m
| 37,417 |
utf_8
|
385e097e99302c6cc85b41c7f39c5a64
|
function Control_GUI
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('UI for faults and damages at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('Toolbar','none',...
'MenuBar','none',...
'IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('UI for faults and damages at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
global oversize_param
oversize_param=0;
Main = uipanel('Parent',hf,'Title','Main Panel','FontSize',20,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 -oversize_param 0.95 1+oversize_param]);
uicontrol('Style','Slider','Parent',hf,... % Slider
'Units','normalized','Position',[0.97 0 0.03 1],...
'Value',1,'Callback',{@slider_callback1,Main});
uicontrol('Parent',Main,...
'Style','text','FontSize',16,...
'Units','normalized',...
'Position',[0 1-0.06 0.95 0.05],...
'String','This GUI allows the user to inputs faults, changes in control surfaces and airframe, as well as, control the learning proces of ANNs',...
'Backgroundcolor',[1 1 1]);
%% Control surfaces
panel_control = uipanel('Parent',Main,'Title','Control surfaces','FontSize',12, 'Units','normalized','Position',[.02 .25 .45 .7]);
% Blockades
panel_control_blockades = uipanel('Parent',panel_control,'Title','Blockades','FontSize',10, 'Units','normalized','Position',[.05 .5 .9 .49]);
string={'Elev_L','Elev_R','Ail_L','Ail_R','Rudd','LEF_L','LEF_R'};
panel_control_blockades_at = uipanel('Parent',panel_control_blockades,'Title','Blockade at:','FontSize',10, 'Units','normalized','Position',[.01 .4 .98 .55]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_at,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_blockades_at,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7,0.3]);
uicontrol('Parent',panel_control_blockades_at,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Block','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Blockat_CurrentValue_Callback,Val_h{i},i}) ;
end
panel_control_blockades_now = uipanel('Parent',panel_control_blockades,'Title','Blockade NOW','FontSize',10,'Units','normalized','Position',[.01 .02 .98 .36]);
% Individual
for i=1:7
uicontrol('Parent',panel_control_blockades_now,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_blockades_now,'Style','togglebutton','Tag',['Block_now',num2str(i)],'String','Block now','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Blocknow_CurrentValue_Callback,i}) ;
end
% Floating or loss
panel_control_Float = uipanel('Parent',panel_control,'Title','Floating or loss','FontSize',10,'Units','normalized','Position',[.05 .30 .9 .17]);
for i=1:7
uicontrol('Parent',panel_control_Float,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7,0.2]);
uicontrol('Parent',panel_control_Float,'Style','togglebutton','Tag',['Float',num2str(i)],'String','Lose or float','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.6],...
'Callback',{@Float_loss_Callback,i}) ;
end
% Lose effectivenes or surface
panel_control_Area = uipanel('Parent',panel_control,'Title','Loss effectiveness or Surface: Input % lost','FontSize',10,'Units','normalized','Position',[.05 .02 .9 .27]);
for i=1:7
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'BackgroundColor','white','String',string{i},'Units','normalized','Position',[0.02+0.95/7*(i-1),0.8,0.95/7-0.02,0.15]);
Val_h{i} = uicontrol('Parent',panel_control_Area,'Style','edit','FontSize',10,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/7*(i-1),0.5,0.95/7-0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/7*(i)-0.03,0.4,0.03,0.3]);
uicontrol('Parent',panel_control_Area,'Style','togglebutton','Tag',['Block_at',num2str(i)],'String','Affect','Units','normalized','Position',[0.02+0.95/7*(i-1),0.1,0.95/7,0.3],...
'Callback',{@Loss_area_Callback,Val_h{i},i}) ;
end
%% Structural changes
panel_control2 = uipanel('Parent',Main,'Title','Airframe and global changes','FontSize',12,'Units','normalized','Position',[.5 .25 .48 .7]);
panel_control_massprop = uipanel('Parent',panel_control2,'Title','Mass properties changes','FontSize',10,...
'Units','normalized','Position',[.05 .57 .9 .4]);
Val_h={};
% mass and xcg
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta mass(%) of 9295.4kg','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{1}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','x_cg position in% of CMA(0.3%)','Units','normalized','Position',[0.02+0.95/2*(i-1),0.8,0.95/2-0.03,0.15]);
Val_h{2}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0.3','Units','normalized','Position',[0.02+0.95/2*(i-1),0.5,0.95/2-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/2*(i)-0.03,0.55,0.03,0.15]);
% Moments of inertia
i=1;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_y(%) of 75673.6kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{3}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_xz(%) of 1331.4kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{4}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_z(%) of 85552.1kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{5}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
i=4;
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta J_x(%) of 12874.8kg.m^2','Units','normalized','Position',[0.02+0.95/4*(i-1),0.3,0.95/4-0.03,0.2]);
Val_h{6}=uicontrol('Parent',panel_control_massprop,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/4*(i-1),0.0,0.95/4-0.03,0.3]);
uicontrol('Parent',panel_control_massprop,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/4*(i)-0.03,0.05,0.03,0.15]);
panel_control_AeroAndArea = uipanel('Parent',panel_control2,'Title','Aerodynamics and surfaces changes','FontSize',10,...
'Units','normalized','Position',[.05 .17 .9 .4]);
% Surface changes
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Left wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{7}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Right wing surface loss(%) of 11.14m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{8}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',12,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Fin surface loss(%) of 6.56m^2','Units','normalized','Position',[0.02+0.95/3*(i-1),0.75,0.95/3-0.03,0.2]);
Val_h{9}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.5,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'String','%','Units','normalized','Position',[0.02+0.95/3*(i)-0.03,0.55,0.03,0.15]);
% DElta coeffs
i=1;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Lift (additionally to ~0.2)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{10}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=2;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_Drag (additionally to ~0.036)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{11}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
i=3;
uicontrol('Parent',panel_control_AeroAndArea,'Style','text','FontSize',10,'BackgroundColor','white','String','Delta C_pitch_moment (additionally to ~ - 0.054)','Units','normalized','Position',[0.02+0.95/3*(i-1),0.3,0.95/3-0.03,0.2]);
Val_h{12}=uicontrol('Parent',panel_control_AeroAndArea,'Style','edit','FontSize',12,'BackgroundColor','white','String','0','Units','normalized','Position',[0.02+0.95/3*(i-1),0.0,0.95/3-0.03,0.3]);
uicontrol('Parent',panel_control2,'String','Update Changes','FontSize',16,'Units','normalized',...
'Position',[0.65 0.02 0.3 0.13],'Callback',{@Surf_and_Mass_changes,Val_h});
%% ANN control
panel_controlANN = uipanel('Parent',Main,'Title','ANNs control','FontSize',12,'Units','normalized','Position',[.02 .02 .96 .22]);
% Roll
panel_control_Roll = uipanel('Parent',panel_controlANN,'Title','Roll chanel','FontSize',12,...
'Units','normalized','Position',[.01 .02 .98/4-0.01 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Roll,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Roll,'Tag','Roll_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','up'}});
uicontrol('Parent',panel_control_Roll,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Roll_reg','down'}});
% Long chanel
panel_control_Long = uipanel('Parent',panel_controlANN,'Title','Long chanel','FontSize',12,...
'Units','normalized','Position',[0.98/4+0.005 .02 .98/4-0.005 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_learn','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Long,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Long,'Tag','Long_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Long_reg','up'}});
uicontrol('Parent',panel_control_Long,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Long_reg','down'}});
% Yaw chanel
panel_control_Yaw = uipanel('Parent',panel_controlANN,'Title','Yaw chanel chanel','FontSize',12,...
'Units','normalized','Position',[2*.98/4+0.005 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Yaw,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Yaw,'Tag','Yaw_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','up'}});
uicontrol('Parent',panel_control_Yaw,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'Yaw_reg','down'}});
% Complete ANN
panel_control_Com = uipanel('Parent',panel_controlANN,'Title','Complete ANN','FontSize',12,...
'Units','normalized','Position',[3*.98/4+0.01 .02 .98/4 0.95]);
% Learning rate
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Learning Rate (~20)','Units','normalized',...
'Position',[0.02 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_learn','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.28 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Speed-up','Units','normalized',...
'Position',[0.02 0.43 0.25 0.35],'Callback',{@Change_params,{'C_learn','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Slow-down','Units','normalized',...
'Position',[0.02 0.05 0.25 0.35],'Callback',{@Change_params,{'C_learn','down'}});
% Regularization param
uicontrol('Parent',panel_control_Com,'Style','text','FontSize',11,'BackgroundColor','white','String','Reg. Param (~1)','Units','normalized',...
'Position',[0.52 .82 .45 0.22]);
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
uicontrol('Parent',panel_control_Com,'Tag','C_reg','Style','text','FontSize',14,'BackgroundColor','white','String',Actual_val,'Units','normalized',...
'Position',[0.78 .35 .15 0.25]);
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Underfit','Units','normalized',...
'Position',[0.52 0.43 0.25 0.35],'Callback',{@Change_params,{'C_reg','up'}});
uicontrol('Parent',panel_control_Com,'FontSize',10,'String','Overfit','Units','normalized',...
'Position',[0.52 0.05 0.25 0.35],'Callback',{@Change_params,{'C_reg','down'}});
function Change_params(hObject, eventdata,handles)
MDL = 'F16ASYM_Controlled';
Str_to_change= findall(get(hObject,'parent'),'Tag',handles{1});
switch handles{1}
% Roll
case {'Roll_learn'}
Block_search = find_system(MDL, 'Name', 'Roll_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Roll_reg'}
Block_search = find_system(MDL, 'Name', 'Roll_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Long
case {'Long_learn'}
Block_search = find_system(MDL, 'Name', 'Long_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Long_reg'}
Block_search = find_system(MDL, 'Name', 'Long_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Yaw
case {'Yaw_learn'}
Block_search = find_system(MDL, 'Name', 'Yaw_learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'Yaw_reg'}
Block_search = find_system(MDL, 'Name', 'Yaw_reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
% Completed
case {'C_learn'}
Block_search = find_system(MDL, 'Name', 'C learning rate','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
case{'C_reg'}
Block_search = find_system(MDL, 'Name', 'C reg param','Blocktype','Constant');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch handles{2}
case {'up'}
Actual_val = Actual_val+0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
case {'down'}
Actual_val = Actual_val-0.1;
set_param(char(Block_search),'Value',num2str(Actual_val));
end
Actual_val = get_param(Block_search,'Value');
set(Str_to_change,'String',Actual_val);
end
function Surf_and_Mass_changes(hObject, eventdata,handles)
% Data from mdl
MDL = 'F16ASYM_Controlled';
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
switch str{i}
case {'delta_mass'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
case {'xcg'}
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=3:6
NewStrVal = get(handles{i}, 'String');
Actual_val(i-2) = str2double(NewStrVal)/100;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% 'delta_S_L','delta_S_R','delta_S_fin'
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
NewStrVal = get(handles{i}, 'String');
Actual_val = str2double(NewStrVal)/100;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
for i=10:12
NewStrVal = get(handles{i}, 'String');
Actual_val(i-9) = str2double(NewStrVal);
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Loss_area_Callback(hObject, eventdata,handles, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = 1-str2double(NewStrVal)/100;
set(hObject,'String','Affected');
set(Elem,'Visible','off')
else
Actual_val(1,num) = 1;
set(hObject,'String','Affect');
set(Elem,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Float_loss_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Block_at',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 0;
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 1;
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blockat_CurrentValue_Callback(hObject, eventdata, handles,num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_now',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
NewStrVal = get(handles, 'String');
Actual_val(1,num) = str2double(NewStrVal);
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = NaN;
set(hObject,'String','Block');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function Blocknow_CurrentValue_Callback(hObject, eventdata, num)
% Data from mdl
MDL = 'F16ASYM_Controlled';
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
Actual_val = get_param(Block_search,'Value');
Actual_val = eval(char(Actual_val));
% Disappear the other blocking option
hf = get(hObject,'parent');
hf = get(hf,'parent');hf = get(hf,'parent');hf = get(hf,'parent');
Elem = findall(hf,'Tag',['Block_at',num2str(num)]);
Elem2 = findall(hf,'Tag',['Float',num2str(num)]);
on=get(hObject, 'Value');
if on
Actual_val(1,num) = 1;
set(hObject,'String','Blocked');
set(Elem,'Visible','off')
set(Elem2,'Visible','off')
else
Actual_val(1,num) = 0;
set(hObject,'String','Block now');
set(Elem,'Visible','on')
set(Elem2,'Visible','on')
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function slider_callback1(hObject, eventdata, handles)
global oversize_param
val = get(hObject,'Value');
set(handles,'Position',[0.02 -oversize_param*val 0.95 1+oversize_param])
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
MDL = 'F16ASYM_Controlled';
% Reseting effectiveness
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'effectiveness');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)),']']);
% Blockades at
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades at');
set_param(char(Block_search),'Value',['[',num2str(ones(1,7)*NaN),']']);
% Blockades now
Block_search = find_system([MDL,'/Faults injection'], 'Name', 'Blockades now');
set_param(char(Block_search),'Value',['[',num2str(zeros(1,7)),']']);
% Airframe parameters
str= {'delta_mass','xcg','Delta_J','Delta_J','Delta_J','Delta_J','delta_S_L','delta_S_R','delta_S_fin','delta_coef','delta_coef','delta_coef'};
% 'delta_mass','xcg'
Actual_val=[];
for i=1:2
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
switch str{i}
case {'delta_mass'}
Actual_val = 0;
case {'xcg'}
Actual_val = 0.3;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% 'delta_S_L','delta_S_R','delta_S_fin'
Actual_val=[];
for i=7:9
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{i} );
Actual_val = 0;
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
end
% Delta_J
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{5} );
for i=3:6
Actual_val(i-2) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
% delta_coef
Actual_val=[];
Block_search = find_system([MDL,'/Faults injection'], 'Name', str{10} );
for i=10:12
Actual_val(i-9) = 0;
end
set_param(char(Block_search),'Value',['[',num2str(Actual_val),']']);
delete(hObject)
% close all Force
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
FE_plot.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/7dof FCS Development/FE_plot.m
| 2,767 |
utf_8
|
33f67ce7964a466b12f76d5a8029b6ce
|
function FE_plot
modelName = 'F16ASYM_Controlled';
% Do some simple error checking on the input
if ~localValidateInputs(modelName)
estr = sprintf('The model %s.mdl cannot be found.',modelName);
errordlg(estr,'Model not found error','modal');
return
end
% Do some simple error checking on varargout
error(nargoutchk(0,1,nargout));
% Create the UI if one does not already exist.
% Bring the UI to the front if one does already exist.
hfi = findall(0,'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName));
if isempty(hfi)
% Create a UI
hfi = localCreateUI(modelName);
figure(hfi);
else
% Bring it to the front
figure(hfi);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function to create the user interface
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function hf = localCreateUI(modelName)
% Create the figure, setting appropriate properties
hf = figure('IntegerHandle','off',...
'Units','normalized',...
'Resize','on',...
'NumberTitle','off',...
'HandleVisibility','callback',...
'Name',sprintf('Plot of Flight envelope position at %s.mdl',modelName),...
'CloseRequestFcn',@localCloseRequestFcn,...
'Visible','off');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Main Panel
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MDL = 'F16ASYM_Controlled';
Main = uipanel('Parent',hf,'Title','Flight Envelope plot','FontSize',15,...
'BackgroundColor','white','Units','normalized',...
'Position',[0.02 0.02 0.95 0.95]);
% Plots and axis
global hplot htext hlist
AX=axes('Parent',Main,'Units','normalized ','Position',[0.1 0.1 0.85 0.85]);
load('FlightEnvelope.mat')
plot(AX,F_envelope.M_1g ,F_envelope.H_1g ,'r')
xlabel(AX,'Mach')
ylabel(AX,'Alt (m)')
% PLot th epoint
hold(AX)
hplot=scatter(AX,0,0,'o','filled');
hChildren = get(hplot, 'Children');
set(hChildren, 'Markersize', 10)
htext = text(0,0,[' YOU ';'\downarrow'],'HorizontalAlignment','Center','VerticalAlignment','Bottom','FontSize',18,'Parent', AX);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add Listener
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Block_search = [MDL,'/Environment params Estimations/ALT_and_M_GAIN_LIST'];
hlist = add_exec_event_listener(Block_search, 'PostOutputs', @localEventListener);
function modelExists = localValidateInputs(modelName)
num = exist(modelName,'file');
if num == 4
modelExists = true;
else
modelExists = false;
end
function localCloseRequestFcn(hObject,eventdata,ad) %#ok
global hplot hlist
try
delete(hlist)
delete(hObject)
catch
close all Force
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
tgear.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/7dof FCS Development/Used Functions/tgear.m
| 535 |
utf_8
|
f0c3d6ed53bf5e044ed13e3251d92c3b
|
%=====================================================
% tgear.m
%
% Author : Ying Huo
%
% power command vs. thtl. relationship used
% in F-16 model
%=====================================================
function tgear_value = tgear ( thtl )
if ( thtl <= 0.77 )
tgear_value = 64.94 * thtl;
else
tgear_value = 217.38 * thtl - 117.38;
end
|
github
|
DavidTorresOcana/Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master
|
trimfun.m
|
.m
|
Adaptive_and_Fault_Tolerant_Flight_Control_Systems-master/src/7dof FCS Development/Used Functions/trimfun.m
| 4,041 |
utf_8
|
908902ca2678a4efb48b714eddeca553
|
%=====================================================
% F16 nonlinear model trim cost function
% for longitudinal motion, steady level flight
% (cost = sum of weighted squared state derivatives)
%
% Author: T. Keviczky
% Date: April 29, 2002
%
% Added addtional functionality.
% This trim function can now trim at three
% additional flight conditions
% - Steady Turning Flight given turn rate
% - Steady Pull-up flight - given pull-up rate
% - Steady Roll - given roll rate
%
% Coauthor: Richard S. Russell
% Date: November 7th, 2002
%
%
%=====================================================
%%**********************************************%%
% Altered to work as a trimming function %
% for the HIFI F_16 Model %
%%**********************************************%%
function [cost, Xdot, xu] = trimfun(UX0)
global phi psi p q r phi_weight theta_weight psi_weight pow
global altitude velocity fi_flag_Simulink
% UX0 = [throttle, elevator, beta, alpha, aileron, rudder]
% Implementing limits:
% Thrust limits
if UX0(1) > 1
UX0(1) = 1;
elseif UX0(1) < 0
UX0(1) = 0;
end;
% elevator limits
if UX0(2) > 25
UX0(2) = 25;
elseif UX0(2) < -25
UX0(2) = -25;
end;
% sideslip limits
if (fi_flag_Simulink == 0)
if UX0(3) > 45*pi/180
UX0(3) = 45*pi/180;
elseif UX0(3) < -10*pi/180
UX0(3) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(3) > 30*pi/180
UX0(3) = 30*pi/180;
elseif UX0(3) < -20*pi/180
UX0(3) = -20*pi/180;
end
end
% angle of attack limits
if (fi_flag_Simulink == 0)
if UX0(4) > 45*pi/180
UX0(4) = 45*pi/180;
elseif UX0(4) < -10*pi/180
UX0(4) = -10*pi/180;
end
elseif (fi_flag_Simulink == 1)
if UX0(4) > 90*pi/180
UX0(4) = 90*pi/180;
elseif UX0(4) < -20*pi/180
UX0(4) = -20*pi/180;
end
end
% Aileron limits
if UX0(5) > 21.5
UX0(5) = 21.5;
elseif UX0(5) < -21.5
UX0(5) = -21.5;
end;
% Rudder limits
if UX0(6) > 30
UX0(6) = 30;
elseif UX0(6) < -30
UX0(6) = -30;
end;
if (fi_flag_Simulink == 1)
% Calculating qbar, ps and steady state leading edge flap deflection:
% (see pg. 43 NASA report)
rho0 = 1.225; tfac = 1 - 6.5e-3/288.15*altitude;
temp = 288.15*tfac; if (altitude >= 11000) temp = 216.65; end;
rho = rho0*(tfac.^4.2586);
qbar = 0.5*rho*velocity^2;
ps = 287*rho*temp;
dLEF = 1.38*UX0(4)*180/pi - 9.05*qbar/ps + 1.45;
elseif (fi_flag_Simulink == 0)
dLEF = 0.0;
end
% Verify that the calculated leading edge flap
% have not been violated.
if (dLEF > 25)
dLEF = 25;
elseif (dLEF < 0)
dLEF = 0;
end;
xu = [ 0 ... %npos (m)
0 ... %epos (m)
altitude ... %altitude (m)
phi*(pi/180) ... %phi (rad)
UX0(4) ... %theta (rad)
psi*(pi/180) ... %psi (rad)
velocity ... %velocity (m/s)
UX0(4) ... %alpha (rad)
UX0(3) ... %beta (rad)
p*(pi/180) ... %p (rad/s)
q*(pi/180) ... %q (rad/s)
r*(pi/180) ... %r (rad/s)
tgear(UX0(1)) ... % pow
UX0(1) ... %throttle (0-1)
UX0(2) ... %ele (deg)
UX0(5) ... %ail (deg)
UX0(6) ... %rud (deg)
dLEF ... %dLEF (deg)
fi_flag_Simulink ...% fidelity flag
]';
OUT = feval('nlplant',xu);
Xdot = OUT(1:13,1);
% Create weight function
weight = [ 0 ...%npos_dot
0 ...%epos_dot
5 ...%alt_dot
phi_weight ...%phi_dot
theta_weight ...%theta_dot
psi_weight ...%psi_dot
2 ...%V_dot
10 ...%alpha_dpt
10 ...%beta_dot
10 ...%P_dot
10 ...%Q_dot
10 ...%R_dot
5 ...% pow_dot
];
cost = weight*(Xdot.*Xdot); % Mean Square to be minimized
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
ardimat2.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECG_MATLAB/ardimat2.m
| 2,232 |
utf_8
|
f0795d79ef6f7d685d3c6ba301b1ef69
|
% Yu Hin Hau
% 7/9/2013
% **CLOSE PLOT TO END SESSION
function ardimat2
instrumentObjects=instrfind; % don't pass it anything - find all of them.
delete(instrumentObjects);
clear all;
clc;
%User Defined Properties
serialPort = 'COM1'; % define COM port #
plotTitle = 'Serial Data Log'; % plot title
xLabel = 'Elapsed Time (s)'; % x-axis label
yLabel = 'Data'; % y-axis label
plotGrid = 'on'; % 'off' to turn off grid
min = -1.5; % set y-min
max = 1.5; % set y-max
scrollWidth = 10; % display period in plot, plot entire data log if <= 0
delay = .01; % make sure sample faster than resolution
%Define Function Variables
time = 0;
data = 0;
count = 0;
%Set up Plot
plotGraph = plot(time,data,'-mo',...
'LineWidth',1,...
'MarkerEdgeColor','k',...
'MarkerFaceColor',[.49 1 .63],...
'MarkerSize',2);
title(plotTitle,'FontSize',25);
xlabel(xLabel,'FontSize',15);
ylabel(yLabel,'FontSize',15);
axis([0 10 min max]);
grid(plotGrid);
%Open Serial COM Port
s = serial(serialPort)
disp('Close Plot to End Session');
fopen(s);
tic
while ishandle(plotGraph) %Loop when Plot is Active
dat = fscanf(s); %Read Data from Serial as Float
disp(dat);
if(~isempty(dat)) %Make sure Data Type is Correct
count = count + 1;
time(count) = toc; %Extract Elapsed Time
data(count) = dat(1); %Extract 1st Data Element
%Set Axis according to Scroll Width
if(scrollWidth > 0)
set(plotGraph,'XData',time(time > time(count)-scrollWidth),'YData',data(time > time(count)-scrollWidth));
axis([time(count)-scrollWidth time(count) min max]);
else
set(plotGraph,'XData',time,'YData',data);
axis([0 time(count) min max]);
end
%Allow MATLAB to Update Plot
pause(delay);
end
end
%Close Serial COM Port and Delete useless Variables
fclose(s);
clear count dat delay max min plotGraph plotGrid plotTitle s ...
scrollWidth serialPort xLabel yLabel;
disp('Session Terminated...');
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
progressbar.m
|
.m
|
ECG-based-Biometric-Authentication-master/MATLAB_ECG/progressbar.m
| 11,767 |
utf_8
|
06705e480618e134da62478338e8251c
|
function progressbar(varargin)
% Description:
% progressbar() provides an indication of the progress of some task using
% graphics and text. Calling progressbar repeatedly will update the figure and
% automatically estimate the amount of time remaining.
% This implementation of progressbar is intended to be extremely simple to use
% while providing a high quality user experience.
%
% Features:
% - Can add progressbar to existing m-files with a single line of code.
% - Supports multiple bars in one figure to show progress of nested loops.
% - Optional labels on bars.
% - Figure closes automatically when task is complete.
% - Only one figure can exist so old figures don't clutter the desktop.
% - Remaining time estimate is accurate even if the figure gets closed.
% - Minimal execution time. Won't slow down code.
% - Randomized color. When a programmer gets bored...
%
% Example Function Calls For Single Bar Usage:
% progressbar % Initialize/reset
% progressbar(0) % Initialize/reset
% progressbar('Label') % Initialize/reset and label the bar
% progressbar(0.5) % Update
% progressbar(1) % Close
%
% Example Function Calls For Multi Bar Usage:
% progressbar(0, 0) % Initialize/reset two bars
% progressbar('A', '') % Initialize/reset two bars with one label
% progressbar('', 'B') % Initialize/reset two bars with one label
% progressbar('A', 'B') % Initialize/reset two bars with two labels
% progressbar(0.3) % Update 1st bar
% progressbar(0.3, []) % Update 1st bar
% progressbar([], 0.3) % Update 2nd bar
% progressbar(0.7, 0.9) % Update both bars
% progressbar(1) % Close
% progressbar(1, []) % Close
% progressbar(1, 0.4) % Close
%
% Notes:
% For best results, call progressbar with all zero (or all string) inputs
% before any processing. This sets the proper starting time reference to
% calculate time remaining.
% Bar color is choosen randomly when the figure is created or reset. Clicking
% the bar will cause a random color change.
%
% Demos:
% % Single bar
% m = 500;
% progressbar % Init single bar
% for i = 1:m
% pause(0.01) % Do something important
% progressbar(i/m) % Update progress bar
% end
%
% % Simple multi bar (update one bar at a time)
% m = 4;
% n = 3;
% p = 100;
% progressbar(0,0,0) % Init 3 bars
% for i = 1:m
% progressbar([],0) % Reset 2nd bar
% for j = 1:n
% progressbar([],[],0) % Reset 3rd bar
% for k = 1:p
% pause(0.01) % Do something important
% progressbar([],[],k/p) % Update 3rd bar
% end
% progressbar([],j/n) % Update 2nd bar
% end
% progressbar(i/m) % Update 1st bar
% end
%
% % Fancy multi bar (use labels and update all bars at once)
% m = 4;
% n = 3;
% p = 100;
% progressbar('Monte Carlo Trials','Simulation','Component') % Init 3 bars
% for i = 1:m
% for j = 1:n
% for k = 1:p
% pause(0.01) % Do something important
% % Update all bars
% frac3 = k/p;
% frac2 = ((j-1) + frac3) / n;
% frac1 = ((i-1) + frac2) / m;
% progressbar(frac1, frac2, frac3)
% end
% end
% end
%
% Author:
% Steve Hoelzer
%
% Revisions:
% 2002-Feb-27 Created function
% 2002-Mar-19 Updated title text order
% 2002-Apr-11 Use floor instead of round for percentdone
% 2002-Jun-06 Updated for speed using patch (Thanks to waitbar.m)
% 2002-Jun-19 Choose random patch color when a new figure is created
% 2002-Jun-24 Click on bar or axes to choose new random color
% 2002-Jun-27 Calc time left, reset progress bar when fractiondone == 0
% 2002-Jun-28 Remove extraText var, add position var
% 2002-Jul-18 fractiondone input is optional
% 2002-Jul-19 Allow position to specify screen coordinates
% 2002-Jul-22 Clear vars used in color change callback routine
% 2002-Jul-29 Position input is always specified in pixels
% 2002-Sep-09 Change order of title bar text
% 2003-Jun-13 Change 'min' to 'm' because of built in function 'min'
% 2003-Sep-08 Use callback for changing color instead of string
% 2003-Sep-10 Use persistent vars for speed, modify titlebarstr
% 2003-Sep-25 Correct titlebarstr for 0% case
% 2003-Nov-25 Clear all persistent vars when percentdone = 100
% 2004-Jan-22 Cleaner reset process, don't create figure if percentdone = 100
% 2004-Jan-27 Handle incorrect position input
% 2004-Feb-16 Minimum time interval between updates
% 2004-Apr-01 Cleaner process of enforcing minimum time interval
% 2004-Oct-08 Seperate function for timeleftstr, expand to include days
% 2004-Oct-20 Efficient if-else structure for sec2timestr
% 2006-Sep-11 Width is a multiple of height (don't stretch on widescreens)
% 2010-Sep-21 Major overhaul to support multiple bars and add labels
%
persistent progfig progdata lastupdate
% Get inputs
if nargin > 0
input = varargin;
ninput = nargin;
else
% If no inputs, init with a single bar
input = {0};
ninput = 1;
end
% If task completed, close figure and clear vars, then exit
if input{1} == 1
if ishandle(progfig)
delete(progfig) % Close progress bar
end
clear progfig progdata lastupdate % Clear persistent vars
drawnow
return
end
% Init reset flag
resetflag = false;
% Set reset flag if first input is a string
if ischar(input{1})
resetflag = true;
end
% Set reset flag if all inputs are zero
if input{1} == 0
% If the quick check above passes, need to check all inputs
if all([input{:}] == 0) && (length([input{:}]) == ninput)
resetflag = true;
end
end
% Set reset flag if more inputs than bars
if ninput > length(progdata)
resetflag = true;
end
% If reset needed, close figure and forget old data
if resetflag
if ishandle(progfig)
delete(progfig) % Close progress bar
end
progfig = [];
progdata = []; % Forget obsolete data
end
% Create new progress bar if needed
if ishandle(progfig)
else % This strange if-else works when progfig is empty (~ishandle() does not)
% Define figure size and axes padding for the single bar case
height = 0.03;
width = height * 8;
hpad = 0.02;
vpad = 0.25;
% Figure out how many bars to draw
nbars = max(ninput, length(progdata));
% Adjust figure size and axes padding for number of bars
heightfactor = (1 - vpad) * nbars + vpad;
height = height * heightfactor;
vpad = vpad / heightfactor;
% Initialize progress bar figure
left = (1 - width) / 2;
bottom = (1 - height) / 2;
progfig = figure(...
'Units', 'normalized',...
'Position', [left bottom width height],...
'NumberTitle', 'off',...
'Resize', 'off',...
'MenuBar', 'none' );
% Initialize axes, patch, and text for each bar
left = hpad;
width = 1 - 2*hpad;
vpadtotal = vpad * (nbars + 1);
height = (1 - vpadtotal) / nbars;
for ndx = 1:nbars
% Create axes, patch, and text
bottom = vpad + (vpad + height) * (nbars - ndx);
progdata(ndx).progaxes = axes( ...
'Position', [left bottom width height], ...
'XLim', [0 1], ...
'YLim', [0 1], ...
'Box', 'on', ...
'ytick', [], ...
'xtick', [] );
progdata(ndx).progpatch = patch( ...
'XData', [0 0 0 0], ...
'YData', [0 0 1 1] );
progdata(ndx).progtext = text(0.99, 0.5, '', ...
'HorizontalAlignment', 'Right', ...
'FontUnits', 'Normalized', ...
'FontSize', 0.7 );
progdata(ndx).proglabel = text(0.01, 0.5, '', ...
'HorizontalAlignment', 'Left', ...
'FontUnits', 'Normalized', ...
'FontSize', 0.7 );
if ischar(input{ndx})
set(progdata(ndx).proglabel, 'String', input{ndx})
input{ndx} = 0;
end
% Set callbacks to change color on mouse click
set(progdata(ndx).progaxes, 'ButtonDownFcn', {@changecolor, progdata(ndx).progpatch})
set(progdata(ndx).progpatch, 'ButtonDownFcn', {@changecolor, progdata(ndx).progpatch})
set(progdata(ndx).progtext, 'ButtonDownFcn', {@changecolor, progdata(ndx).progpatch})
set(progdata(ndx).proglabel, 'ButtonDownFcn', {@changecolor, progdata(ndx).progpatch})
% Pick a random color for this patch
changecolor([], [], progdata(ndx).progpatch)
% Set starting time reference
if ~isfield(progdata(ndx), 'starttime') || isempty(progdata(ndx).starttime)
progdata(ndx).starttime = clock;
end
end
% Set time of last update to ensure a redraw
lastupdate = clock - 1;
end
% Process inputs and update state of progdata
for ndx = 1:ninput
if ~isempty(input{ndx})
progdata(ndx).fractiondone = input{ndx};
progdata(ndx).clock = clock;
end
end
% Enforce a minimum time interval between graphics updates
myclock = clock;
if abs(myclock(6) - lastupdate(6)) < 0.01 % Could use etime() but this is faster
return
end
% Update progress patch
for ndx = 1:length(progdata)
set(progdata(ndx).progpatch, 'XData', ...
[0, progdata(ndx).fractiondone, progdata(ndx).fractiondone, 0])
end
% Update progress text if there is more than one bar
if length(progdata) > 1
for ndx = 1:length(progdata)
set(progdata(ndx).progtext, 'String', ...
sprintf('%1d%%', floor(100*progdata(ndx).fractiondone)))
end
end
% Update progress figure title bar
if progdata(1).fractiondone > 0
runtime = etime(progdata(1).clock, progdata(1).starttime);
timeleft = runtime / progdata(1).fractiondone - runtime;
timeleftstr = sec2timestr(timeleft);
titlebarstr = sprintf('%2d%% %s remaining', ...
floor(100*progdata(1).fractiondone), timeleftstr);
else
titlebarstr = ' 0%';
end
set(progfig, 'Name', titlebarstr)
% Force redraw to show changes
drawnow
% Record time of this update
lastupdate = clock;
% ------------------------------------------------------------------------------
function changecolor(h, e, progpatch) %#ok<INUSL>
% Change the color of the progress bar patch
% Prevent color from being too dark or too light
colormin = 1.5;
colormax = 2.8;
thiscolor = rand(1, 3);
while (sum(thiscolor) < colormin) || (sum(thiscolor) > colormax)
thiscolor = rand(1, 3);
end
set(progpatch, 'FaceColor', thiscolor)
% ------------------------------------------------------------------------------
function timestr = sec2timestr(sec)
% Convert a time measurement from seconds into a human readable string.
% Convert seconds to other units
w = floor(sec/604800); % Weeks
sec = sec - w*604800;
d = floor(sec/86400); % Days
sec = sec - d*86400;
h = floor(sec/3600); % Hours
sec = sec - h*3600;
m = floor(sec/60); % Minutes
sec = sec - m*60;
s = floor(sec); % Seconds
% Create time string
if w > 0
if w > 9
timestr = sprintf('%d week', w);
else
timestr = sprintf('%d week, %d day', w, d);
end
elseif d > 0
if d > 9
timestr = sprintf('%d day', d);
else
timestr = sprintf('%d day, %d hr', d, h);
end
elseif h > 0
if h > 9
timestr = sprintf('%d hr', h);
else
timestr = sprintf('%d hr, %d min', h, m);
end
elseif m > 0
if m > 9
timestr = sprintf('%d min', m);
else
timestr = sprintf('%d min, %d sec', m, s);
end
else
timestr = sprintf('%d sec', s);
end
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
untitled.m
|
.m
|
ECG-based-Biometric-Authentication-master/MATLAB_ECG/untitled.m
| 14,583 |
utf_8
|
1035b4a62875e9877dfb1ab7653f5b47
|
function varargout = untitled(varargin)
% UNTITLED MATLAB code for untitled.fig
% UNTITLED, by itself, creates a new UNTITLED or raises the existing
% singleton*.
%
% H = UNTITLED returns the handle to a new UNTITLED or the handle to
% the existing singleton*.
%
% UNTITLED('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in UNTITLED.M with the given input arguments.
%
% UNTITLED('Property','Value',...) creates a new UNTITLED or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before untitled_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to untitled_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help untitled
% Last Modified by GUIDE v2.5 08-Apr-2017 21:17:21
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @untitled_OpeningFcn, ...
'gui_OutputFcn', @untitled_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before untitled is made visible.
function untitled_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to untitled (see VARARGIN)
% Choose default command line output for untitled
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes untitled wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = untitled_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
% --- Executes on selection change in popupmenu2.
function popupmenu2_Callback(hObject, eventdata, handles)
% hObject handle to popupmenu2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: contents = cellstr(get(hObject,'String')) returns popupmenu2 contents as cell array
% contents{get(hObject,'Value')} returns selected item from popupmenu2
%contents = cellstr(get(hObject,'String'));
%aaaa=contents{get(hObject,'Value')};
% --- Executes during object creation, after setting all properties.
function popupmenu2_CreateFcn(hObject, eventdata, handles)
% hObject handle to popupmenu2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: popupmenu controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
cla reset;
aa=load('Person_02.txt');
N=aa(:,1);
X=aa(:,2);
plot(handles.axes1,N,X);
function edit1_Callback(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit1 as text
% str2double(get(hObject,'String')) returns contents of edit1 as a double
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton9.
function pushbutton9_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton9 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
cla reset;
ecg=load('Person_02.txt');
N=ecg(:,1);
X=ecg(:,2);
[qrs_amp_raw,qrs_i_raw,delay,ecg_d, NOISL_buf1, SIGL_buf1, THRS_buf1, locs, ecg_h]=pan_tompkin1(X,500,0);
plot(handles.axes1,ecg_h);
hold on,scatter(handles.axes1,qrs_i_raw,qrs_amp_raw,'m');
hold on,plot(handles.axes1,locs,NOISL_buf1,'LineWidth',2,'Linestyle','--','color','k');
hold on,plot(handles.axes1,locs,SIGL_buf1,'LineWidth',2,'Linestyle','-.','color','r');
hold on,plot(handles.axes1,locs,THRS_buf1,'LineWidth',2,'Linestyle','-.','color','g');
% --- Executes on button press in pushbutton10.
function pushbutton10_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton10 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
%[N1,X1]=R_Peak(N,X);
%plot(handles.axes1,N,X);
%plot(handles.axes1,N1,X1,'ro');
%----
%----
% --- Executes on button press in pushbutton11.
function pushbutton11_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton11 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
cla reset;
ecg=load('Person_02.txt');
N=ecg(:,1);
X=ecg(:,2);
[qrs_amp_raw,qrs_i_raw,delay,ecg_d, NOISL_buf1, SIGL_buf1, THRS_buf1, locs, ecg_h]=pan_tompkin1(X,500,0);
plot(handles.axes1,N,ecg_d);
disp(handles);
function edit2_Callback(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit2 as text
% str2double(get(hObject,'String')) returns contents of edit2 as a double
% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function edit3_Callback(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit3 as text
% str2double(get(hObject,'String')) returns contents of edit3 as a double
% --- Executes during object creation, after setting all properties.
function edit3_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton12.
function pushbutton12_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton12 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
folder_name = uigetdir('C:\Users\hp1\Desktop');
folder_name=cellstr(folder_name);
set(handles.edit2,'string',folder_name);
%disp(class(folder_name));
%disp(folder_name);
% --- Executes on button press in pushbutton14.
function pushbutton14_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton14 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
folder_name = uigetdir('C:\Users\hp1\Desktop');
folder_name=cellstr(folder_name);
set(handles.edit3,'string',folder_name);
% --- Executes on button press in pushbutton15.
function pushbutton15_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton15 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
%h=zoom;
%disp(h.Enable);
%if(h.Enable=='off')
% zoom on;
%else
% zoom off;
%end;
data = handles.pushbutton15;
%if(data.String=='+')
zoom on;
% data.String='-';
%else
% zoom out;
% data.String='+';
%end;
disp(class(data.String));
% --- Executes on button press in pushbutton16.
function pushbutton16_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton16 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
zoom out;
zoom off;
function edit4_Callback(hObject, eventdata, handles)
% hObject handle to edit4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit4 as text
% str2double(get(hObject,'String')) returns contents of edit4 as a double
% --- Executes during object creation, after setting all properties.
function edit4_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in pushbutton17.
function pushbutton17_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton17 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
%disp(handles.edit2);
xx=pwd;
xx1=strcat(pwd,'\');
train=handles.edit2.String;
test=handles.edit3.String;
disp(strrep(char(test),xx1,''));
%acc= dwt_verify(strrep(char(test),xx1,''),strrep(char(train),xx1,''));
acc= dwt_verify(char(test),char(train));
disp(strcat('sddssdds',acc));
set(handles.edit4,'String',num2str(acc));
% --- Executes on button press in pushbutton19.
function pushbutton19_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton19 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
xx=pwd;
xx1=strcat(pwd,'\');
train=handles.edit2.String;
test=handles.edit3.String;
disp(strrep(char(test),xx1,''));
%acc= dwt_verify(strrep(char(test),xx1,''),strrep(char(train),xx1,''));
acc= dwt_verify(char(test),char(train));
set(handles.edit4,'String',num2str(acc));
% --- Executes during object creation, after setting all properties.
function pushbutton19_CreateFcn(hObject, eventdata, handles)
% hObject handle to pushbutton19 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% --- Executes on button press in pushbutton18.
function pushbutton18_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton18 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
xx=pwd;
xx1=strcat(pwd,'\');
train=handles.edit2.String;
test=handles.edit3.String;
disp(strrep(char(test),xx1,''));
%acc= dwt_verify(strrep(char(test),xx1,''),strrep(char(train),xx1,''));
N=5; %total number of parfor iterations
hbar = parfor_progressbar(N,'Computing...'); %create the progress bar
parfor i=1:N,
acc{i}= dwt_verify(char(test),char(train)); % computation
hbar.iterate(1); % update progress by one iteration
end
close(hbar); %close progress bar
%end
%end
set(handles.edit4,'string',num2str(acc{N}));
% --- Executes when figure1 is resized.
function figure1_SizeChangedFcn(hObject, eventdata, handles)
% hObject handle to figure1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- Executes on key press with focus on pushbutton18 and none of its controls.
function pushbutton18_KeyPressFcn(hObject, eventdata, handles)
% hObject handle to pushbutton18 (see GCBO)
% eventdata structure with the following fields (see MATLAB.UI.CONTROL.UICONTROL)
% Key: name of the key that was pressed, in lower case
% Character: character interpretation of the key(s) that was pressed
% Modifier: name(s) of the modifier key(s) (i.e., control, shift) pressed
% handles structure with handles and user data (see GUIDATA)
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
bxb.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/bxb.m
| 3,461 |
utf_8
|
57b3c3892ca3780599004ec45c9df76d
|
function varargout=bxb(varargin)
%
% report=bxb(recName,refAnn,testAnn,reportFile,beginTime,stopTime,matchWindow)
%
% Wrapper to WFDB BXB:
% http://www.physionet.org/physiotools/wag/bxb-1.htm
%
% Creates a report file ("reportFile) using
% ANSI/AAMI-standard beat-by-beat annotation comparator.
%
% Ouput Parameters:
%
% report (Optional)
% Returns a structure containing information on the 'reportFile'.
% This can be used to read report File that has been previously
% generated by BXB (see Example 2 below), into the workspace.
% The structure has the following fields:
% report.data -Numerical data matching the Algorithm table
% report.textdata -Text data describing the Algorithm table
%
%Input Parameters:
% recName
% String specifying the WFDB record file.
%
% refAnn
% String specifying the reference WFDB annotation file.
%
% testAnn
% String specifying the test WFDB annotation file.
%
% reportFile
% String representing the file at which the report will be
% written to.
%
% beginTime (Optional)
% String specifying the begin time in WFDB time format. The
% WFDB time format is described at
% http://www.physionet.org/physiotools/wag/intro.htm#time.
% Default starts comparison after 5 minutes.
%
% stopTime (Optional)
% String specifying the stop time in WFDB format (default is end of
% record).
%
% matchWindow (Optional)
% 1x1 WFDB Time specifying the match window size (default = 0.15 s).
%
%
% Written by Ikaro Silva, 2013
% Last Modified: May 28, 2014
% Version 1.1
% Since 0.9.0
%
% %Example (this will generate a /mitdb/100.qrs file at your directory):
% %Compares SQRS detetor with the MITDB ATR annotations
%
% [refAnn]=rdann('mitdb/100','atr');
% sqrs('mitdb/100');
% [testAnn]=rdann('mitdb/100','qrs');
% report=bxb('mitdb/100','atr','qrs','bxbReport.txt')
%
%
% %Example 2 - Load variables from a report file that has been previously
% %generated
% report=bxb([],[],[],'bxbReport.txt')
%
%
% See also RDANN, MXM, WFDBTIME
%endOfHelp
persistent javaWfdbExec
if(isempty(javaWfdbExec))
javaWfdbExec=getWfdbClass('bxb');
end
%Set default pararamter values
inputs={'recName','refAnn','testAnn','reportFile','beginTime','stopTime','matchWindow'};
recName=[];
refAnn=[];
testAnn=[];
reportFile=[];
beginTime=[];
stopTime=[];
matchWindow=[];
for n=1:nargin
if(~isempty(varargin{n}))
eval([inputs{n} '=varargin{n};'])
end
end
if(~isempty(recName))
%Only execute this if recName is defined, otherwise we assume
%that the user just want to load the 'reporFile' variable into the
%workspace based on a previously generated 'reportFile'
wfdb_argument={'-r',recName,'-a',refAnn,testAnn,'-S',reportFile,'-v'};
if(~isempty(beginTime))
wfdb_argument{end+1}='-f';
wfdb_argument{end+1}=beginTime;
end
if(~isempty(stopTime))
wfdb_argument{end+1}='-t';
wfdb_argument{end+1}=stopTime;
end
if(~isempty(matchWindow))
wfdb_argument{end+1}='-w';
wfdb_argument{end+1}=matchWindow;
end
report=javaWfdbExec.execToStringList(wfdb_argument);
end
if(nargout>0)
varargout{1}=bxbReader(reportFile);
end
function reportData = bxbReader(fileName)
%load file
reportData = importdata(fileName);
%get rid of unimportant stuff
reportData.data(end,:) = [];
reportData.textdata(end,:) = [];
reportData.textdata(:,end) = [];
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
surrogate.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/surrogate.m
| 1,986 |
utf_8
|
4dce61f40839e472d48a46aa980d311b
|
function Y=surrogate(x,M)
%
% Y=surrogate(x,M)
%
% Generates M amplitude adjusted phase shuffled surrogate time series from x.
% Useufel for testing the underlying assumption that the null hypothesis consists
% of linear dynamics with possibly non-linear, monotonically increasing,
% measurement function.
%
% Required Input Parameters:
%
% x
% Nx1 vector of doubles
%
% M
% 1x1 scalar specifying the number of surrogate time series to
% generate.
%
% Required Output Parameters:
%
% Y
% NxM vector of doubles
%
%
%
% References:
%
%[1] Kaplan, Daniel, and Leon Glass. Understanding nonlinear dynamics. Vol. 19. Springer, 1995.
%
%
% Written by Ikaro Silva, 2014
% Last Modified: November 20, 2014
% Version 1.0
% Since 0.9.8
%
%
%
%
% See also MSENTROPY, SURROGATE
%endOfHelp
% 1. Amp transform original data to Gaussian distribution
% 2. Phase randomize #1
% 3. Amp transform #2 to original
% Auto-correlation function should be similar but not exact!
x=x(:);
N=length(x);
Y=zeros(N,M);
for m=1:M
%Step 1
y=randn(N,1);
y=amplitudeTransform(x,y,N);
%Step 2
y=phaseShuffle(y,N);
%Step 3
y=amplitudeTransform(y,x,N);
Y(:,m)=y;
end
%%% Helper functions
function target=amplitudeTransform(x,target,N)
%Steps:
%1. Sort the source by increasing amp
%2. Sort target as #1
%3. Swap source amp by target amp
%4. Sort #3 by increasing time index of #1
X=[[1:N]' x];
X=sortrows(X,2);
target=[X(:,1) sort(target)];
target=sortrows(target,1);
target=target(:,2);
function y=phaseShuffle(x,N)
%%Shuffle spectrum
X=fft(x);
Y=X;
mid=floor(N/2)+ mod(N,2);
phi=2*pi*rand(mid-1,1); %Generate random phase
Y(2:mid)=abs(X(2:mid)).*cos(phi) + j*abs(X(2:mid)).*sin(phi);
if(~mod(N,2))
%Even series has Nyquist in the middle+1 because of DC
Y(mid+2:end)=conj(flipud(Y(2:mid)));
Y(mid+1)=X(mid+1);
else
%Odd series is fully symetric except for DC
Y(mid+1:end)=conj(flipud(Y(2:mid)));
end
y=real(ifft(Y));
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
mat2wfdb.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/mat2wfdb.m
| 10,214 |
utf_8
|
ccd1af8befc8050ad893caab1a0463e0
|
function [varargout]=mat2wfdb(varargin)
%
% [xbit]=mat2wfdb(X,fname,Fs,bit_res,adu,info,gain,sg_name,baseline,isint)
%
% Convert data readable in matlab into WFDB Physionet format.
%
% Input Paramater are:
%
% X -(required) NxM matrix of M signals with N samples each. The
% signals can be of type double.The signals are assumed to be
% in physical units already and will be converted to
% ADU.
% fname -(required) String where the the header (*.hea) and data (*.dat)
% files will be saved (one single name for both, with no sufix).
% Fs -(Optional) 1x1 sampling frequency in Hz (all signals must have
% been sampled at the same frquency). Default is 1 Hz.
% bit_res -(Optional) 1xM (or Mx1):scalar determining the bit depth of the conversion for
% each signal.
% 1x1 : If all the signals should have the same bit depth
% Options are: 8, 16, and 32 ( all are signed types). 16 is the default.
% adu -(Optional) Cell array of strings describing the physical units (default is 'V').
% If only one string is entered all signals will have the same physical units.
% If multiple physical units, the total units entered has to equal M (number of
% channels). Units are delimited by '/'. See examples below.
% info -(Optional) String that will be added to the comment section of the header file.
% gain -(Optional) Scalar, if provided, no automatic scaling will be applied before the
% quantitzation of the signal. If a gain is passed, in will be the same one set
% on the header file. The signal will be scaled by this gain prior to the quantization
% process. Use this options if you want to have a standard gain and quantization
% process for all signals in a dataset (the function will not attempt to quantitized
% individual waveforms based on their individual range and baseline).
%baseline -(Optional) Offset (ADC zero) Mx1 array of integers that represents the amplitude (sample
% value) that would be observed if the analog signal present at the ADC inputs had a
% level that fell exactly in the middle of the input range of the ADC.
% sg_name -(Optional) Cell array of strings describing signal names.
%
% isint -(Optional) Logical value (default=0). Use this option if you know
% the signal is already quantitized, and you want to remove round-off
% error by setting the original values to integers prior to fixed
% point conversion.
%
% Ouput Parameters are:
%
% xbit -(Optional) NxM the quantitized signals that written to file (possible
% rescaled if no gain was provided at input). Useful for comparing
% and estimating quatitization error with the input double signal X
% (see examples below).
%
%
% NOTE: The signals can have different amplitudes, they will all be scaled to
% a reference gain, with the scaling factor saved in the *.hea file.
%
%Written by Ikaro Silva 2010
%Modified by Louis Mayaud 2011
% Version 1.0
%
% Since 0.0.1
% See also wrsamp, wfdbdesc
%
%%%%%%%%%% Example 1 %%%%%%%%%%%%
%
% display('***This example will write a Ex1.dat and Ex1.hea file to your current directory!')
% s=input('Hit "ctrl + c" to quit or "Enter" to continue!');
%
% %Generate 3 different signals and convert them to signed 16 bit in WFDB format
% clear all;clc;close all
% N=1024;
% Fs=48000;
% tm=[0:1/Fs:(N-1)/Fs]';
% adu='V/mV/V';
% info='Example 1';
%
%
% %First signal a ramp with 2^16 unique levels and is set to (+-) 2^15 (Volts)
% %Thus the header file should have one quant step equal to (2^15-(-2^15))/(2^16) V.
% sig1=double(int16(linspace(-2^15,2^15,N)'));
%
% %Second signal is a sine wave with 2^8 unique levels and set to (+-) 1 (mV)
% %Thus the header file should one quant step equal a (1--1)/(2^16) adu step
% sig2=double(int8(sin(2*pi*tm*1000).*(2^7)))./(2^7);
%
% %Third signal is a random binary signal set to to (+-) 1 (V) with DC (to be discarded)
% %Thus the header file should have one quant step equal a 1/(2^16) adu step.
% sig3=(rand(N,1) > 0.97)*2 -1 + 2^16;
%
% %Concatenate all signals and convert to WFDB format with default 16 bits (empty brackets)
% sig=[sig1 sig2 sig3];
% mat2wfdb(sig,'Ex1',Fs,[],adu,info)
%
% % %NOTE: If you have WFDB installed you can check the conversion by
% % %uncomenting and this section and running (notice that all signals are scaled
% % %to unit amplitude during conversion, with the header files keeping the gain info):
%
% % !rdsamp -r Ex1 > foo
% % x=dlmread('foo');
% % subplot(211)
% % plot(sig)
% % subplot(212)
% % plot(x(:,1),x(:,2));hold on;plot(x(:,1),x(:,3),'k');plot(x(:,1),x(:,4),'r')
%
%%%%%%%% End of Example 1%%%%%%%%%
%endOfHelp
machine_format='l';
skip=0;
%Set default parameters
params={'x','fname','Fs','bit_res','adu','info','gain','sg_name','baseline','isint'};
Fs=1;
adu=[];
info=[];
isint=0;
%Use cell array for baseline and gain in case of empty conditions
baseline=[];
gain=[];
sg_name=[];
x=[];
fname=[];
%Convert signal from double to appropiate type
bit_res = 16 ;
bit_res_suport=[8 16 32];
for i=1:nargin
if(~isempty(varargin{i}))
eval([params{i} '= varargin{i};'])
end
end
[N,M]=size(x);
adu=regexp(adu,'/','split');
if(isempty(gain))
gain=cell(M,1); %Generate empty cells as default
elseif(length(gain)==1)
gain=repmat(gain,[M 1]);
gain=num2cell(gain);
else
gain=gain;
end
if(isempty(sg_name))
sg_name=repmat({''},[M 1]);
end
if(isempty(adu))
adu=repmat({'V'},[M 1]);
end
if ~isempty(setdiff(bit_res,bit_res_suport))
error(['Bit res should be any of: ' num2str(bit_res_suport)]);
end
if(isempty(baseline))
baseline=cell(M,1); %Generate empty cells as default
elseif(length(baseline)==1)
baseline=repmat(baseline,[M 1]);
baseline=num2cell(baseline);
end
%Header string
head_str=cell(M+1,1);
head_str(1)={[fname ' ' num2str(M) ' ' num2str(Fs) ' ' num2str(N)]};
%Loop through all signals, digitizing them and generating lines in header
%file
eval(['y=int' num2str(bit_res) '(zeros(N,M));']) %allocate space
for m=1:M
nameArray = regexp(fname,'/','split');
if ~isempty(nameArray)
fname = nameArray{end};
end
[tmp_bit1,bit_gain,baseline_tmp,ck_sum]=quant(x(:,m), ...
bit_res,gain{m},baseline{m},isint);
y(:,m)=tmp_bit1;
head_str(m+1)={[fname '.dat ' num2str(bit_res) ' ' num2str(bit_gain) '(' ...
num2str(baseline_tmp) ')/' adu{m} ' ' '0 0 0 ' num2str(ck_sum) ' 0 ' sg_name{m}]};
end
if(length(y)<1)
error(['Converted data is empty. Exiting without saving file...'])
end
%Write *.dat file
fid = fopen([fname '.dat'],'wb',machine_format);
if(~fid)
error(['Could not create data file for writing: ' fname])
end
count=fwrite(fid,y',['int' num2str(bit_res)],skip,machine_format);
if(~count)
fclose(fid);
error(['Could not data write to file: ' fname])
end
fprintf(['Generated *.dat file: ' fname '\n'])
fclose(fid);
%Write *.hea file
fid = fopen([fname '.hea'],'w');
for m=1:M+1
if(~fid)
error(['Could not create header file for writing: ' fname])
end
fprintf(fid,'%s\n',head_str{m});
end
if(~isempty(info))
count=fprintf(fid,'#%s',info);
end
if(nargout==1)
varargout(1)={y};
end
fprintf(['Generated *.hea file: ' fname '\n'])
fclose(fid);
%%%End of Main %%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Helper function
function [y,adc_gain,baseline,check_sum]=quant(x,bit_res,gain,baseline,isint)
%shift so that the signal midrange is at 0
min_x=min(x(~isnan(x)));
nan_ind=isnan(x);
rg=max(x(~isnan(x)))-min_x;
if(isempty(baseline))
baseline=min_x + (rg/2);
end
x=x-baseline;
if(isempty(gain))
%ADC gain (ADC units per physical unit). This value is a floating-point number
%that specifies the difference in sample values that would be observed if a step
%of one physical unit occurred in the original analog signal. For ECGs, the gain
%is usually roughly equal to the R-wave amplitude in a lead that is roughly parallel
%to the mean cardiac electrical axis. If the gain is zero or missing, this indicates
%that the signal amplitude is uncalibrated; in such cases, a value of 200 (DEFGAIN,
%defined in <wfdb/wfdb.h>) ADC units per physical unit may be assumed.
%Dynamic range of encoding / Dynamic Range of Data --but leave 1 quant level for NaN
adc_gain=(2^(bit_res-1)-1)/(rg/2);
y=x.*adc_gain;
if(isint)
%Use this option if you know the signal is quantitized, and you
%want to remove round-off error by setting the original values to
%integers prior to fixed point conversion
df_db=min(diff(sort(unique(y))));
y=y/df_db;
adc_gain=adc_gain/df_db;
end
else
%if gain is alreay passed don't do anything to the signal
%the gain will be used in the header file only
%Convert the signal to integers before encoding in order minimize round off
%error
adc_gain=gain;
y=x;
end
%convert to appropiate bit type
eval(['y=int' num2str(bit_res) '(y);'])
%Shift WFDB NaN int value to a lower value so that they will not be read as NaN's by WFDB
WFDBNAN=-32768;
iswfdbnan=find(y==WFDBNAN); %-12^15 are NaNs in WFDB
if(~isempty(iswfdbnan))
y(iswfdbnan)=WFDBNAN-1;
end
%Set NaNs to WFDBNAN
y(nan_ind)=WFDBNAN;
%Calculate the 16-bit signed checksum of all samples in the signal
check_sum=sum(y);
M=check_sum/(2^15);
if(M<0)
check_sum=mod(check_sum,-2^15);
if(~check_sum && abs(M)<1)
check_sum=-2^15;
elseif (mod(ceil(M),2))
check_sum=2^15 + check_sum;
end
else
check_sum=mod(check_sum,2^15);
if(mod(floor(M),2))
check_sum=-2^15+check_sum;
end
end
%Calculate baseline (ADC units):
%The baseline is an integer that specifies the sample
%value corresponding to 0 physical units.
baseline=baseline.*adc_gain;
baseline=-round(baseline);
function y=get_names(str,deli)
y={};
old=1;
ind=regexp(str,deli);
ind(end+1)=length(str)+1;
for i=1:length(ind)
y(end+1)={str(old:ind(i)-1)};
old=ind(i)+1;
end
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
wfdbloadlib.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/wfdbloadlib.m
| 5,910 |
utf_8
|
feb96d305ef53118d12317d29239fc2c
|
function [varargout]=wfdbloadlib(varargin)
%
% [isloaded,config]=wfdbloadlib(debugLevel,networkWaitTime)
%
% Loads the WDFDB libarary if it has not been loaded already into the
% MATLAB classpath. And optionally prints configuration environment and debug information
% regarding the settings used by the classes in the JAR file.
%
% Inputs:
%
% debugLevel
% (Optional) 1x1 integer between 0 and 5 represeting the level of debug information to output from
% Java class when output configuration information. Level 0 (no debug information),
% level =5 is maximum level of information output by the class (logger set to finest). Default is level 0.
%
% networkWaitTime
% (Optional) 1x1 integer representing the longest time in
% milliseconds for which the JVM should wait for a data stream from
% PhysioNet (default is =1000 , ie one second). If you need to change this time to a
% longer value across the entire toolbox, it is better modify to default value in the source
% code below and restart MATLAB.
%
%
% Written by Ikaro Silva, 2013
% Last Modified: December 3, 2014
% Since 0.0.1
%
%
%endOfHelp
mlock
persistent isloaded wfdb_path wfdb_native_path
%%%%% SYSTEM WIDE CONFIGURATION PARAMETERS %%%%%%%
%%% Change these values for system wide configuration of the WFDB binaries
%If you are using your own custom version of the WFDB binaries, set this to true
%NOTE: this parameter is completely ignored if the 'WFDB_COMMAND_PATH' parameter
%described above is set (i.e.: the library will used the WFDB commands located
% according to the path in 'WFDB_COMMAND_PATH').
%You will need to restart MATLAB/Octave if to sync the changes.
%The default is to used commands shipped with the toolbox, this location can be obtained by running the command:
%[~,config]=wfdbloadlib; config.WFDB_NATIVE_BIN
WFDB_CUSTOMLIB=0;
%WFDB_PATH: If empty, will use the default given config.WFDB_PATH
%this is where the toolbox searches for data files (*.dat, *.hea etc).
%When unistalling the toolbox, you may wish to clear this directory to save space.
%See http://www.physionet.org/physiotools/wag/setwfd-1.htm for more details.
WFDB_PATH=[];
%WFDBCAL: If empty, will use the default giveng confing.WFDBCAL
%The WFDB library require calibration data in order to convert between sample values
%(expressed in analog-to-digital converter units, or adus) and physical units.
%See http://www.physionet.org/physiotools/wag/wfdbca-5.htm for more details.
WFDBCAL=[];
%debugLevel: Ouput JVM information while running commands
debugLevel=0;
%networkWaitTime: Setting maximum waiting period for fetching data from
%PhysioNet servers (default location: http://physionet.org/physiobank).
networkWaitTime=1000;
%%%% END OF SYSTEM WIDE CONFIGURATION PARAMETERS
inputs={'debugLevel','networkWaitTime'};
for n=1:nargin
if(~isempty(varargin{n}))
eval([inputs{n} '=varargin{n};'])
end
end
inOctave=is_octave;
fsep=filesep;
if(ispc && inOctave)
fsep=['\\']; %Need to escape '\' for regexp in Octave and Windows
end
if(isempty(isloaded))
jar_path=which('wfdbloadlib');
cut=strfind(jar_path,'wfdbloadlib.m');
wfdb_path=jar_path(1:cut-1);
if(~inOctave)
ml_jar_version=version('-java');
else
%In Octave
ml_jar_version=javaMethod('getProperty','java.lang.System','java.version');
ml_jar_version=['Java ' ml_jar_version];
end
%Check if path has not been added yet
if(~isempty(strfind(ml_jar_version,'Java 1.6')))
wfdb_path=[wfdb_path 'wfdb-app-JVM6-0-9-9.jar'];
elseif(~isempty(strfind(ml_jar_version,'Java 1.7')))
wfdb_path=[wfdb_path 'wfdb-app-JVM7-0-9-9.jar'];
else
error(['Cannot load on unsupported JVM: ' ml_jar_version])
end
javaaddpath(wfdb_path)
isloaded=1;
end
outputs={'isloaded','config'};
for n=1:nargout
if(n>1)
config.MATLAB_VERSION=version;
config.inOctave=inOctave;
if(inOctave)
javaWfdbExec=javaObject('org.physionet.wfdb.Wfdbexec','wfdb-config',WFDB_CUSTOMLIB);
javaWfdbExec.setLogLevel(debugLevel);
config.WFDB_VERSION=char(javaMethod('execToStringList',javaWfdbExec,{'--version'}));
else
javaWfdbExec=org.physionet.wfdb.Wfdbexec('wfdb-config',WFDB_CUSTOMLIB);
javaWfdbExec.setLogLevel(debugLevel);
config.WFDB_VERSION=char(javaWfdbExec.execToStringList('--version'));
end
env=regexp(char(javaWfdbExec.getEnvironment),',','split');
for e=1:length(env)
tmpstr=regexp(env{e},'=','split');
varname=strrep(tmpstr{1},'[','');
varname=strrep(varname,' ','');
varname=strrep(varname,']','');
eval(['config.' varname '=''' tmpstr{2} ''';'])
end
config.MATLAB_PATH=strrep(which('wfdbloadlib'),'wfdbloadlib.m','');
config.SUPPORT_EMAIL='[email protected]';
wver=regexp(wfdb_path,fsep,'split');
config.WFDB_JAVA_VERSION=wver{end};
config.DEBUG_LEVEL=debugLevel;
config.NETWORK_WAIT_TIME=networkWaitTime;
config.MATLAB_ARCH=computer('arch');
%Remove empty spaces from arch name
del=strfind(config.osName,' ');
config.osName(del)=[];
%Define WFDB Environment variables
if(isempty(WFDB_PATH))
WFDB_PATH=['. ' 'file:// ' config.MATLAB_PATH 'database http://physionet.org/physiobank/database'];
end
if(isempty(WFDBCAL))
WFDBCAL=[config.WFDB_JAVA_HOME fsep 'database' fsep 'wfdbcal'];
end
config.WFDB_PATH=WFDB_PATH;
config.WFDBCAL=WFDBCAL;
config.WFDB_CUSTOMLIB=WFDB_CUSTOMLIB;
end
eval(['varargout{n}=' outputs{n} ';'])
end
%% subfunction that checks if we are in octave
function r = is_octave ()
r = exist ('OCTAVE_VERSION', 'builtin')>0;
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
woody.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/woody.m
| 6,574 |
utf_8
|
0679ae612c072e1ba908279a60af43e0
|
function [out]=woody(x,varargin)
%
% [out]=woody(x,tol,max_it,est_mthd,xcorr_mthd)
%
% Weighted average using Woody average for a signal
% with jitter. Parameters:
%
% x Signal measurements. Each COLUMN represents
% and independent measure of the signal (or channel).
% tol Tolerance paremeter to stop average (default is 0.1)
% max_it Maximum number of iterations done on the average (default is 100).
% est_mthd Estimation method to use. Options are:
% 'woody' : classical approach (default)
% 'thornton' : implements the Thornton approach that is also useful for different noise sources.
% xcorr_mthd Determines what estimation method to use for the estimating the correlaation function using the
% XCORR function. Options are:
% 'biased' - scales the raw cross-correlation by 1/M.
% 'unbiased' - scales the raw correlation by 1/(M-abs(lags)). (Default)
% out Final averaged waveform (time aligned).
%
%
%
% Written by Ikaro Silva
%
% Since 0.9.5
%
% %%%Example 1 %%%%
% t=[0:1/1000:1];
% N=1001;
% x=sin(2*pi*t)+sin(4*pi*t)+sin(8*pi*t);
% y=exp(0.01*[-1*[500:-1:1] 0 -1*[1:500]]);
% s=x.*y;
% sig1=0;
% sig2=0.1;
% M=100;
% S=zeros(N,M);
% center=501;
% TAU=round((rand(1,M)-0.5)*160);
% for i=1:M,
% tau=TAU(i);
%
% if(tau<0)
% S(:,i)=[s(-1*tau:end)'; zeros(-1*(tau+1),1)];
% else
% S(:,i)=[zeros(tau,1);s(1:N-tau)'; ];
% end
% if(i<50)
% S(:,i)=S(:,i) + randn(N,1).*sig1;
% else
% S(:,i)=S(:,i) + randn(N,1).*sig2;
% end
% end
%
% [wood]=woody(S,[],[],'woody','biased');
% [thor]=woody(S,[],[],'thornton','biased');
% figure;
% subplot(211)
% plot(s,'b','LineWidth',2);grid on;hold on;plot(S,'r');plot(s,'b','LineWidth',2)
% legend('Signal','Measurements')
% subplot(212)
% plot(s);hold on;plot(mean(S,2),'r');plot(wood,'g');plot(thor,'k')
% legend('Signal','Normal Ave','Woody Ave','Thornton Ave');grid on
%endOfHelp
%Default parameter values
tol= 0.1;
max_it=100;
est_mthd='woody';
xcorr_mthd='unbiased';
thornton_sub=3; %number of subaverages to use in the thornton procedure
if(nargin>1)
if(~isempty(varargin{1}))
tol=varargin{1};
end
if(nargin>2)
if(~isempty(varargin{2}))
max_it=varargin{2};
end
if(nargin>3)
if(~isempty(varargin{3}))
est_mthd=varargin{3};
end
if(nargin>4)
if(~isempty(varargin{4}))
xcorr_mthd=varargin{4};
end
end
end
end
end
%Call repective averaging technique
switch est_mthd
case 'woody'
out=woody_core(x,tol,max_it,xcorr_mthd);
case 'thornton'
%Implement procedure from Thornton 2008
[N,M]=size(x);
K=floor(M/thornton_sub);
%Call woody several times implementing the subaverages
for k=1:K
sub=thornton_sub*k;
ind=round(linspace(1,M,sub+1));
if((length(ind)-2) > (M/2))
%Number of subaverages is equal to or just less than
%half the number of trials, move to the final stage
%and exit loop
[out,est_lags]=woody_core(x,tol,max_it,xcorr_mthd);
break
end
%Get woody average from the subaverages
%procedure converges when there is no lag changes
y=gen_subave(x,ind); %Generate sub averages
y_old=y;
err=1;
while(err)
[trash,est_lags]=woody_core(y,tol,max_it,xcorr_mthd);
x=shift_data(x,est_lags,ind,N,M);
y=gen_subave(x,ind); %Re-generate sub averages
err=sum(abs(y(:)-y_old(:)));
y_old=y;
end
end
otherwise
error(['Invalid option for est_mthd parameter: ' xcorr_mthd ' valid options are: woody, weighted, and thornton'])
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%End of Maing Function%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%Helper Functions%%%%%%%%%%%%
function x=shift_data(x,est_lags,ind,N,M)
%Shifts individual trials within each subaverage
K=length(est_lags);
for k=1:K
lag=est_lags(k);
if(lag)
if(k~=K)
sel_ind=[ind(k):ind(k+1)-1];
else
sel_ind=[ind(k):M];
end
pad=length(sel_ind);
if(lag>0)
x(:,sel_ind)=[zeros(lag-1,pad); x(lag:end,sel_ind)];
%x(:,sel_ind)=[randn(lag-1,pad).*mean(std(x(:,sel_ind))).*0.001; x(lag:end,sel_ind)];
elseif(lag<0)
x(:,sel_ind)=[x(1:N+lag,sel_ind); zeros(lag*-1,pad)];
%x(:,sel_ind)=[x(1:N+lag,sel_ind); randn(lag*-1,pad).*mean(std(x(:,sel_ind))).*0.001];
end
end
end
function [out,varargout]=woody_core(x,tol,max_it,xcorr_mthd)
[N,M]=size(x);
mx=mean(x,2);
p=zeros(N,1);
conv=1;
run=0;
sig_x=diag(sqrt(x'*x));
X=xcorr(mx);
ref=length(X)/2;
if(mod(ref,2))
ref=ceil(ref);
else
ref=floor(ref);
end
if(nargout>1)
%In this case we output the lag of the trials as well
lag_data=zeros(1,M);
end
while(conv*(run<max_it))
z=zeros(N,1);
w=ones(N,1);
for i=1:M,
y=x(:,i);
xy=xcorr(mx,y,xcorr_mthd);
[val,ind]=max(xy);
if(ind>ref)
lag=ref-ind-1;
else
lag=ref-ind;
end
if(lag>0)
num=w(lag:end)-1;
z(1:N-lag+1)=( z(1:N-lag+1).*num + y(lag:end))./w(lag:end);
w(lag:end)=w(lag:end)+1;
elseif(lag<0)
num=w(lag*(-1)+1:end)-1;
z(lag*(-1)+1:end)=( z(lag*(-1)+1:end).*num + y(1:N+lag) )./w(lag*(-1)+1:end);
w(lag*(-1)+1:end)=w(lag*(-1)+1:end)+1;
else
z=z.*(w-1)./w + y./w;
w=w+1;
end
if(exist('lag_data','var'))
lag_data(i)=lag;
end
end
old_mx=mx;
mx=z;
p_old=p;
p=mx'*x./(sqrt(mx'*mx).*sig_x');
p=sum(p)./M;
err=abs(p-p_old);
if(err<tol)
conv=0;
end
run=run+1;
end
out=mx;
if(exist('lag_data','var'))
varargout(1)={lag_data};
end
function [y]=gen_subave(x,ind)
[N,M]=size(x);
T=length(ind)-1;
y=zeros(N,T);
%Generate Subaverages
for i=1:T-1
y(:,i)=mean(x(:,ind(i):ind(i+1)-1),2);
end
y(:,end)=mean(x(:,ind(T):end),2);
|
github
|
dhirajhr/ECG-based-Biometric-Authentication-master
|
wfdbRecordViewer.m
|
.m
|
ECG-based-Biometric-Authentication-master/ECGMatlab_Project/Toolbox/wfdb-app-toolbox-0-9-9/mcode/wfdbRecordViewer.m
| 27,253 |
utf_8
|
c0504c65c81a11015aa85c985db1c311
|
function varargout = wfdbRecordViewer(varargin)
% WFDBRECORDVIEWER MATLAB code for wfdbRecordViewer.fig
% WFDBRECORDVIEWER, by itself, creates a new WFDBRECORDVIEWER or raises the existing
% singleton*.
%
% H = WFDBRECORDVIEWER returns the handle to a new WFDBRECORDVIEWER or the handle to
% the existing singleton*.
%
% WFDBRECORDVIEWER('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in WFDBRECORDVIEWER.M with the given input arguments.
%
% WFDBRECORDVIEWER('Property','Value',...) creates a new WFDBRECORDVIEWER or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before wfdbRecordViewer_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to wfdbRecordViewer_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help wfdbRecordViewer
% Last Modified by GUIDE v2.5 30-Jan-2015 12:05:48
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @wfdbRecordViewer_OpeningFcn, ...
'gui_OutputFcn', @wfdbRecordViewer_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before wfdbRecordViewer is made visible.
function wfdbRecordViewer_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to wfdbRecordViewer (see VARARGIN)
global current_record records tm tm_step signalDescription
% Choose default command line output for wfdbRecordViewer
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
[filename,directoryname] = uigetfile('*.hea','Select signal header file:');
cd(directoryname)
tmp=dir('*.hea');
N=length(tmp);
records=cell(N,1);
current_record=1;
for n=1:N
fname=tmp(n).name;
records(n)={fname(1:end-4)};
if(strcmp(fname,filename))
current_record=n;
end
end
set(handles.RecorListMenu,'String',records)
set(handles.RecorListMenu,'Value',current_record)
loadRecord(records{current_record})
set(handles.signalList,'String',signalDescription)
loadAnnotationList(records{current_record},handles);
set(handles.slider1,'Max',tm(end))
set(handles.slider1,'Min',tm(1))
set(handles.slider1,'SliderStep',[1 1]);
sliderStep=get(handles.slider1,'SliderStep');
tm_step=(tm(end)-tm(1)).*sliderStep(1);
wfdbplot(handles)
function varargout = wfdbRecordViewer_OutputFcn(~,~, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
function PreviousButton_Callback(hObject, eventdata, handles)
global current_record records
current_record=current_record - 1;
set(handles.RecorListMenu,'Value',current_record);
Refresh(hObject, eventdata, handles)
function NextButton_Callback(hObject, eventdata, handles)
global current_record records
current_record=current_record + 1;
set(handles.RecorListMenu,'Value',current_record);
Refresh(hObject, eventdata, handles)
% --------------------------------------------------------------------
function FileMenu_Callback(hObject, eventdata, handles)
% hObject handle to FileMenu (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --------------------------------------------------------------------
function OpenMenuItem_Callback(hObject, eventdata, handles)
file = uigetfile('*.fig');
if ~isequal(file, 0)
open(file);
end
% --------------------------------------------------------------------
function PrintMenuItem_Callback(hObject, eventdata, handles)
printdlg(handles.figure1)
% --------------------------------------------------------------------
function CloseMenuItem_Callback(hObject, eventdata, handles)
selection = questdlg(['Close ' get(handles.figure1,'Name') '?'],...
['Close ' get(handles.figure1,'Name') '...'],...
'Yes','No','Yes');
if strcmp(selection,'No')
return;
end
delete(handles.figure1)
% --- Executes on selection change in RecorListMenu.
function RecorListMenu_Callback(hObject, eventdata, handles)
global current_record records
current_record=get(handles.RecorListMenu,'Value');
Refresh(hObject, eventdata, handles)
% --- Executes during object creation, after setting all properties.
function RecorListMenu_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on slider movement.
function slider1_Callback(hObject, eventdata, handles)
wfdbplot(handles)
% --- Executes during object creation, after setting all properties.
function slider1_CreateFcn(hObject, eventdata, handles)
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
function loadRecord(fname)
global tm signal info tm_step signalDescription analysisSignal analysisTime
h = waitbar(0,'Loading Data. Please wait...');
try
[tm,signal]=rdmat(fname);
catch
[tm,signal]=rdsamp(fname);
end
info=wfdbdesc(fname);
R=length(info);
analysisSignal=[];
analysisTime=[];
signalDescription=cell(R,1);
for r=1:R
signalDescription(r)={info(r).Description};
end
close(h)
function loadAnn1(fname,annName)
global ann1
h = waitbar(0,'Loading Annotations. Please wait...');
if(strcmp(fname,'none'))
ann1=[];
else
[ann1,type,subtype,chan,num,comments]=rdann(fname,annName);
end
close(h)
function loadAnn2(fname,annName)
global ann2
h = waitbar(0,'Loading Annotations. Please wait...');
if(strcmp(fname,'none'))
ann1=[];
else
[ann2,type,subtype,chan,num,comments]=rdann(fname,annName);
end
close(h)
function loadAnnotationList(fname,handles)
global ann1 ann2 annDiff
ann1=[];
ann2=[];
annDiff=[];
tmp=dir([fname '*']);
annotations={'none'};
exclude={'dat','hea','edf','mat'};
for i=1:length(tmp)
name=tmp(i).name;
st=strfind(name,'.');
if(~isempty(st))
tmp_ann=name(st+1:end);
enter=1;
for k=1:length(exclude)
if(strcmp(tmp_ann,exclude{k}))
enter=0;
end
end
if(enter)
annotations(end+1)={tmp_ann};
end
end
end
set(handles.Ann1Menu,'String',annotations)
set(handles.Ann2Menu,'String',annotations)
function wfdbplot(handles)
global tm signal info tm_step ann1 ann2 annDiff ann1RR analysisSignal analysisTime analysisUnits analysisYAxis
axes(handles.axes1);
cla;
%Normalize each signal and plot them with an offset
[N,CH]=size(signal);
offset=0.5;
%Get time info
center=get(handles.slider1,'Value');
maxSlide=get(handles.slider1,'Max');
minSlide=get(handles.slider1,'Min');
if(tm_step == ( tm(end)-tm(1) ))
tm_start=tm(1);
tm_end=tm(end);
elseif(center==maxSlide)
tm_end=tm(end);
tm_start=tm_end - tm_step;
elseif(center==minSlide)
tm_start=tm(1);
tm_end=tm_start + tm_step;
else
tm_start=center - tm_step/2;
tm_end=center + tm_step/2;
end
[~,ind_start]=min(abs(tm-tm_start));
[~,ind_end]=min(abs(tm-tm_end));
DC=min(signal(ind_start:ind_end,:),[],1);
sig=signal - repmat(DC,[N 1]);
SCALE=max(sig(ind_start:ind_end,:),[],1);
SCALE(SCALE==0)=1;
sig=offset.*sig./repmat(SCALE,[N 1]);
OFFSET=offset.*[1:CH];
sig=sig + repmat(OFFSET,[N 1]);
for ch=1:CH;
plot(tm(ind_start:ind_end),sig(ind_start:ind_end,ch))
hold on ; grid on
if(~isempty(ann1))
tmp_ann1=ann1((ann1>ind_start) & (ann1<ind_end));
if(~isempty(tmp_ann1))
if(length(tmp_ann1)<30)
msize=8;
else
msize=5;
end
plot(tm(tmp_ann1),OFFSET(ch),'go','MarkerSize',msize,'MarkerFaceColor','g')
end
end
if(~isempty(ann2))
tmp_ann2=ann2((ann2>ind_start) & (ann2<ind_end));
if(~isempty(tmp_ann2))
if(length(tmp_ann2)<30)
msize=8;
else
msize=5;
end
plot(tm(tmp_ann2),OFFSET(ch),'r*','MarkerSize',msize,'MarkerFaceColor','r')
end
end
if(~isempty(info(ch).Description))
text(tm(ind_start),ch*offset+0.85*offset,info(ch).Description,'FontWeight','bold','FontSize',12)
end
end
set(gca,'YTick',[])
set(gca,'YTickLabel',[])
set(gca,'FontSize',10)
set(gca,'FontWeight','bold')
xlabel('Time (seconds)')
xlim([tm(ind_start) tm(ind_end)])
%Plot annotations in analysis window
if(~isempty(annDiff) & (get(handles.AnnotationMenu,'Value')==2))
axes(handles.AnalysisAxes);
df=annDiff((ann1>ind_start) & (ann1<ind_end));
plot(tm(tmp_ann1),df,'k*-')
text(tm(tmp_ann1(1)),max(df),'Ann Diff','FontWeight','bold','FontSize',12)
grid on
ylabel('Diff (seconds)')
xlim([tm(ind_start) tm(ind_end)])
end
%Plot custom signal in the analysis window
if(~isempty(analysisSignal))
axes(handles.AnalysisAxes);
if(isempty(analysisYAxis))
%Standard 2D Plot
plot(analysisTime,analysisSignal,'k')
grid on;
else
if(isfield(analysisYAxis,'isImage') && analysisYAxis.isImage)
%Plot scaled image
imagesc(analysisSignal)
else
%3D Plot with colormap
surf(analysisTime,analysisYAxis.values,analysisSignal,'EdgeColor','none');
axis xy; axis tight; colormap(analysisYAxis.map); view(0,90);
end
ylim([analysisYAxis.minY analysisYAxis.maxY])
end
xlim([tm(ind_start) tm(ind_end)])
if(~isempty(analysisUnits))
ylabel(analysisUnits)
end
else
%Plot RR series in analysis window
if(~isempty(ann1RR) & (get(handles.AnnotationMenu,'Value')==3))
Nann=length(ann1);
axes(handles.AnalysisAxes);
ind=(ann1(1:end)>ind_start) & (ann1(1:end)<ind_end);
ind=find(ind==1)+1;
if(~isempty(ind) && ind(end)> Nann)
ind(end)=[];
end
tm_ind=ann1(ind);
del_ind=find(tm_ind>N);
if(~isempty(del_ind))
ind(ann1(ind)==tm_ind(del_ind))=[];
tm_ind(del_ind)=[];
end
if(~isempty(ind) && ind(end)>length(ann1RR))
del_ind=find(ind>length(ann1RR));
ind(del_ind)=[];
tm_ind(del_ind)=[];
end
plot(tm(tm_ind),ann1RR(ind),'k*-')
text(tm(tm_ind(1)),max(df),'RR Series','FontWeight','bold','FontSize',12)
grid on
ylabel('Interval (seconds)')
if(~isnan(ind_start) && ~isnan(ind_end) && ~(ind_start==ind_end))
xlim([tm(ind_start) tm(ind_end)])
end
end
end
% --- Executes on selection change in TimeScaleSelection.
function TimeScaleSelection_Callback(hObject, eventdata, handles)
global tm_step tm
TM_SC=[tm(end)-tm(1) 120 60 30 15 10 5 1];
index = get(handles.TimeScaleSelection, 'Value');
%Normalize step to time range
if(TM_SC(index)>TM_SC(1))
index=1;
end
stp=TM_SC(index)/TM_SC(1);
set(handles.slider1,'SliderStep',[stp stp*10]);
tm_step=TM_SC(1).*stp(1);
axes(handles.axes1);
cla;
wfdbplot(handles)
% --- Executes during object creation, after setting all properties.
function TimeScaleSelection_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on selection change in AmplitudeScale.
function AmplitudeScale_Callback(hObject, eventdata, handles)
wfdbplot(handles)
% --- Executes during object creation, after setting all properties.
function AmplitudeScale_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on selection change in Ann1Menu.
function Ann1Menu_Callback(hObject, eventdata, handles)
global ann1 records current_record
ind = get(handles.Ann1Menu, 'Value');
annStr=get(handles.Ann1Menu, 'String');
loadAnn1(records{current_record},annStr{ind})
wfdbplot(handles)
% --- Executes during object creation, after setting all properties.
function Ann1Menu_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on selection change in Ann2Menu.
function Ann2Menu_Callback(hObject, eventdata, handles)
global ann2 records current_record
ind = get(handles.Ann2Menu, 'Value');
annStr=get(handles.Ann2Menu, 'String');
loadAnn2(records{current_record},annStr{ind})
wfdbplot(handles)
% --- Executes during object creation, after setting all properties.
function Ann2Menu_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function AnnotationMenu_Callback(hObject, eventdata, handles)
global ann1 ann1RR info tm ann2
tips=0;
Fs=double(info(1).SamplingFrequency);
annStr=get(handles.AnnotationMenu,'String');
index=get(handles.AnnotationMenu,'Value');
switch(annStr{index})
case 'Plot Annotation Differences'
h = waitbar(0,'Comparing Annotations. Please wait...');
annDiff=[];
%Compare annotation with ann1menu being the reference
N=length(ann1);
if(~isempty(ann2))
[A1,A2]=meshgrid(ann1,ann2);
annDiff=min(abs(A1-A2))./Fs;
end
close(h)
wfdbplot(handles)
case 'Plot RR Series Ann1'
h = waitbar(0,'Generating RR Series. Please wait...');
%Compare annotation with ann1menu being the reference
ann1RR=diff(ann1)./double(info(1).SamplingFrequency);
close(h)
wfdbplot(handles)
case 'Add annotations to Ann1'
%Get closest sample using ginput
if(tips)
helpdlg('Left click to add multiple annotations. Hit Enter when done.','Adding Annotations');
end
axes(handles.axes1);
[x,~]= ginput;
%Convert to samples ann to ann1
x=round(x*Fs);
ann1=sort([ann1;x]);
%Refresh annotation plot
wfdbplot(handles)
case 'Delete annotations from Ann1'
%Get closest sample using ginput
if(tips)
helpdlg('Left click on annotations to remove multiple. Hit Enter when done.','Removing Annotations');
end
axes(handles.axes1);
[x,~]= ginput;
rmN=length(x);
rm_ind=zeros(rmN,1);
for n=1:rmN
[~,tmp_ind]=min(abs(x(n)-tm(ann1)));
rm_ind(n)=tmp_ind;
end
if~(isempty(rm_ind))
ann1(rm_ind)=[];
end
%Refresh annotation plot
wfdbplot(handles)
case 'Delete annotations in a range from Ann1'
%Get closest sample using ginput
if(tips)
helpdlg('Left click on start and end regions. Hit Enter when done.','Removing Annotations');
end
axes(handles.axes1);
[x,~]= ginput;
[~,start_ind]=min(abs(x(end-1)-tm(ann1)));
[~,end_ind]=min(abs(x(end)-tm(ann1)));
ann1(start_ind:end_ind)=[];
%Refresh annotation plot
wfdbplot(handles)
case 'Edit annotations in Ann1'
%Modify closest sample using ginput
if(tips)
helpdlg('Left click on waveform will shift closest annotation to the clicked point. Hit Enter when done.','Adding Annotations');
end
axes(handles.axes1);
[x,~]= ginput;
editN=length(x);
edit_ind=zeros(editN,1);
for n=1:editN
[~,tmp_ind]=min(abs(x(n)-tm(ann1)));
edit_ind(n)=tmp_ind;
end
if~(isempty(edit_ind))
ann1(edit_ind)=round(x*Fs);
end
%Refresh annotation plot
wfdbplot(handles)
case 'Add annotations in a range from Ann2 to Ann2'
global ann2
if(tips)
helpdlg('Left click on waveform to select start and end of region to add from Ann2 to Ann1. Hit Enter when done.','Adding Annotations');
end
axes(handles.axes1);
[x,~]= ginput;
[~,start_ind]=min(abs(x(1)-tm(ann2)));
[~,end_ind]=min(abs(x(2)-tm(ann2)));
ann1=sort([ann1;ann2(start_ind:end_ind)]);
%Refresh annotation plot
wfdbplot(handles)
case 'Save modified annotations of Ann1'
global records current_record
defaultAnn=get(handles.Ann1Menu,'String');
defaultInd=get(handles.Ann1Menu,'Value');
defName={[defaultAnn{defaultInd} '_x']};
newAnn=inputdlg('Enter new annotation name:','Save Annotation',1,defName);
h=waitbar(0,['Saving annotation file: ' records{current_record} '.' newAnn{1}]);
wrann(records{current_record},newAnn{1},ann1);
close(h)
end
function AnnotationMenu_CreateFcn(hObject, eventdata, handles)
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function Refresh(hObject, eventdata, handles)
global records current_record
loadRecord(records{current_record})
loadAnnotationList(records{current_record},handles)
Ann1Menu_Callback(hObject, eventdata, handles)
Ann2Menu_Callback(hObject, eventdata, handles)
%AnalysisMenu_Callback(hObject, eventdata, handles)
% --- Executes on selection change in SignalMenu.
function SignalMenu_Callback(hObject, eventdata, handles)
% hObject handle to SignalMenu (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: contents = cellstr(get(hObject,'String')) returns SignalMenu contents as cell array
% contents{get(hObject,'Value')} returns selected item from SignalMenu
global tm signal info analysisSignal analysisTime analysisUnits analysisYAxis
contents = cellstr(get(hObject,'String'));
ind=get(handles.signalList,'Value');
str= contents{get(hObject,'Value')};
%Get Raw Signal
analysisTime=tm;
analysisSignal=signal(:,ind);
analysisUnits=strsplit(info(ind).Gain,'/');
if(length(analysisUnits)>1)
analysisUnits=analysisUnits{2};
else
analysisUnits=[];
end
Fs=double(info(ind).SamplingFrequency);
analysisYAxis=[];
switch str
case 'Plot Raw Signal'
wfdbplot(handles);
case 'Apply General Filter'
[analysisSignal]=wfdbFilter(analysisSignal);
wfdbplot(handles);
case '60/50 Hz Notch Filter'
[analysisSignal]=wfdbNotch(analysisSignal,Fs);
wfdbplot(handles);
case 'Resonator Filter'
[analysisSignal]=wfdbResonator(analysisSignal,Fs);
wfdbplot(handles);
case 'Custom Function'
[analysisSignal,analysisTime]=wfdbFunction(analysisSignal,analysisTime,Fs);
wfdbplot(handles);
case 'Spectogram Analysis'
[analysisSignal,analysisTime,analysisYAxis,analysisUnits]=wfdbSpect(analysisSignal,Fs);
wfdbplot(handles);
case 'Wavelets Analysis'
[analysisSignal,analysisYAxis,analysisUnits]=wfdbWavelets(analysisSignal,Fs);
wfdbplot(handles);
end
% --- Executes during object creation, after setting all properties.
function SignalMenu_CreateFcn(hObject, eventdata, handles)
% hObject handle to SignalMenu (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: popupmenu controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on selection change in signalList.
function signalList_Callback(hObject, eventdata, handles)
% hObject handle to signalList (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: contents = cellstr(get(hObject,'String')) returns signalList contents as cell array
% contents{get(hObject,'Value')} returns selected item from signalList
% --- Executes during object creation, after setting all properties.
function signalList_CreateFcn(hObject, eventdata, handles)
% hObject handle to signalList (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: popupmenu controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function [analysisSignal]=wfdbFilter(analysisSignal)
%Set Low-pass default values
dlgParam.prompt={'Filter Design Function (should return "a" and "b", for use by FILTFILT ):'};
dlgParam.defaultanswer={'b=fir1(48,[0.1 0.5]);a=1;'};
dlgParam.name='Filter Design Command';
dlgParam.numlines=1;
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Filtering Data. Please wait...');
try
eval([answer{1} ';']);
analysisSignal=filtfilt(b,a,analysisSignal);
catch
errordlg(['Unable to filter data! Error: ' lasterr])
end
close(h)
function [analysisSignal]=wfdbNotch(analysisSignal,Fs)
% References:
% *Rangayyan (2002), "Biomedical Signal Analysis", IEEE Press Series in BME
%
% *Hayes (1999), "Digital Signal Processing", Schaum's Outline
%Set Low-pass default values
dlgParam.prompt={'Control Paramter (0 < r < 1 ):','Notch Frequency (Hz):'};
dlgParam.defaultanswer={'0.995','60'};
dlgParam.name='Notch Filter Design';
dlgParam.numlines=1;
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Filtering Data. Please wait...');
r = str2num(answer{1}); % Control parameter. 0 < r < 1.
fn= str2num(answer{2});
cW = cos(2*pi*fn/Fs);
b=[1 -2*cW 1];
a=[1 -2*r*cW r^2];
try
eval([answer{1} ';']);
analysisSignal=filtfilt(b,a,analysisSignal);
catch
errordlg(['Unable to filter data! Error: ' lasterr])
end
close(h)
function [analysisSignal]=wfdbResonator(analysisSignal,Fs)
% References:
% *Rangayyan (2002), "Biomedical Signal Analysis", IEEE Press Series in BME
%
% *Hayes (1999), "Digital Signal Processing", Schaum's Outline
%Set Low-pass default values
dlgParam.prompt={'Resonating Frequency (Hz):','Q factor:'};
dlgParam.defaultanswer={num2str(Fs/5),'50'};
dlgParam.name='Resonator Filter Design';
dlgParam.numlines=1;
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Filtering Data. Please wait...');
fn= str2num(answer{1});
K= str2num(answer{2});
%Similar to 'Q1' but more accurate
%For details see IEEE SP 2008 (5), pg 113
beta=1+K;
f=pi*fn/Fs;
numA=tan(pi/4 - f);
denA=sin(2*f)+cos(2*f)*numA;
A=numA/denA;
b=[1 -2*A A.^2];
a=[ (beta + K*(A^2)) -2*A*(beta+K) ((A^2)*beta + K)];
try
eval([answer{1} ';']);
analysisSignal=filtfilt(b,a,analysisSignal);
catch
errordlg(['Unable to filter data! Error: ' lasterr])
end
close(h)
function [analysisSignal,analysisTime]=wfdbFunction(analysisSignal,analysisTime,Fs)
dlgParam.prompt={'Custom Function must output variables ''analysisSignal'' and ''analysisTime'''};
dlgParam.defaultanswer={'[analysisSignal,analysisTime]=foo(analysisSignal,analysisTime,Fs)'};
dlgParam.name='Evaluate Command:';
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Executing code on signal. Please wait...');
try
eval([answer{1} ';']);
analysisSignal=filtfilt(b,a,analysisSignal);
catch
errordlg(['Unable to execute code!! Error: ' lasterr])
end
close(h)
function [analysisSignal,analysisTime,analysisYAxis,analysisUnits]=wfdbSpect(analysisSignal,Fs)
persistent dlgParam
if(isempty(dlgParam))
dlgParam.prompt={'window size','overlap size','Min Frequency (Hz)','Max Frequency (Hz)','colormap'};
dlgParam.window=2^10;
dlgParam.minY= 0;
dlgParam.maxY= floor(Fs/2);
dlgParam.noverlap=round(dlgParam.window/2);
dlgParam.map='jet';
dlgParam.name='Spectogram Parameters';
dlgParam.numlines=1;
end
dlgParam.defaultanswer={num2str(dlgParam.window),num2str(dlgParam.noverlap),...
num2str(dlgParam.minY),num2str(dlgParam.maxY),dlgParam.map};
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Calculating spectogram. Please wait...');
dlgParam.window= str2num(answer{1});
dlgParam.noverlap= str2num(answer{2});
analysisYAxis.minY= str2num(answer{3});
analysisYAxis.maxY= str2num(answer{4});
analysisYAxis.map=answer{5};
dlgParam.minY=analysisYAxis.minY;
dlgParam.maxY=analysisYAxis.maxY;
dlgParam.map=analysisYAxis.map;
[~,F,analysisTime,analysisSignal] = spectrogram(analysisSignal,dlgParam.window,...
dlgParam.noverlap,dlgParam.window,Fs,'yaxis');
analysisSignal=10*log10(abs(analysisSignal));
analysisYAxis.values=F;
analysisUnits='Frequency (Hz)';
close(h)
function [analysisSignal,analysisYAxis,analysisUnits]=wfdbWavelets(analysisSignal,Fs)
persistent dlgParam
if(isempty(dlgParam))
dlgParam.prompt={'wavelet','scales','colormap','logScale'};
dlgParam.wavelet='coif2';
dlgParam.scales='1:28';
dlgParam.map='jet';
dlgParam.log='false';
dlgParam.name='Wavelet Parameters';
dlgParam.numlines=1;
end
dlgParam.defaultanswer={num2str(dlgParam.wavelet),num2str(dlgParam.scales),dlgParam.map,dlgParam.log};
answer=inputdlg(dlgParam.prompt,dlgParam.name,dlgParam.numlines,dlgParam.defaultanswer);
h = waitbar(0,'Calculating wavelets. Please wait...');
dlgParam.wavelet= answer{1};
dlgParam.scales = str2num(answer{2});
dlgParam.map= answer{3};
dlgParam.log= answer{4};
analysisYAxis.minY= dlgParam.scales(1);
analysisYAxis.maxY= dlgParam.scales(end);
analysisYAxis.map=dlgParam.map;
analysisYAxis.isImage=1;
coefs = cwt(analysisSignal,dlgParam.scales,dlgParam.wavelet);
analysisSignal = wscalogram('',coefs);
if(strcmp(dlgParam.log,'true'))
analysisSignal=log(analysisSignal);
end
analysisYAxis.values=dlgParam.scales;
analysisUnits='Scale';
close(h)
|
github
|
smaillot/3D_pose_estimation-master
|
DLT_system.m
|
.m
|
3D_pose_estimation-master/DLT_system.m
| 218 |
utf_8
|
680c2d45bf8b0c87f45b63317d5ff0b0
|
function A = DLT_system(u, x)
A = [];
for i=1:length(u)
A = [A ; DLT_point2vec(u(i,:), x(i,:))];
end
end
function A = DLT_point2vec(u, x)
A = kron(eye(2), [x,1]);
A = [A , -u' * [x,1]];
end
|
github
|
shenwei1231/caffe-LDLForests-master
|
classification_demo.m
|
.m
|
caffe-LDLForests-master/matlab/demo/classification_demo.m
| 5,412 |
utf_8
|
8f46deabe6cde287c4759f3bc8b7f819
|
function [scores, maxlabel] = classification_demo(im, use_gpu)
% [scores, maxlabel] = classification_demo(im, use_gpu)
%
% Image classification demo using BVLC CaffeNet.
%
% IMPORTANT: before you run this demo, you should download BVLC CaffeNet
% from Model Zoo (http://caffe.berkeleyvision.org/model_zoo.html)
%
% ****************************************************************************
% For detailed documentation and usage on Caffe's Matlab interface, please
% refer to Caffe Interface Tutorial at
% http://caffe.berkeleyvision.org/tutorial/interfaces.html#matlab
% ****************************************************************************
%
% input
% im color image as uint8 HxWx3
% use_gpu 1 to use the GPU, 0 to use the CPU
%
% output
% scores 1000-dimensional ILSVRC score vector
% maxlabel the label of the highest score
%
% You may need to do the following before you start matlab:
% $ export LD_LIBRARY_PATH=/opt/intel/mkl/lib/intel64:/usr/local/cuda-5.5/lib64
% $ export LD_PRELOAD=/usr/lib/x86_64-linux-gnu/libstdc++.so.6
% Or the equivalent based on where things are installed on your system
%
% Usage:
% im = imread('../../examples/images/cat.jpg');
% scores = classification_demo(im, 1);
% [score, class] = max(scores);
% Five things to be aware of:
% caffe uses row-major order
% matlab uses column-major order
% caffe uses BGR color channel order
% matlab uses RGB color channel order
% images need to have the data mean subtracted
% Data coming in from matlab needs to be in the order
% [width, height, channels, images]
% where width is the fastest dimension.
% Here is the rough matlab for putting image data into the correct
% format in W x H x C with BGR channels:
% % permute channels from RGB to BGR
% im_data = im(:, :, [3, 2, 1]);
% % flip width and height to make width the fastest dimension
% im_data = permute(im_data, [2, 1, 3]);
% % convert from uint8 to single
% im_data = single(im_data);
% % reshape to a fixed size (e.g., 227x227).
% im_data = imresize(im_data, [IMAGE_DIM IMAGE_DIM], 'bilinear');
% % subtract mean_data (already in W x H x C with BGR channels)
% im_data = im_data - mean_data;
% If you have multiple images, cat them with cat(4, ...)
% Add caffe/matlab to you Matlab search PATH to use matcaffe
if exist('../+caffe', 'dir')
addpath('..');
else
error('Please run this demo from caffe/matlab/demo');
end
% Set caffe mode
if exist('use_gpu', 'var') && use_gpu
caffe.set_mode_gpu();
gpu_id = 0; % we will use the first gpu in this demo
caffe.set_device(gpu_id);
else
caffe.set_mode_cpu();
end
% Initialize the network using BVLC CaffeNet for image classification
% Weights (parameter) file needs to be downloaded from Model Zoo.
model_dir = '../../models/bvlc_reference_caffenet/';
net_model = [model_dir 'deploy.prototxt'];
net_weights = [model_dir 'bvlc_reference_caffenet.caffemodel'];
phase = 'test'; % run with phase test (so that dropout isn't applied)
if ~exist(net_weights, 'file')
error('Please download CaffeNet from Model Zoo before you run this demo');
end
% Initialize a network
net = caffe.Net(net_model, net_weights, phase);
if nargin < 1
% For demo purposes we will use the cat image
fprintf('using caffe/examples/images/cat.jpg as input image\n');
im = imread('../../examples/images/cat.jpg');
end
% prepare oversampled input
% input_data is Height x Width x Channel x Num
tic;
input_data = {prepare_image(im)};
toc;
% do forward pass to get scores
% scores are now Channels x Num, where Channels == 1000
tic;
% The net forward function. It takes in a cell array of N-D arrays
% (where N == 4 here) containing data of input blob(s) and outputs a cell
% array containing data from output blob(s)
scores = net.forward(input_data);
toc;
scores = scores{1};
scores = mean(scores, 2); % take average scores over 10 crops
[~, maxlabel] = max(scores);
% call caffe.reset_all() to reset caffe
caffe.reset_all();
% ------------------------------------------------------------------------
function crops_data = prepare_image(im)
% ------------------------------------------------------------------------
% caffe/matlab/+caffe/imagenet/ilsvrc_2012_mean.mat contains mean_data that
% is already in W x H x C with BGR channels
d = load('../+caffe/imagenet/ilsvrc_2012_mean.mat');
mean_data = d.mean_data;
IMAGE_DIM = 256;
CROPPED_DIM = 227;
% Convert an image returned by Matlab's imread to im_data in caffe's data
% format: W x H x C with BGR channels
im_data = im(:, :, [3, 2, 1]); % permute channels from RGB to BGR
im_data = permute(im_data, [2, 1, 3]); % flip width and height
im_data = single(im_data); % convert from uint8 to single
im_data = imresize(im_data, [IMAGE_DIM IMAGE_DIM], 'bilinear'); % resize im_data
im_data = im_data - mean_data; % subtract mean_data (already in W x H x C, BGR)
% oversample (4 corners, center, and their x-axis flips)
crops_data = zeros(CROPPED_DIM, CROPPED_DIM, 3, 10, 'single');
indices = [0 IMAGE_DIM-CROPPED_DIM] + 1;
n = 1;
for i = indices
for j = indices
crops_data(:, :, :, n) = im_data(i:i+CROPPED_DIM-1, j:j+CROPPED_DIM-1, :);
crops_data(:, :, :, n+5) = crops_data(end:-1:1, :, :, n);
n = n + 1;
end
end
center = floor(indices(2) / 2) + 1;
crops_data(:,:,:,5) = ...
im_data(center:center+CROPPED_DIM-1,center:center+CROPPED_DIM-1,:);
crops_data(:,:,:,10) = crops_data(end:-1:1, :, :, 5);
|
github
|
xhuang31/AANE_MATLAB-master
|
Performance.m
|
.m
|
AANE_MATLAB-master/Performance.m
| 3,202 |
utf_8
|
ad6f8f3b492868c911c6b76ecf5768ec
|
function [F1macro,F1micro] = Performance(Xtrain,Xtest,Ytrain,Ytest)
%Evaluate the performance of classification for both multi-class and multi-label Classification
% [F1macro,F1micro] = Performance(Xtrain,Xtest,Ytrain,Ytest)
%
% Xtrain is the training data with row denotes instances, column denotes features
% Xtest is the test data with row denotes instances, column denotes features
% Ytrain is the training labels with row denotes instances
% Ytest is the test labels
% Copyright 2017, Xiao Huang and Jundong Li.
% $Revision: 1.0.0 $ $Date: 2017/10/18 00:00:00 $
%% Multi class Classification
if size(Ytrain,2) == 1 && length(unique(Ytrain)) > 2
t = templateSVM('Standardize',true);
model = fitcecoc(Xtrain,Ytrain,'Learners',t);
pred_label = predict(model,Xtest);
[micro, macro] = micro_macro_PR(pred_label,Ytest);
F1macro = macro.fscore;
F1micro = micro.fscore;
else
%% For multi-label classification, computer micro and macro
rng default % For repeatability
NumLabel = size(Ytest,2);
macroTP = zeros(NumLabel,1);
macroFP = zeros(NumLabel,1);
macroFN = zeros(NumLabel,1);
macroF = zeros(NumLabel,1);
for i = 1:NumLabel
model = fitcsvm(Xtrain,Ytrain(:,i),'Standardize',true,'KernelFunction','RBF','KernelScale','auto');
pred_label = predict(model,Xtest);
mat = confusionmat(Ytest(:,i), pred_label);
if size(mat,1) == 1
macroTP(i) = sum(pred_label);
macroFP(i) = 0;
macroFN(i) = 0;
if macroTP(i) ~= 0
macroF(i) = 1;
end
else
macroTP(i) = mat(2,2);
macroFP(i) = mat(1,2);
macroFN(i) = mat(2,1);
macroF(i) = 2*macroTP(i)/(2*macroTP(i)+macroFP(i)+macroFN(i));
end
end
F1macro = mean(macroF);
F1micro = 2*sum(macroTP)/(2*sum(macroTP)+sum(macroFP)+sum(macroFN));
end
end
function [micro, macro] = micro_macro_PR(pred_label,orig_label)
% computer micro and macro: precision, recall and fscore
mat = confusionmat(orig_label, pred_label);
len = size(mat,1);
macroTP = zeros(len,1);
macroFP = zeros(len,1);
macroFN = zeros(len,1);
macroP = zeros(len,1);
macroR = zeros(len,1);
macroF = zeros(len,1);
for i = 1:len
macroTP(i) = mat(i,i);
macroFP(i) = sum(mat(:, i))-mat(i,i);
macroFN(i) = sum(mat(i,:))-mat(i,i);
macroP(i) = macroTP(i)/(macroTP(i)+macroFP(i));
macroR(i) = macroTP(i)/(macroTP(i)+macroFN(i));
macroF(i) = 2*macroP(i)*macroR(i)/(macroP(i)+macroR(i));
end
% macroP(isnan(macroP)) = 0;
% macroR(isnan(macroR)) = 0;
macroF(isnan(macroF)) = 0;
% macro.precision = mean(macroP);
% macro.recall = mean(macroR);
macro.fscore = mean(macroF);
micro.precision = sum(macroTP)/(sum(macroTP)+sum(macroFP));
micro.recall = sum(macroTP)/(sum(macroTP)+sum(macroFN));
micro.fscore = 2*micro.precision*micro.recall/(micro.precision+micro.recall);
end
|
github
|
wincle626/HLS_Legup-master
|
sobel.m
|
.m
|
HLS_Legup-master/legup-4.0/examples/multipump/sobel/sobel.m
| 926 |
utf_8
|
071ab66f3b2a331ededc44016739b25a
|
% from http://angeljohnsy.blogspot.ca/2011/12/sobel-edge-detection.html
function sobel(image, Thresh)
if (nargin < 2) Thresh = 100; end
A=imread(image);
B=rgb2gray(A);
C=double(B);
for i=1:size(C,1)-2
for j=1:size(C,2)-2
%Sobel mask for x-direction:
Gx=((2*C(i+2,j+1)+C(i+2,j)+C(i+2,j+2))-(2*C(i,j+1)+C(i,j)+C(i,j+2)));
%Sobel mask for y-direction:
Gy=((2*C(i+1,j+2)+C(i,j+2)+C(i+2,j+2))-(2*C(i+1,j)+C(i,j)+C(i+2,j)));
%The gradient of the image
%keyboard;
B(i,j)=sqrt(Gx.^2+Gy.^2);
C(i,j)=abs(Gx)+abs(Gy);
end
end
%keyboard
%figure,imshow(A); title('Original');
%figure,imshow(B); title('Sobel gradient');
B=max(B,Thresh);
B(B==round(Thresh))=0;
B=uint8(B);
%keyboard
figure,imshow(B~=0);title('Edge detected Image');
C=max(C,Thresh);
C(C==round(Thresh))=0;
C=uint8(C);
figure,imshow(C~=0);title('Approx Edge detected Image');
|
github
|
wincle626/HLS_Legup-master
|
dct8x8.m
|
.m
|
HLS_Legup-master/legup-4.0/examples/multipump/idct/dct8x8.m
| 1,576 |
utf_8
|
5665ac4c6e35b7683e7a75ef560e7ce9
|
% from: http://www.mathworks.com/matlabcentral/fileexchange/15494-2-d-dctidct-for-jpeg-compression
function O = DCT_8X8(I)
cosines = [1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.9808 0.8315 0.5556 0.1951 -0.1951 -0.5556 -0.8315 -0.9808
0.9239 0.3827 -0.3827 -0.9239 -0.9239 -0.3827 0.3827 0.9239
0.8315 -0.1951 -0.9808 -0.5556 0.5556 0.9808 0.1951 -0.8315
0.7071 -0.7071 -0.7071 0.7071 0.7071 -0.7071 -0.7071 0.7071
0.5556 -0.9808 0.1951 0.8315 -0.8315 -0.1951 0.9808 -0.5556
0.3827 -0.9239 0.9239 -0.3827 -0.3827 0.9239 -0.9239 0.3827
0.1951 -0.5556 0.8315 -0.9808 0.9808 -0.8315 0.5556 -0.1951];
alpha = [0.1250 0.1768 0.1768 0.1768 0.1768 0.1768 0.1768 0.1768
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500];
O = double(zeros(8,8));
for p = 1 : 8
for q = 1 : 8
s = double(0);
for m = 1 : 8
for n = 1 : 8
s = s + (double(I(m,n)) * cosines(p,m) * cosines(q,n));
end
end
O(p,q) = alpha(p,q) * s;
end
end
return
|
github
|
wincle626/HLS_Legup-master
|
idct8x8.m
|
.m
|
HLS_Legup-master/legup-4.0/examples/multipump/idct/idct8x8.m
| 1,732 |
utf_8
|
b81ad096903d006ddfd0dadbbe6d41c2
|
% from: http://www.mathworks.com/matlabcentral/fileexchange/15494-2-d-dctidct-for-jpeg-compression
% a = int32(255*rand(8,8))
% a-int32(idct8x8(dct8x8(a)))
% a-int32(idct2(dct2(a)))
% correct to within a decimal place
% idct2(a)-idct8x8(a)>0.1
function O = IDCT_8X8(I)
cosines = [1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.9808 0.8315 0.5556 0.1951 -0.1951 -0.5556 -0.8315 -0.9808
0.9239 0.3827 -0.3827 -0.9239 -0.9239 -0.3827 0.3827 0.9239
0.8315 -0.1951 -0.9808 -0.5556 0.5556 0.9808 0.1951 -0.8315
0.7071 -0.7071 -0.7071 0.7071 0.7071 -0.7071 -0.7071 0.7071
0.5556 -0.9808 0.1951 0.8315 -0.8315 -0.1951 0.9808 -0.5556
0.3827 -0.9239 0.9239 -0.3827 -0.3827 0.9239 -0.9239 0.3827
0.1951 -0.5556 0.8315 -0.9808 0.9808 -0.8315 0.5556 -0.1951];
alpha = [0.1250 0.1768 0.1768 0.1768 0.1768 0.1768 0.1768 0.1768
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
0.1768 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500];
O = double(zeros(8,8));
for m = 1 : 8
for n = 1 : 8
s = double(0);
for p = 1 : 8
for q = 1 : 8
s = s + (alpha(p,q) * double(I(p,q)) * cosines(p,m) * cosines(q,n));
end
end
O(m,n) = s;
end
end
return
|
github
|
swchao/personFrameworkDetectCMU-master
|
classification_demo.m
|
.m
|
personFrameworkDetectCMU-master/3rdparty/caffe/matlab/demo/classification_demo.m
| 5,466 |
utf_8
|
45745fb7cfe37ef723c307dfa06f1b97
|
function [scores, maxlabel] = classification_demo(im, use_gpu)
% [scores, maxlabel] = classification_demo(im, use_gpu)
%
% Image classification demo using BVLC CaffeNet.
%
% IMPORTANT: before you run this demo, you should download BVLC CaffeNet
% from Model Zoo (http://caffe.berkeleyvision.org/model_zoo.html)
%
% ****************************************************************************
% For detailed documentation and usage on Caffe's Matlab interface, please
% refer to the Caffe Interface Tutorial at
% http://caffe.berkeleyvision.org/tutorial/interfaces.html#matlab
% ****************************************************************************
%
% input
% im color image as uint8 HxWx3
% use_gpu 1 to use the GPU, 0 to use the CPU
%
% output
% scores 1000-dimensional ILSVRC score vector
% maxlabel the label of the highest score
%
% You may need to do the following before you start matlab:
% $ export LD_LIBRARY_PATH=/opt/intel/mkl/lib/intel64:/usr/local/cuda-5.5/lib64
% $ export LD_PRELOAD=/usr/lib/x86_64-linux-gnu/libstdc++.so.6
% Or the equivalent based on where things are installed on your system
% and what versions are installed.
%
% Usage:
% im = imread('../../examples/images/cat.jpg');
% scores = classification_demo(im, 1);
% [score, class] = max(scores);
% Five things to be aware of:
% caffe uses row-major order
% matlab uses column-major order
% caffe uses BGR color channel order
% matlab uses RGB color channel order
% images need to have the data mean subtracted
% Data coming in from matlab needs to be in the order
% [width, height, channels, images]
% where width is the fastest dimension.
% Here is the rough matlab code for putting image data into the correct
% format in W x H x C with BGR channels:
% % permute channels from RGB to BGR
% im_data = im(:, :, [3, 2, 1]);
% % flip width and height to make width the fastest dimension
% im_data = permute(im_data, [2, 1, 3]);
% % convert from uint8 to single
% im_data = single(im_data);
% % reshape to a fixed size (e.g., 227x227).
% im_data = imresize(im_data, [IMAGE_DIM IMAGE_DIM], 'bilinear');
% % subtract mean_data (already in W x H x C with BGR channels)
% im_data = im_data - mean_data;
% If you have multiple images, cat them with cat(4, ...)
% Add caffe/matlab to your Matlab search PATH in order to use matcaffe
if exist('../+caffe', 'dir')
addpath('..');
else
error('Please run this demo from caffe/matlab/demo');
end
% Set caffe mode
if exist('use_gpu', 'var') && use_gpu
caffe.set_mode_gpu();
gpu_id = 0; % we will use the first gpu in this demo
caffe.set_device(gpu_id);
else
caffe.set_mode_cpu();
end
% Initialize the network using BVLC CaffeNet for image classification
% Weights (parameter) file needs to be downloaded from Model Zoo.
model_dir = '../../models/bvlc_reference_caffenet/';
net_model = [model_dir 'deploy.prototxt'];
net_weights = [model_dir 'bvlc_reference_caffenet.caffemodel'];
phase = 'test'; % run with phase test (so that dropout isn't applied)
if ~exist(net_weights, 'file')
error('Please download CaffeNet from Model Zoo before you run this demo');
end
% Initialize a network
net = caffe.Net(net_model, net_weights, phase);
if nargin < 1
% For demo purposes we will use the cat image
fprintf('using caffe/examples/images/cat.jpg as input image\n');
im = imread('../../examples/images/cat.jpg');
end
% prepare oversampled input
% input_data is Height x Width x Channel x Num
tic;
input_data = {prepare_image(im)};
toc;
% do forward pass to get scores
% scores are now Channels x Num, where Channels == 1000
tic;
% The net forward function. It takes in a cell array of N-D arrays
% (where N == 4 here) containing data of input blob(s) and outputs a cell
% array containing data from output blob(s)
scores = net.forward(input_data);
toc;
scores = scores{1};
scores = mean(scores, 2); % take average scores over 10 crops
[~, maxlabel] = max(scores);
% call caffe.reset_all() to reset caffe
caffe.reset_all();
% ------------------------------------------------------------------------
function crops_data = prepare_image(im)
% ------------------------------------------------------------------------
% caffe/matlab/+caffe/imagenet/ilsvrc_2012_mean.mat contains mean_data that
% is already in W x H x C with BGR channels
d = load('../+caffe/imagenet/ilsvrc_2012_mean.mat');
mean_data = d.mean_data;
IMAGE_DIM = 256;
CROPPED_DIM = 227;
% Convert an image returned by Matlab's imread to im_data in caffe's data
% format: W x H x C with BGR channels
im_data = im(:, :, [3, 2, 1]); % permute channels from RGB to BGR
im_data = permute(im_data, [2, 1, 3]); % flip width and height
im_data = single(im_data); % convert from uint8 to single
im_data = imresize(im_data, [IMAGE_DIM IMAGE_DIM], 'bilinear'); % resize im_data
im_data = im_data - mean_data; % subtract mean_data (already in W x H x C, BGR)
% oversample (4 corners, center, and their x-axis flips)
crops_data = zeros(CROPPED_DIM, CROPPED_DIM, 3, 10, 'single');
indices = [0 IMAGE_DIM-CROPPED_DIM] + 1;
n = 1;
for i = indices
for j = indices
crops_data(:, :, :, n) = im_data(i:i+CROPPED_DIM-1, j:j+CROPPED_DIM-1, :);
crops_data(:, :, :, n+5) = crops_data(end:-1:1, :, :, n);
n = n + 1;
end
end
center = floor(indices(2) / 2) + 1;
crops_data(:,:,:,5) = ...
im_data(center:center+CROPPED_DIM-1,center:center+CROPPED_DIM-1,:);
crops_data(:,:,:,10) = crops_data(end:-1:1, :, :, 5);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
format_ticks.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/cepstrum/format_ticks.m
| 17,920 |
utf_8
|
9451fdec572f520b405113bde2e3fb6c
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% BEGIN HEADER
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Name: format_tick.m
%
%Usage: [hx,hy] = ...
% format_tick(h,tickx,ticky,tickposx,tickposy,rotx,roty,offset,...
% varargin);
%
%Description: Replace or appends XTickLabels and YTickLabels of axis handle
% h with input tickx and ticky array
%
%***NOTE!***: BE SURE TO DELETE ANY PREVIOUS TEXT OBJECTS CREATED BY THIS
% FUNCTION BEFORE RUNNING THIS ON THE SAME FIGURE TWICE
%
%Required Inputs:
% h : handle of axis to change tick labels (can use gca)
% tickx : cell array of tick labels or string to append to current
% labels
% (Defaults to appending degree symbols if not input)
%
%Optional Inputs
% ticky : cell array of tick labels or string to append to current
% labels (Can use [] or not specify to ignore)
% tickposx : Vector of x positions where you want the tick labels
% (Can use [] or not specify to ignore)
% tickposy : Vector of y positions where you want the tick labels
% (Can use [] or not specify to ignore)
% rotx : Number of degrees to rotate x tick labels
% (Can use [] or not specify to ignore) Default = 0.0
% roty : Number of degrees to rotate y tick labels
% (Can use [] or not specify to ignore) Default = 0.0
% offset : Label offsets from axis in fraction of total range
% (Can use [] or not specify to ignore) Default = 0.0
%
%Optional Inputs:%
% Any standard text formatting parameters such as
% 'FontSize','FontWeight',etc.
% Use the same way you would in a set command after putting
% in the required input values.
%
%Outputs:
% hx: handle of text objects created for XTickLabels
% hy: handle of text objects created for YTickLabels
%
%Function Calls:
% None
%
%Required Data Files:
% None
%
%
%Example:
% ;Example 1: Append Degree Symbols to X-Axis of a Plot
% figure;
% plot(1:10,1:10);
% [hx,hy] = format_ticks(gca);
%
% ;Example 2: Append Degree Symbolts to X and Y Axes of a Plot
% figure;
% plot(1:10,1:10);
% [hx,hy] = format_ticks(gca,'^{\circ}','^{\circ}');
%
% ;Example 2: Append Degree Symbolts to X and Y Axes of a Plot and
% ; put a 45 degree tilt on them
% figure;
% plot(1:10,1:10);
% [hx,hy] = format_ticks(gca,'^{\circ}','^{\circ}',[],[],45,45);
%
% ;Example 3: Make a plot with fractions on the x tick labels
% figure
% plot(1:10,1:10);
% [hx,hy] = format_ticks(gca,{'$1$','$2\frac{1}{2}$','$9\frac{1}{2}$'},...
% [],[1,2.5,9.5]);
%
% ;Example 4: Make a plot with degrees on y tick label and fractions
% ; on x
% figure
% plot(0:10,0:10);
% [hx,hy] = format_ticks(gca,...
% {'$0$','$2\frac{1}{2}$','$5$','$7\frac{1}{2}$','$10$'},...
% '$^{\circ}$',[0,2.5,5,7.5,10],[],0,45,[],...
% 'FontSize',16,'FontWeight','Bold');
%
%Change Log:
% 08/19/2007: Origin Version Created by Alex Hayes
% ([email protected])
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% BEGIN FUNCTION
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [hx,hy] = ...
format_ticks(h,tickx,ticky,tickposx,tickposy,rotx,roty,offset,varargin)
%define axis text offset (percentage of total range)
if ~exist('offset','var');
offset = 0.02;
elseif length(offset) == 0;
offset = 0.02;
end;
%make sure the axis handle input really exists
if ~exist('h','var');
h = gca;
warning(['Axis handle NOT Input, Defaulting to Current Axes, '...
num2str(h)]);
elseif length(h) == 0;
h = gca;
warning(['Axis Handle NOT Input, Defaulting to Current Axes, '...
num2str(h)]);
elseif ~ishandle(h(1))
warning(['Input (' num2str(h(1)) ') is NOT an axis handle, ' ...
'defaulting to current axis, ' num2str(h)]);
h = gca;
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%BEGIN: FIRST THE X-AXIS TICK LABELS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%fix the XTickLabels if they have been erased in the past
if length(get(h,'XTickLabel'))==0;
set(h,'XTickLabel',get(h,'XTick'));
end;
%set the xtick positions if entered
if exist('tickposx','var');
if length(tickposx) > 0;
set(h,'XTick',tickposx);
end;
tickposx = get(h,'XTick');
set(h,'XTickLabel',tickposx);
end;
%make sure the xtick positions are in the xlimit range
if exist('tickposx','var');
if length(tickposx) > 0;
lim = get(h,'XLim');
if lim(1) > min(tickposx);
lim(1) = min(tickposx);
end;
if lim(2) < max(tickposx);
lim(2) = max(tickposx);
end;
set(h,'XLim',lim);
end;
end;
%get the tick labels and positions if the user did not input them
if ~exist('tickx','var');
tickx = get(h,'XTickLabel');
if ischar(tickx);
temp = tickx;
tickx = cell(1,size(temp,1));
for j=1:size(temp,1);
tickx{j} = strtrim( temp(j,:) );
end;
end;
append = '^{\circ}';
for j=1:length(tickx);
tickx{j} = [tickx{j} append];
end;
elseif length(tickx) == 0;
tickx = get(h,'XTickLabel');
if ischar(tickx);
temp = tickx;
tickx = cell(1,size(temp,1));
for j=1:size(temp,1);
tickx{j} = strtrim( temp(j,:) );
end;
end;
append = '^{\circ}';
for j=1:length(tickx);
tickx{j} = [tickx{j} append];
end;
elseif isstr(tickx);
append = tickx;
tickx = get(h,'XTickLabel');
if ischar(tickx);
temp = tickx;
tickx = cell(1,size(temp,1));
for j=1:size(temp,1);
tickx{j} = strtrim( temp(j,:) );
end;
end;
if strcmp(append(1),'$');
for j=1:length(tickx);
tickx{j} = ['$' tickx{j} append(2:end)];
end;
else;
for j=1:length(tickx);
tickx{j} = [tickx{j} append];
end;
end;
elseif ~iscell(tickx );
warning(['Input TICKX variable is not a compatible string ' ...
'or cell array! Returning...']);
return;
end;
%find out if we have to use the LaTex interpreter
temp = tickx{1};
if strcmp(temp(1),'$');
latex_on = 1;
else;
latex_on = 0;
end;
%erase the current tick label
set(h,'XTickLabel',{});
%get the x tick positions if the user did not input them
if ~exist('tickposx','var');
tickposx = get(h,'XTick');
elseif length(tickx) == 0;
tickposx = get(h,'XTick');
end;
%get the y tick positions if the user did not input them
if ~exist('tickposy','var');
tickposy = get(h,'YTick');
elseif length(tickposy) == 0;
tickposy = get(h,'YTick');
end;
%set the new tick positions
set(h,'YTick',tickposy);
set(h,'XTick',tickposx);
%check the lengths of the xtick positions and xtick labels
l1 = length(tickx);
l2 = length(tickposx);
if l1==0;
set(h,'XTickLabel',tickx);
end;
if l1~=l2;
disp(['Length of XTick = ' num2str(length(tickposx))]);
disp(['Length of XTickLabel = ' num2str(length(tickx))]);
if l2 < l1;
warning(['Reducing Length of XTickLabel!']);
else;
warning(['Reducing Length of XTick!']);
end;
l3 = min([l1,l2]);
tickx = tickx{1:l3};
tickposx = tickposx(1:l3);
end;
%set rotation to 0 if not input
if ~exist('rotx','var');
rotx = 0;
elseif length(rotx) == 0;
rotx = 0;
end;
%Convert the cell labels to a character string
%tickx = char(tickx);
tickx = cellstr(tickx);
%Make the XTICKS!
lim = get(h,'YLim');
if min(tickposy) < lim(1);
lim(1) = min(tickposy);
end;
if max(tickposy) > lim(2);
lim(2) = max(tickposy);
end;
if rotx == 0;
if latex_on;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposx),1),...
tickx,'HorizontalAlignment','center',...
'VerticalAlignment','top','rotation',rotx,'interpreter','LaTex');
else;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposx),1),...
tickx,'HorizontalAlignment','center',...
'VerticalAlignment','top','rotation',rotx);
end;
elseif rotx < 0;
if latex_on;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposx),1),...
tickx,'HorizontalAlignment','left','interpreter','LaTex',...
'VerticalAlignment','middlefi','rotation',rotx);
else;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposx),1),...
tickx,'HorizontalAlignment','left',...
'VerticalAlignment','middle','rotation',rotx);
end;
else;
if latex_on;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposx),1),...
tickx,'HorizontalAlignment','right','interpreter','LaTex',...
'VerticalAlignment','middle','rotation',rotx);
else;
hx = text(tickposx,...
repmat(lim(1)-offset*(lim(2)-lim(2)),length(tickposx),1),...
tickx,'HorizontalAlignment','right',...
'VerticalAlignment','middle','rotation',rotx);
end;
end;
%Get and set the text size and weight
set(hx,'FontSize',get(h,'FontSize'));
set(hx,'FontWeight',get(h,'FontWeight'));
%Set the additional parameters if they were input
if length(varargin) > 2;
command_string = ['set(hx'];
for j=1:2:length(varargin);
command_string = [command_string ',' ...
'''' varargin{j} ''',varargin{' num2str(j+1) '}'];
end;
command_string = [command_string ');'];
eval(command_string);
end;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%END: FIRST THE X-AXIS TICK LABELS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%BEGIN: NOW THE Y-AXIS TICK LABELS
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%only move forward if we are doing anything to the yticks
if ~exist('ticky');
hy = -1;
elseif length(ticky)==0;
hy = -1;
else;
%fix the YTickLabels if they have been erased in the past
if length(get(h,'YTickLabel'))==0;
set(h,'YTickLabel',get(h,'YTick'));
end;
%set the ytick positions if entered
if exist('tickposy','var');
if length(tickposy) > 0;
set(h,'YTick',tickposy);
set(h,'YTickLabel',tickposy);
end;
end;
%make sure the xtick positions are in the xlimit range
if exist('tickposy','var');
if length(tickposy) > 0;
lim = get(h,'YLim');
if lim(1) > min(tickposy);
lim(1) = min(tickposy);
end;
if lim(2) < max(tickposy);
lim(2) = max(tickposy);
end;
set(h,'YLim',lim);
end;
end;
%get the tick labels and positions if the user did not input them
if ~exist('ticky','var');
ticky = get(h,'YTickLabel');
if ischar(ticky);
temp = ticky;
ticky = cell(1,size(temp,1));
for j=1:size(temp,1);
ticky{j} = strtrim( temp(j,:) );
end;
end;
append = '^{\circ}';
for j=1:length(ticky);
ticky{j} = [ticky{j} append];
end;
elseif length(ticky) == 0;
ticky = get(h,'YTickLabel');
if ischar(ticky);
temp = ticky;
ticky = cell(1,size(temp,1));
for j=1:size(temp,1);
ticky{j} = strtrim( temp(j,:) );
end;
end;
append = '^{\circ}';
for j=1:length(ticky);
ticky{j} = [ticky{j} append];
end;
elseif isstr(ticky);
append = ticky;
ticky = get(h,'YTickLabel');
if ischar(ticky);
temp = ticky;
ticky = cell(1,size(temp,1));
for j=1:size(temp,1);
ticky{j} = strtrim( temp(j,:) );
end;
end;
if strcmp(append(1),'$');
for j=1:length(ticky);
ticky{j} = ['$' ticky{j} append(2:end)];
end;
else;
for j=1:length(ticky);
ticky{j} = [ticky{j} append];
end;
end;
elseif ~iscell(ticky );
warning(['Input TICKY variable is not a compatible string ' ...
'or cell array! Returning...']);
return;
end;
%find out if we have to use the LaTex interpreter
temp = ticky{1};
if strcmp(temp(1),'$');
latex_on = 1;
else;
latex_on = 0;
end;
%erase the current tick label
set(h,'YTickLabel',{});
%get the x tick positions if the user did not input them
if ~exist('tickposy','var');
tickposy = get(h,'YTick');
elseif length(ticky) == 0;
tickposy = get(h,'YTick');
end;
%get the x tick positions if the user did not input them
if ~exist('tickposx','var');
tickposx = get(h,'YTick');
elseif length(tickposx) == 0;
tickposx = get(h,'XTick');
end;
%set the new tick positions
set(h,'YTick',tickposy);
% set(h,'XTick',tickposx);
%check the lengths of the xtick positions and xtick labels
l1 = length(ticky);
l2 = length(tickposy);
if l1==0;
set(h,'YTickLabel',ticky);
end;
if l1~=l2;
disp(['Length of YTick = ' num2str(length(tickposy))]);
disp(['Length of YTickLabel = ' num2str(length(ticky))]);
if l2 < l1;
warning(['Reducing Length of YTickLabel!']);
else;
warning(['Reducing Length of YTick!']);
end;
l3 = min([l1,l2]);
ticky = ticky{1:l3};
tickposy = tickposy(1:l3);
end;
%set rotation to 0 if not input
if ~exist('roty','var');
roty = 0;
elseif length(roty) == 0;
roty = 0;
end;
%Convert the cell labels to a character string
%ticky = char(ticky);
ticky = cellstr(ticky);
%Make the YTICKS!
lim = get(h,'XLim');
if min(tickposx) < lim(1);
lim(1) = min(tickposx);
end;
if max(tickposx) > lim(2);
lim(2) = max(tickposx);
end;
if roty == 0;
if latex_on;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty,'interpreter','LaTex');
else;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty);
end;
elseif roty < 180;
if latex_on;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty,'interpreter','LaTex');
else;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty);
end;
else;
if latex_on;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty,'interpreter','LaTex');
else;
hy = text(...
repmat(lim(1)-offset*(lim(2)-lim(1)),length(tickposy),1),...
tickposy,...
ticky,'VerticalAlignment','middle',...
'HorizontalAlignment','right','rotation',roty);
end;
end;
%Get and set the text size and weight
set(hy,'FontSize',get(h,'FontSize'));
set(hy,'FontWeight',get(h,'FontWeight'));
%Set the additional parameters if they were input
if length(varargin) > 2;
command_string = ['set(hy'];
for j=1:2:length(varargin);
command_string = [command_string ',' ...
'''' varargin{j} ''',varargin{' num2str(j+1) '}'];
end;
command_string = [command_string ');'];
eval(command_string);
end;
end;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
Hungarian.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/newton-fractal/Hungarian.m
| 9,328 |
utf_8
|
51e60bc9f1f362bfdc0b4f6d67c44e80
|
function [Matching,Cost] = Hungarian(Perf)
%
% [MATCHING,COST] = Hungarian_New(WEIGHTS)
%
% A function for finding a minimum edge weight matching given a MxN Edge
% weight matrix WEIGHTS using the Hungarian Algorithm.
%
% An edge weight of Inf indicates that the pair of vertices given by its
% position have no adjacent edge.
%
% MATCHING return a MxN matrix with ones in the place of the matchings and
% zeros elsewhere.
%
% COST returns the cost of the minimum matching
% Written by: Alex Melin 30 June 2006
% Initialize Variables
Matching = zeros(size(Perf));
% Condense the Performance Matrix by removing any unconnected vertices to
% increase the speed of the algorithm
% Find the number in each column that are connected
num_y = sum(~isinf(Perf),1);
% Find the number in each row that are connected
num_x = sum(~isinf(Perf),2);
% Find the columns(vertices) and rows(vertices) that are isolated
x_con = find(num_x~=0);
y_con = find(num_y~=0);
% Assemble Condensed Performance Matrix
P_size = max(length(x_con),length(y_con));
P_cond = zeros(P_size);
P_cond(1:length(x_con),1:length(y_con)) = Perf(x_con,y_con);
if isempty(P_cond)
Cost = 0;
return
end
% Ensure that a perfect matching exists
% Calculate a form of the Edge Matrix
Edge = P_cond;
Edge(P_cond~=Inf) = 0;
% Find the deficiency(CNUM) in the Edge Matrix
cnum = min_line_cover(Edge);
% Project additional vertices and edges so that a perfect matching
% exists
Pmax = max(max(P_cond(P_cond~=Inf)));
P_size = length(P_cond)+cnum;
P_cond = ones(P_size)*Pmax;
P_cond(1:length(x_con),1:length(y_con)) = Perf(x_con,y_con);
%*************************************************
% MAIN PROGRAM: CONTROLS WHICH STEP IS EXECUTED
%*************************************************
exit_flag = 1;
stepnum = 1;
while exit_flag
switch stepnum
case 1
[P_cond,stepnum] = step1(P_cond);
case 2
[r_cov,c_cov,M,stepnum] = step2(P_cond);
case 3
[c_cov,stepnum] = step3(M,P_size);
case 4
[M,r_cov,c_cov,Z_r,Z_c,stepnum] = step4(P_cond,r_cov,c_cov,M);
case 5
[M,r_cov,c_cov,stepnum] = step5(M,Z_r,Z_c,r_cov,c_cov);
case 6
[P_cond,stepnum] = step6(P_cond,r_cov,c_cov);
case 7
exit_flag = 0;
end
end
% Remove all the virtual satellites and targets and uncondense the
% Matching to the size of the original performance matrix.
Matching(x_con,y_con) = M(1:length(x_con),1:length(y_con));
Cost = sum(sum(Perf(Matching==1)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% STEP 1: Find the smallest number of zeros in each row
% and subtract that minimum from its row
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [P_cond,stepnum] = step1(P_cond)
P_size = length(P_cond);
% Loop throught each row
for ii = 1:P_size
rmin = min(P_cond(ii,:));
P_cond(ii,:) = P_cond(ii,:)-rmin;
end
stepnum = 2;
%**************************************************************************
% STEP 2: Find a zero in P_cond. If there are no starred zeros in its
% column or row start the zero. Repeat for each zero
%**************************************************************************
function [r_cov,c_cov,M,stepnum] = step2(P_cond)
% Define variables
P_size = length(P_cond);
r_cov = zeros(P_size,1); % A vector that shows if a row is covered
c_cov = zeros(P_size,1); % A vector that shows if a column is covered
M = zeros(P_size); % A mask that shows if a position is starred or primed
for ii = 1:P_size
for jj = 1:P_size
if P_cond(ii,jj) == 0 && r_cov(ii) == 0 && c_cov(jj) == 0
M(ii,jj) = 1;
r_cov(ii) = 1;
c_cov(jj) = 1;
end
end
end
% Re-initialize the cover vectors
r_cov = zeros(P_size,1); % A vector that shows if a row is covered
c_cov = zeros(P_size,1); % A vector that shows if a column is covered
stepnum = 3;
%**************************************************************************
% STEP 3: Cover each column with a starred zero. If all the columns are
% covered then the matching is maximum
%**************************************************************************
function [c_cov,stepnum] = step3(M,P_size)
c_cov = sum(M,1);
if sum(c_cov) == P_size
stepnum = 7;
else
stepnum = 4;
end
%**************************************************************************
% STEP 4: Find a noncovered zero and prime it. If there is no starred
% zero in the row containing this primed zero, Go to Step 5.
% Otherwise, cover this row and uncover the column containing
% the starred zero. Continue in this manner until there are no
% uncovered zeros left. Save the smallest uncovered value and
% Go to Step 6.
%**************************************************************************
function [M,r_cov,c_cov,Z_r,Z_c,stepnum] = step4(P_cond,r_cov,c_cov,M)
P_size = length(P_cond);
zflag = 1;
while zflag
% Find the first uncovered zero
row = 0; col = 0; exit_flag = 1;
ii = 1; jj = 1;
while exit_flag
if P_cond(ii,jj) == 0 && r_cov(ii) == 0 && c_cov(jj) == 0
row = ii;
col = jj;
exit_flag = 0;
end
jj = jj + 1;
if jj > P_size; jj = 1; ii = ii+1; end
if ii > P_size; exit_flag = 0; end
end
% If there are no uncovered zeros go to step 6
if row == 0
stepnum = 6;
zflag = 0;
Z_r = 0;
Z_c = 0;
else
% Prime the uncovered zero
M(row,col) = 2;
% If there is a starred zero in that row
% Cover the row and uncover the column containing the zero
if sum(find(M(row,:)==1)) ~= 0
r_cov(row) = 1;
zcol = find(M(row,:)==1);
c_cov(zcol) = 0;
else
stepnum = 5;
zflag = 0;
Z_r = row;
Z_c = col;
end
end
end
%**************************************************************************
% STEP 5: Construct a series of alternating primed and starred zeros as
% follows. Let Z0 represent the uncovered primed zero found in Step 4.
% Let Z1 denote the starred zero in the column of Z0 (if any).
% Let Z2 denote the primed zero in the row of Z1 (there will always
% be one). Continue until the series terminates at a primed zero
% that has no starred zero in its column. Unstar each starred
% zero of the series, star each primed zero of the series, erase
% all primes and uncover every line in the matrix. Return to Step 3.
%**************************************************************************
function [M,r_cov,c_cov,stepnum] = step5(M,Z_r,Z_c,r_cov,c_cov)
zflag = 1;
ii = 1;
while zflag
% Find the index number of the starred zero in the column
rindex = find(M(:,Z_c(ii))==1);
if rindex > 0
% Save the starred zero
ii = ii+1;
% Save the row of the starred zero
Z_r(ii,1) = rindex;
% The column of the starred zero is the same as the column of the
% primed zero
Z_c(ii,1) = Z_c(ii-1);
else
zflag = 0;
end
% Continue if there is a starred zero in the column of the primed zero
if zflag == 1;
% Find the column of the primed zero in the last starred zeros row
cindex = find(M(Z_r(ii),:)==2);
ii = ii+1;
Z_r(ii,1) = Z_r(ii-1);
Z_c(ii,1) = cindex;
end
end
% UNSTAR all the starred zeros in the path and STAR all primed zeros
for ii = 1:length(Z_r)
if M(Z_r(ii),Z_c(ii)) == 1
M(Z_r(ii),Z_c(ii)) = 0;
else
M(Z_r(ii),Z_c(ii)) = 1;
end
end
% Clear the covers
r_cov = r_cov.*0;
c_cov = c_cov.*0;
% Remove all the primes
M(M==2) = 0;
stepnum = 3;
% *************************************************************************
% STEP 6: Add the minimum uncovered value to every element of each covered
% row, and subtract it from every element of each uncovered column.
% Return to Step 4 without altering any stars, primes, or covered lines.
%**************************************************************************
function [P_cond,stepnum] = step6(P_cond,r_cov,c_cov)
a = find(r_cov == 0);
b = find(c_cov == 0);
minval = min(min(P_cond(a,b)));
P_cond(find(r_cov == 1),:) = P_cond(find(r_cov == 1),:) + minval;
P_cond(:,find(c_cov == 0)) = P_cond(:,find(c_cov == 0)) - minval;
stepnum = 4;
function cnum = min_line_cover(Edge)
% Step 2
[r_cov,c_cov,M,stepnum] = step2(Edge);
% Step 3
[c_cov,stepnum] = step3(M,length(Edge));
% Step 4
[M,r_cov,c_cov,Z_r,Z_c,stepnum] = step4(Edge,r_cov,c_cov,M);
% Calculate the deficiency
cnum = length(Edge)-sum(r_cov)-sum(c_cov);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
glasso_solver.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/graphical-lasso/glasso_solver.m
| 2,722 |
utf_8
|
6796909c4c43ae392d5d83535db957be
|
% Graphical Lasso function
% Author: Xiaohui Chen ([email protected])
% Version: 2012-Feb
function [Theta W] = glasso_solver(S, rho, maxIt, tol)
% Solve the graphical Lasso
% minimize_{Theta > 0} tr(S*Theta) - logdet(Theta) + rho * ||Theta||_1
% Ref: Friedman et al. (2007) Sparse inverse covariance estimation with the
% graphical lasso. Biostatistics.
% Note: This function needs to call an algorithm that solves the Lasso
% problem. Here, we choose to use to the function *lassoShooting* (shooting
% algorithm) for this purpose. However, any Lasso algorithm in the
% penelized form will work.
%
% Input:
% S -- sample covariance matrix
% rho -- regularization parameter
% maxIt -- maximum number of iterations
% tol -- convergence tolerance level
%
% Output:
% Theta -- inverse covariance matrix estimate
% W -- regularized covariance matrix estimate, W = Theta^-1
p = size(S,1);
if nargin < 4, tol = 1e-6; end
if nargin < 3, maxIt = 1e2; end
% Initialization
W = S + rho * eye(p); % diagonal of W remains unchanged
W_old = W;
i = 0;
% Graphical Lasso loop
while i < maxIt,
i = i+1;
for j = p:-1:1,
jminus = setdiff(1:p,j);
[V D] = eig(W(jminus,jminus));
d = diag(D);
X = V * diag(sqrt(d)) * V'; % W_11^(1/2)
Y = V * diag(1./sqrt(d)) * V' * S(jminus,j); % W_11^(-1/2) * s_12
b = lassoShooting(X, Y, rho, maxIt, tol);
W(jminus,j) = W(jminus,jminus) * b;
W(j,jminus) = W(jminus,j)';
end
% Stop criterion
if norm(W-W_old,1) < tol,
break;
end
W_old = W;
end
if i == maxIt,
fprintf('%s\n', 'Maximum number of iteration reached, glasso may not converge.');
end
Theta = W^-1;
% Shooting algorithm for Lasso (unstandardized version)
function b = lassoShooting(X, Y, lambda, maxIt, tol),
if nargin < 4, tol = 1e-6; end
if nargin < 3, maxIt = 1e2; end
% Initialization
[n,p] = size(X);
if p > n,
b = zeros(p,1); % From the null model, if p > n
else
b = X \ Y; % From the OLS estimate, if p <= n
end
b_old = b;
i = 0;
% Precompute X'X and X'Y
XTX = X'*X;
XTY = X'*Y;
% Shooting loop
while i < maxIt,
i = i+1;
for j = 1:p,
jminus = setdiff(1:p,j);
S0 = XTX(j,jminus)*b(jminus) - XTY(j); % S0 = X(:,j)'*(X(:,jminus)*b(jminus)-Y)
if S0 > lambda,
b(j) = (lambda-S0) / norm(X(:,j),2)^2;
elseif S0 < -lambda,
b(j) = -(lambda+S0) / norm(X(:,j),2)^2;
else
b(j) = 0;
end
end
delta = norm(b-b_old,1); % Norm change during successive iterations
if delta < tol, break; end
b_old = b;
end
if i == maxIt,
fprintf('%s\n', 'Maximum number of iteration reached, shooting may not converge.');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
plot_quadtree.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/cart/toolbox-cart/plot_quadtree.m
| 2,304 |
utf_8
|
36dc15aa95e9dab104a6f90ce381d27c
|
function plot_quadtree(W, f, options)
% plot_quadtree - plot an image quadtree
%
% plot_quadtree(T, f, options);
%
% f is a background image.
%
% Copyright (c) 2010 Gabriel Peyre
options.null = 0;
if nargin<2
f = [];
end
n = size(f,1);
J = length(W);
str = 'r';
str_geom = 'b';
hold on;
% display image
if ~isempty(f)
%f = f';
%f = f(end:-1:1,:);
%f = fliplr(f);
imagesc([0 1],[0 1],f);
colormap gray(256);
end
plot_square([0,0], 1, str);
axis square;
axis off;
axis equal;
cx = [.5];
cy = [.5];
v = 1;
for j=1:J
z = v(:)*0; z(v(:)) = 1:length(v(:));
w = 1/2^j; % width of a square
for k=1:length(W{j})
if W{j}(k)==0
plot_cross([cy(z(k)) cx(z(k))], w*2, str);
end
end
% update for the next scale
cx1 = zeros(2^j,2^j);
cx1(1:2:end,1:2:end) = cx-w/2;
cx1(2:2:end,1:2:end) = cx+w/2;
cx1(1:2:end,2:2:end) = cx-w/2;
cx1(2:2:end,2:2:end) = cx+w/2;
cy1 = zeros(2^j,2^j);
cy1(1:2:end,1:2:end) = cy-w/2;
cy1(2:2:end,1:2:end) = cy-w/2;
cy1(1:2:end,2:2:end) = cy+w/2;
cy1(2:2:end,2:2:end) = cy+w/2;
cx = cx1;
cy = cy1;
% update for the next scale
v1 = zeros(2^j,2^j);
v1(1:2:end,1:2:end) = v*4-3;
v1(2:2:end,1:2:end) = v*4-2;
v1(1:2:end,2:2:end) = v*4-1;
v1(2:2:end,2:2:end) = v*4;
v = v1;
end
axis ij
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function plot_cross(pos, w, str)
pos = swap_pos(pos);
if nargin<3
str = 'r';
end
x = [pos(1)-w/2, pos(1)+w/2];
y = [pos(2), pos(2)];
plot(x,y, str);
x = [pos(1), pos(1)];
y = [pos(2)-w/2, pos(2)+w/2];
plot(x,y, str);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function plot_square(pos, w, str)
% pos = swap_pos(pos);
if nargin<3
str = 'r';
end
x = [pos(1), pos(1)+w, pos(1)+w, pos(1), pos(1)];
y = [pos(2), pos(2), pos(2)+w, pos(2)+w, pos(2)];
plot(x,y, str);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function plot_square_geometry(theta,pos,w, str)
if nargin<4
str = 'b';
end
% pos = pos(2:-1:1);
x = pos(1)+w/2 + w/2*[cos(theta), -cos(theta)];
y = pos(2)+w/2 + w/2*[sin(theta), -sin(theta)];
plot(x,y, str);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function pos1 = swap_pos(pos)
pos1 = pos;
% pos1 = pos(2:-1:1);
%% pos1(1) = 1-pos1(1);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
plot_tree.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/cart/toolbox-cart/plot_tree.m
| 1,658 |
utf_8
|
e6be3a012e8a2f5c2eb29c0eecc71e9e
|
function plot_tree(Tree)
% plot_tree - display a tree
%
% plot_tree(Tree);
%
% Copyright (c) 2007 Gabriel Peyre
J = length(Tree);
% branching factor
q = length(Tree{2})/length(Tree{1});
% edge
edgecolor = 'b';
% leaf
leafcolor = 'r.';
leafsize = 20;
% node
nodecolor = 'b.';
nodesize = 15;
delta = [-0.018,-0.045];
textsize = 20;
% clf;
hold on;
for j=1:J
t = Tree{j};
hj = 1-(j-1)*1/J;
Hj = 1-j*1/J;
nj = q^(j-1); % number of nodes
xj = linspace(0,1,nj+2); xj(1) = []; xj(end) = [];
Xj = linspace(0,1,nj*q+2); Xj(1) = []; Xj(end) = [];
for i=1:nj
if t(i)==0
% plot two branch
for s=1:q
plot([xj(i) Xj(q*(i-1)+s)], [hj Hj], edgecolor);
end
% plot([xj(i) Xj(2*i)], [hj Hj], edgecolor);
plot_point(xj(i), hj, nodecolor, nodesize);
% plot the choice
if 0
h = text( xj(i)+delta(1), hj+delta(2), num2str(t(i)) );
set(h, 'FontSize', textsize);
set(h, 'FontWeight', 'bold');
end
if j==J
plot_point(Xj(2*i-1), Hj, leafcolor, leafsize);
plot_point(Xj(2*i), Hj, leafcolor, leafsize);
end
elseif t(i)==+1
plot_point(xj(i), hj, leafcolor, leafsize);
elseif t(i)==-1
% plot_point(xj(i), hj, 'k', leafsize/2);
end
end
end
% plot invisible bouding box
h = plot([0 1 1 0], [0 0 1 1]);
set(h, 'LineStyle', 'none');
hold off;
axis tight; axis off;
%%%
function plot_point(x,y,c,s)
h = plot(x, y, c);
set(h, 'MarkerSize', s);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
patcht.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-param/patcht.m
| 4,383 |
utf_8
|
bdaee35efdd1e4a99596366a2d565917
|
function patcht(FF,VV,TF,VT,I,Options)
%%
% This function PATCHT, will show a triangulated mesh like Matlab function
% Patch but then with a texture.
%
% patcht(FF,VV,TF,VT,I,Options);
%
% inputs,
% FF : Face list 3 x N with vertex indices
% VV : Vertices 3 x M
% TF : Texture list 3 x N with texture vertex indices
% VT : Texture Coordinates s 2 x K, range must be [0..1] or real pixel postions
% I : The texture-image RGB [O x P x 3] or Grayscale [O x P]
% Options : Structure with options for the textured patch such as
% EdgeColor, EdgeAlpha see help "Surface Properties :: Functions"
%
% Options.PSize : Special option, defines the image texturesize for each
% individual polygon, a low number gives a more block
% like texture, defaults to 64;
%
% note:
% On a normal PC displaying 10,000 faces will take about 6 sec.
%
% Example,
%
% % Load Data;
% load testdata;
% % Show the textured patch
% figure, patcht(FF,VV,TF,VT,I);
% % Allow Camera Control (with left, right and center mouse button)
% mouse3d
%
% Function is written by D.Kroon University of Twente (July 2010)
% FaceColor is a texture
Options.FaceColor='texturemap';
% Size of texture image used for every triangle
if(isfield(Options,'PSize'))
sizep=round(Options.PSize(1));
Options=rmfield(Options,'PSize');
else
sizep=64;
end
% Check input sizes
if(size(FF,2)~=size(TF,2))
error('patcht:inputs','Face list must be equal in size to texture-index list');
end
if((ndims(I)~=2)&&(ndims(I)~=3))
error('patcht:inputs','No valid Input texture image');
end
% Detect if grayscale or color image
switch(size(I,3))
case 1
iscolor=false;
case 3
iscolor=true;
otherwise
error('patcht:inputs','No valid Input texture image');
end
if(max(VT(:))<2)
% Remap texture coordinates to image coordinates
VT2(:,1)=(size(I,1)-1)*(VT(:,1))+1;
VT2(:,2)=(size(I,2)-1)*(VT(:,2))+1;
else
VT2=VT;
end
% Calculate the texture interpolation values
[lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep);
% Split texture-image in r,g,b to allow fast 1D index
Ir=I(:,:,1); if(iscolor), Ig=I(:,:,2); Ib=I(:,:,3); end
% The Patch used for every triangle (rgb)
Jr=zeros([(sizep+1) (sizep+1) 1],class(I));
if(iscolor)
Jg=zeros([(sizep+1) (sizep+1) 1],class(I));
Jb=zeros([(sizep+1) (sizep+1) 1],class(I));
end
hold on;
% Loop through all triangles of the mesh
for i=1:size(FF,1)
% Get current triangle vertices and current texture-vertices
V=VV(FF(i,:),:);
Vt=VT2(TF(i,:),:);
% Define the triangle as a surface
x=[V(1,1) V(2,1); V(3,1) V(3,1)];
y=[V(1,2) V(2,2); V(3,2) V(3,2)];
z=[V(1,3) V(2,3); V(3,3) V(3,3)];
% Define the texture coordinates of the surface
tx=[Vt(1,1) Vt(2,1) Vt(3,1) Vt(3,1)];
ty=[Vt(1,2) Vt(2,2) Vt(3,2) Vt(3,2)] ;
xy=[tx(1) ty(1); tx(2) ty(2); tx(3) ty(3); tx(3) ty(3)];
% Calculate texture interpolation coordinates
pos(:,1)=xy(1,1)*lambda1+xy(2,1)*lambda2+xy(3,1)*lambda3;
pos(:,2)=xy(1,2)*lambda1+xy(2,2)*lambda2+xy(3,2)*lambda3;
pos=round(pos); pos=max(pos,1); pos(:,1)=min(pos(:,1),size(I,1)); pos(:,2)=min(pos(:,2),size(I,2));
posind=(pos(:,1)-1)+(pos(:,2)-1)*size(I,1)+1;
% Map texture to surface image
Jr(jind)=Ir(posind);
J(:,:,1)=Jr;
if(iscolor)
Jg(jind)=Ig(posind);
Jb(jind)=Ib(posind);
J(:,:,2)=Jg;
J(:,:,3)=Jb;
end
% Show the surface
surface(x,y,z,J,Options);
end
hold off;
function [lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep)
% Define a triangle in the upperpart of an square, because only that
% part is used by the surface function
% x1=sizep; y1=sizep; x2=sizep; y2=0; x3=0 ;y3=0;
x1=sizep; y1=sizep; x2=sizep; y2=0; x3=0 ;y3=sizep;
% Calculate the bary centric coordinates (instead of creating a 2D image
% with the interpolation values, we map them directly to an 1D vector)
detT = (x1-x3)*(y2-y3) - (x2-x3)*(y1-y3);
[x,y]=ndgrid(0:sizep,0:sizep); x=x(:); y=y(:);
lambda1=((y2-y3).*(x-x3)+(x3-x2).*(y-y3))/detT;
lambda2=((y3-y1).*(x-x3)+(x1-x3).*(y-y3))/detT;
lambda3=1-lambda1-lambda2;
% Make from 2D (surface)image indices 1D image indices
[jx jy]=ndgrid(sizep-(0:sizep)+1,sizep-(0:sizep)+1);
jind=(jx(:)-1)+(jy(:)-1)*(sizep+1)+1;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
compute_boundary.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-param/compute_boundary.m
| 2,537 |
utf_8
|
1722359a4efff29fd344fc6e14eddba5
|
function boundary=compute_boundary(face, options)
% compute_boundary - compute the vertices on the boundary of a 3D mesh
%
% boundary=compute_boundary(face);
%
% Copyright (c) 2007 Gabriel Peyre
if size(face,1)<size(face,2)
face=face';
end
%% compute edges (i,j) that are adjacent to only 1 face
A = compute_edge_face_ring(face);
[i,j,v] = find(A);
i = i(v==-1);
j = j(v==-1);
%% build the boundary by traversing the edges
boundary = i(1); i(1) = []; j(1) = [];
while not(isempty(i))
b = boundary(end);
I = find(i==b);
if isempty(I)
I = find(j==b);
if isempty(I)
warning('Problem with boundary');
break;
end
boundary(end+1) = i(I);
else
boundary(end+1) = j(I);
end
i(I) = []; j(I) = [];
end
return;
%% OLD CODE %%
nvert=max(max(face));
nface=size(face,1);
% count number of faces adjacent to a vertex
A=sparse(nvert,nvert);
for i=1:nface
if verb
progressbar(i,nface);
end
f=face(i,:);
A(f(1),f(2))=A(f(1),f(2))+1;
A(f(1),f(3))=A(f(1),f(3))+1;
A(f(3),f(2))=A(f(3),f(2))+1;
end
A=A+A';
for i=1:nvert
u=find(A(i,:)==1);
if ~isempty(u)
boundary=[i u(1)];
break;
end
end
s=boundary(2);
i=2;
while(i<=nvert)
u=find(A(s,:)==1);
if length(u)~=2
warning('problem in boundary');
end
if u(1)==boundary(i-1)
s=u(2);
else
s=u(1);
end
if s~=boundary(1)
boundary=[boundary s];
else
break;
end
i=i+1;
end
if i>nvert
warning('problem in boundary');
end
%%% OLD %%%
function v = compute_boundary_old(faces)
nvert = max(face(:));
ring = compute_vertex_ring( face );
% compute boundary
v = -1;
for i=1:nvert % first find a starting vertex
f = ring{i};
if f(end)<0
v = i;
break;
end
end
if v<0
error('No boundary found.');
end
boundary = [v];
prev = -1;
while true
f = ring{v};
if f(end)>=0
error('Problem in boundary');
end
if f(1)~=prev
prev = v;
v = f(1);
else
prev = v;
v = f(end-1);
end
if ~isempty( find(boundary==v) )
% we have reach the begining of the boundary
if v~=boundary(1)
warning('Begining and end of boundary doesn''t match.');
else
break;
end
end
boundary = [boundary,v];
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
check_face_vertex.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-param/check_face_vertex.m
| 671 |
utf_8
|
21c65f119991c973909eedd356838dad
|
function [vertex,face] = check_face_vertex(vertex,face, options)
% check_face_vertex - check that vertices and faces have the correct size
%
% [vertex,face] = check_face_vertex(vertex,face);
%
% Copyright (c) 2007 Gabriel Peyre
vertex = check_size(vertex,2,4);
face = check_size(face,3,4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = check_size(a,vmin,vmax)
if isempty(a)
return;
end
if size(a,1)>size(a,2)
a = a';
end
if size(a,1)<3 && size(a,2)==3
a = a';
end
if size(a,1)<=3 && size(a,2)>=3 && sum(abs(a(:,3)))==0
% for flat triangles
% a = a';
end
if size(a,1)<vmin || size(a,1)>vmax
error('face or vertex is not of correct size');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
patcht.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-param/patcht/patcht.m
| 4,465 |
utf_8
|
aff599d5c7bab679b7b543addd97579b
|
function patcht(FF,VV,TF,VT,I,Options)
% This function PATCHT, will show a triangulated mesh like Matlab function
% Patch but then with a texture.
%
% patcht(FF,VV,TF,VT,I,Options);
%
% inputs,
% FF : Face list 3 x N with vertex indices
% VV : Vertices 3 x M
% TF : Texture list 3 x N with texture vertex indices
% VT : Texture Coordinates s 2 x K, range must be [0..1] or real pixel postions
% I : The texture-image RGB [O x P x 3] or Grayscale [O x P]
% Options : Structure with options for the textured patch such as
% EdgeColor, EdgeAlpha see help "Surface Properties :: Functions"
%
% Options.PSize : Special option, defines the image texturesize for each
% individual polygon, a low number gives a more block
% like texture, defaults to 64;
%
% note:
% On a normal PC displaying 10,000 faces will take about 6 sec.
%
% Example,
%
% % Load Data;
% load testdata;
% % Show the textured patch
% figure, patcht(FF,VV,TF,VT,I);
% % Allow Camera Control (with left, right and center mouse button)
% mouse3d
%
% Function is written by D.Kroon University of Twente (July 2010)
% FaceColor is a texture
Options.FaceColor='texturemap';
% Size of texture image used for every triangle
if(isfield(Options,'PSize'))
sizep=round(Options.PSize(1));
Options=rmfield(Options,'PSize');
else
sizep=64;
end
% Check input sizes
if(size(FF,2)~=size(TF,2))
error('patcht:inputs','Face list must be equal in size to texture-index list');
end
if((ndims(I)~=2)&&(ndims(I)~=3))
error('patcht:inputs','No valid Input texture image');
end
% Detect if grayscale or color image
switch(size(I,3))
case 1
iscolor=false;
case 3
iscolor=true;
otherwise
error('patcht:inputs','No valid Input texture image');
end
if(max(VT(:))<2)
% Remap texture coordinates to image coordinates
VT2(:,1)=(size(I,1)-1)*(VT(:,1))+1;
VT2(:,2)=(size(I,2)-1)*(VT(:,2))+1;
else
VT2=VT;
end
% Calculate the texture interpolation values
[lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep);
% Split texture-image in r,g,b to allow fast 1D index
Ir=I(:,:,1); if(iscolor), Ig=I(:,:,2); Ib=I(:,:,3); end
% The Patch used for every triangle (rgb)
Jr=zeros([(sizep+1) (sizep+1) 1],class(I));
if(iscolor)
Jg=zeros([(sizep+1) (sizep+1) 1],class(I));
Jb=zeros([(sizep+1) (sizep+1) 1],class(I));
end
hold on;
% Loop through all triangles of the mesh
for i=1:size(FF,1)
% Get current triangle vertices and current texture-vertices
V=VV(FF(i,:),:);
Vt=VT2(TF(i,:),:);
% Define the triangle as a surface
x=[V(1,1) V(2,1); V(3,1) V(3,1)];
y=[V(1,2) V(2,2); V(3,2) V(3,2)];
z=[V(1,3) V(2,3); V(3,3) V(3,3)];
% Define the texture coordinates of the surface
tx=[Vt(1,1) Vt(2,1) Vt(3,1) Vt(3,1)];
ty=[Vt(1,2) Vt(2,2) Vt(3,2) Vt(3,2)] ;
xy=[tx(1) ty(1); tx(2) ty(2); tx(3) ty(3); tx(3) ty(3)];
% Calculate texture interpolation coordinates
pos(:,1)=xy(1,1)*lambda1+xy(2,1)*lambda2+xy(3,1)*lambda3;
pos(:,2)=xy(1,2)*lambda1+xy(2,2)*lambda2+xy(3,2)*lambda3;
pos=round(pos); pos=max(pos,1); pos(:,1)=min(pos(:,1),size(I,1)); pos(:,2)=min(pos(:,2),size(I,2));
posind=(pos(:,1)-1)+(pos(:,2)-1)*size(I,1)+1;
% Map texture to surface image
Jr(jind)=Ir(posind);
J(:,:,1)=Jr;
if(iscolor)
Jg(jind)=Ig(posind);
Jb(jind)=Ib(posind);
J(:,:,2)=Jg;
J(:,:,3)=Jb;
end
% Show the surface
surface(x,y,z,J,Options)
end
hold off;
function [lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep)
% Define a triangle in the upperpart of an square, because only that
% part is used by the surface function
x1=sizep; y1=sizep; x2=sizep; y2=0; x3=0 ;y3=0;
% Calculate the bary centric coordinates (instead of creating a 2D image
% with the interpolation values, we map them directly to an 1D vector)
detT = (x1-x3)*(y2-y3) - (x2-x3)*(y1-y3);
[x,y]=ndgrid(0:sizep,0:sizep); x=x(:); y=y(:);
lambda1=((y2-y3).*(x-x3)+(x3-x2).*(y-y3))/detT;
lambda2=((y3-y1).*(x-x3)+(x1-x3).*(y-y3))/detT;
lambda3=1-lambda1-lambda2;
% Make from 2D (surface)image indices 1D image indices
[jx jy]=ndgrid(sizep-(0:sizep)+1,sizep-(0:sizep)+1);
jind=(jx(:)-1)+(jy(:)-1)*(sizep+1)+1;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
mouse3d.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-param/patcht/mouse3d.m
| 11,755 |
utf_8
|
21e012d7de63f0c8898540286a7e366c
|
function mouse3d(varargin)
% This function MOUSE3D enables mouse camera control on an certain figure
% axes.
%
% Enable mouse control with mouse3d(axis-handle) or just mouse3d
%
%
% MouseButtons
% Left : Rotate
% Right : Zoom
% Center : Pan
% Keys
% 'r' : Change mouse rotation from inplane to outplane
% 'i' : Go back to initial view
%
% Example,
% [X,Y,Z] = peaks(30);
% surf(X,Y,Z)
% colormap hsv
% % Enable mouse control
% mouse3d
%
% Function is written by D.Kroon University of Twente (July 2010)
if(nargin<1)
handle=gca;
else
handle=varargin{1};
if(ishandle(handle))
if(~strcmpi(get(handle,'Type'),'axes'))
error('mouse3d:input','no valid axis handle');
end
else
error('mouse3d:input','no valid axis handle');
end
end
handles.figure1=get(handle,'Parent');
handles.axes1=handle;
mouse3d_OpeningFcn(gcf, handles, varargin);
% --- Executes just before mouse3d is made visible.
function mouse3d_OpeningFcn(hObject, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to mouse3d (see VARARGIN)
% Choose default command line output for mouse3d
handles.output = hObject;
% UIWAIT makes mouse3d wait for user response (see UIRESUME)
% uiwait(handles.figure1);
data.mouse_position_pressed=[0 0];
data.mouse_position=[0 0];
data.mouse_position_last=[0 0];
data.mouse_pressed=false;
data.mouse_button='';
data.firsttime=true;
data.mouse_rotate=true;
data=loadmousepointershapes(data);
data.handles=handles;
data.trans=[0 0 0];
data.Mview=[1 0 0 0;0 1 0 0; 0 0 1 0; 0 0 0 1];
setMyData(data);
set(data.handles.axes1,'ButtonDownFcn',@axes1_ButtonDownFcn);
set(data.handles.figure1,'WindowButtonMotionFcn',@figure1_WindowButtonMotionFcn);
set(data.handles.figure1,'WindowButtonUpFcn',@figure1_WindowButtonUpFcn);
set(data.handles.figure1,'KeyPressFcn',@figure1_KeyPressFcn);
function setViewMatrix()
data=getMyData; if(isempty(data)), return, end
Mview=data.Mview;
UpVector=Mview(1,1:3);
Camtar=[0 0 0];
XYZ=Mview(2,1:3);
Forward=Mview(3,1:3);
UpVector=cross(cross(UpVector,Forward),Forward);
trans2=Mview(1:3,1:3)\data.trans(:);
Camtar=Camtar-Mview(1:3,4)'+trans2(1:3)'*data.scale;
XYZ=(XYZ-Mview(1:3,4)'+trans2(1:3)')*data.scale;
set(data.handles.axes1,'CameraUpVector', UpVector);
set(data.handles.axes1,'CameraPosition', XYZ+data.center);
set(data.handles.axes1,'CameraTarget', Camtar+data.center);
drawnow;
function setWindow()
data=getMyData; if(isempty(data)), return, end
c=get(data.handles.axes1,'Children');
jx=0; jy=0; jz=0;
if(~isempty(c))
pmin=zeros(length(c),3);
pmax=zeros(length(c),3);
for i=1:length(c)
c2=get(c(i));
if(isfield(c2,'XData')),
xd=c2.XData(:); xd(isnan(xd))=[];
jx=jx+1;
pmin(jx,1)= min(xd);
pmax(jx,1)= max(xd);
end
if(isfield(c2,'YData')),
yd=c2.YData(:); yd(isnan(yd))=[];
jy=jy+1;
pmin(jy,2)= min(yd);
pmax(jy,2)= max(yd);
end
if(isfield(c2,'ZData')),
zd=c2.ZData(:); zd(isnan(zd))=[];
jz=jz+1;
pmin(jz,3)= min(zd);
pmax(jz,3)= max(zd);
end
end
jx(jx==0)=1; jy(jy==0)=1; jz(jz==0)=1;
pmin=[min(pmin(1:jx,1)) min(pmin(1:jy,2)) min(pmin(1:jz,3))];
pmax=[max(pmax(1:jx,1)) max(pmax(1:jy,2)) max(pmax(1:jz,3))];
data.center=(pmax+pmin)/2;
data.scale=max(pmax-pmin)/2;
else
data.center=[0 0 0];
data.scale=1;
end
setMyData(data);
axis([-1 1 -1 1 -1 1]*data.scale+[data.center(1) data.center(1) data.center(2) data.center(2) data.center(3) data.center(3)]);
drawnow
set(data.handles.axes1,'CameraPositionMode','manual');
set(data.handles.axes1,'CameraUpVectorMode','manual');
set(data.handles.axes1,'CameraTargetMode','manual');
set(data.handles.axes1,'CameraViewAngleMode','manual');
set(data.handles.axes1,'PlotBoxAspectRatioMode','manual');
set(data.handles.axes1,'DataAspectRatioMode','manual');
set(data.handles.axes1,'CameraViewAngle',100);
set(get(data.handles.axes1,'Children'),'ButtonDownFcn',@axes1_ButtonDownFcn);
set(data.handles.axes1,'ButtonDownFcn',@axes1_ButtonDownFcn);
setViewMatrix()
function figure1_WindowButtonMotionFcn(hObject, eventdata)
cursor_position_in_axes();
data=getMyData(); if(isempty(data)), return, end
if(data.firsttime)
data.firsttime=false; setMyData(data);
setWindow();
end
if(data.mouse_pressed)
t1=(data.mouse_position_last(1)-data.mouse_position(1));
t2=(data.mouse_position_last(2)-data.mouse_position(2));
switch(data.mouse_button)
case 'rotate1'
R=RotationMatrix([t1 0 t2]);
data.Mview=R*data.Mview;
setMyData(data);
setViewMatrix()
case 'rotate2'
R=RotationMatrix([0 0.5*(t1+t2) 0]);
data.Mview=R*data.Mview;
setMyData(data);
setViewMatrix()
case 'pan'
data.trans=data.trans+[-t2/100 0 -t1/100];
setMyData(data);
setViewMatrix()
case 'zoom'
z=1-t2/100;
R=ResizeMatrix([z z z]);
data.Mview=R*data.Mview;
setMyData(data);
setViewMatrix()
otherwise
end
end
function R=RotationMatrix(r)
% Determine the rotation matrix (View matrix) for rotation angles xyz ...
Rx=[1 0 0 0; 0 cosd(r(1)) -sind(r(1)) 0; 0 sind(r(1)) cosd(r(1)) 0; 0 0 0 1];
Ry=[cosd(r(2)) 0 sind(r(2)) 0; 0 1 0 0; -sind(r(2)) 0 cosd(r(2)) 0; 0 0 0 1];
Rz=[cosd(r(3)) -sind(r(3)) 0 0; sind(r(3)) cosd(r(3)) 0 0; 0 0 1 0; 0 0 0 1];
R=Rx*Ry*Rz;
function M=ResizeMatrix(s)
M=[1/s(1) 0 0 0;
0 1/s(2) 0 0;
0 0 1/s(3) 0;
0 0 0 1];
function axes1_ButtonDownFcn(hObject, eventdata)
data=getMyData(); if(isempty(data)), return, end
handles=data.handles;
data.mouse_pressed=true;
data.mouse_button=get(handles.figure1,'SelectionType');
data.mouse_position_pressed=data.mouse_position;
if(strcmp(data.mouse_button,'normal'))
if(data.mouse_rotate)
data.mouse_button='rotate1';
set_mouse_shape('rotate1',data);
else
data.mouse_button='rotate2';
set_mouse_shape('rotate2',data);
end
end
if(strcmp(data.mouse_button,'open'))
end
if(strcmp(data.mouse_button,'extend'))
data.mouse_button='pan';
set_mouse_shape('pan',data);
end
if(strcmp(data.mouse_button,'alt'))
data.mouse_button='zoom';
set_mouse_shape('zoom',data);
end
setMyData(data);
function data=loadmousepointershapes(data)
I=[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0; 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0;
0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0; 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0;
0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1; 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1;
1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1; 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1;
0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1; 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0;
0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0];
I(I==0)=NaN; data.icon_mouse_rotate1=I;
I=[1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0; 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0;
1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0; 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0;
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0; 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0;
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1;
0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1; 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1;
0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1; 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1;
0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1; 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1];
I(I==0)=NaN; data.icon_mouse_rotate2=I;
I=[0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0; 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0;
0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0; 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0;
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0; 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0;
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0; 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0;
0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0; 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0;
0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0;
0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0;
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1];
I(I==0)=NaN; data.icon_mouse_zoom=I;
I=[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0; 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0;
0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0; 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0;
0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0; 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0;
0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0; 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0;
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];
I(I==0)=NaN; data.icon_mouse_pan=I;
function set_mouse_shape(type,data)
switch(type)
case 'rotate1'
set(gcf,'Pointer','custom','PointerShapeCData',data.icon_mouse_rotate1,'PointerShapeHotSpot',round(size(data.icon_mouse_rotate1)/2))
set(data.handles.figure1,'Pointer','custom');
case 'rotate2'
set(gcf,'Pointer','custom','PointerShapeCData',data.icon_mouse_rotate2,'PointerShapeHotSpot',round(size(data.icon_mouse_rotate2)/2))
set(data.handles.figure1,'Pointer','custom');
case 'select_distance'
set(data.handles.figure1,'Pointer','crosshair')
case 'select_landmark'
set(data.handles.figure1,'Pointer','crosshair')
case 'select_roi'
set(data.handles.figure1,'Pointer','crosshair')
case 'normal'
set(data.handles.figure1,'Pointer','arrow')
case 'alt'
set(data.handles.figure1,'Pointer','arrow')
case 'open'
set(data.handles.figure1,'Pointer','arrow')
case 'zoom'
set(gcf,'Pointer','custom','PointerShapeCData',data.icon_mouse_zoom,'PointerShapeHotSpot',round(size(data.icon_mouse_zoom)/2))
set(data.handles.figure1,'Pointer','custom');
case 'pan'
set(gcf,'Pointer','custom','PointerShapeCData',data.icon_mouse_pan,'PointerShapeHotSpot',round(size(data.icon_mouse_pan)/2))
set(data.handles.figure1,'Pointer','custom');
otherwise
set(data.handles.figure1,'Pointer',type);
end
% --- Executes on mouse press over figure background, over a disabled or
% --- inactive control, or over an axes background.
function figure1_WindowButtonUpFcn(hObject, eventdata)
data=getMyData(); if(isempty(data)), return, end
if(data.mouse_pressed)
data.mouse_pressed=false;
setMyData(data);
end
set_mouse_shape('arrow',data)
function cursor_position_in_axes()
data=getMyData(); if(isempty(data)), return, end;
data.mouse_position_last=data.mouse_position;
p = get(0, 'PointerLocation');
data.mouse_position=[p(1, 1) p(1, 2)];
setMyData(data);
function setMyData(data)
% Store data struct in figure
setappdata(gcf,'data3d',data);
function data=getMyData()
% Get data struct stored in figure
data=getappdata(gcf,'data3d');
% --- Executes on key press with focus on figure1 and none of its controls.
function figure1_KeyPressFcn(hObject, eventdata)
data=getappdata(gcf,'data3d');
switch(eventdata.Character)
case 'i'
data.trans=[0 0 0];
data.Mview=[1 0 0 0;0 1 0 0; 0 0 1 0; 0 0 0 1];
setMyData(data);
setViewMatrix();
case 'r'
data.mouse_rotate=~data.mouse_rotate;
setMyData(data)
otherwise
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_signal.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/fourier-signal/load_signal.m
| 12,338 |
utf_8
|
b70e4cb57d6b467ae9c90d4b3310a81f
|
function y = load_signal(name, n, options)
% load_signal - load a 1D signal
%
% y = load_signal(name, n, options);
%
% name is a string that can be :
% 'regular' (options.alpha gives regularity)
% 'step', 'rand',
% 'gaussiannoise' (options.sigma gives width of filtering in pixels),
% [natural signals]
% 'tiger', 'bell', 'bird'
% [WAVELAB signals]
% 'HeaviSine', 'Bumps', 'Blocks',
% 'Doppler', 'Ramp', 'Cusp', 'Sing', 'HiSine',
% 'LoSine', 'LinChirp', 'TwoChirp', 'QuadChirp',
% 'MishMash', 'WernerSorrows' (Heisenberg),
% 'Leopold' (Kronecker), 'Piece-Regular' (Piece-Wise Smooth),
% 'Riemann','HypChirps','LinChirps', 'Chirps', 'Gabor'
% 'sineoneoverx','Cusp2','SmoothCusp','Gaussian'
% 'Piece-Polynomial' (Piece-Wise 3rd degree polynomial)
if nargin<2
n = 1024;
end
options.null = 0;
if isfield(options, 'alpha')
alpha = options.alpha;
else
alpha = 2;
end
options.rep = '';
switch lower(name)
case 'regular'
y = gen_signal(n,alpha);
case 'step'
y = linspace(0,1,n)>0.5;
case 'stepregular'
y = linspace(0,1,n)>0.5; y=y(:);
a = gen_signal(n,2); a = a(:);
a = rescale(a,-0.1,0.1);
y = y+a;
case 'gaussiannoise'
% filtered gaussian noise
y = randn(n,1);
if isfield(options, 'sigma')
sigma = options.sigma; % variance in number of pixels
else
sigma = 20;
end
m = min(n, 6*round(sigma/2)+1);
h = compute_gaussian_filter(m,sigma/(4*n),n);
options.bound = 'per';
y = perform_convolution(y,h, options);
case 'rand'
if isfield(options, 'p1')
p1 = options.p1;
else
c = 10;
p1 = 1:c; p1 = p1/sum(p1);
end
p1 = p1(:); c = length(p1);
if isfield(options, 'p2')
p2 = options.p2;
else
if isfield(options, 'evol')
evol = options.evol;
else
evol = 0;
end
p2 = p1(:) + evol*(rand(c,1)-0.5);
p2 = max(p2,0); p2 = p2/sum(p2);
end
y = zeros(n,1);
for i=1:n
a = (i-1)/(n-1);
p = a*p1+(1-a)*p2; p = p/sum(p);
y(i) = rand_discr(p, 1);
end
case 'bird'
[y,fs] = load_sound([name '.wav'], n, options);
case 'tiger'
[y,fs] = load_sound([name '.au'], n, options);
case 'bell'
[y,fs] = load_sound([name '.wav'], n, options);
otherwise
y = MakeSignal(name,n);
end
y = y(:);
function y = gen_signal(n,alpha)
% gen_signal - generate a 1D C^\alpha signal of length n.
%
% y = gen_signal(n,alpha);
%
% The signal is scaled in [0,1].
%
% Copyright (c) 2003 Gabriel Peyr?
if nargin<2
alpha = 2;
end
y = randn(n,1);
fy = fft(y);
fy = fftshift(fy);
% filter with |omega|^{-\alpha}
h = (-n/2+1):(n/2);
h = (abs(h)+1).^(-alpha-0.5);
fy = fy.*h';
fy = fftshift(fy);
y = real( ifft(fy) );
y = (y-min(y))/(max(y)-min(y));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sig = MakeSignal(Name,n)
% MakeSignal -- Make artificial signal
% Usage
% sig = MakeSignal(Name,n)
% Inputs
% Name string: 'HeaviSine', 'Bumps', 'Blocks',
% 'Doppler', 'Ramp', 'Cusp', 'Sing', 'HiSine',
% 'LoSine', 'LinChirp', 'TwoChirp', 'QuadChirp',
% 'MishMash', 'WernerSorrows' (Heisenberg),
% 'Leopold' (Kronecker), 'Piece-Regular' (Piece-Wise Smooth),
% 'Riemann','HypChirps','LinChirps', 'Chirps', 'Gabor'
% 'sineoneoverx','Cusp2','SmoothCusp','Gaussian'
% 'Piece-Polynomial' (Piece-Wise 3rd degree polynomial)
% n desired signal length
% Outputs
% sig 1-d signal
%
% References
% Various articles of D.L. Donoho and I.M. Johnstone
%
if nargin > 1,
t = (1:n) ./n;
end
Name = lower(Name);
if strcmp(Name,'heavisine'),
sig = 4.*sin(4*pi.*t);
sig = sig - sign(t - .3) - sign(.72 - t);
elseif strcmp(Name,'bumps'),
pos = [ .1 .13 .15 .23 .25 .40 .44 .65 .76 .78 .81];
hgt = [ 4 5 3 4 5 4.2 2.1 4.3 3.1 5.1 4.2];
wth = [.005 .005 .006 .01 .01 .03 .01 .01 .005 .008 .005];
sig = zeros(size(t));
for j =1:length(pos)
sig = sig + hgt(j)./( 1 + abs((t - pos(j))./wth(j))).^4;
end
elseif strcmp(Name,'blocks'),
pos = [ .1 .13 .15 .23 .25 .40 .44 .65 .76 .78 .81];
hgt = [4 (-5) 3 (-4) 5 (-4.2) 2.1 4.3 (-3.1) 2.1 (-4.2)];
sig = zeros(size(t));
for j=1:length(pos)
sig = sig + (1 + sign(t-pos(j))).*(hgt(j)/2) ;
end
elseif strcmp(Name,'doppler'),
sig = sqrt(t.*(1-t)).*sin((2*pi*1.05) ./(t+.05));
elseif strcmp(Name,'ramp'),
sig = t - (t >= .37);
elseif strcmp(Name,'cusp'),
sig = sqrt(abs(t - .37));
elseif strcmp(Name,'sing'),
k = floor(n * .37);
sig = 1 ./abs(t - (k+.5)/n);
elseif strcmp(Name,'hisine'),
sig = sin( pi * (n * .6902) .* t);
elseif strcmp(Name,'losine'),
sig = sin( pi * (n * .3333) .* t);
elseif strcmp(Name,'linchirp'),
sig = sin(pi .* t .* ((n .* .500) .* t));
elseif strcmp(Name,'twochirp'),
sig = sin(pi .* t .* (n .* t)) + sin((pi/3) .* t .* (n .* t));
elseif strcmp(Name,'quadchirp'),
sig = sin( (pi/3) .* t .* (n .* t.^2));
elseif strcmp(Name,'mishmash'), % QuadChirp + LinChirp + HiSine
sig = sin( (pi/3) .* t .* (n .* t.^2)) ;
sig = sig + sin( pi * (n * .6902) .* t);
sig = sig + sin(pi .* t .* (n .* .125 .* t));
elseif strcmp(Name,'wernersorrows'),
sig = sin( pi .* t .* (n/2 .* t.^2)) ;
sig = sig + sin( pi * (n * .6902) .* t);
sig = sig + sin(pi .* t .* (n .* t));
pos = [ .1 .13 .15 .23 .25 .40 .44 .65 .76 .78 .81];
hgt = [ 4 5 3 4 5 4.2 2.1 4.3 3.1 5.1 4.2];
wth = [.005 .005 .006 .01 .01 .03 .01 .01 .005 .008 .005];
for j =1:length(pos)
sig = sig + hgt(j)./( 1 + abs((t - pos(j))./wth(j))).^4;
end
elseif strcmp(Name,'leopold'),
sig = (t == floor(.37 * n)/n); % Kronecker
elseif strcmp(Name,'riemann'),
sqn = round(sqrt(n));
sig = t .* 0; % Riemann's Non-differentiable Function
sig((1:sqn).^2) = 1. ./ (1:sqn);
sig = real(ifft(sig));
elseif strcmp(Name,'hypchirps'), % Hyperbolic Chirps of Mallat's book
alpha = 15*n*pi/1024;
beta = 5*n*pi/1024;
t = (1.001:1:n+.001)./n;
f1 = zeros(1,n);
f2 = zeros(1,n);
f1 = sin(alpha./(.8-t)).*(0.1<t).*(t<0.68);
f2 = sin(beta./(.8-t)).*(0.1<t).*(t<0.75);
M = round(0.65*n);
P = floor(M/4);
enveloppe = ones(1,M); % the rising cutoff function
enveloppe(1:P) = (1+sin(-pi/2+((1:P)-ones(1,P))./(P-1)*pi))/2;
enveloppe(M-P+1:M) = reverse(enveloppe(1:P));
env = zeros(1,n);
env(ceil(n/10):M+ceil(n/10)-1) = enveloppe(1:M);
sig = (f1+f2).*env;
elseif strcmp(Name,'linchirps'), % Linear Chirps of Mallat's book
b = 100*n*pi/1024;
a = 250*n*pi/1024;
t = (1:n)./n;
A1 = sqrt((t-1/n).*(1-t));
sig = A1.*(cos((a*(t).^2)) + cos((b*t+a*(t).^2)));
elseif strcmp(Name,'chirps'), % Mixture of Chirps of Mallat's book
t = (1:n)./n.*10.*pi;
f1 = cos(t.^2*n/1024);
a = 30*n/1024;
t = (1:n)./n.*pi;
f2 = cos(a.*(t.^3));
f2 = reverse(f2);
ix = (-n:n)./n.*20;
g = exp(-ix.^2*4*n/1024);
i1 = (n/2+1:n/2+n);
i2 = (n/8+1:n/8+n);
j = (1:n)/n;
f3 = g(i1).*cos(50.*pi.*j*n/1024);
f4 = g(i2).*cos(350.*pi.*j*n/1024);
sig = f1+f2+f3+f4;
enveloppe = ones(1,n); % the rising cutoff function
enveloppe(1:n/8) = (1+sin(-pi/2+((1:n/8)-ones(1,n/8))./(n/8-1)*pi))/2;
enveloppe(7*n/8+1:n) = reverse(enveloppe(1:n/8));
sig = sig.*enveloppe;
elseif strcmp(Name,'gabor'), % two modulated Gabor functions in
% Mallat's book
N = 512;
t = (-N:N)*5/N;
j = (1:N)./N;
g = exp(-t.^2*20);
i1 = (2*N/4+1:2*N/4+N);
i2 = (N/4+1:N/4+N);
sig1 = 3*g(i1).*exp(i*N/16.*pi.*j);
sig2 = 3*g(i2).*exp(i*N/4.*pi.*j);
sig = sig1+sig2;
elseif strcmp(Name,'sineoneoverx'), % sin(1/x) in Mallat's book
N = 1024;
a = (-N+1:N);
a(N) = 1/100;
a = a./(N-1);
sig = sin(1.5./(i));
sig = sig(513:1536);
elseif strcmp(Name,'cusp2'),
N = 64;
a = (1:N)./N;
x = (1-sqrt(a)) + a/2 -.5;
M = 8*N;
sig = zeros(1,M);
sig(M-1.5.*N+1:M-.5*N) = x;
sig(M-2.5*N+2:M-1.5.*N+1) = reverse(x);
sig(3*N+1:3*N + N) = .5*ones(1,N);
elseif strcmp(Name,'smoothcusp'),
sig = MakeSignal('Cusp2');
N = 64;
M = 8*N;
t = (1:M)/M;
sigma = 0.01;
g = exp(-.5.*(abs(t-.5)./sigma).^2)./sigma./sqrt(2*pi);
g = fftshift(g);
sig2 = iconv(g',sig)'/M;
elseif strcmp(Name,'piece-regular'),
sig1=-15*MakeSignal('Bumps',n);
t = (1:fix(n/12)) ./fix(n/12);
sig2=-exp(4*t);
t = (1:fix(n/7)) ./fix(n/7);
sig5=exp(4*t)-exp(4);
t = (1:fix(n/3)) ./fix(n/3);
sigma=6/40;
sig6=-70*exp(-((t-1/2).*(t-1/2))/(2*sigma^2));
sig(1:fix(n/7))= sig6(1:fix(n/7));
sig((fix(n/7)+1):fix(n/5))=0.5*sig6((fix(n/7)+1):fix(n/5));
sig((fix(n/5)+1):fix(n/3))=sig6((fix(n/5)+1):fix(n/3));
sig((fix(n/3)+1):fix(n/2))=sig1((fix(n/3)+1):fix(n/2));
sig((fix(n/2)+1):(fix(n/2)+fix(n/12)))=sig2;
sig((fix(n/2)+2*fix(n/12)):-1:(fix(n/2)+fix(n/12)+1))=sig2;
sig(fix(n/2)+2*fix(n/12)+fix(n/20)+1:(fix(n/2)+2*fix(n/12)+3*fix(n/20)))=...
-ones(1,fix(n/2)+2*fix(n/12)+3*fix(n/20)-fix(n/2)-2*fix(n/12)-fix(n/20))*25;
k=fix(n/2)+2*fix(n/12)+3*fix(n/20);
sig((k+1):(k+fix(n/7)))=sig5;
diff=n-5*fix(n/5);
sig(5*fix(n/5)+1:n)=sig(diff:-1:1);
% zero-mean
bias=sum(sig)/n;
sig=bias-sig;
elseif strcmp(Name,'piece-polynomial'),
t = (1:fix(n/5)) ./fix(n/5);
sig1=20*(t.^3+t.^2+4);
sig3=40*(2.*t.^3+t) + 100;
sig2=10.*t.^3 + 45;
sig4=16*t.^2+8.*t+16;
sig5=20*(t+4);
sig6(1:fix(n/10))=ones(1,fix(n/10));
sig6=sig6*20;
sig(1:fix(n/5))=sig1;
sig(2*fix(n/5):-1:(fix(n/5)+1))=sig2;
sig((2*fix(n/5)+1):3*fix(n/5))=sig3;
sig((3*fix(n/5)+1):4*fix(n/5))=sig4;
sig((4*fix(n/5)+1):5*fix(n/5))=sig5(fix(n/5):-1:1);
diff=n-5*fix(n/5);
sig(5*fix(n/5)+1:n)=sig(diff:-1:1);
%sig((fix(n/20)+1):(fix(n/20)+fix(n/10)))=-ones(1,fix(n/10))*20;
sig((fix(n/20)+1):(fix(n/20)+fix(n/10)))=ones(1,fix(n/10))*10;
sig((n-fix(n/10)+1):(n+fix(n/20)-fix(n/10)))=ones(1,fix(n/20))*150;
% zero-mean
bias=sum(sig)/n;
sig=sig-bias;
elseif strcmp(Name,'gaussian'),
sig=GWN(n,beta);
g=zeros(1,n);
lim=alpha*n;
mult=pi/(2*alpha*n);
g(1:lim)=(cos(mult*(1:lim))).^2;
g((n/2+1):n)=g((n/2):-1:1);
g = rnshift(g,n/2);
g=g/norm(g);
sig=iconv(g,sig);
else
disp(sprintf('MakeSignal: I don*t recognize <<%s>>',Name))
disp('Allowable Names are:')
disp('HeaviSine'),
disp('Bumps'),
disp('Blocks'),
disp('Doppler'),
disp('Ramp'),
disp('Cusp'),
disp('Crease'),
disp('Sing'),
disp('HiSine'),
disp('LoSine'),
disp('LinChirp'),
disp('TwoChirp'),
disp('QuadChirp'),
disp('MishMash'),
disp('WernerSorrows'),
disp('Leopold'),
disp('Sing'),
disp('HiSine'),
disp('LoSine'),
disp('LinChirp'),
disp('TwoChirp'),
disp('QuadChirp'),
disp('MishMash'),
disp('WernerSorrows'),
disp('Leopold'),
disp('Riemann'),
disp('HypChirps'),
disp('LinChirps'),
disp('Chirps'),
disp('sineoneoverx'),
disp('Cusp2'),
disp('SmoothCusp'),
disp('Gabor'),
disp('Piece-Regular');
disp('Piece-Polynomial');
disp('Gaussian');
end
%
% Originally made by David L. Donoho.
% Function has been enhanced.
%
% Part of WaveLab Version 802
% Built Sunday, October 3, 1999 8:52:27 AM
% This is Copyrighted Material
% For Copying permissions see COPYING.m
% Comments? e-mail [email protected]
%
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
GameOfLife.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/cellular/GameOfLife.m
| 3,374 |
utf_8
|
a30e18a0dce03b6f6d490e96282b1f1f
|
function GameOfLife
% This is a simple simulation of Conway Game of life GoL
% it is good for understanding Cellular Automata (CA) concept
% GoL Rules:
% 1. Survival: an alive cell live if it has 2 or 3 alive neighbors
% 2. Birth: a dead cell will be alive if it has 3 alive neighbors
% 3. Deaths:
% Lonless: alive cell dies if it has 0 or 1 alive neighbors
% Overcrowding: alive cell dies if it has 4 or more alive neighbors
% Any questions related to CA are welcome
% By: Ibraheem Al-Dhamari
clc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% size= 500x500
% different random initial values
%A= rand(500,500);
%A= ones(500,500);
% periodic configuration
%A= zeros(500,500);
% A(100,200)=1;
% A(100,201)=1;
% A(100,202)=1;
% initial from image
A=imread('CA02.JPG');
% convert to binary--> % states={0,1}
A=im2bw(A);
% visualize the initial states
disp('the binary image')
imshow(A);
% pause
% boundary type: 0= reflection
% 1= doublication
% 2= null, zeros
% this step enlarge A with 4 virtual vectors
A=Bnd(A,0);
[d1,d2]=size(A);
% disp('the extended binary image')
% whos A
imshow(A);
pause
B=A;
t=0;
stp=false; % to stop when if no new configrations
%B is the CA in time t
%A is the CA in time t+1
%t is the number of generations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Play ^_^
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
while ~stp & (t<10) % repeat for 10 generations
% for each cell in the CA
for i=2:d1-1
for j=2:d2-1
% apply Game of life rule
A(i,j)=GOL(A,B,i,j) ;
end
end
% visualize what happened
disp('the CA image')
imshow(A);
drawnow;
% pause
% save B
if A==B
stp=true; % no more new states
end
B=A;
t=t+1
end
%==========================================
% Game of Life Rules
%==========================================
function s=GOL (A,B,i,j)
% game of life rule
sm=0;
% count number of alive neighbors
sm=sm+ B(i-1,j-1)+B(i-1,j)+B(i-1,j+1);
sm=sm+ B(i,j-1)+ B(i,j+1);
sm=sm+ B(i+1,j-1)+B(i+1,j)+B(i+1,j+1);
% compute the new state of the current cell
s=B(i,j);
if B(i,j)==1
if (sm>1)&&(sm<4)
s=1;
else
s=0 ;
end
else
if sm==3
s=1;
end
end
%==========================================
% Boundary Type
%==========================================
function bA= Bnd(A,k)
% add new four vectors based on boundary type
[d1, d2]=size(A);
d1=d1+2; d2=d2+2;
X=ones(d1,d2);
X=im2bw(X);
X(2:d1-1,2:d2-1)=A;
imshow(X);
whos A X
if k==0 % Reflection
X( 1 , 2:d2-1)=A(end , :);
X( d1 , 2:d2-1)=A( 1 , :);
X( 2:d1-1 , 1 )=A(: , end);
X( 2:d1-1 , d2 )=A(: , 1 );
X(1,1) =A(end,end);
X(1,end) =A(end,1);
X(end,1) =A(1,end);
X(end,end)=A(1,1);
elseif k==1 % Double
X( 1 , 2:d2-1)=A( 1 , :);
X( d1 , 2:d2-1)=A(end , :);
X( 2:d1-1 , 1 )=A(: , 1 );
X( 2:d1-1 , d2 )=A(: , end);
X(1,1) =A(end,1);
X(1,end) =A(end,end);
X(end,1) =A(1,1);
X(end,end)=A(1,end);
else % k==2 % zeros
X( 1 ,:)=0;
X( end ,:)=0;
X(: , 1 )=0;
X(: , end )=0;
end
bA=X;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_gear.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/gears-non-circ/load_gear.m
| 4,615 |
utf_8
|
aed61f3cb53895649282de68959df88e
|
function x = load_gear(name, n, center, tooth, smoothing)
% load_gear - create default gears
%
% x = load_gear(name, n, center, tooth, smoothing);
%
% n is the number of points used for the discretization.
% center is the coordinate of the center of rotation (detaul is [0 0])
% tooth gives the parameters for the tooth extrusion.
%
% Copyright (c) 2010 Gabriel Peyre
theta = (0:n-1)'/n*2*pi;
if nargin<3
center = [0 0];
end
if nargin<4
tooth.transition =.2;
tooth.nbr = 30;
tooth.height = .05;
end
if nargin<5
smoothing=0;
end
switch name
case 'ellipse-focal'
% ellipse, focal
bmin = 1;
epsilon = .5;
x = bmin*(1-epsilon^2)./( 1-epsilon*cos(theta) );
case 'ellipse-centered'
% ellipse, centered
bmin = 1;
bmax = 3;
x = bmin*bmax./sqrt( (bmin*cos(theta)).^2 + (bmax*sin(theta)).^2 );
case {'random' 'random-strong'}
if strcmp(name, 'random')
bmin = 1; bmax = 1.5;
p = 6;
else
bmin = 1; bmax = 4;
p = 10;
end
x = zeros(n,1);
x(1:p) = exp(2i*rand(p,1));
x = real(ifft(x));
x = (x-min(x))/(max(x)-min(x));
x = x*(bmax-bmin)+bmin;
case 'petal'
x = sin(4*theta)+1.5;
case 'petal-8'
x = sin(8*theta).^2+2;
case 'circle'
x = theta*0+1;
case 'cardioid'
x = 1.2+cos(theta);
case 'engrenage-16'
eta = 16;
x = 10+ abs(cos(theta*eta)).^.2 .* sign(cos(theta*eta));
case 'discont'
x = .5*theta/2*pi + 1;
case 'discont-2'
x = mod(theta/(2*pi),.5)*3 + 1;
case 'square'
a = genpolygon_regular(4,n);
case 'triangle'
a = genpolygon_regular(3,n);
case 'hexagon'
a = genpolygon_regular(6,n);
end
%% add tooths
if not(exist('a'))
%% convert to rectangular
a = gear2cart(x);
end
a(:,1) = a(:,1) + center(1);
a(:,2) = a(:,2) + center(2);
if smoothing>0
niter = round(n * smoothing);
a = smooth(a,niter);
end
if tooth.nbr>0
q = n*10; % number of point for the profile curve
t = mod((0:q-1)'/q, 1/tooth.nbr)*tooth.nbr;
e = (tooth_profile(t, tooth.transition)) * 2 * tooth.height;
% normal
asmooth = smooth(a,.02);
u = compute_normal(asmooth);
s = compute_curvabs(a);
e1 = interp1( linspace(0,1,q+1), [e;e(1)], s );
% offset
a = a + u .* repmat(e1, [1 2]);
end
x = cart2gear(a);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = smooth(a,s)
n = size(a,1);
t = (-n/2:n/2-1)';
h = exp( -(t.^2)/(2*s^2) );
h = h/sum(h);
% recenter the filter for fft use
h1 = fftshift(h);
filter = @(u)real(ifft(fft(h1).*fft(u)));
a(:,1) = filter(a(:,1));
a(:,2) = filter(a(:,2));
return;
if nargin<2
niter = 1;
end
for i=1:niter
a = (a + a([2:end 1],:) + a([end 1:end-1],:) )/3;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function s = compute_curvabs(a)
u = a([2:end 1],:) - a([end 1:end-1],:);
s = sqrt(sum(u.^2,2));
s = [0;cumsum(s)];
s = s/s(end);
s = s(1:end-1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function u = compute_normal(a)
u = a([2:end 1],:) - a([end 1:end-1],:);
u = u ./ repmat( sqrt(sum(u.^2,2)), [1 2] );
u = [-u(:,2) u(:,1)];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function e = tooth_profile(t, a)
d = 1/2-a;
e = double(t<d) + double(t>=d & t<a+d).*(d+a-t)/(a) + ...
double(t>=1-a).*(t-(1-a))/(a);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = normal_extrude(a)
n = a-a(:,[2:end 1]);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = genpolygon_regular(p,n)
theta = linspace(0,2*pi,p+1)';
theta(end) = [];
A = [cos(theta), sin(theta)];
a = genpolygon(A,n);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = genpolygon(A,n)
p = size(A,1);
a = [];
for i=1:p
j = mod(i,p)+1;
if i<p
k = floor(n/p);
else
k = n - (p-1)*floor(n/p);
end
t = (0:k-1)'/k;
a(end+1:end+k,:) = (1-t)*A(i,:) + t*A(j,:);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function x = cart2gear(a)
n = size(a,1);
[theta,r] = cart2pol(a(:,1), a(:,2));
theta = theta - theta(1);
theta(theta<0) = theta(theta<0) + 2*pi;
theta(end+1) = 2*pi; r(end+1) = r(1);
theta0 = (0:n-1)'/n*2*pi;
x = interp1(theta,r,theta0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = gear2cart(x)
n = length(x);
theta = (0:n-1)'/n*2*pi;
a = [x.*cos(theta), x.*sin(theta)];
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
hilbert.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/hilbert-curve/hilbert.m
| 416 |
utf_8
|
be622fc6b0e538e3287a391980e5091d
|
function [x,y] = hilbert(n)
%HILBERT Hilbert curve.
%
% [x,y]=hilbert(n) gives the vector coordinates of points
% in n-th order Hilbert curve of area 1.
%
% Example: plot of 5-th order curve
%
% [x,y]=hilbert(5);line(x,y)
%
% Copyright (c) by Federico Forte
% Date: 2000/10/06
if n<=0
x=0;
y=0;
else
[xo,yo]=hilbert(n-1);
x=.5*[-.5+yo -.5+xo .5+xo .5-yo];
y=.5*[-.5+xo .5+yo .5+yo -.5-xo];
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
plot_tensor_field.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/tensor-diffusion/plot_tensor_field.m
| 5,736 |
utf_8
|
08ad2346cf316598da10c6b1d5c367d3
|
function h = plot_tensor_field(H, M, options)
% plot_tensor_field - display a tensor field
%
% h = plot_tensor_field(H, M, options);
%
% options.sub controls sub-sampling
% options.color controls color
%
% Copyright (c) 2006 Gabriel Peyre
if nargin<3
options.null = 0;
end
if not( isstruct(options) )
sub = options;
clear options;
options.sub = sub;
end
% sub = getoptions(options, 'sub', 1);
sub = getoptions(options, 'sub', round(size(H,1)/30) );
color = getoptions(options, 'color', 'r');
if nargin<2
M = [];
end
if not(isempty(M)) && size(M,3)==1
M = repmat(M, [1 1 3]); % ensure B&W image
end
if size(H,3)==3 && size(H,4)==1
H = cat(3, H(:,:,1), H(:,:,3), H(:,:,3), H(:,:,2) );
H = reshape(H, size(H,1), size(H,2), 2, 2);
if 0
% flip the main eigen-axes
[e1,e2,l1,l2] = perform_tensor_decomp(H);
H = perform_tensor_recomp(e2,e1,l1,l2);
end
h = plot_tensor_field(H, M, sub);
return;
end
% swap X and Y axis
%%% TODO
a = H(:,:,2,2);
H(:,:,2,2) = H(:,:,1,1);
H(:,:,1,1) = a;
hold on;
if ~isempty(M)
imagesc(rescale(M)); drawnow;
end
h = fn_tensordisplay(H(:,:,1,1),H(:,:,1,2), H(:,:,2,2), 'sub', sub, 'color', color);
axis image; axis off;
colormap jet(256);
% hold off;
function h = fn_tensordisplay(varargin)
% function h = fn_tensordisplay([X,Y,]Txx,Txy,Tyy[,'sigma',sigma][,'sub',sub][,color][,patch options...]])
% function h = fn_tensordisplay([X,Y,]e[,'sigma',sigma][,'sub',sub][,color][,patch options...]])
% X,Y,Txx,Txy,Tyy
if isstruct(varargin{1}) || isstruct(varargin{3})
if isstruct(varargin{1}), nextarg=1; else nextarg=3; end
e = varargin{nextarg};
Txx = e.ytyt;
Txy = -e.ytyx;
Tyy = e.yxyx;
if nextarg==1
[nj ni] = size(Txx);
[X Y] = meshgrid(1:ni,1:nj);
else
[X Y] = deal(varargin{1:2});
end
nextarg = nextarg+1;
else
[nj ni] = size(varargin{3});
if nargin<5 || ischar(varargin{4}) || ischar(varargin{5}) || any(size(varargin{5})~=[nj ni])
[X Y] = meshgrid(1:ni,1:nj);
nextarg = 1;
else
[X Y] = deal(varargin{1:2});
nextarg = 3;
end
[Txx Txy Tyy] = deal(varargin{nextarg:nextarg+2});
nextarg = nextarg+3;
end
if any(size(X)==1), [X Y] = meshgrid(X,Y); end
[nj,ni] = size(X);
if any(size(Y)~=[nj ni]) || ...
any(size(Txx)~=[nj ni]) || any(size(Txy)~=[nj ni]) || any(size(Tyy)~=[nj ni])
error('Matrices must be same size')
end
% sigma, sub, color
color = 'r';
while nextarg<=nargin
flag = varargin{nextarg};
nextarg=nextarg+1;
if ~ischar(flag), color = flag; continue, end
switch lower(flag)
case 'sigma'
sigma = varargin{nextarg};
nextarg = nextarg+1;
switch length(sigma)
case 1
sigmax = sigma;
sigmay = sigma;
case 2
sigmax = sigma(1);
sigmay = sigma(2);
otherwise
error('sigma definition should entail two values');
end
h = fspecial('gaussian',[ceil(2*sigmay) 1],sigmay)*fspecial('gaussian',[1 ceil(2*sigmax)],sigmax);
Txx = imfilter(Txx,h,'replicate');
Txy = imfilter(Txy,h,'replicate');
Tyy = imfilter(Tyy,h,'replicate');
case 'sub'
sub = varargin{nextarg};
nextarg = nextarg+1;
switch length(sub)
case 1
[x y] = meshgrid(1:sub:ni,1:sub:nj);
sub = y+nj*(x-1);
case 2
[x y] = meshgrid(1:sub(1):ni,1:sub(2):nj);
sub = y+nj*(x-1);
end
X = X(sub); Y = Y(sub);
Txx = Txx(sub); Txy = Txy(sub); Tyy = Tyy(sub);
[nj ni] = size(sub);
case 'color'
color = varargin{nextarg};
nextarg = nextarg+1;
otherwise
break
end
end
% options
options = {varargin{nextarg:end}};
npoints = 50;
theta = (0:npoints-1)*(2*pi/npoints);
circle = [cos(theta) ; sin(theta)];
Tensor = cat(3,Txx,Txy,Txy,Tyy); % jdisplay x idisplay x tensor
Tensor = reshape(Tensor,2*nj*ni,2); % (display x 1tensor) x 2tensor
Ellipse = Tensor * circle; % (display x uv) x npoints
Ellipse = reshape(Ellipse,nj*ni,2,npoints); % display x uv x npoints
XX = repmat(X(:),1,npoints); % display x npoints
YY = repmat(Y(:),1,npoints); % display x npoints
U = reshape(Ellipse(:,1,:),nj*ni,npoints); % display x npoints
V = reshape(Ellipse(:,2,:),nj*ni,npoints); % display x npoints
umax = max(U')'; vmax = max(V')';
umax(umax==0)=1; vmax(vmax==0)=1;
if ni==1, dx=1; else dx = X(1,2)-X(1,1); end
if nj==1, dy=1; else dy = Y(2,1)-Y(1,1); end
fact = min(dx./umax,dy./vmax)*.35;
fact = repmat(fact,1,npoints);
U = XX + fact.*U;
V = YY + fact.*V;
%-----------
MM = mmax(Txx+Tyy);
mm = mmin(Txx+Tyy);
[S1, S2] = size(U);
Colormap = zeros(S2, S1, 3);
Map = colormap(jet(256));
for k =1:npoints
Colormap(k,:,1) = Map(floor(255*(Txx(:)+Tyy(:)-mm)/(MM-mm)) + 1, 1);
Colormap(k,:,2) = Map(floor(255*(Txx(:)+Tyy(:)-mm)/(MM-mm)) + 1, 2);
Colormap(k,:,3) = Map(floor(255*(Txx(:)+Tyy(:)-mm)/(MM-mm)) + 1, 3);
end
%-----------
h = fill(U',V',color,'EdgeColor',color,options{:});
%h = fill(U',V',Colormap,'EdgeColor', 'interp');
axis ij;
if nargout==0, clear h, end
function a=mmax(a)
a = max(a(:));
function a=mmin(a)
a = min(a(:));
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
inpolyhedron.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/wave-heat-3d/inpolyhedron.m
| 22,756 |
utf_8
|
16738ef64a83b8c37c57511248fb93cf
|
function IN = inpolyhedron(varargin)
%INPOLYHEDRON Tests if points are inside a 3D triangulated (faces/vertices) surface
% BY CONVENTION, SURFACE NORMALS SHOULD POINT OUT from the object. (see
% FLIPNORMALS option below for details)
%
% IN = INPOLYHEDRON(FV,QPTS) tests if the query points (QPTS) are inside the
% patch/surface/polyhedron defined by FV (a structure with fields 'vertices' and
% 'faces'). QPTS is an N-by-3 set of XYZ coordinates. IN is an N-by-1 logical
% vector which will be TRUE for each query point inside the surface.
%
% INPOLYHEDRON(FACES,VERTICES,...) takes faces/vertices separately, rather than in
% an FV structure.
%
% IN = INPOLYHEDRON(..., X, Y, Z) voxelises a mask of 3D gridded query points
% rather than an N-by-3 array of points. X, Y, and Z coordinates of the grid
% supplied in XVEC, YVEC, and ZVEC respectively. IN will return as a 3D logical
% volume with SIZE(IN) = [LENGTH(YVEC) LENGTH(XVEC) LENGTH(ZVEC)], equivalent to
% syntax used by MESHGRID. INPOLYHEDRON handles this input faster and with a lower
% memory footprint than using MESHGRID to make full X, Y, Z query points matrices.
%
% INPOLYHEDRON(...,'PropertyName',VALUE,'PropertyName',VALUE,...) tests query
% points using the following optional property values:
%
% TOL - Tolerance on the tests for "inside" the surface. You can think of
% tol as the distance a point may possibly lie above/below the surface, and still
% be perceived as on the surface. Due to numerical rounding nothing can ever be
% done exactly here. Defaults to ZERO. Note that in the current implementation TOL
% only affects points lying above/below a surface triangle (in the Z-direction).
% Points coincident with a vertex in the XY plane are considered INside the surface.
% More formal rules can be implemented with input/feedback from users.
%
% GRIDSIZE - Internally, INPOLYHEDRON uses a divide-and-conquer algorithm to
% split all faces into a chessboard-like grid of GRIDSIZE-by-GRIDSIZE regions.
% Performance will be a tradeoff between a small GRIDSIZE (few iterations, more
% data per iteration) and a large GRIDSIZE (many iterations of small data
% calculations). The sweet-spot has been experimentally determined (on a win64
% system) to be correlated with the number of faces/vertices. You can overwrite
% this automatically computed choice by specifying a GRIDSIZE parameter.
%
% FACENORMALS - By default, the normals to the FACE triangles are computed as the
% cross-product of the first two triangle edges. You may optionally specify face
% normals here if they have been pre-computed.
%
% FLIPNORMALS - (Defaults FALSE). To match a wider convention, triangle
% face normals are presumed to point OUT from the object's surface. If
% your surface normals are defined pointing IN, then you should set the
% FLIPNORMALS option to TRUE to use the reverse of this convention.
%
% Example:
% tmpvol = zeros(20,20,20); % Empty voxel volume
% tmpvol(5:15,8:12,8:12) = 1; % Turn some voxels on
% tmpvol(8:12,5:15,8:12) = 1;
% tmpvol(8:12,8:12,5:15) = 1;
% fv = isosurface(tmpvol, 0.99); % Create the patch object
% fv.faces = fliplr(fv.faces); % Ensure normals point OUT
% % Test SCATTERED query points
% pts = rand(200,3)*12 + 4; % Make some query points
% in = inpolyhedron(fv, pts); % Test which are inside the patch
% figure, hold on, view(3) % Display the result
% patch(fv,'FaceColor','g','FaceAlpha',0.2)
% plot3(pts(in,1),pts(in,2),pts(in,3),'bo','MarkerFaceColor','b')
% plot3(pts(~in,1),pts(~in,2),pts(~in,3),'ro'), axis image
% % Test STRUCTURED GRID of query points
% gridLocs = 3:2.1:19;
% [x,y,z] = meshgrid(gridLocs,gridLocs,gridLocs);
% in = inpolyhedron(fv, gridLocs,gridLocs,gridLocs);
% figure, hold on, view(3) % Display the result
% patch(fv,'FaceColor','g','FaceAlpha',0.2)
% plot3(x(in), y(in), z(in),'bo','MarkerFaceColor','b')
% plot3(x(~in),y(~in),z(~in),'ro'), axis image
%
% See also: UNIFYMESHNORMALS (on the <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=43013">file exchange</a>)
% TODO-list
% - Optmise overall memory footprint. (need examples with MEM errors)
% - Implement an "ignore these" step to speed up calculations for:
% * Query points outside the convex hull of the faces/vertices input
% - Get a better/best gridSize calculation. User feedback?
% - Detect cases where X-rays or Y-rays would be better than Z-rays?
%
% Author: Sven Holcombe
% - 10 Jun 2012: Version 1.0
% - 28 Aug 2012: Version 1.1 - Speedup using accumarray
% - 07 Nov 2012: Version 2.0 - BEHAVIOUR CHANGE
% Query points coincident with a VERTEX are now IN an XY triangle
% - 18 Aug 2013: Version 2.1 - Gridded query point handling with low memory footprint.
% - 10 Sep 2013: Version 3.0 - BEHAVIOUR CHANGE
% NEW CONVENTION ADOPTED to expect face normals pointing IN
% Vertically oriented faces are now ignored. Speeds up
% computation and fixes bug where presence of vertical faces
% produced NaN distance from a query pt to facet, making all
% query points under facet erroneously NOT IN polyhedron.
% - 25 Sep 2013: Version 3.1 - Dropped nested unique call which was made
% mostly redundant via v2.1 gridded point handling. Also
% refreshed grid size selection via optimisation.
% - 25 Feb 2014: Version 3.2 - Fixed indeterminate behaviour for query
% points *exactly* in line with an "overhanging" vertex.
%%
% FACETS is an unpacked arrangement of faces/vertices. It is [3-by-3-by-N],
% with 3 1-by-3 XYZ coordinates of N faces.
[facets, qPts, options] = parseInputs(varargin{:});
numFaces = size(facets,3);
if ~options.griddedInput % SCATTERED QUERY POINTS
numQPoints = size(qPts,1);
else % STRUCTURED QUERY POINTS
numQPoints = prod(cellfun(@numel,qPts(1:2)));
end
% Precompute 3d normals to all facets (triangles). Do this via the cross
% product of the first edge vector with the second. Normalise the result.
allEdgeVecs = facets([2 3 1],:,:) - facets(:,:,:);
if isempty(options.facenormals)
allFacetNormals = bsxfun(@times, allEdgeVecs(1,[2 3 1],:), allEdgeVecs(2,[3 1 2],:)) - ...
bsxfun(@times, allEdgeVecs(2,[2 3 1],:), allEdgeVecs(1,[3 1 2],:));
allFacetNormals = bsxfun(@rdivide, allFacetNormals, sqrt(sum(allFacetNormals.^2,2)));
else
allFacetNormals = permute(options.facenormals,[3 2 1]);
end
if options.flipnormals
allFacetNormals = -allFacetNormals;
end
% We use a Z-ray intersection so we don't even need to consider facets that
% are purely vertically oriented (have zero Z-component).
isFacetUseful = allFacetNormals(:,3,:) ~= 0;
%% Setup grid referencing system
% Function speed can be thought of as a function of grid size. A small number of grid
% squares means iterating over fewer regions (good) but with more faces/qPts to
% consider each time (bad). For any given mesh/queryPt configuration, there will be a
% sweet spot that minimises computation time. There will also be a constraint from
% memory available - low grid sizes means considering many queryPt/faces at once,
% which will require a larger memory footprint. Here we will let the user specify
% gridsize directly, or we will estimate the optimum size based on prior testing.
if ~isempty(options.gridsize)
gridSize = options.gridsize;
else
% Coefficients (with 95% confidence bounds):
p00 = -47; p10 = 12.83; p01 = 20.89;
p20 = 0.7578; p11 = -6.511; p02 = -2.586;
p30 = -0.1802; p21 = 0.2085; p12 = 0.7521;
p03 = 0.09984; p40 = 0.005815; p31 = 0.007775;
p22 = -0.02129; p13 = -0.02309;
GSfit = @(x,y)p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2 + p13*x*y^3;
gridSize = min(150 ,max(1, ceil(GSfit(log(numQPoints),log(numFaces)))));
if isnan(gridSize), gridSize = 1; end
end
%% Find candidate qPts -> triangles pairs
% We have a large set of query points. For each query point, find potential
% triangles that would be pierced by vertical rays through the qPt. First,
% a simple filter by XY bounding box
% Calculate the bounding box of each facet
minFacetCoords = permute(min(facets(:,1:2,:),[],1),[3 2 1]);
maxFacetCoords = permute(max(facets(:,1:2,:),[],1),[3 2 1]);
% Set rescale values to rescale all vertices between 0(-eps) and 1(+eps)
scalingOffsetsXY = min(minFacetCoords,[],1) - eps;
scalingRangeXY = max(maxFacetCoords,[],1) - scalingOffsetsXY + 2*eps;
% Based on scaled min/max facet coords, get the [lowX lowY highX highY] "grid" index
% of all faces
lowToHighGridIdxs = floor(bsxfun(@rdivide, ...
bsxfun(@minus, ... % Use min/max coordinates of each facet (+/- the tolerance)
[minFacetCoords-options.tol maxFacetCoords+options.tol],...
[scalingOffsetsXY scalingOffsetsXY]),...
[scalingRangeXY scalingRangeXY]) * gridSize) + 1;
% Build a grid of cells. In each cell, place the facet indices that encroach into
% that grid region. Similarly, each query point will be assigned to a grid region.
% Note that query points will be assigned only one grid region, facets can cover many
% regions. Furthermore, we will add a tolerance to facet region assignment to ensure
% a query point will be compared to facets even if it falls only on the edge of a
% facet's bounding box, rather than inside it.
cells = cell(gridSize);
[unqLHgrids,~,facetInds] = unique(lowToHighGridIdxs,'rows');
tmpInds = accumarray(facetInds(isFacetUseful),find(isFacetUseful),[size(unqLHgrids,1),1],@(x){x});
for xi = 1:gridSize
xyMinMask = xi >= unqLHgrids(:,1) & xi <= unqLHgrids(:,3);
for yi = 1:gridSize
cells{yi,xi} = cat(1,tmpInds{xyMinMask & yi >= unqLHgrids(:,2) & yi <= unqLHgrids(:,4)});
% The above line (with accumarray) is faster with equiv results than:
% % cells{yi,xi} = find(ismember(facetInds, xyInds));
end
end
% With large number of facets, memory may be important:
clear lowToHightGridIdxs LHgrids facetInds tmpInds xyMinMask minFacetCoords maxFacetCoords
%% Compute edge unit vectors and dot products
% Precompute the 2d unit vectors making up each facet's edges in the XY plane.
allEdgeUVecs = bsxfun(@rdivide, allEdgeVecs(:,1:2,:), sqrt(sum(allEdgeVecs(:,1:2,:).^2,2)));
% Precompute the inner product between edgeA.edgeC, edgeB.edgeA, edgeC.edgeB
allEdgeEdgeDotPs = sum(allEdgeUVecs .* -allEdgeUVecs([3 1 2],:,:),2) - 1e-9;
%% Gather XY query locations
% Since query points are most likely given as a (3D) grid of query locations, we only
% need to consider the unique XY locations when asking which facets a vertical ray
% through an XY location would pierce.
if ~options.griddedInput % SCATTERED QUERY POINTS
qPtsXY = @(varargin)qPts(:,1:2);
qPtsXYZViaUnqIndice = @(ind)qPts(ind,:);
outPxIndsViaUnqIndiceMask = @(ind,mask)ind(mask);
outputSize = [size(qPts,1),1];
reshapeINfcn = @(INMASK)INMASK;
minFacetDistanceFcn = @minFacetToQptDistance;
else % STRUCTURED QUERY POINTS
[xmat,ymat] = meshgrid(qPts{1:2});
qPtsXY = [xmat(:) ymat(:)];
% A standard set of Z locations will be shifted around by different
% unqQpts XY coordinates.
zCoords = qPts{3}(:) * [0 0 1];
qPtsXYZViaUnqIndice = @(ind)bsxfun(@plus, zCoords, [qPtsXY(ind,:) 0]);
% From a given indice and mask, we will turn on/off the IN points under
% that indice based on the mask. The easiest calculation is to setup
% the IN matrix as a numZpts-by-numUnqPts mask. At the end, we must
% unpack/reshape this 2D mask to a full 3D logical mask
numZpts = size(zCoords,1);
baseZinds = 1:numZpts;
outPxIndsViaUnqIndiceMask = @(ind,mask)(ind-1)*numZpts + baseZinds(mask);
outputSize = [numZpts, size(qPtsXY,1)];
reshapeINfcn = @(INMASK)reshape(INMASK', cellfun(@numel, qPts([2 1 3])));
minFacetDistanceFcn = @minFacetToQptsDistance;
end
% Start with every query point NOT inside the polyhedron. We will
% iteratively find those query points that ARE inside.
IN = false(outputSize);
% Determine with grids each query point falls into.
qPtGridXY = floor(bsxfun(@rdivide, bsxfun(@minus, qPtsXY(:,:), scalingOffsetsXY),...
scalingRangeXY) * gridSize) + 1;
[unqQgridXY,~,qPtGridInds] = unique(qPtGridXY,'rows');
% We need only consider grid indices within those already set up
ptsToConsidMask = ~any(qPtGridXY<1 | qPtGridXY>gridSize, 2);
if ~any(ptsToConsidMask)
IN = reshapeINfcn(IN);
return;
end
% Build the reference list
cellQptContents = accumarray(qPtGridInds(ptsToConsidMask),find(ptsToConsidMask), [],@(x){x});
gridsToCheck = unqQgridXY(~any(unqQgridXY<1 | unqQgridXY>gridSize, 2),:);
cellQptContents(cellfun('isempty',cellQptContents)) = [];
gridIndsToCheck = sub2ind(size(cells), gridsToCheck(:,2), gridsToCheck(:,1));
% For ease of multiplication, reshape qPt XY coords to [1-by-2-by-1-by-N]
qPtsXY = permute(qPtsXY(:,:),[4 2 3 1]);
% There will be some grid indices with query points but without facets.
emptyMask = cellfun('isempty',cells(gridIndsToCheck))';
for i = find(~emptyMask)
% We get all the facet coordinates (ie, triangle vertices) of triangles
% that intrude into this grid location. The size is [3-by-2-by-N], for
% the [3vertices-by-XY-by-Ntriangles]
allFacetInds = cells{gridIndsToCheck(i)};
candVerts = facets(:,1:2,allFacetInds);
% We need the XY coordinates of query points falling into this grid.
allqPtInds = cellQptContents{i};
queryPtsXY = qPtsXY(:,:,:,allqPtInds);
% Get unit vectors pointing from each triangle vertex to my query point(s)
vert2ptVecs = bsxfun(@minus, queryPtsXY, candVerts);
vert2ptUVecs = bsxfun(@rdivide, vert2ptVecs, sqrt(sum(vert2ptVecs.^2,2)));
% Get unit vectors pointing around each triangle (along edge A, edge B, edge C)
edgeUVecs = allEdgeUVecs(:,:,allFacetInds);
% Get the inner product between edgeA.edgeC, edgeB.edgeA, edgeC.edgeB
edgeEdgeDotPs = allEdgeEdgeDotPs(:,:,allFacetInds);
% Get inner products between each edge unit vec and the UVs from qPt to vertex
edgeQPntDotPs = sum(bsxfun(@times, edgeUVecs, vert2ptUVecs),2);
qPntEdgeDotPs = sum(bsxfun(@times,vert2ptUVecs, -edgeUVecs([3 1 2],:,:)),2);
% If both inner products 2 edges to the query point are greater than the inner
% product between the two edges themselves, the query point is between the V
% shape made by the two edges. If this is true for all 3 edge pair, the query
% point is inside the triangle.
resultIN = all(bsxfun(@gt, edgeQPntDotPs, edgeEdgeDotPs) & bsxfun(@gt, qPntEdgeDotPs, edgeEdgeDotPs),1);
resultONVERTEX = any(any(isnan(vert2ptUVecs),2),1);
result = resultIN | resultONVERTEX;
qPtHitsTriangles = any(result,3);
% If NONE of the query points pierce ANY triangles, we can skip forward
if ~any(qPtHitsTriangles), continue, end
% In the next step, we'll need to know the indices of ALL the query points at
% each of the distinct XY coordinates. Let's get their indices into "qPts" as a
% cell of length M, where M is the number of unique XY points we had found.
for ptNo = find(qPtHitsTriangles(:))'
% Which facets does it pierce?
piercedFacetInds = allFacetInds(result(1,1,:,ptNo));
% Get the 1-by-3-by-N set of triangle normals that this qPt pierces
piercedTriNorms = allFacetNormals(:,:,piercedFacetInds);
% Pick the first vertex as the "origin" of a plane through the facet. Get the
% vectors from each query point to each facet origin
facetToQptVectors = bsxfun(@minus, ...
qPtsXYZViaUnqIndice(allqPtInds(ptNo)),...
facets(1,:,piercedFacetInds));
% Calculate how far you need to go up/down to pierce the facet's plane.
% Positive direction means "inside" the facet, negative direction means
% outside.
facetToQptDists = bsxfun(@rdivide, ...
sum(bsxfun(@times,piercedTriNorms,facetToQptVectors),2), ...
abs(piercedTriNorms(:,3,:)));
% Since it's possible for two triangles sharing the same vertex to
% be the same distance away, I want to sum up all the distances of
% triangles that are closest to the query point. Simple case: The
% closest triangle is unique Edge case: The closest triangle is one
% of many the same distance and direction away. Tricky case: The
% closes triangle has another triangle the equivalent distance
% but facing the opposite direction
IN( outPxIndsViaUnqIndiceMask(allqPtInds(ptNo), ...
minFacetDistanceFcn(facetToQptDists)<options.tol...
)) = true;
end
end
% If they provided X,Y,Z vectors of query points, our output is currently a
% 2D mask and must be reshaped to [LEN(Y) LEN(X) LEN(Z)].
IN = reshapeINfcn(IN);
%% Called subfunctions
% vertices = [
% 0.9046 0.1355 -0.0900
% 0.8999 0.3836 -0.0914
% 1.0572 0.2964 -0.0907
% 0.8735 0.1423 -0.1166
% 0.8685 0.4027 -0.1180
% 1.0337 0.3112 -0.1173
% 0.9358 0.1287 -0.0634
% 0.9313 0.3644 -0.0647
% 1.0808 0.2816 -0.0641
% ];
% faces = [
% 1 2 5
% 1 5 4
% 2 3 6
% 2 6 5
% 3 1 4
% 3 4 6
% 6 4 5
% 2 1 8
% 8 1 7
% 3 2 9
% 9 2 8
% 1 3 7
% 7 3 9
% 7 9 8
% ];
% point = [vertices(3,1),vertices(3,2),1.5];
function closestTriDistance = minFacetToQptDistance(facetToQptDists)
% FacetToQptDists is a 1pt-by-1-by-Nfacets array of how far you need to go
% up/down to pierce each facet's plane. If the Qpt was directly over an
% "overhang" vertex, then two facets with opposite orientation will be
% equally distant from the Qpt, with one distance positive and one
% negative. In such cases, it is impossible for the Qpt to actually be
% "inside" this pair of facets, so their distance is updated to Inf.
[~,minInd] = min(abs(facetToQptDists),[],3);
while any( abs(facetToQptDists + facetToQptDists(minInd)) < 1e-15 )
% Since the above comparison is made every time, but the below variable
% setting is done only in the rare case that a query point coincides
% with an overhang vertex, it is more efficient to re-compute the
% equality when it's true, rather than store the result every time.
facetToQptDists( abs(facetToQptDists) - abs(facetToQptDists(minInd)) < 1e-15) = inf;
if ~any(isfinite(facetToQptDists))
break;
end
[~,minInd] = min(abs(facetToQptDists),[],3);
end
closestTriDistance = facetToQptDists(minInd);
function closestTriDistance = minFacetToQptsDistance(facetToQptDists)
% As above, but facetToQptDists is an Mpts-by-1-by-Nfacets array.
% The multi-point version is a little more tricky. While below is quite a
% bit slower when the while loop is entered, it is very rarely entered and
% very fast to make just the initial comparison.
[minVals,minInds] = min(abs(facetToQptDists),[],3);
while any(...
any(abs(bsxfun(@plus,minVals,facetToQptDists))<1e-15,3) & ...
any(abs(bsxfun(@minus,minVals,facetToQptDists))<1e-15,3))
maskP = abs(bsxfun(@plus,minVals,facetToQptDists))<1e-15;
maskN = abs(bsxfun(@minus,minVals,facetToQptDists))<1e-15;
mustAlterMask = any(maskP,3) & any(maskN,3);
for i = find(mustAlterMask)'
facetToQptDists(i,:,maskP(i,:,:) | maskN(i,:,:)) = inf;
end
[newMv,newMinInds] = min(abs(facetToQptDists(mustAlterMask,:,:)),[],3);
minInds(mustAlterMask) = newMinInds(:);
minVals(mustAlterMask) = newMv(:);
end
% Below is a tiny speedup on basically a sub2ind call.
closestTriDistance = facetToQptDists((minInds-1)*size(facetToQptDists,1) + (1:size(facetToQptDists,1))');
%% Input handling subfunctions
function [facets, qPts, options] = parseInputs(varargin)
% Gather FACES and VERTICES
if isstruct(varargin{1}) % inpolyhedron(FVstruct, ...)
if ~all(isfield(varargin{1},{'vertices','faces'}))
error( 'Structure FV must have "faces" and "vertices" fields' );
end
faces = varargin{1}.faces;
vertices = varargin{1}.vertices;
varargin(1) = []; % Chomp off the faces/vertices
else % inpolyhedron(FACES, VERTICES, ...)
faces = varargin{1};
vertices = varargin{2};
varargin(1:2) = []; % Chomp off the faces/vertices
end
% Unpack the faces/vertices into [3-by-3-by-N] facets. It's better to
% perform this now and have FACETS only in memory in the main program,
% rather than FACETS, FACES and VERTICES
facets = vertices';
facets = permute(reshape(facets(:,faces'), 3, 3, []),[2 1 3]);
% Extract query points
if length(varargin)<2 || ischar(varargin{2}) % inpolyhedron(F, V, [x(:) y(:) z(:)], ...)
qPts = varargin{1};
varargin(1) = []; % Chomp off the query points
else % inpolyhedron(F, V, xVec, yVec, zVec, ...)
qPts = varargin(1:3);
% Chomp off the query points and tell the world that it's gridded input.
varargin(1:3) = [];
varargin = [varargin {'griddedInput',true}];
end
% Extract configurable options
options = parseOptions(varargin{:});
% Check if face normals are unified
if options.testNormals
options.normalsAreUnified = checkNormalUnification(faces);
end
function options = parseOptions(varargin)
IP = inputParser;
IP.addParamValue('gridsize',[], @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('tol', 0, @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('tol_ang', 1e-5, @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('facenormals',[]);
IP.addParamValue('flipnormals',false);
IP.addParamValue('griddedInput',false);
IP.addParamValue('testNormals',false);
IP.parse(varargin{:});
options = IP.Results;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_image.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/wass-barycenters/toolbox/load_image.m
| 19,798 |
utf_8
|
df61d87c209e587d6199fa36bbe979bf
|
function M = load_image(type, n, options)
% load_image - load benchmark images.
%
% M = load_image(name, n, options);
%
% name can be:
% Synthetic images:
% 'chessboard1', 'chessboard', 'square', 'squareregular', 'disk', 'diskregular', 'quaterdisk', '3contours', 'line',
% 'line_vertical', 'line_horizontal', 'line_diagonal', 'line_circle',
% 'parabola', 'sin', 'phantom', 'circ_oscil',
% 'fnoise' (1/f^alpha noise).
% Natural images:
% 'boat', 'lena', 'goldhill', 'mandrill', 'maurice', 'polygons_blurred', or your own.
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<2
n = 512;
end
options.null = 0;
if iscell(type)
for i=1:length(type)
M{i} = load_image(type{i},n,options);
end
return;
end
type = lower(type);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters for geometric objects
eta = getoptions(options, 'eta', .1);
gamma = getoptions(options, 'gamma', 1/sqrt(2));
radius = getoptions(options, 'radius', 10);
center = getoptions(options, 'center', [0 0]);
center1 = getoptions(options, 'center1', [0 0]);
w = getoptions(options, 'tube_width', 0.06);
nb_points = getoptions(options, 'nb_points', 9);
scaling = getoptions(options, 'scaling', 1);
theta = getoptions(options, 'theta', 30 * 2*pi/360);
eccentricity = getoptions(options, 'eccentricity', 1.3);
sigma = getoptions(options, 'sigma', 0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for the line, can be vertical / horizontal / diagonal / any
if strcmp(type, 'line_vertical')
eta = 0.5; % translation
gamma = 0; % slope
elseif strcmp(type, 'line_horizontal')
eta = 0.5; % translation
gamma = Inf; % slope
elseif strcmp(type, 'line_diagonal')
eta = 0; % translation
gamma = 1; % slope
end
if strcmp(type(1:min(12,end)), 'square-tube-')
k = str2double(type(13:end));
c1 = [.22 .5]; c2 = [1-c1(1) .5];
eta = 1.5;
r1 = [c1 c1] + .21*[-1 -eta 1 eta];
r2 = [c2 c2] + .21*[-1 -eta 1 eta];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
if mod(k,2)==0
sel = n/2-k/2+1:n/2+k/2;
else
sel = n/2-(k-1)/2:n/2+(k-1)/2;
end
M( round(.25*n:.75*n), sel ) = 1;
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch lower(type)
case 'constant'
M = ones(n);
case 'ramp'
x = linspace(0,1,n);
[Y,M] = meshgrid(x,x);
case 'bump'
s = getoptions(options, 'bump_size', .5);
c = getoptions(options, 'center', [0 0]);
if length(s)==1
s = [s s];
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
X = (X-c(1))/s(1); Y = (Y-c(2))/s(2);
M = exp( -(X.^2+Y.^2)/2 );
case 'periodic'
x = linspace(-pi,pi,n)/1.1;
[Y,X] = meshgrid(x,x);
f = getoptions(options, 'freq', 6);
M = (1+cos(f*X)).*(1+cos(f*Y));
case {'letter-x' 'letter-v' 'letter-z' 'letter-y'}
M = create_letter(type(8), radius, n);
case 'l'
r1 = [.1 .1 .3 .9];
r2 = [.1 .1 .9 .4];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
case 'ellipse'
c1 = [0.15 0.5];
c2 = [0.85 0.5];
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
d = sqrt((X-c1(1)).^2 + (Y-c1(2)).^2) + sqrt((X-c2(1)).^2 + (Y-c2(2)).^2);
M = double( d<=eccentricity*sqrt( sum((c1-c2).^2) ) );
case 'ellipse-thin'
options.eccentricity = 1.06;
M = load_image('ellipse', n, options);
case 'ellipse-fat'
options.eccentricity = 1.3;
M = load_image('ellipse', n, options);
case 'square-tube'
c1 = [.25 .5];
c2 = [.75 .5];
r1 = [c1 c1] + .18*[-1 -1 1 1];
r2 = [c2 c2] + .18*[-1 -1 1 1];
r3 = [c1(1)-w c1(2)-w c2(1)+w c2(2)+w];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) | draw_rectangle(r3,n) );
case 'square-tube-1'
options.tube_width = 0.03;
M = load_image('square-tube', n, options);
case 'square-tube-2'
options.tube_width = 0.06;
M = load_image('square-tube', n, options);
case 'square-tube-3'
options.im = 0.09;
M = load_image('square-tube', n, options);
case 'polygon'
theta = sort( rand(nb_points,1)*2*pi );
radius = scaling*rescale(rand(nb_points,1), 0.1, 0.93);
points = [cos(theta) sin(theta)] .* repmat(radius, 1,2);
points = (points+1)/2*(n-1)+1; points(end+1,:) = points(1,:);
M = draw_polygons(zeros(n),0.8,{points'});
[x,y] = ind2sub(size(M),find(M));
p = 100; m = length(x);
lambda = linspace(0,1,p);
X = n/2 + repmat(x-n/2, [1 p]) .* repmat(lambda, [m 1]);
Y = n/2 + repmat(y-n/2, [1 p]) .* repmat(lambda, [m 1]);
I = round(X) + (round(Y)-1)*n;
M = zeros(n); M(I) = 1;
case 'polygon-8'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-10'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-12'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'pacman'
options.radius = 0.45;
options.center = [.5 .5];
M = load_image('disk', n, options);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
T =atan2(Y,X);
M = M .* (1-(abs(T-pi/2)<theta/2));
case 'square-hole'
options.radius = 0.45;
M = load_image('disk', n, options);
options.scaling = 0.5;
M = M - load_image('polygon-10', n, options);
case 'grid-circles'
if isempty(n)
n = 256;
end
f = getoptions(options, 'frequency', 30);
eta = getoptions(options, 'width', .3);
x = linspace(-n/2,n/2,n) - round(n*0.03);
y = linspace(0,n,n);
[Y,X] = meshgrid(y,x);
R = sqrt(X.^2+Y.^2);
theta = 0.05*pi/2;
X1 = cos(theta)*X+sin(theta)*Y;
Y1 = -sin(theta)*X+cos(theta)*Y;
A1 = abs(cos(2*pi*R/f))<eta;
A2 = max( abs(cos(2*pi*X1/f))<eta, abs(cos(2*pi*Y1/f))<eta );
M = A1;
M(X1>0) = A2(X1>0);
case 'chessboard1'
x = -1:2/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (2*(Y>=0)-1).*(2*(X>=0)-1);
case 'chessboard'
width = getoptions(options, 'width', round(n/16) );
[Y,X] = meshgrid(0:n-1,0:n-1);
M = mod( floor(X/width)+floor(Y/width), 2 ) == 0;
case 'square'
if ~isfield( options, 'radius' )
radius = 0.6;
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M = max( abs(X),abs(Y) )<radius;
case 'squareregular'
M = rescale(load_image('square',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'regular1'
options.alpha = 1;
M = load_image('fnoise',n,options);
case 'regular2'
options.alpha = 2;
M = load_image('fnoise',n,options);
case 'regular3'
options.alpha = 3;
M = load_image('fnoise',n,options);
case 'sparsecurves'
options.alpha = 3;
M = load_image('fnoise',n,options);
M = rescale(M);
ncurves = 3;
M = cos(2*pi*ncurves);
case 'geometrical'
J = getoptions(options, 'Jgeometrical', 4);
sgeom = 100*n/256;
options.bound = 'per';
A = ones(n);
for j=0:J-1
B = A;
for k=1:2^j
I = find(B==k);
U = perform_blurring(randn(n),sgeom,options);
s = median(U(I));
I1 = find( (B==k) & (U>s) );
I2 = find( (B==k) & (U<=s) );
A(I1) = 2*k-1;
A(I2) = 2*k;
end
end
M = A;
case 'lic-texture'
disp('Computing random tensor field.');
options.sigma_tensor = getoptions(options, 'lic_regularity', 50*n/256);
T = compute_tensor_field_random(n,options);
Flow = perform_tensor_decomp(T); % extract eigenfield.
options.isoriented = 0; % no orientation in streamlines
% initial texture
lic_width = getoptions(options, 'lic_width', 0);
M0 = perform_blurring(randn(n),lic_width);
M0 = perform_histogram_equalization( M0, 'linear');
options.histogram = 'linear';
options.dt = 0.4;
options.M0 = M0;
options.verb = 1;
options.flow_correction = 1;
options.niter_lic = 3;
w = 30;
M = perform_lic(Flow, w, options);
case 'square_texture'
M = load_image('square',n);
M = rescale(M);
% make a texture patch
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M(I) = M(I) + lambda * sin( x(I) * 2*pi / eta );
case 'tv-image'
M = rand(n);
tau = compute_total_variation(M);
options.niter = 400;
[M,err_tv,err_l2] = perform_tv_projection(M,tau/1000,options);
M = perform_histogram_equalization(M,'linear');
case 'oscillatory_texture'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M = sin( x * 2*pi / eta );
case {'line', 'line_vertical', 'line_horizontal', 'line_diagonal'}
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
if gamma~=Inf
M = (X-eta) - gamma*Y < 0;
else
M = (Y-eta) < 0;
end
case 'line-windowed'
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
eta = .3;
gamma = getoptions(options, 'gamma', pi/10);
parabola = getoptions(options, 'parabola', 0);
M = (X-eta) - gamma*Y - parabola*Y.^2 < 0;
f = sin( pi*x ).^2;
M = M .* ( f'*f );
case 'grating'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
theta = getoptions(options, 'theta', .2);
freq = getoptions(options, 'freq', .2);
X = cos(theta)*X + sin(theta)*Y;
M = sin(2*pi*X/freq);
case 'disk'
if ~isfield( options, 'radius' )
radius = 0.35;
end
if ~isfield( options, 'center' )
center = [0.5, 0.5]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'twodisks'
M = zeros(n);
options.center = [.25 .25];
M = load_image('disk', n, options);
options.center = [.75 .75];
M = M + load_image('disk', n, options);
case 'diskregular'
M = rescale(load_image('disk',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'quarterdisk'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'fading_contour'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
theta = 2/pi*atan2(Y,X);
h = 0.5;
M = exp(-(1-theta).^2/h^2).*M;
case '3contours'
radius = 1.3;
center = [-1, 1];
radius1 = 0.8;
center1 = [0, 0];
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
f1 = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
f2 = (X-center1(1)).^2 + (Y-center1(2)).^2 < radius1^2;
M = f1 + 0.5*f2.*(1-f1);
case 'line_circle'
gamma = 1/sqrt(2);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M1 = double( X>gamma*Y+0.25 );
M2 = X.^2 + Y.^2 < 0.6^2;
M = 20 + max(0.5*M1,M2) * 216;
case 'fnoise'
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
alpha = getoptions(options, 'alpha', 1);
M = gen_noisy_image(n,alpha);
case 'gaussiannoise'
% generate an image of filtered noise with gaussian
sigma = getoptions(options, 'sigma', 10);
M = randn(n);
m = 51;
h = compute_gaussian_filter([m m],sigma/(4*n),[n n]);
M = perform_convolution(M,h);
return;
case {'bwhorizontal','bwvertical','bwcircle'}
[Y,X] = meshgrid(0:n-1,0:n-1);
if strcmp(type, 'bwhorizontal')
d = X;
elseif strcmp(type, 'bwvertical')
d = Y;
elseif strcmp(type, 'bwcircle')
d = sqrt( (X-(n-1)/2).^2 + (Y-(n-1)/2).^2 );
end
if isfield(options, 'stripe_width')
stripe_width = options.stripe_width;
else
stripe_width = 5;
end
if isfield(options, 'black_prop')
black_prop = options.black_prop;
else
black_prop = 0.5;
end
M = double( mod( d/(2*stripe_width),1 )>=black_prop );
case 'parabola'
% curvature
c = getoptions(c, 'c', .1);
% angle
theta = getoptions(options, 'theta', pi/sqrt(2));
x = -0.5:1/(n-1):0.5;
[Y,X] = meshgrid(x,x);
Xs = X*cos(theta) + Y*sin(theta);
Y =-X*sin(theta) + Y*cos(theta); X = Xs;
M = Y>c*X.^2;
case 'sin'
[Y,X] = meshgrid(-1:2/(n-1):1, -1:2/(n-1):1);
M = Y >= 0.6*cos(pi*X);
M = double(M);
case 'circ_oscil'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
R = sqrt(X.^2+Y.^2);
M = cos(R.^3*50);
case 'phantom'
M = phantom(n);
case 'periodic_bumps'
nbr_periods = getoptions(options, 'nbr_periods', 8);
theta = getoptions(options, 'theta', 1/sqrt(2));
skew = getoptions(options, 'skew', 1/sqrt(2) );
A = [cos(theta), -sin(theta); sin(theta), cos(theta)];
B = [1 skew; 0 1];
T = B*A;
x = (0:n-1)*2*pi*nbr_periods/(n-1);
[Y,X] = meshgrid(x,x);
pos = [X(:)'; Y(:)'];
pos = T*pos;
X = reshape(pos(1,:), n,n);
Y = reshape(pos(2,:), n,n);
M = cos(X).*sin(Y);
case 'noise'
sigma = getoptions(options, 'sigma', 1);
M = randn(n) * sigma;
case 'disk-corner'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
rho = .3; eta = .1;
M1 = rho*X+eta<Y;
c = [0 .2]; r = .85;
d = (X-c(1)).^2 + (Y-c(2)).^2;
M2 = d<r^2;
M = M1.*M2;
otherwise
ext = {'gif', 'png', 'jpg', 'bmp', 'tiff', 'pgm', 'ppm'};
for i=1:length(ext)
name = [type '.' ext{i}];
if( exist(name) )
M = imread( name );
M = double(M);
if not(isempty(n)) && (n~=size(M, 1) || n~=size(M, 2)) && nargin>=2
M = image_resize(M,n,n);
end
if strcmp(type, 'peppers-bw')
M(:,1) = M(:,2);
M(1,:) = M(2,:);
end
if sigma>0
M = perform_blurring(M,sigma);
end
return;
end
end
error( ['Image ' type ' does not exists.'] );
end
M = double(M);
if sigma>0
M = perform_blurring(M,sigma);
end
M = rescale(M);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = create_letter(a, r, n)
c = 0.2;
p1 = [c;c];
p2 = [c; 1-c];
p3 = [1-c; 1-c];
p4 = [1-c; c];
p4 = [1-c; c];
pc = [0.5;0.5];
pu = [0.5; c];
switch a
case 'x'
point_list = { [p1 p3] [p2 p4] };
case 'z'
point_list = { [p2 p3 p1 p4] };
case 'v'
point_list = { [p2 pu p3] };
case 'y'
point_list = { [p2 pc pu] [pc p3] };
end
% fit image
for i=1:length(point_list)
a = point_list{i}(2:-1:1,:);
a(1,:) = 1-a(1,:);
point_list{i} = round( a*(n-1)+1 );
end
M = draw_polygons(zeros(n),r,point_list);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_polygons(mask,r,point_list)
sk = mask*0;
for i=1:length(point_list)
pl = point_list{i};
for k=2:length(pl)
sk = draw_line(sk,pl(1,k-1),pl(2,k-1),pl(1,k),pl(2,k),r);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_line(sk,x1,y1,x2,y2,r)
n = size(sk,1);
[Y,X] = meshgrid(1:n,1:n);
q = 100;
t = linspace(0,1,q);
x = x1*t+x2*(1-t); y = y1*t+y2*(1-t);
if r==0
x = round( x ); y = round( y );
sk( x+(y-1)*n ) = 1;
else
for k=1:q
I = find((X-x(k)).^2 + (Y-y(k)).^2 <= r^2 );
sk(I) = 1;
end
end
function M = gen_noisy_image(n,alpha)
% gen_noisy_image - generate a noisy cloud-like image.
%
% M = gen_noisy_image(n,alpha);
%
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<1
n = 128;
end
if nargin<2
alpha = 1.5;
end
if mod(n(1),2)==0
x = -n/2:n/2-1;
else
x = -(n-1)/2:(n-1)/2;
end
[Y,X] = meshgrid(x,x);
d = sqrt(X.^2 + Y.^2) + 0.1;
f = rand(n)*2*pi;
M = (d.^(-alpha)) .* exp(f*1i);
% M = real(ifft2(fftshift(M)));
M = ifftshift(M);
M = real( ifft2(M) );
function y = gen_signal_2d(n,alpha)
% gen_signal_2d - generate a 2D C^\alpha signal of length n x n.
% gen_signal_2d(n,alpha) generate a 2D signal C^alpha.
%
% The signal is scale in [0,1].
%
% Copyright (c) 2003 Gabriel Peyre
% new new method
[Y,X] = meshgrid(0:n-1, 0:n-1);
A = X+Y+1;
B = X-Y+n+1;
a = gen_signal(2*n+1, alpha);
b = gen_signal(2*n+1, alpha);
y = a(A).*b(B);
% M = a(1:n)*b(1:n)';
return;
% new method
h = (-n/2+1):(n/2); h(n/2)=1;
[X,Y] = meshgrid(h,h);
h = sqrt(X.^2+Y.^2+1).^(-alpha-1/2);
h = h .* exp( 2i*pi*rand(n,n) );
h = fftshift(h);
y = real( ifft2(h) );
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
return;
%% old code
y = rand(n,n);
y = y - mean(mean(y));
for i=1:alpha
y = cumsum(cumsum(y)')';
y = y - mean(mean(y));
end
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = draw_rectangle(r,n)
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
M = double( (X>=r(1)) & (X<=r(3)) & (Y>=r(2)) & (Y<=r(4)) ) ;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
imageplot.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/wass-barycenters/toolbox/imageplot.m
| 2,996 |
utf_8
|
bb6359ff3ad5e82264a744d41ba24582
|
function h1 = imageplot(M,str, a,b,c)
% imageplot - diplay an image and a title
%
% Example of usages:
% imageplot(M);
% imageplot(M,title);
% imageplot(M,title,1,2,1); % to make subplot(1,2,1);
%
% imageplot(M,options);
%
% If you want to display several images:
% imageplot({M1 M2}, {'title1', 'title2'});
%
% Copyright (c) 2007 Gabriel Peyre
if nargin<2
str = [];
end
options.null = 0;
if isstruct(str)
options = str;
str = '';
end
nbdims = nb_dims(M);
if iscell(M)
q = length(M);
if nargin<5
c = 1;
end
if nargin<4
a = ceil(q/4);
end
if nargin<3
b = ceil(q/a);
end
if (c-1+q)>(a*b)
warning('a and c parameters not large enough');
a = ceil((c-1+q)/4);
b = ceil((c-1+q)/a);
end
for i=1:q
if iscell(str)
str1 = str{i};
else
str1 = str;
end
h{i} = imageplot(M{i},str1, a,b,c-1+i);
end
global axlist;
if not(isempty(axlist))
linkaxes(axlist, 'xy');
end
if nargout>0
if exist('h')
h1 = h;
else
h1 = [];
end
end
return;
end
if nargin==5
global axlist;
global imageplot_size;
if c==1 || isempty(imageplot_size) || imageplot_size~=size(M,1)
clear axlist;
global axlist;
axlist = [];
imageplot_size = size(M,1);
end
axlist(end+1) = subplot(a,b,c);
end
if nbdims==1
h = plot(M); axis tight;
elseif size(M,3)<=3
% gray-scale or color image
if size(M,3)==2
M = cat(3,M, zeros(size(M,1),size(M,2)));
end
if not(isreal(M))
if size(M,3)==1
% turn into color matrix
M = cat(3, real(M), imag(M), zeros(size(M,1),size(M,2)));
else
warning('Complex data');
M = real(M);
end
end
if size(M,3)==1
colormap gray(256);
else
colormap jet(256);
end
h = imagesc(rescale(M)); axis image; axis off;
else
if not(isfield(options, 'center') )
options.center = .5; % here a value in [0,1]
end
if not(isfield(options, 'sigma'))
options.sigma = .08; % control the width of the non-transparent region
end
a = compute_alpha_map('gaussian', options); % you can plot(a) to see the alphamap
% volumetric image
h = vol3d('cdata',rescale(M),'texture','2D');
view(3);
axis tight; % daspect([1 1 .4])
colormap bone(256);
% alphamap('rampup');
% alphamap(.06 .* alphamap);
vol3d(h);
end
if not(isempty(str))
title(str);
end
if nargout>0
if exist('h')
h1 = h;
else
h1 = [];
end
end
if nargin==5 && c==a*b
linkaxes(axlist, 'xy');
end
function d = nb_dims(x)
% nb_dims - debugged version of ndims.
%
% d = nb_dims(x);
%
% Copyright (c) 2004 Gabriel Peyre
if isempty(x)
d = 0;
return;
end
d = ndims(x);
if d==2 && (size(x,1)==1 || size(x,2)==1)
d = 1;
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
check_face_vertex.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/silouhette/check_face_vertex.m
| 671 |
utf_8
|
21c65f119991c973909eedd356838dad
|
function [vertex,face] = check_face_vertex(vertex,face, options)
% check_face_vertex - check that vertices and faces have the correct size
%
% [vertex,face] = check_face_vertex(vertex,face);
%
% Copyright (c) 2007 Gabriel Peyre
vertex = check_size(vertex,2,4);
face = check_size(face,3,4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = check_size(a,vmin,vmax)
if isempty(a)
return;
end
if size(a,1)>size(a,2)
a = a';
end
if size(a,1)<3 && size(a,2)==3
a = a';
end
if size(a,1)<=3 && size(a,2)>=3 && sum(abs(a(:,3)))==0
% for flat triangles
% a = a';
end
if size(a,1)<vmin || size(a,1)>vmax
error('face or vertex is not of correct size');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_image.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/load_image.m
| 19,798 |
utf_8
|
df61d87c209e587d6199fa36bbe979bf
|
function M = load_image(type, n, options)
% load_image - load benchmark images.
%
% M = load_image(name, n, options);
%
% name can be:
% Synthetic images:
% 'chessboard1', 'chessboard', 'square', 'squareregular', 'disk', 'diskregular', 'quaterdisk', '3contours', 'line',
% 'line_vertical', 'line_horizontal', 'line_diagonal', 'line_circle',
% 'parabola', 'sin', 'phantom', 'circ_oscil',
% 'fnoise' (1/f^alpha noise).
% Natural images:
% 'boat', 'lena', 'goldhill', 'mandrill', 'maurice', 'polygons_blurred', or your own.
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<2
n = 512;
end
options.null = 0;
if iscell(type)
for i=1:length(type)
M{i} = load_image(type{i},n,options);
end
return;
end
type = lower(type);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters for geometric objects
eta = getoptions(options, 'eta', .1);
gamma = getoptions(options, 'gamma', 1/sqrt(2));
radius = getoptions(options, 'radius', 10);
center = getoptions(options, 'center', [0 0]);
center1 = getoptions(options, 'center1', [0 0]);
w = getoptions(options, 'tube_width', 0.06);
nb_points = getoptions(options, 'nb_points', 9);
scaling = getoptions(options, 'scaling', 1);
theta = getoptions(options, 'theta', 30 * 2*pi/360);
eccentricity = getoptions(options, 'eccentricity', 1.3);
sigma = getoptions(options, 'sigma', 0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for the line, can be vertical / horizontal / diagonal / any
if strcmp(type, 'line_vertical')
eta = 0.5; % translation
gamma = 0; % slope
elseif strcmp(type, 'line_horizontal')
eta = 0.5; % translation
gamma = Inf; % slope
elseif strcmp(type, 'line_diagonal')
eta = 0; % translation
gamma = 1; % slope
end
if strcmp(type(1:min(12,end)), 'square-tube-')
k = str2double(type(13:end));
c1 = [.22 .5]; c2 = [1-c1(1) .5];
eta = 1.5;
r1 = [c1 c1] + .21*[-1 -eta 1 eta];
r2 = [c2 c2] + .21*[-1 -eta 1 eta];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
if mod(k,2)==0
sel = n/2-k/2+1:n/2+k/2;
else
sel = n/2-(k-1)/2:n/2+(k-1)/2;
end
M( round(.25*n:.75*n), sel ) = 1;
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch lower(type)
case 'constant'
M = ones(n);
case 'ramp'
x = linspace(0,1,n);
[Y,M] = meshgrid(x,x);
case 'bump'
s = getoptions(options, 'bump_size', .5);
c = getoptions(options, 'center', [0 0]);
if length(s)==1
s = [s s];
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
X = (X-c(1))/s(1); Y = (Y-c(2))/s(2);
M = exp( -(X.^2+Y.^2)/2 );
case 'periodic'
x = linspace(-pi,pi,n)/1.1;
[Y,X] = meshgrid(x,x);
f = getoptions(options, 'freq', 6);
M = (1+cos(f*X)).*(1+cos(f*Y));
case {'letter-x' 'letter-v' 'letter-z' 'letter-y'}
M = create_letter(type(8), radius, n);
case 'l'
r1 = [.1 .1 .3 .9];
r2 = [.1 .1 .9 .4];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
case 'ellipse'
c1 = [0.15 0.5];
c2 = [0.85 0.5];
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
d = sqrt((X-c1(1)).^2 + (Y-c1(2)).^2) + sqrt((X-c2(1)).^2 + (Y-c2(2)).^2);
M = double( d<=eccentricity*sqrt( sum((c1-c2).^2) ) );
case 'ellipse-thin'
options.eccentricity = 1.06;
M = load_image('ellipse', n, options);
case 'ellipse-fat'
options.eccentricity = 1.3;
M = load_image('ellipse', n, options);
case 'square-tube'
c1 = [.25 .5];
c2 = [.75 .5];
r1 = [c1 c1] + .18*[-1 -1 1 1];
r2 = [c2 c2] + .18*[-1 -1 1 1];
r3 = [c1(1)-w c1(2)-w c2(1)+w c2(2)+w];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) | draw_rectangle(r3,n) );
case 'square-tube-1'
options.tube_width = 0.03;
M = load_image('square-tube', n, options);
case 'square-tube-2'
options.tube_width = 0.06;
M = load_image('square-tube', n, options);
case 'square-tube-3'
options.im = 0.09;
M = load_image('square-tube', n, options);
case 'polygon'
theta = sort( rand(nb_points,1)*2*pi );
radius = scaling*rescale(rand(nb_points,1), 0.1, 0.93);
points = [cos(theta) sin(theta)] .* repmat(radius, 1,2);
points = (points+1)/2*(n-1)+1; points(end+1,:) = points(1,:);
M = draw_polygons(zeros(n),0.8,{points'});
[x,y] = ind2sub(size(M),find(M));
p = 100; m = length(x);
lambda = linspace(0,1,p);
X = n/2 + repmat(x-n/2, [1 p]) .* repmat(lambda, [m 1]);
Y = n/2 + repmat(y-n/2, [1 p]) .* repmat(lambda, [m 1]);
I = round(X) + (round(Y)-1)*n;
M = zeros(n); M(I) = 1;
case 'polygon-8'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-10'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-12'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'pacman'
options.radius = 0.45;
options.center = [.5 .5];
M = load_image('disk', n, options);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
T =atan2(Y,X);
M = M .* (1-(abs(T-pi/2)<theta/2));
case 'square-hole'
options.radius = 0.45;
M = load_image('disk', n, options);
options.scaling = 0.5;
M = M - load_image('polygon-10', n, options);
case 'grid-circles'
if isempty(n)
n = 256;
end
f = getoptions(options, 'frequency', 30);
eta = getoptions(options, 'width', .3);
x = linspace(-n/2,n/2,n) - round(n*0.03);
y = linspace(0,n,n);
[Y,X] = meshgrid(y,x);
R = sqrt(X.^2+Y.^2);
theta = 0.05*pi/2;
X1 = cos(theta)*X+sin(theta)*Y;
Y1 = -sin(theta)*X+cos(theta)*Y;
A1 = abs(cos(2*pi*R/f))<eta;
A2 = max( abs(cos(2*pi*X1/f))<eta, abs(cos(2*pi*Y1/f))<eta );
M = A1;
M(X1>0) = A2(X1>0);
case 'chessboard1'
x = -1:2/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (2*(Y>=0)-1).*(2*(X>=0)-1);
case 'chessboard'
width = getoptions(options, 'width', round(n/16) );
[Y,X] = meshgrid(0:n-1,0:n-1);
M = mod( floor(X/width)+floor(Y/width), 2 ) == 0;
case 'square'
if ~isfield( options, 'radius' )
radius = 0.6;
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M = max( abs(X),abs(Y) )<radius;
case 'squareregular'
M = rescale(load_image('square',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'regular1'
options.alpha = 1;
M = load_image('fnoise',n,options);
case 'regular2'
options.alpha = 2;
M = load_image('fnoise',n,options);
case 'regular3'
options.alpha = 3;
M = load_image('fnoise',n,options);
case 'sparsecurves'
options.alpha = 3;
M = load_image('fnoise',n,options);
M = rescale(M);
ncurves = 3;
M = cos(2*pi*ncurves);
case 'geometrical'
J = getoptions(options, 'Jgeometrical', 4);
sgeom = 100*n/256;
options.bound = 'per';
A = ones(n);
for j=0:J-1
B = A;
for k=1:2^j
I = find(B==k);
U = perform_blurring(randn(n),sgeom,options);
s = median(U(I));
I1 = find( (B==k) & (U>s) );
I2 = find( (B==k) & (U<=s) );
A(I1) = 2*k-1;
A(I2) = 2*k;
end
end
M = A;
case 'lic-texture'
disp('Computing random tensor field.');
options.sigma_tensor = getoptions(options, 'lic_regularity', 50*n/256);
T = compute_tensor_field_random(n,options);
Flow = perform_tensor_decomp(T); % extract eigenfield.
options.isoriented = 0; % no orientation in streamlines
% initial texture
lic_width = getoptions(options, 'lic_width', 0);
M0 = perform_blurring(randn(n),lic_width);
M0 = perform_histogram_equalization( M0, 'linear');
options.histogram = 'linear';
options.dt = 0.4;
options.M0 = M0;
options.verb = 1;
options.flow_correction = 1;
options.niter_lic = 3;
w = 30;
M = perform_lic(Flow, w, options);
case 'square_texture'
M = load_image('square',n);
M = rescale(M);
% make a texture patch
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M(I) = M(I) + lambda * sin( x(I) * 2*pi / eta );
case 'tv-image'
M = rand(n);
tau = compute_total_variation(M);
options.niter = 400;
[M,err_tv,err_l2] = perform_tv_projection(M,tau/1000,options);
M = perform_histogram_equalization(M,'linear');
case 'oscillatory_texture'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M = sin( x * 2*pi / eta );
case {'line', 'line_vertical', 'line_horizontal', 'line_diagonal'}
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
if gamma~=Inf
M = (X-eta) - gamma*Y < 0;
else
M = (Y-eta) < 0;
end
case 'line-windowed'
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
eta = .3;
gamma = getoptions(options, 'gamma', pi/10);
parabola = getoptions(options, 'parabola', 0);
M = (X-eta) - gamma*Y - parabola*Y.^2 < 0;
f = sin( pi*x ).^2;
M = M .* ( f'*f );
case 'grating'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
theta = getoptions(options, 'theta', .2);
freq = getoptions(options, 'freq', .2);
X = cos(theta)*X + sin(theta)*Y;
M = sin(2*pi*X/freq);
case 'disk'
if ~isfield( options, 'radius' )
radius = 0.35;
end
if ~isfield( options, 'center' )
center = [0.5, 0.5]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'twodisks'
M = zeros(n);
options.center = [.25 .25];
M = load_image('disk', n, options);
options.center = [.75 .75];
M = M + load_image('disk', n, options);
case 'diskregular'
M = rescale(load_image('disk',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'quarterdisk'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'fading_contour'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
theta = 2/pi*atan2(Y,X);
h = 0.5;
M = exp(-(1-theta).^2/h^2).*M;
case '3contours'
radius = 1.3;
center = [-1, 1];
radius1 = 0.8;
center1 = [0, 0];
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
f1 = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
f2 = (X-center1(1)).^2 + (Y-center1(2)).^2 < radius1^2;
M = f1 + 0.5*f2.*(1-f1);
case 'line_circle'
gamma = 1/sqrt(2);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M1 = double( X>gamma*Y+0.25 );
M2 = X.^2 + Y.^2 < 0.6^2;
M = 20 + max(0.5*M1,M2) * 216;
case 'fnoise'
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
alpha = getoptions(options, 'alpha', 1);
M = gen_noisy_image(n,alpha);
case 'gaussiannoise'
% generate an image of filtered noise with gaussian
sigma = getoptions(options, 'sigma', 10);
M = randn(n);
m = 51;
h = compute_gaussian_filter([m m],sigma/(4*n),[n n]);
M = perform_convolution(M,h);
return;
case {'bwhorizontal','bwvertical','bwcircle'}
[Y,X] = meshgrid(0:n-1,0:n-1);
if strcmp(type, 'bwhorizontal')
d = X;
elseif strcmp(type, 'bwvertical')
d = Y;
elseif strcmp(type, 'bwcircle')
d = sqrt( (X-(n-1)/2).^2 + (Y-(n-1)/2).^2 );
end
if isfield(options, 'stripe_width')
stripe_width = options.stripe_width;
else
stripe_width = 5;
end
if isfield(options, 'black_prop')
black_prop = options.black_prop;
else
black_prop = 0.5;
end
M = double( mod( d/(2*stripe_width),1 )>=black_prop );
case 'parabola'
% curvature
c = getoptions(c, 'c', .1);
% angle
theta = getoptions(options, 'theta', pi/sqrt(2));
x = -0.5:1/(n-1):0.5;
[Y,X] = meshgrid(x,x);
Xs = X*cos(theta) + Y*sin(theta);
Y =-X*sin(theta) + Y*cos(theta); X = Xs;
M = Y>c*X.^2;
case 'sin'
[Y,X] = meshgrid(-1:2/(n-1):1, -1:2/(n-1):1);
M = Y >= 0.6*cos(pi*X);
M = double(M);
case 'circ_oscil'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
R = sqrt(X.^2+Y.^2);
M = cos(R.^3*50);
case 'phantom'
M = phantom(n);
case 'periodic_bumps'
nbr_periods = getoptions(options, 'nbr_periods', 8);
theta = getoptions(options, 'theta', 1/sqrt(2));
skew = getoptions(options, 'skew', 1/sqrt(2) );
A = [cos(theta), -sin(theta); sin(theta), cos(theta)];
B = [1 skew; 0 1];
T = B*A;
x = (0:n-1)*2*pi*nbr_periods/(n-1);
[Y,X] = meshgrid(x,x);
pos = [X(:)'; Y(:)'];
pos = T*pos;
X = reshape(pos(1,:), n,n);
Y = reshape(pos(2,:), n,n);
M = cos(X).*sin(Y);
case 'noise'
sigma = getoptions(options, 'sigma', 1);
M = randn(n) * sigma;
case 'disk-corner'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
rho = .3; eta = .1;
M1 = rho*X+eta<Y;
c = [0 .2]; r = .85;
d = (X-c(1)).^2 + (Y-c(2)).^2;
M2 = d<r^2;
M = M1.*M2;
otherwise
ext = {'gif', 'png', 'jpg', 'bmp', 'tiff', 'pgm', 'ppm'};
for i=1:length(ext)
name = [type '.' ext{i}];
if( exist(name) )
M = imread( name );
M = double(M);
if not(isempty(n)) && (n~=size(M, 1) || n~=size(M, 2)) && nargin>=2
M = image_resize(M,n,n);
end
if strcmp(type, 'peppers-bw')
M(:,1) = M(:,2);
M(1,:) = M(2,:);
end
if sigma>0
M = perform_blurring(M,sigma);
end
return;
end
end
error( ['Image ' type ' does not exists.'] );
end
M = double(M);
if sigma>0
M = perform_blurring(M,sigma);
end
M = rescale(M);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = create_letter(a, r, n)
c = 0.2;
p1 = [c;c];
p2 = [c; 1-c];
p3 = [1-c; 1-c];
p4 = [1-c; c];
p4 = [1-c; c];
pc = [0.5;0.5];
pu = [0.5; c];
switch a
case 'x'
point_list = { [p1 p3] [p2 p4] };
case 'z'
point_list = { [p2 p3 p1 p4] };
case 'v'
point_list = { [p2 pu p3] };
case 'y'
point_list = { [p2 pc pu] [pc p3] };
end
% fit image
for i=1:length(point_list)
a = point_list{i}(2:-1:1,:);
a(1,:) = 1-a(1,:);
point_list{i} = round( a*(n-1)+1 );
end
M = draw_polygons(zeros(n),r,point_list);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_polygons(mask,r,point_list)
sk = mask*0;
for i=1:length(point_list)
pl = point_list{i};
for k=2:length(pl)
sk = draw_line(sk,pl(1,k-1),pl(2,k-1),pl(1,k),pl(2,k),r);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_line(sk,x1,y1,x2,y2,r)
n = size(sk,1);
[Y,X] = meshgrid(1:n,1:n);
q = 100;
t = linspace(0,1,q);
x = x1*t+x2*(1-t); y = y1*t+y2*(1-t);
if r==0
x = round( x ); y = round( y );
sk( x+(y-1)*n ) = 1;
else
for k=1:q
I = find((X-x(k)).^2 + (Y-y(k)).^2 <= r^2 );
sk(I) = 1;
end
end
function M = gen_noisy_image(n,alpha)
% gen_noisy_image - generate a noisy cloud-like image.
%
% M = gen_noisy_image(n,alpha);
%
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<1
n = 128;
end
if nargin<2
alpha = 1.5;
end
if mod(n(1),2)==0
x = -n/2:n/2-1;
else
x = -(n-1)/2:(n-1)/2;
end
[Y,X] = meshgrid(x,x);
d = sqrt(X.^2 + Y.^2) + 0.1;
f = rand(n)*2*pi;
M = (d.^(-alpha)) .* exp(f*1i);
% M = real(ifft2(fftshift(M)));
M = ifftshift(M);
M = real( ifft2(M) );
function y = gen_signal_2d(n,alpha)
% gen_signal_2d - generate a 2D C^\alpha signal of length n x n.
% gen_signal_2d(n,alpha) generate a 2D signal C^alpha.
%
% The signal is scale in [0,1].
%
% Copyright (c) 2003 Gabriel Peyre
% new new method
[Y,X] = meshgrid(0:n-1, 0:n-1);
A = X+Y+1;
B = X-Y+n+1;
a = gen_signal(2*n+1, alpha);
b = gen_signal(2*n+1, alpha);
y = a(A).*b(B);
% M = a(1:n)*b(1:n)';
return;
% new method
h = (-n/2+1):(n/2); h(n/2)=1;
[X,Y] = meshgrid(h,h);
h = sqrt(X.^2+Y.^2+1).^(-alpha-1/2);
h = h .* exp( 2i*pi*rand(n,n) );
h = fftshift(h);
y = real( ifft2(h) );
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
return;
%% old code
y = rand(n,n);
y = y - mean(mean(y));
for i=1:alpha
y = cumsum(cumsum(y)')';
y = y - mean(mean(y));
end
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = draw_rectangle(r,n)
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
M = double( (X>=r(1)) & (X<=r(3)) & (Y>=r(2)) & (Y<=r(4)) ) ;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
check_face_vertex.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/check_face_vertex.m
| 669 |
utf_8
|
c940a837f5afef7c3a7f7aed3aff9f7a
|
function [vertex,face] = check_face_vertex(vertex,face, options)
% check_face_vertex - check that vertices and faces have the correct size
%
% [vertex,face] = check_face_vertex(vertex,face);
%
% Copyright (c) 2007 Gabriel Peyre
vertex = check_size(vertex,2,4);
face = check_size(face,3,4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = check_size(a,vmin,vmax)
if isempty(a)
return;
end
if size(a,1)>size(a,2)
a = a';
end
if size(a,1)<3 && size(a,2)==3
a = a';
end
if size(a,1)<=3 && size(a,2)>=3 && sum(abs(a(:,3)))==0
% for flat triangles
a = a';
end
if size(a,1)<vmin || size(a,1)>vmax
error('face or vertex is not of correct size');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
imageplot.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/imageplot.m
| 2,996 |
utf_8
|
bb6359ff3ad5e82264a744d41ba24582
|
function h1 = imageplot(M,str, a,b,c)
% imageplot - diplay an image and a title
%
% Example of usages:
% imageplot(M);
% imageplot(M,title);
% imageplot(M,title,1,2,1); % to make subplot(1,2,1);
%
% imageplot(M,options);
%
% If you want to display several images:
% imageplot({M1 M2}, {'title1', 'title2'});
%
% Copyright (c) 2007 Gabriel Peyre
if nargin<2
str = [];
end
options.null = 0;
if isstruct(str)
options = str;
str = '';
end
nbdims = nb_dims(M);
if iscell(M)
q = length(M);
if nargin<5
c = 1;
end
if nargin<4
a = ceil(q/4);
end
if nargin<3
b = ceil(q/a);
end
if (c-1+q)>(a*b)
warning('a and c parameters not large enough');
a = ceil((c-1+q)/4);
b = ceil((c-1+q)/a);
end
for i=1:q
if iscell(str)
str1 = str{i};
else
str1 = str;
end
h{i} = imageplot(M{i},str1, a,b,c-1+i);
end
global axlist;
if not(isempty(axlist))
linkaxes(axlist, 'xy');
end
if nargout>0
if exist('h')
h1 = h;
else
h1 = [];
end
end
return;
end
if nargin==5
global axlist;
global imageplot_size;
if c==1 || isempty(imageplot_size) || imageplot_size~=size(M,1)
clear axlist;
global axlist;
axlist = [];
imageplot_size = size(M,1);
end
axlist(end+1) = subplot(a,b,c);
end
if nbdims==1
h = plot(M); axis tight;
elseif size(M,3)<=3
% gray-scale or color image
if size(M,3)==2
M = cat(3,M, zeros(size(M,1),size(M,2)));
end
if not(isreal(M))
if size(M,3)==1
% turn into color matrix
M = cat(3, real(M), imag(M), zeros(size(M,1),size(M,2)));
else
warning('Complex data');
M = real(M);
end
end
if size(M,3)==1
colormap gray(256);
else
colormap jet(256);
end
h = imagesc(rescale(M)); axis image; axis off;
else
if not(isfield(options, 'center') )
options.center = .5; % here a value in [0,1]
end
if not(isfield(options, 'sigma'))
options.sigma = .08; % control the width of the non-transparent region
end
a = compute_alpha_map('gaussian', options); % you can plot(a) to see the alphamap
% volumetric image
h = vol3d('cdata',rescale(M),'texture','2D');
view(3);
axis tight; % daspect([1 1 .4])
colormap bone(256);
% alphamap('rampup');
% alphamap(.06 .* alphamap);
vol3d(h);
end
if not(isempty(str))
title(str);
end
if nargout>0
if exist('h')
h1 = h;
else
h1 = [];
end
end
if nargin==5 && c==a*b
linkaxes(axlist, 'xy');
end
function d = nb_dims(x)
% nb_dims - debugged version of ndims.
%
% d = nb_dims(x);
%
% Copyright (c) 2004 Gabriel Peyre
if isempty(x)
d = 0;
return;
end
d = ndims(x);
if d==2 && (size(x,1)==1 || size(x,2)==1)
d = 1;
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
plot_mesh.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/plot_mesh.m
| 11,184 |
utf_8
|
0dcb199b54eb7b66240316a0359d9127
|
function h = plot_mesh(vertex,face,options)
% plot_mesh - plot a 3D mesh.
%
% plot_mesh(vertex,face, options);
%
% 'options' is a structure that may contains:
% - 'normal' : a (nvertx x 3) array specifying the normals at each vertex.
% - 'edge_color' : a float specifying the color of the edges.
% - 'face_color' : a float specifying the color of the faces.
% - 'face_vertex_color' : a color per vertex or face.
% - 'vertex'
% - 'texture' : a 2-D image to be mapped on the surface
% - 'texture_coords' : a (nvertx x 2) array specifying the texture
% coordinates in [0,1] of the vertices in the texture.
% - 'tmesh' : set it to 1 if this corresponds to a volumetric tet mesh.
%
% See also: mesh_previewer.
%
% Copyright (c) 2004 Gabriel Peyr?
if nargin<2
error('Not enough arguments.');
end
options.null = 0;
name = getoptions(options, 'name', '');
normal = getoptions(options, 'normal', []);
face_color = getoptions(options, 'face_color', [.7 .7 .7]);
edge_color = getoptions(options, 'edge_color', [0 0 0]);
normal_scaling = getoptions(options, 'normal_scaling', .8);
sanity_check = getoptions(options, 'sanity_check', 1);
view_param = getoptions(options, 'view_param', []);
texture = getoptions(options, 'texture', []);
texture_coords = getoptions(options, 'texture_coords', []);
tmesh = getoptions(options, 'tmesh', 0);
if size(vertex,1)==2
% 2D triangulation
% vertex = cat(1,vertex, zeros(1,size(vertex,2)));
plot_graph(triangulation2adjacency(face),vertex);
return;
end
% can flip to accept data in correct ordering
%[vertex,face] = check_face_vertex(vertex,face);
if size(face,1)==4 && tmesh==1
%%%% tet mesh %%%%
% normal to the plane <x,w><=a
w = getoptions(options, 'cutting_plane', [0.2 0 1]');
w = w(:)/sqrt(sum(w.^2));
t = sum(vertex.*repmat(w,[1 size(vertex,2)]));
a = getoptions(options, 'cutting_offs', median(t(:)) );
b = getoptions(options, 'cutting_interactive', 0);
plot_points = getoptions(options, 'plot_points', 0);
while true;
% in/out
I = ( t<=a );
% trim
e = sum(I(face));
J = find(e==4);
facetrim = face(:,J);
% convert to triangular mesh
hold on;
if not(isempty(facetrim))
face1 = tet2tri(facetrim, vertex, 1);
% options.method = 'slow';
face1 = perform_faces_reorientation(vertex,face1, options);
h{1} = plot_mesh(vertex,face1, options);
end
view(3); % camlight;
shading faceted;
if plot_points
K = find(e==0);
K = face(:,K); K = unique(K(:));
h{2} = plot3(vertex(1,K), vertex(2,K), vertex(3,K), 'k.');
end
hold off;
if b==0
break;
end
[x,y,b] = ginput(1);
if b==1
a = a+.03;
elseif b==3
a = a-.03;
else
break;
end
end
return;
end
vertex = vertex';
face = face';
if strcmp(name, 'bunny') || strcmp(name, 'pieta')
% vertex = -vertex;
end
if strcmp(name, 'armadillo')
vertex(:,3) = -vertex(:,3);
end
if sanity_check && ( (size(face,2)~=3 && size(face,2)~=4) || (size(vertex,2)~=3 && size(vertex,2)~=2))
error('face or vertex does not have correct format.');
end
% if ~isfield(options, 'face_vertex_color') || isempty(options.face_vertex_color)
% options.face_vertex_color = zeros(size(vertex,1),1);
% end
face_vertex_color = getoptions(options, 'face_vertex_color', []);
if not(isempty(texture))
%%% textured mesh %%%
if isempty(texture_coords)
error('You need to provide texture_coord.');
end
if size(texture_coords,2)~=2
texture_coords = texture_coords';
end
opts.EdgeColor = 'none';
patcht(face,vertex,face,texture_coords,texture',opts);
if size(texture,3)==1
colormap gray(256);
else
colormap jet(256);
end
set_view(name, view_param);
axis off; axis equal;
% camlight; % problem with pithon notebook
shading faceted;
return;
end
shading_type = 'interp';
if isempty(face_vertex_color)
h = patch('vertices',vertex,'faces',face,'facecolor', face_color(:)','edgecolor',edge_color(:)');
else
nverts = size(vertex,1);
% vertex_color = rand(nverts,1);
if size(face_vertex_color,1)==size(vertex,1)
shading_type = 'interp';
else
shading_type = 'flat';
end
h = patch('vertices',vertex,'faces',face,'FaceVertexCData',face_vertex_color, 'FaceColor',shading_type);
end
colormap gray(256);
lighting phong;
% camlight infinite;
camproj('perspective');
axis square;
axis off;
if ~isempty(normal)
%%% plot the normals %%%
n = size(vertex,1);
subsample_normal = getoptions(options, 'subsample_normal', min(4000/n,1) );
sel = randperm(n); sel = sel(1:floor(end*subsample_normal));
hold on;
quiver3(vertex(sel,1),vertex(sel,2),vertex(sel,3),normal(1,sel)',normal(2,sel)',normal(3,sel)',normal_scaling);
hold off;
end
% camlight;
set_view(name, view_param);
shading(shading_type);
% camlight; %% BUG WITH PYTHON
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function set_view(name, view_param)
switch lower(name)
case 'hammerheadtriang'
view(150,-45);
case 'horse'
view(134,-61);
case 'skull'
view(21.5,-12);
case 'mushroom'
view(160,-75);
case 'bunny'
% view(0,-55);
view(0,90);
case 'david_head'
view(-100,10);
case 'screwdriver'
view(-10,25);
case 'pieta'
view(15,31);
case 'mannequin'
view(25,15);
view(27,6);
case 'david-low'
view(40,3);
case 'david-head'
view(-150,5);
case 'brain'
view(30,40);
case 'pelvis'
view(5,-15);
case 'fandisk'
view(36,-34);
case 'earth'
view(125,35);
case 'camel'
view(-123,-5);
camroll(-90);
case 'beetle'
view(-117,-5);
camroll(-90);
zoom(.85);
case 'cat'
view(-60,15);
case 'nefertiti'
view(-20,65);
end
if not(isempty(view_param))
view(view_param(1),view_param(2));
end
axis tight;
axis equal;
if strcmp(name, 'david50kf') || strcmp(name, 'hand')
zoom(.85);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function patcht(FF,VV,TF,VT,I,Options)
% This function PATCHT, will show a triangulated mesh like Matlab function
% Patch but then with a texture.
%
% patcht(FF,VV,TF,VT,I,Options);
%
% inputs,
% FF : Face list 3 x N with vertex indices
% VV : Vertices 3 x M
% TF : Texture list 3 x N with texture vertex indices
% VT : Texture Coordinates s 2 x K, range must be [0..1] or real pixel postions
% I : The texture-image RGB [O x P x 3] or Grayscale [O x P]
% Options : Structure with options for the textured patch such as
% EdgeColor, EdgeAlpha see help "Surface Properties :: Functions"
%
% Options.PSize : Special option, defines the image texturesize for each
% individual polygon, a low number gives a more block
% like texture, defaults to 64;
%
% note:
% On a normal PC displaying 10,000 faces will take about 6 sec.
%
% Example,
%
% % Load Data;
% load testdata;
% % Show the textured patch
% figure, patcht(FF,VV,TF,VT,I);
% % Allow Camera Control (with left, right and center mouse button)
% mouse3d
%
% Function is written by D.Kroon University of Twente (July 2010)
% FaceColor is a texture
Options.FaceColor='texturemap';
% Size of texture image used for every triangle
if(isfield(Options,'PSize'))
sizep=round(Options.PSize(1));
Options=rmfield(Options,'PSize');
else
sizep=64;
end
% Check input sizes
if(size(FF,2)~=size(TF,2))
error('patcht:inputs','Face list must be equal in size to texture-index list');
end
if((ndims(I)~=2)&&(ndims(I)~=3))
error('patcht:inputs','No valid Input texture image');
end
% Detect if grayscale or color image
switch(size(I,3))
case 1
iscolor=false;
case 3
iscolor=true;
otherwise
error('patcht:inputs','No valid Input texture image');
end
if(max(VT(:))<2)
% Remap texture coordinates to image coordinates
VT2(:,1)=(size(I,1)-1)*(VT(:,1))+1;
VT2(:,2)=(size(I,2)-1)*(VT(:,2))+1;
else
VT2=VT;
end
% Calculate the texture interpolation values
[lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep);
% Split texture-image in r,g,b to allow fast 1D index
Ir=I(:,:,1); if(iscolor), Ig=I(:,:,2); Ib=I(:,:,3); end
% The Patch used for every triangle (rgb)
Jr=zeros([(sizep+1) (sizep+1) 1],class(I));
if(iscolor)
Jg=zeros([(sizep+1) (sizep+1) 1],class(I));
Jb=zeros([(sizep+1) (sizep+1) 1],class(I));
end
hold on;
% Loop through all triangles of the mesh
for i=1:size(FF,1)
% Get current triangle vertices and current texture-vertices
V=VV(FF(i,:),:);
Vt=VT2(TF(i,:),:);
% Define the triangle as a surface
x=[V(1,1) V(2,1); V(3,1) V(3,1)];
y=[V(1,2) V(2,2); V(3,2) V(3,2)];
z=[V(1,3) V(2,3); V(3,3) V(3,3)];
% Define the texture coordinates of the surface
tx=[Vt(1,1) Vt(2,1) Vt(3,1) Vt(3,1)];
ty=[Vt(1,2) Vt(2,2) Vt(3,2) Vt(3,2)] ;
xy=[tx(1) ty(1); tx(2) ty(2); tx(3) ty(3); tx(3) ty(3)];
% Calculate texture interpolation coordinates
pos(:,1)=xy(1,1)*lambda1+xy(2,1)*lambda2+xy(3,1)*lambda3;
pos(:,2)=xy(1,2)*lambda1+xy(2,2)*lambda2+xy(3,2)*lambda3;
pos=round(pos); pos=max(pos,1); pos(:,1)=min(pos(:,1),size(I,1)); pos(:,2)=min(pos(:,2),size(I,2));
posind=(pos(:,1)-1)+(pos(:,2)-1)*size(I,1)+1;
% Map texture to surface image
Jr(jind)=Ir(posind);
J(:,:,1)=Jr;
if(iscolor)
Jg(jind)=Ig(posind);
Jb(jind)=Ib(posind);
J(:,:,2)=Jg;
J(:,:,3)=Jb;
end
% Show the surface
surface(x,y,z,J,Options);
end
hold off;
function [lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep)
% Define a triangle in the upperpart of an square, because only that
% part is used by the surface function
x1=sizep; y1=sizep; x2=sizep; y2=0; x3=0 ;y3=0;
% Calculate the bary centric coordinates (instead of creating a 2D image
% with the interpolation values, we map them directly to an 1D vector)
detT = (x1-x3)*(y2-y3) - (x2-x3)*(y1-y3);
[x,y]=ndgrid(0:sizep,0:sizep); x=x(:); y=y(:);
lambda1=((y2-y3).*(x-x3)+(x3-x2).*(y-y3))/detT;
lambda2=((y3-y1).*(x-x3)+(x1-x3).*(y-y3))/detT;
lambda3=1-lambda1-lambda2;
% Make from 2D (surface)image indices 1D image indices
[jx jy]=ndgrid(sizep-(0:sizep)+1,sizep-(0:sizep)+1);
jind=(jx(:)-1)+(jy(:)-1)*(sizep+1)+1;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
distinguishable_colors.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/distinguishable_colors.m
| 5,753 |
utf_8
|
57960cf5d13cead2f1e291d1288bccb2
|
function colors = distinguishable_colors(n_colors,bg,func)
% DISTINGUISHABLE_COLORS: pick colors that are maximally perceptually distinct
%
% When plotting a set of lines, you may want to distinguish them by color.
% By default, Matlab chooses a small set of colors and cycles among them,
% and so if you have more than a few lines there will be confusion about
% which line is which. To fix this problem, one would want to be able to
% pick a much larger set of distinct colors, where the number of colors
% equals or exceeds the number of lines you want to plot. Because our
% ability to distinguish among colors has limits, one should choose these
% colors to be "maximally perceptually distinguishable."
%
% This function generates a set of colors which are distinguishable
% by reference to the "Lab" color space, which more closely matches
% human color perception than RGB. Given an initial large list of possible
% colors, it iteratively chooses the entry in the list that is farthest (in
% Lab space) from all previously-chosen entries. While this "greedy"
% algorithm does not yield a global maximum, it is simple and efficient.
% Moreover, the sequence of colors is consistent no matter how many you
% request, which facilitates the users' ability to learn the color order
% and avoids major changes in the appearance of plots when adding or
% removing lines.
%
% Syntax:
% colors = distinguishable_colors(n_colors)
% Specify the number of colors you want as a scalar, n_colors. This will
% generate an n_colors-by-3 matrix, each row representing an RGB
% color triple. If you don't precisely know how many you will need in
% advance, there is no harm (other than execution time) in specifying
% slightly more than you think you will need.
%
% colors = distinguishable_colors(n_colors,bg)
% This syntax allows you to specify the background color, to make sure that
% your colors are also distinguishable from the background. Default value
% is white. bg may be specified as an RGB triple or as one of the standard
% "ColorSpec" strings. You can even specify multiple colors:
% bg = {'w','k'}
% or
% bg = [1 1 1; 0 0 0]
% will only produce colors that are distinguishable from both white and
% black.
%
% colors = distinguishable_colors(n_colors,bg,rgb2labfunc)
% By default, distinguishable_colors uses the image processing toolbox's
% color conversion functions makecform and applycform. Alternatively, you
% can supply your own color conversion function.
%
% Example:
% c = distinguishable_colors(25);
% figure
% image(reshape(c,[1 size(c)]))
%
% Example using the file exchange's 'colorspace':
% func = @(x) colorspace('RGB->Lab',x);
% c = distinguishable_colors(25,'w',func);
% Copyright 2010-2011 by Timothy E. Holy
% Parse the inputs
if (nargin < 2)
bg = [1 1 1]; % default white background
else
if iscell(bg)
% User specified a list of colors as a cell aray
bgc = bg;
for i = 1:length(bgc)
bgc{i} = parsecolor(bgc{i});
end
bg = cat(1,bgc{:});
else
% User specified a numeric array of colors (n-by-3)
bg = parsecolor(bg);
end
end
% Generate a sizable number of RGB triples. This represents our space of
% possible choices. By starting in RGB space, we ensure that all of the
% colors can be generated by the monitor.
n_grid = 30; % number of grid divisions along each axis in RGB space
x = linspace(0,1,n_grid);
[R,G,B] = ndgrid(x,x,x);
rgb = [R(:) G(:) B(:)];
if (n_colors > size(rgb,1)/3)
error('You can''t readily distinguish that many colors');
end
% Convert to Lab color space, which more closely represents human
% perception
if (nargin > 2)
lab = func(rgb);
bglab = func(bg);
else
C = makecform('srgb2lab');
lab = applycform(rgb,C);
bglab = applycform(bg,C);
end
% If the user specified multiple background colors, compute distances
% from the candidate colors to the background colors
mindist2 = inf(size(rgb,1),1);
for i = 1:size(bglab,1)-1
dX = bsxfun(@minus,lab,bglab(i,:)); % displacement all colors from bg
dist2 = sum(dX.^2,2); % square distance
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color
end
% Iteratively pick the color that maximizes the distance to the nearest
% already-picked color
colors = zeros(n_colors,3);
lastlab = bglab(end,:); % initialize by making the "previous" color equal to background
for i = 1:n_colors
dX = bsxfun(@minus,lab,lastlab); % displacement of last from all colors on list
dist2 = sum(dX.^2,2); % square distance
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color
[~,index] = max(mindist2); % find the entry farthest from all previously-chosen colors
colors(i,:) = rgb(index,:); % save for output
lastlab = lab(index,:); % prepare for next iteration
end
end
function c = parsecolor(s)
if ischar(s)
c = colorstr2rgb(s);
elseif isnumeric(s) && size(s,2) == 3
c = s;
else
error('MATLAB:InvalidColorSpec','Color specification cannot be parsed.');
end
end
function c = colorstr2rgb(c)
% Convert a color string to an RGB value.
% This is cribbed from Matlab's whitebg function.
% Why don't they make this a stand-alone function?
rgbspec = [1 0 0;0 1 0;0 0 1;1 1 1;0 1 1;1 0 1;1 1 0;0 0 0];
cspec = 'rgbwcmyk';
k = find(cspec==c(1));
if isempty(k)
error('MATLAB:InvalidColorString','Unknown color string.');
end
if k~=3 || length(c)==1,
c = rgbspec(k,:);
elseif length(c)>2,
if strcmpi(c(1:3),'bla')
c = [0 0 0];
elseif strcmpi(c(1:3),'blu')
c = [0 0 1];
else
error('MATLAB:UnknownColorString', 'Unknown color string.');
end
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
perform_haar_transf.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/toolbox/perform_haar_transf.m
| 3,170 |
utf_8
|
14b7d7fd610eca05949ef196c55d7b83
|
function f = perform_haar_transf(f, Jmin, dir, options)
% perform_haar_transf - peform fast Haar transform
%
% y = perform_haar_transf(x, Jmin, dir);
%
% Implement a Haar wavelets.
% Works in any dimension.
%
% Copyright (c) 2008 Gabriel Peyre
n = size(f,1);
Jmax = log2(n)-1;
if dir==1
%%% FORWARD %%%
for j=Jmax:-1:Jmin
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
Coarse = ( subselectdim(a,1:2:size(a,d),d) + subselectdim(a,2:2:size(a,d),d) )/sqrt(2);
Detail = ( subselectdim(a,1:2:size(a,d),d) - subselectdim(a,2:2:size(a,d),d) )/sqrt(2);
a = cat(d, Coarse, Detail );
end
f = subassign(f,sel,a);
end
else
%%% BACKWARD %%%
for j=Jmin:Jmax
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
Detail = subselectdim(a,2^j+1:2^(j+1),d);
Coarse = subselectdim(a,1:2^j,d);
a = subassigndim(a, 1:2:2^(j+1), ( Coarse + Detail )/sqrt(2),d );
a = subassigndim(a, 2:2:2^(j+1), ( Coarse - Detail )/sqrt(2),d );
end
f = subassign(f,sel,a);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselect(f,sel)
switch nb_dims(f)
case 1
f = f(sel);
case 2
f = f(sel,sel);
case 3
f = f(sel,sel,sel);
case 4
f = f(sel,sel,sel,sel);
case 5
f = f(sel,sel,sel,sel,sel);
case 6
f = f(sel,sel,sel,sel,sel,sel);
case 7
f = f(sel,sel,sel,sel,sel,sel,sel);
case 8
f = f(sel,sel,sel,sel,sel,sel,sel,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselectdim(f,sel,d)
switch d
case 1
f = f(sel,:,:,:,:,:,:,:);
case 2
f = f(:,sel,:,:,:,:,:,:);
case 3
f = f(:,:,sel,:,:,:,:,:);
case 4
f = f(:,:,:,sel,:,:,:,:);
case 5
f = f(:,:,:,:,sel,:,:,:);
case 6
f = f(:,:,:,:,:,sel,:,:);
case 7
f = f(:,:,:,:,:,:,sel,:);
case 8
f = f(:,:,:,:,:,:,:,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subassign(f,sel,g)
switch nb_dims(f)
case 1
f(sel) = g;
case 2
f(sel,sel) = g;
case 3
f(sel,sel,sel) = g;
case 4
f(sel,sel,sel,sel) = g;
case 5
f(sel,sel,sel,sel,sel) = g;
case 6
f(sel,sel,sel,sel,sel,sel) = g;
case 7
f(sel,sel,sel,sel,sel,sel,sel) = g;
case 8
f(sel,sel,sel,sel,sel,sel,sel,sel) = g;
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subassigndim(f,sel,g,d)
switch d
case 1
f(sel,:,:,:,:,:,:,:) = g;
case 2
f(:,sel,:,:,:,:,:,:) = g;
case 3
f(:,:,sel,:,:,:,:,:) = g;
case 4
f(:,:,:,sel,:,:,:,:) = g;
case 5
f(:,:,:,:,sel,:,:,:) = g;
case 6
f(:,:,:,:,:,sel,:,:) = g;
case 7
f(:,:,:,:,:,:,sel,:) = g;
case 8
f(:,:,:,:,:,:,:,sel) = g;
otherwise
error('Not implemented');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_image.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/wasserstein-flows/toolbox/load_image.m
| 19,798 |
utf_8
|
df61d87c209e587d6199fa36bbe979bf
|
function M = load_image(type, n, options)
% load_image - load benchmark images.
%
% M = load_image(name, n, options);
%
% name can be:
% Synthetic images:
% 'chessboard1', 'chessboard', 'square', 'squareregular', 'disk', 'diskregular', 'quaterdisk', '3contours', 'line',
% 'line_vertical', 'line_horizontal', 'line_diagonal', 'line_circle',
% 'parabola', 'sin', 'phantom', 'circ_oscil',
% 'fnoise' (1/f^alpha noise).
% Natural images:
% 'boat', 'lena', 'goldhill', 'mandrill', 'maurice', 'polygons_blurred', or your own.
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<2
n = 512;
end
options.null = 0;
if iscell(type)
for i=1:length(type)
M{i} = load_image(type{i},n,options);
end
return;
end
type = lower(type);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters for geometric objects
eta = getoptions(options, 'eta', .1);
gamma = getoptions(options, 'gamma', 1/sqrt(2));
radius = getoptions(options, 'radius', 10);
center = getoptions(options, 'center', [0 0]);
center1 = getoptions(options, 'center1', [0 0]);
w = getoptions(options, 'tube_width', 0.06);
nb_points = getoptions(options, 'nb_points', 9);
scaling = getoptions(options, 'scaling', 1);
theta = getoptions(options, 'theta', 30 * 2*pi/360);
eccentricity = getoptions(options, 'eccentricity', 1.3);
sigma = getoptions(options, 'sigma', 0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for the line, can be vertical / horizontal / diagonal / any
if strcmp(type, 'line_vertical')
eta = 0.5; % translation
gamma = 0; % slope
elseif strcmp(type, 'line_horizontal')
eta = 0.5; % translation
gamma = Inf; % slope
elseif strcmp(type, 'line_diagonal')
eta = 0; % translation
gamma = 1; % slope
end
if strcmp(type(1:min(12,end)), 'square-tube-')
k = str2double(type(13:end));
c1 = [.22 .5]; c2 = [1-c1(1) .5];
eta = 1.5;
r1 = [c1 c1] + .21*[-1 -eta 1 eta];
r2 = [c2 c2] + .21*[-1 -eta 1 eta];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
if mod(k,2)==0
sel = n/2-k/2+1:n/2+k/2;
else
sel = n/2-(k-1)/2:n/2+(k-1)/2;
end
M( round(.25*n:.75*n), sel ) = 1;
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch lower(type)
case 'constant'
M = ones(n);
case 'ramp'
x = linspace(0,1,n);
[Y,M] = meshgrid(x,x);
case 'bump'
s = getoptions(options, 'bump_size', .5);
c = getoptions(options, 'center', [0 0]);
if length(s)==1
s = [s s];
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
X = (X-c(1))/s(1); Y = (Y-c(2))/s(2);
M = exp( -(X.^2+Y.^2)/2 );
case 'periodic'
x = linspace(-pi,pi,n)/1.1;
[Y,X] = meshgrid(x,x);
f = getoptions(options, 'freq', 6);
M = (1+cos(f*X)).*(1+cos(f*Y));
case {'letter-x' 'letter-v' 'letter-z' 'letter-y'}
M = create_letter(type(8), radius, n);
case 'l'
r1 = [.1 .1 .3 .9];
r2 = [.1 .1 .9 .4];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
case 'ellipse'
c1 = [0.15 0.5];
c2 = [0.85 0.5];
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
d = sqrt((X-c1(1)).^2 + (Y-c1(2)).^2) + sqrt((X-c2(1)).^2 + (Y-c2(2)).^2);
M = double( d<=eccentricity*sqrt( sum((c1-c2).^2) ) );
case 'ellipse-thin'
options.eccentricity = 1.06;
M = load_image('ellipse', n, options);
case 'ellipse-fat'
options.eccentricity = 1.3;
M = load_image('ellipse', n, options);
case 'square-tube'
c1 = [.25 .5];
c2 = [.75 .5];
r1 = [c1 c1] + .18*[-1 -1 1 1];
r2 = [c2 c2] + .18*[-1 -1 1 1];
r3 = [c1(1)-w c1(2)-w c2(1)+w c2(2)+w];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) | draw_rectangle(r3,n) );
case 'square-tube-1'
options.tube_width = 0.03;
M = load_image('square-tube', n, options);
case 'square-tube-2'
options.tube_width = 0.06;
M = load_image('square-tube', n, options);
case 'square-tube-3'
options.im = 0.09;
M = load_image('square-tube', n, options);
case 'polygon'
theta = sort( rand(nb_points,1)*2*pi );
radius = scaling*rescale(rand(nb_points,1), 0.1, 0.93);
points = [cos(theta) sin(theta)] .* repmat(radius, 1,2);
points = (points+1)/2*(n-1)+1; points(end+1,:) = points(1,:);
M = draw_polygons(zeros(n),0.8,{points'});
[x,y] = ind2sub(size(M),find(M));
p = 100; m = length(x);
lambda = linspace(0,1,p);
X = n/2 + repmat(x-n/2, [1 p]) .* repmat(lambda, [m 1]);
Y = n/2 + repmat(y-n/2, [1 p]) .* repmat(lambda, [m 1]);
I = round(X) + (round(Y)-1)*n;
M = zeros(n); M(I) = 1;
case 'polygon-8'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-10'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-12'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'pacman'
options.radius = 0.45;
options.center = [.5 .5];
M = load_image('disk', n, options);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
T =atan2(Y,X);
M = M .* (1-(abs(T-pi/2)<theta/2));
case 'square-hole'
options.radius = 0.45;
M = load_image('disk', n, options);
options.scaling = 0.5;
M = M - load_image('polygon-10', n, options);
case 'grid-circles'
if isempty(n)
n = 256;
end
f = getoptions(options, 'frequency', 30);
eta = getoptions(options, 'width', .3);
x = linspace(-n/2,n/2,n) - round(n*0.03);
y = linspace(0,n,n);
[Y,X] = meshgrid(y,x);
R = sqrt(X.^2+Y.^2);
theta = 0.05*pi/2;
X1 = cos(theta)*X+sin(theta)*Y;
Y1 = -sin(theta)*X+cos(theta)*Y;
A1 = abs(cos(2*pi*R/f))<eta;
A2 = max( abs(cos(2*pi*X1/f))<eta, abs(cos(2*pi*Y1/f))<eta );
M = A1;
M(X1>0) = A2(X1>0);
case 'chessboard1'
x = -1:2/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (2*(Y>=0)-1).*(2*(X>=0)-1);
case 'chessboard'
width = getoptions(options, 'width', round(n/16) );
[Y,X] = meshgrid(0:n-1,0:n-1);
M = mod( floor(X/width)+floor(Y/width), 2 ) == 0;
case 'square'
if ~isfield( options, 'radius' )
radius = 0.6;
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M = max( abs(X),abs(Y) )<radius;
case 'squareregular'
M = rescale(load_image('square',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'regular1'
options.alpha = 1;
M = load_image('fnoise',n,options);
case 'regular2'
options.alpha = 2;
M = load_image('fnoise',n,options);
case 'regular3'
options.alpha = 3;
M = load_image('fnoise',n,options);
case 'sparsecurves'
options.alpha = 3;
M = load_image('fnoise',n,options);
M = rescale(M);
ncurves = 3;
M = cos(2*pi*ncurves);
case 'geometrical'
J = getoptions(options, 'Jgeometrical', 4);
sgeom = 100*n/256;
options.bound = 'per';
A = ones(n);
for j=0:J-1
B = A;
for k=1:2^j
I = find(B==k);
U = perform_blurring(randn(n),sgeom,options);
s = median(U(I));
I1 = find( (B==k) & (U>s) );
I2 = find( (B==k) & (U<=s) );
A(I1) = 2*k-1;
A(I2) = 2*k;
end
end
M = A;
case 'lic-texture'
disp('Computing random tensor field.');
options.sigma_tensor = getoptions(options, 'lic_regularity', 50*n/256);
T = compute_tensor_field_random(n,options);
Flow = perform_tensor_decomp(T); % extract eigenfield.
options.isoriented = 0; % no orientation in streamlines
% initial texture
lic_width = getoptions(options, 'lic_width', 0);
M0 = perform_blurring(randn(n),lic_width);
M0 = perform_histogram_equalization( M0, 'linear');
options.histogram = 'linear';
options.dt = 0.4;
options.M0 = M0;
options.verb = 1;
options.flow_correction = 1;
options.niter_lic = 3;
w = 30;
M = perform_lic(Flow, w, options);
case 'square_texture'
M = load_image('square',n);
M = rescale(M);
% make a texture patch
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M(I) = M(I) + lambda * sin( x(I) * 2*pi / eta );
case 'tv-image'
M = rand(n);
tau = compute_total_variation(M);
options.niter = 400;
[M,err_tv,err_l2] = perform_tv_projection(M,tau/1000,options);
M = perform_histogram_equalization(M,'linear');
case 'oscillatory_texture'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M = sin( x * 2*pi / eta );
case {'line', 'line_vertical', 'line_horizontal', 'line_diagonal'}
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
if gamma~=Inf
M = (X-eta) - gamma*Y < 0;
else
M = (Y-eta) < 0;
end
case 'line-windowed'
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
eta = .3;
gamma = getoptions(options, 'gamma', pi/10);
parabola = getoptions(options, 'parabola', 0);
M = (X-eta) - gamma*Y - parabola*Y.^2 < 0;
f = sin( pi*x ).^2;
M = M .* ( f'*f );
case 'grating'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
theta = getoptions(options, 'theta', .2);
freq = getoptions(options, 'freq', .2);
X = cos(theta)*X + sin(theta)*Y;
M = sin(2*pi*X/freq);
case 'disk'
if ~isfield( options, 'radius' )
radius = 0.35;
end
if ~isfield( options, 'center' )
center = [0.5, 0.5]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'twodisks'
M = zeros(n);
options.center = [.25 .25];
M = load_image('disk', n, options);
options.center = [.75 .75];
M = M + load_image('disk', n, options);
case 'diskregular'
M = rescale(load_image('disk',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'quarterdisk'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'fading_contour'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
theta = 2/pi*atan2(Y,X);
h = 0.5;
M = exp(-(1-theta).^2/h^2).*M;
case '3contours'
radius = 1.3;
center = [-1, 1];
radius1 = 0.8;
center1 = [0, 0];
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
f1 = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
f2 = (X-center1(1)).^2 + (Y-center1(2)).^2 < radius1^2;
M = f1 + 0.5*f2.*(1-f1);
case 'line_circle'
gamma = 1/sqrt(2);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M1 = double( X>gamma*Y+0.25 );
M2 = X.^2 + Y.^2 < 0.6^2;
M = 20 + max(0.5*M1,M2) * 216;
case 'fnoise'
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
alpha = getoptions(options, 'alpha', 1);
M = gen_noisy_image(n,alpha);
case 'gaussiannoise'
% generate an image of filtered noise with gaussian
sigma = getoptions(options, 'sigma', 10);
M = randn(n);
m = 51;
h = compute_gaussian_filter([m m],sigma/(4*n),[n n]);
M = perform_convolution(M,h);
return;
case {'bwhorizontal','bwvertical','bwcircle'}
[Y,X] = meshgrid(0:n-1,0:n-1);
if strcmp(type, 'bwhorizontal')
d = X;
elseif strcmp(type, 'bwvertical')
d = Y;
elseif strcmp(type, 'bwcircle')
d = sqrt( (X-(n-1)/2).^2 + (Y-(n-1)/2).^2 );
end
if isfield(options, 'stripe_width')
stripe_width = options.stripe_width;
else
stripe_width = 5;
end
if isfield(options, 'black_prop')
black_prop = options.black_prop;
else
black_prop = 0.5;
end
M = double( mod( d/(2*stripe_width),1 )>=black_prop );
case 'parabola'
% curvature
c = getoptions(c, 'c', .1);
% angle
theta = getoptions(options, 'theta', pi/sqrt(2));
x = -0.5:1/(n-1):0.5;
[Y,X] = meshgrid(x,x);
Xs = X*cos(theta) + Y*sin(theta);
Y =-X*sin(theta) + Y*cos(theta); X = Xs;
M = Y>c*X.^2;
case 'sin'
[Y,X] = meshgrid(-1:2/(n-1):1, -1:2/(n-1):1);
M = Y >= 0.6*cos(pi*X);
M = double(M);
case 'circ_oscil'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
R = sqrt(X.^2+Y.^2);
M = cos(R.^3*50);
case 'phantom'
M = phantom(n);
case 'periodic_bumps'
nbr_periods = getoptions(options, 'nbr_periods', 8);
theta = getoptions(options, 'theta', 1/sqrt(2));
skew = getoptions(options, 'skew', 1/sqrt(2) );
A = [cos(theta), -sin(theta); sin(theta), cos(theta)];
B = [1 skew; 0 1];
T = B*A;
x = (0:n-1)*2*pi*nbr_periods/(n-1);
[Y,X] = meshgrid(x,x);
pos = [X(:)'; Y(:)'];
pos = T*pos;
X = reshape(pos(1,:), n,n);
Y = reshape(pos(2,:), n,n);
M = cos(X).*sin(Y);
case 'noise'
sigma = getoptions(options, 'sigma', 1);
M = randn(n) * sigma;
case 'disk-corner'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
rho = .3; eta = .1;
M1 = rho*X+eta<Y;
c = [0 .2]; r = .85;
d = (X-c(1)).^2 + (Y-c(2)).^2;
M2 = d<r^2;
M = M1.*M2;
otherwise
ext = {'gif', 'png', 'jpg', 'bmp', 'tiff', 'pgm', 'ppm'};
for i=1:length(ext)
name = [type '.' ext{i}];
if( exist(name) )
M = imread( name );
M = double(M);
if not(isempty(n)) && (n~=size(M, 1) || n~=size(M, 2)) && nargin>=2
M = image_resize(M,n,n);
end
if strcmp(type, 'peppers-bw')
M(:,1) = M(:,2);
M(1,:) = M(2,:);
end
if sigma>0
M = perform_blurring(M,sigma);
end
return;
end
end
error( ['Image ' type ' does not exists.'] );
end
M = double(M);
if sigma>0
M = perform_blurring(M,sigma);
end
M = rescale(M);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = create_letter(a, r, n)
c = 0.2;
p1 = [c;c];
p2 = [c; 1-c];
p3 = [1-c; 1-c];
p4 = [1-c; c];
p4 = [1-c; c];
pc = [0.5;0.5];
pu = [0.5; c];
switch a
case 'x'
point_list = { [p1 p3] [p2 p4] };
case 'z'
point_list = { [p2 p3 p1 p4] };
case 'v'
point_list = { [p2 pu p3] };
case 'y'
point_list = { [p2 pc pu] [pc p3] };
end
% fit image
for i=1:length(point_list)
a = point_list{i}(2:-1:1,:);
a(1,:) = 1-a(1,:);
point_list{i} = round( a*(n-1)+1 );
end
M = draw_polygons(zeros(n),r,point_list);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_polygons(mask,r,point_list)
sk = mask*0;
for i=1:length(point_list)
pl = point_list{i};
for k=2:length(pl)
sk = draw_line(sk,pl(1,k-1),pl(2,k-1),pl(1,k),pl(2,k),r);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_line(sk,x1,y1,x2,y2,r)
n = size(sk,1);
[Y,X] = meshgrid(1:n,1:n);
q = 100;
t = linspace(0,1,q);
x = x1*t+x2*(1-t); y = y1*t+y2*(1-t);
if r==0
x = round( x ); y = round( y );
sk( x+(y-1)*n ) = 1;
else
for k=1:q
I = find((X-x(k)).^2 + (Y-y(k)).^2 <= r^2 );
sk(I) = 1;
end
end
function M = gen_noisy_image(n,alpha)
% gen_noisy_image - generate a noisy cloud-like image.
%
% M = gen_noisy_image(n,alpha);
%
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<1
n = 128;
end
if nargin<2
alpha = 1.5;
end
if mod(n(1),2)==0
x = -n/2:n/2-1;
else
x = -(n-1)/2:(n-1)/2;
end
[Y,X] = meshgrid(x,x);
d = sqrt(X.^2 + Y.^2) + 0.1;
f = rand(n)*2*pi;
M = (d.^(-alpha)) .* exp(f*1i);
% M = real(ifft2(fftshift(M)));
M = ifftshift(M);
M = real( ifft2(M) );
function y = gen_signal_2d(n,alpha)
% gen_signal_2d - generate a 2D C^\alpha signal of length n x n.
% gen_signal_2d(n,alpha) generate a 2D signal C^alpha.
%
% The signal is scale in [0,1].
%
% Copyright (c) 2003 Gabriel Peyre
% new new method
[Y,X] = meshgrid(0:n-1, 0:n-1);
A = X+Y+1;
B = X-Y+n+1;
a = gen_signal(2*n+1, alpha);
b = gen_signal(2*n+1, alpha);
y = a(A).*b(B);
% M = a(1:n)*b(1:n)';
return;
% new method
h = (-n/2+1):(n/2); h(n/2)=1;
[X,Y] = meshgrid(h,h);
h = sqrt(X.^2+Y.^2+1).^(-alpha-1/2);
h = h .* exp( 2i*pi*rand(n,n) );
h = fftshift(h);
y = real( ifft2(h) );
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
return;
%% old code
y = rand(n,n);
y = y - mean(mean(y));
for i=1:alpha
y = cumsum(cumsum(y)')';
y = y - mean(mean(y));
end
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = draw_rectangle(r,n)
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
M = double( (X>=r(1)) & (X<=r(3)) & (Y>=r(2)) & (Y<=r(4)) ) ;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
inpolyhedron.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/level-sets/inpolyhedron.m
| 22,756 |
utf_8
|
16738ef64a83b8c37c57511248fb93cf
|
function IN = inpolyhedron(varargin)
%INPOLYHEDRON Tests if points are inside a 3D triangulated (faces/vertices) surface
% BY CONVENTION, SURFACE NORMALS SHOULD POINT OUT from the object. (see
% FLIPNORMALS option below for details)
%
% IN = INPOLYHEDRON(FV,QPTS) tests if the query points (QPTS) are inside the
% patch/surface/polyhedron defined by FV (a structure with fields 'vertices' and
% 'faces'). QPTS is an N-by-3 set of XYZ coordinates. IN is an N-by-1 logical
% vector which will be TRUE for each query point inside the surface.
%
% INPOLYHEDRON(FACES,VERTICES,...) takes faces/vertices separately, rather than in
% an FV structure.
%
% IN = INPOLYHEDRON(..., X, Y, Z) voxelises a mask of 3D gridded query points
% rather than an N-by-3 array of points. X, Y, and Z coordinates of the grid
% supplied in XVEC, YVEC, and ZVEC respectively. IN will return as a 3D logical
% volume with SIZE(IN) = [LENGTH(YVEC) LENGTH(XVEC) LENGTH(ZVEC)], equivalent to
% syntax used by MESHGRID. INPOLYHEDRON handles this input faster and with a lower
% memory footprint than using MESHGRID to make full X, Y, Z query points matrices.
%
% INPOLYHEDRON(...,'PropertyName',VALUE,'PropertyName',VALUE,...) tests query
% points using the following optional property values:
%
% TOL - Tolerance on the tests for "inside" the surface. You can think of
% tol as the distance a point may possibly lie above/below the surface, and still
% be perceived as on the surface. Due to numerical rounding nothing can ever be
% done exactly here. Defaults to ZERO. Note that in the current implementation TOL
% only affects points lying above/below a surface triangle (in the Z-direction).
% Points coincident with a vertex in the XY plane are considered INside the surface.
% More formal rules can be implemented with input/feedback from users.
%
% GRIDSIZE - Internally, INPOLYHEDRON uses a divide-and-conquer algorithm to
% split all faces into a chessboard-like grid of GRIDSIZE-by-GRIDSIZE regions.
% Performance will be a tradeoff between a small GRIDSIZE (few iterations, more
% data per iteration) and a large GRIDSIZE (many iterations of small data
% calculations). The sweet-spot has been experimentally determined (on a win64
% system) to be correlated with the number of faces/vertices. You can overwrite
% this automatically computed choice by specifying a GRIDSIZE parameter.
%
% FACENORMALS - By default, the normals to the FACE triangles are computed as the
% cross-product of the first two triangle edges. You may optionally specify face
% normals here if they have been pre-computed.
%
% FLIPNORMALS - (Defaults FALSE). To match a wider convention, triangle
% face normals are presumed to point OUT from the object's surface. If
% your surface normals are defined pointing IN, then you should set the
% FLIPNORMALS option to TRUE to use the reverse of this convention.
%
% Example:
% tmpvol = zeros(20,20,20); % Empty voxel volume
% tmpvol(5:15,8:12,8:12) = 1; % Turn some voxels on
% tmpvol(8:12,5:15,8:12) = 1;
% tmpvol(8:12,8:12,5:15) = 1;
% fv = isosurface(tmpvol, 0.99); % Create the patch object
% fv.faces = fliplr(fv.faces); % Ensure normals point OUT
% % Test SCATTERED query points
% pts = rand(200,3)*12 + 4; % Make some query points
% in = inpolyhedron(fv, pts); % Test which are inside the patch
% figure, hold on, view(3) % Display the result
% patch(fv,'FaceColor','g','FaceAlpha',0.2)
% plot3(pts(in,1),pts(in,2),pts(in,3),'bo','MarkerFaceColor','b')
% plot3(pts(~in,1),pts(~in,2),pts(~in,3),'ro'), axis image
% % Test STRUCTURED GRID of query points
% gridLocs = 3:2.1:19;
% [x,y,z] = meshgrid(gridLocs,gridLocs,gridLocs);
% in = inpolyhedron(fv, gridLocs,gridLocs,gridLocs);
% figure, hold on, view(3) % Display the result
% patch(fv,'FaceColor','g','FaceAlpha',0.2)
% plot3(x(in), y(in), z(in),'bo','MarkerFaceColor','b')
% plot3(x(~in),y(~in),z(~in),'ro'), axis image
%
% See also: UNIFYMESHNORMALS (on the <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=43013">file exchange</a>)
% TODO-list
% - Optmise overall memory footprint. (need examples with MEM errors)
% - Implement an "ignore these" step to speed up calculations for:
% * Query points outside the convex hull of the faces/vertices input
% - Get a better/best gridSize calculation. User feedback?
% - Detect cases where X-rays or Y-rays would be better than Z-rays?
%
% Author: Sven Holcombe
% - 10 Jun 2012: Version 1.0
% - 28 Aug 2012: Version 1.1 - Speedup using accumarray
% - 07 Nov 2012: Version 2.0 - BEHAVIOUR CHANGE
% Query points coincident with a VERTEX are now IN an XY triangle
% - 18 Aug 2013: Version 2.1 - Gridded query point handling with low memory footprint.
% - 10 Sep 2013: Version 3.0 - BEHAVIOUR CHANGE
% NEW CONVENTION ADOPTED to expect face normals pointing IN
% Vertically oriented faces are now ignored. Speeds up
% computation and fixes bug where presence of vertical faces
% produced NaN distance from a query pt to facet, making all
% query points under facet erroneously NOT IN polyhedron.
% - 25 Sep 2013: Version 3.1 - Dropped nested unique call which was made
% mostly redundant via v2.1 gridded point handling. Also
% refreshed grid size selection via optimisation.
% - 25 Feb 2014: Version 3.2 - Fixed indeterminate behaviour for query
% points *exactly* in line with an "overhanging" vertex.
%%
% FACETS is an unpacked arrangement of faces/vertices. It is [3-by-3-by-N],
% with 3 1-by-3 XYZ coordinates of N faces.
[facets, qPts, options] = parseInputs(varargin{:});
numFaces = size(facets,3);
if ~options.griddedInput % SCATTERED QUERY POINTS
numQPoints = size(qPts,1);
else % STRUCTURED QUERY POINTS
numQPoints = prod(cellfun(@numel,qPts(1:2)));
end
% Precompute 3d normals to all facets (triangles). Do this via the cross
% product of the first edge vector with the second. Normalise the result.
allEdgeVecs = facets([2 3 1],:,:) - facets(:,:,:);
if isempty(options.facenormals)
allFacetNormals = bsxfun(@times, allEdgeVecs(1,[2 3 1],:), allEdgeVecs(2,[3 1 2],:)) - ...
bsxfun(@times, allEdgeVecs(2,[2 3 1],:), allEdgeVecs(1,[3 1 2],:));
allFacetNormals = bsxfun(@rdivide, allFacetNormals, sqrt(sum(allFacetNormals.^2,2)));
else
allFacetNormals = permute(options.facenormals,[3 2 1]);
end
if options.flipnormals
allFacetNormals = -allFacetNormals;
end
% We use a Z-ray intersection so we don't even need to consider facets that
% are purely vertically oriented (have zero Z-component).
isFacetUseful = allFacetNormals(:,3,:) ~= 0;
%% Setup grid referencing system
% Function speed can be thought of as a function of grid size. A small number of grid
% squares means iterating over fewer regions (good) but with more faces/qPts to
% consider each time (bad). For any given mesh/queryPt configuration, there will be a
% sweet spot that minimises computation time. There will also be a constraint from
% memory available - low grid sizes means considering many queryPt/faces at once,
% which will require a larger memory footprint. Here we will let the user specify
% gridsize directly, or we will estimate the optimum size based on prior testing.
if ~isempty(options.gridsize)
gridSize = options.gridsize;
else
% Coefficients (with 95% confidence bounds):
p00 = -47; p10 = 12.83; p01 = 20.89;
p20 = 0.7578; p11 = -6.511; p02 = -2.586;
p30 = -0.1802; p21 = 0.2085; p12 = 0.7521;
p03 = 0.09984; p40 = 0.005815; p31 = 0.007775;
p22 = -0.02129; p13 = -0.02309;
GSfit = @(x,y)p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y + p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2 + p13*x*y^3;
gridSize = min(150 ,max(1, ceil(GSfit(log(numQPoints),log(numFaces)))));
if isnan(gridSize), gridSize = 1; end
end
%% Find candidate qPts -> triangles pairs
% We have a large set of query points. For each query point, find potential
% triangles that would be pierced by vertical rays through the qPt. First,
% a simple filter by XY bounding box
% Calculate the bounding box of each facet
minFacetCoords = permute(min(facets(:,1:2,:),[],1),[3 2 1]);
maxFacetCoords = permute(max(facets(:,1:2,:),[],1),[3 2 1]);
% Set rescale values to rescale all vertices between 0(-eps) and 1(+eps)
scalingOffsetsXY = min(minFacetCoords,[],1) - eps;
scalingRangeXY = max(maxFacetCoords,[],1) - scalingOffsetsXY + 2*eps;
% Based on scaled min/max facet coords, get the [lowX lowY highX highY] "grid" index
% of all faces
lowToHighGridIdxs = floor(bsxfun(@rdivide, ...
bsxfun(@minus, ... % Use min/max coordinates of each facet (+/- the tolerance)
[minFacetCoords-options.tol maxFacetCoords+options.tol],...
[scalingOffsetsXY scalingOffsetsXY]),...
[scalingRangeXY scalingRangeXY]) * gridSize) + 1;
% Build a grid of cells. In each cell, place the facet indices that encroach into
% that grid region. Similarly, each query point will be assigned to a grid region.
% Note that query points will be assigned only one grid region, facets can cover many
% regions. Furthermore, we will add a tolerance to facet region assignment to ensure
% a query point will be compared to facets even if it falls only on the edge of a
% facet's bounding box, rather than inside it.
cells = cell(gridSize);
[unqLHgrids,~,facetInds] = unique(lowToHighGridIdxs,'rows');
tmpInds = accumarray(facetInds(isFacetUseful),find(isFacetUseful),[size(unqLHgrids,1),1],@(x){x});
for xi = 1:gridSize
xyMinMask = xi >= unqLHgrids(:,1) & xi <= unqLHgrids(:,3);
for yi = 1:gridSize
cells{yi,xi} = cat(1,tmpInds{xyMinMask & yi >= unqLHgrids(:,2) & yi <= unqLHgrids(:,4)});
% The above line (with accumarray) is faster with equiv results than:
% % cells{yi,xi} = find(ismember(facetInds, xyInds));
end
end
% With large number of facets, memory may be important:
clear lowToHightGridIdxs LHgrids facetInds tmpInds xyMinMask minFacetCoords maxFacetCoords
%% Compute edge unit vectors and dot products
% Precompute the 2d unit vectors making up each facet's edges in the XY plane.
allEdgeUVecs = bsxfun(@rdivide, allEdgeVecs(:,1:2,:), sqrt(sum(allEdgeVecs(:,1:2,:).^2,2)));
% Precompute the inner product between edgeA.edgeC, edgeB.edgeA, edgeC.edgeB
allEdgeEdgeDotPs = sum(allEdgeUVecs .* -allEdgeUVecs([3 1 2],:,:),2) - 1e-9;
%% Gather XY query locations
% Since query points are most likely given as a (3D) grid of query locations, we only
% need to consider the unique XY locations when asking which facets a vertical ray
% through an XY location would pierce.
if ~options.griddedInput % SCATTERED QUERY POINTS
qPtsXY = @(varargin)qPts(:,1:2);
qPtsXYZViaUnqIndice = @(ind)qPts(ind,:);
outPxIndsViaUnqIndiceMask = @(ind,mask)ind(mask);
outputSize = [size(qPts,1),1];
reshapeINfcn = @(INMASK)INMASK;
minFacetDistanceFcn = @minFacetToQptDistance;
else % STRUCTURED QUERY POINTS
[xmat,ymat] = meshgrid(qPts{1:2});
qPtsXY = [xmat(:) ymat(:)];
% A standard set of Z locations will be shifted around by different
% unqQpts XY coordinates.
zCoords = qPts{3}(:) * [0 0 1];
qPtsXYZViaUnqIndice = @(ind)bsxfun(@plus, zCoords, [qPtsXY(ind,:) 0]);
% From a given indice and mask, we will turn on/off the IN points under
% that indice based on the mask. The easiest calculation is to setup
% the IN matrix as a numZpts-by-numUnqPts mask. At the end, we must
% unpack/reshape this 2D mask to a full 3D logical mask
numZpts = size(zCoords,1);
baseZinds = 1:numZpts;
outPxIndsViaUnqIndiceMask = @(ind,mask)(ind-1)*numZpts + baseZinds(mask);
outputSize = [numZpts, size(qPtsXY,1)];
reshapeINfcn = @(INMASK)reshape(INMASK', cellfun(@numel, qPts([2 1 3])));
minFacetDistanceFcn = @minFacetToQptsDistance;
end
% Start with every query point NOT inside the polyhedron. We will
% iteratively find those query points that ARE inside.
IN = false(outputSize);
% Determine with grids each query point falls into.
qPtGridXY = floor(bsxfun(@rdivide, bsxfun(@minus, qPtsXY(:,:), scalingOffsetsXY),...
scalingRangeXY) * gridSize) + 1;
[unqQgridXY,~,qPtGridInds] = unique(qPtGridXY,'rows');
% We need only consider grid indices within those already set up
ptsToConsidMask = ~any(qPtGridXY<1 | qPtGridXY>gridSize, 2);
if ~any(ptsToConsidMask)
IN = reshapeINfcn(IN);
return;
end
% Build the reference list
cellQptContents = accumarray(qPtGridInds(ptsToConsidMask),find(ptsToConsidMask), [],@(x){x});
gridsToCheck = unqQgridXY(~any(unqQgridXY<1 | unqQgridXY>gridSize, 2),:);
cellQptContents(cellfun('isempty',cellQptContents)) = [];
gridIndsToCheck = sub2ind(size(cells), gridsToCheck(:,2), gridsToCheck(:,1));
% For ease of multiplication, reshape qPt XY coords to [1-by-2-by-1-by-N]
qPtsXY = permute(qPtsXY(:,:),[4 2 3 1]);
% There will be some grid indices with query points but without facets.
emptyMask = cellfun('isempty',cells(gridIndsToCheck))';
for i = find(~emptyMask)
% We get all the facet coordinates (ie, triangle vertices) of triangles
% that intrude into this grid location. The size is [3-by-2-by-N], for
% the [3vertices-by-XY-by-Ntriangles]
allFacetInds = cells{gridIndsToCheck(i)};
candVerts = facets(:,1:2,allFacetInds);
% We need the XY coordinates of query points falling into this grid.
allqPtInds = cellQptContents{i};
queryPtsXY = qPtsXY(:,:,:,allqPtInds);
% Get unit vectors pointing from each triangle vertex to my query point(s)
vert2ptVecs = bsxfun(@minus, queryPtsXY, candVerts);
vert2ptUVecs = bsxfun(@rdivide, vert2ptVecs, sqrt(sum(vert2ptVecs.^2,2)));
% Get unit vectors pointing around each triangle (along edge A, edge B, edge C)
edgeUVecs = allEdgeUVecs(:,:,allFacetInds);
% Get the inner product between edgeA.edgeC, edgeB.edgeA, edgeC.edgeB
edgeEdgeDotPs = allEdgeEdgeDotPs(:,:,allFacetInds);
% Get inner products between each edge unit vec and the UVs from qPt to vertex
edgeQPntDotPs = sum(bsxfun(@times, edgeUVecs, vert2ptUVecs),2);
qPntEdgeDotPs = sum(bsxfun(@times,vert2ptUVecs, -edgeUVecs([3 1 2],:,:)),2);
% If both inner products 2 edges to the query point are greater than the inner
% product between the two edges themselves, the query point is between the V
% shape made by the two edges. If this is true for all 3 edge pair, the query
% point is inside the triangle.
resultIN = all(bsxfun(@gt, edgeQPntDotPs, edgeEdgeDotPs) & bsxfun(@gt, qPntEdgeDotPs, edgeEdgeDotPs),1);
resultONVERTEX = any(any(isnan(vert2ptUVecs),2),1);
result = resultIN | resultONVERTEX;
qPtHitsTriangles = any(result,3);
% If NONE of the query points pierce ANY triangles, we can skip forward
if ~any(qPtHitsTriangles), continue, end
% In the next step, we'll need to know the indices of ALL the query points at
% each of the distinct XY coordinates. Let's get their indices into "qPts" as a
% cell of length M, where M is the number of unique XY points we had found.
for ptNo = find(qPtHitsTriangles(:))'
% Which facets does it pierce?
piercedFacetInds = allFacetInds(result(1,1,:,ptNo));
% Get the 1-by-3-by-N set of triangle normals that this qPt pierces
piercedTriNorms = allFacetNormals(:,:,piercedFacetInds);
% Pick the first vertex as the "origin" of a plane through the facet. Get the
% vectors from each query point to each facet origin
facetToQptVectors = bsxfun(@minus, ...
qPtsXYZViaUnqIndice(allqPtInds(ptNo)),...
facets(1,:,piercedFacetInds));
% Calculate how far you need to go up/down to pierce the facet's plane.
% Positive direction means "inside" the facet, negative direction means
% outside.
facetToQptDists = bsxfun(@rdivide, ...
sum(bsxfun(@times,piercedTriNorms,facetToQptVectors),2), ...
abs(piercedTriNorms(:,3,:)));
% Since it's possible for two triangles sharing the same vertex to
% be the same distance away, I want to sum up all the distances of
% triangles that are closest to the query point. Simple case: The
% closest triangle is unique Edge case: The closest triangle is one
% of many the same distance and direction away. Tricky case: The
% closes triangle has another triangle the equivalent distance
% but facing the opposite direction
IN( outPxIndsViaUnqIndiceMask(allqPtInds(ptNo), ...
minFacetDistanceFcn(facetToQptDists)<options.tol...
)) = true;
end
end
% If they provided X,Y,Z vectors of query points, our output is currently a
% 2D mask and must be reshaped to [LEN(Y) LEN(X) LEN(Z)].
IN = reshapeINfcn(IN);
%% Called subfunctions
% vertices = [
% 0.9046 0.1355 -0.0900
% 0.8999 0.3836 -0.0914
% 1.0572 0.2964 -0.0907
% 0.8735 0.1423 -0.1166
% 0.8685 0.4027 -0.1180
% 1.0337 0.3112 -0.1173
% 0.9358 0.1287 -0.0634
% 0.9313 0.3644 -0.0647
% 1.0808 0.2816 -0.0641
% ];
% faces = [
% 1 2 5
% 1 5 4
% 2 3 6
% 2 6 5
% 3 1 4
% 3 4 6
% 6 4 5
% 2 1 8
% 8 1 7
% 3 2 9
% 9 2 8
% 1 3 7
% 7 3 9
% 7 9 8
% ];
% point = [vertices(3,1),vertices(3,2),1.5];
function closestTriDistance = minFacetToQptDistance(facetToQptDists)
% FacetToQptDists is a 1pt-by-1-by-Nfacets array of how far you need to go
% up/down to pierce each facet's plane. If the Qpt was directly over an
% "overhang" vertex, then two facets with opposite orientation will be
% equally distant from the Qpt, with one distance positive and one
% negative. In such cases, it is impossible for the Qpt to actually be
% "inside" this pair of facets, so their distance is updated to Inf.
[~,minInd] = min(abs(facetToQptDists),[],3);
while any( abs(facetToQptDists + facetToQptDists(minInd)) < 1e-15 )
% Since the above comparison is made every time, but the below variable
% setting is done only in the rare case that a query point coincides
% with an overhang vertex, it is more efficient to re-compute the
% equality when it's true, rather than store the result every time.
facetToQptDists( abs(facetToQptDists) - abs(facetToQptDists(minInd)) < 1e-15) = inf;
if ~any(isfinite(facetToQptDists))
break;
end
[~,minInd] = min(abs(facetToQptDists),[],3);
end
closestTriDistance = facetToQptDists(minInd);
function closestTriDistance = minFacetToQptsDistance(facetToQptDists)
% As above, but facetToQptDists is an Mpts-by-1-by-Nfacets array.
% The multi-point version is a little more tricky. While below is quite a
% bit slower when the while loop is entered, it is very rarely entered and
% very fast to make just the initial comparison.
[minVals,minInds] = min(abs(facetToQptDists),[],3);
while any(...
any(abs(bsxfun(@plus,minVals,facetToQptDists))<1e-15,3) & ...
any(abs(bsxfun(@minus,minVals,facetToQptDists))<1e-15,3))
maskP = abs(bsxfun(@plus,minVals,facetToQptDists))<1e-15;
maskN = abs(bsxfun(@minus,minVals,facetToQptDists))<1e-15;
mustAlterMask = any(maskP,3) & any(maskN,3);
for i = find(mustAlterMask)'
facetToQptDists(i,:,maskP(i,:,:) | maskN(i,:,:)) = inf;
end
[newMv,newMinInds] = min(abs(facetToQptDists(mustAlterMask,:,:)),[],3);
minInds(mustAlterMask) = newMinInds(:);
minVals(mustAlterMask) = newMv(:);
end
% Below is a tiny speedup on basically a sub2ind call.
closestTriDistance = facetToQptDists((minInds-1)*size(facetToQptDists,1) + (1:size(facetToQptDists,1))');
%% Input handling subfunctions
function [facets, qPts, options] = parseInputs(varargin)
% Gather FACES and VERTICES
if isstruct(varargin{1}) % inpolyhedron(FVstruct, ...)
if ~all(isfield(varargin{1},{'vertices','faces'}))
error( 'Structure FV must have "faces" and "vertices" fields' );
end
faces = varargin{1}.faces;
vertices = varargin{1}.vertices;
varargin(1) = []; % Chomp off the faces/vertices
else % inpolyhedron(FACES, VERTICES, ...)
faces = varargin{1};
vertices = varargin{2};
varargin(1:2) = []; % Chomp off the faces/vertices
end
% Unpack the faces/vertices into [3-by-3-by-N] facets. It's better to
% perform this now and have FACETS only in memory in the main program,
% rather than FACETS, FACES and VERTICES
facets = vertices';
facets = permute(reshape(facets(:,faces'), 3, 3, []),[2 1 3]);
% Extract query points
if length(varargin)<2 || ischar(varargin{2}) % inpolyhedron(F, V, [x(:) y(:) z(:)], ...)
qPts = varargin{1};
varargin(1) = []; % Chomp off the query points
else % inpolyhedron(F, V, xVec, yVec, zVec, ...)
qPts = varargin(1:3);
% Chomp off the query points and tell the world that it's gridded input.
varargin(1:3) = [];
varargin = [varargin {'griddedInput',true}];
end
% Extract configurable options
options = parseOptions(varargin{:});
% Check if face normals are unified
if options.testNormals
options.normalsAreUnified = checkNormalUnification(faces);
end
function options = parseOptions(varargin)
IP = inputParser;
IP.addParamValue('gridsize',[], @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('tol', 0, @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('tol_ang', 1e-5, @(x)isscalar(x) && isnumeric(x))
IP.addParamValue('facenormals',[]);
IP.addParamValue('flipnormals',false);
IP.addParamValue('griddedInput',false);
IP.addParamValue('testNormals',false);
IP.parse(varargin{:});
options = IP.Results;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
knnsearch.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/quantized-rendering/knnsearch.m
| 4,137 |
utf_8
|
40fbf8d0695309e13ce021d477c579c3
|
function [idx,D]=knnsearch(varargin)
% KNNSEARCH Linear k-nearest neighbor (KNN) search
% IDX = knnsearch(Q,R,K) searches the reference data set R (n x d array
% representing n points in a d-dimensional space) to find the k-nearest
% neighbors of each query point represented by eahc row of Q (m x d array).
% The results are stored in the (m x K) index array, IDX.
%
% IDX = knnsearch(Q,R) takes the default value K=1.
%
% IDX = knnsearch(Q) or IDX = knnsearch(Q,[],K) does the search for R = Q.
%
% Rationality
% Linear KNN search is the simplest appraoch of KNN. The search is based on
% calculation of all distances. Therefore, it is normally believed only
% suitable for small data sets. However, other advanced approaches, such as
% kd-tree and delaunary become inefficient when d is large comparing to the
% number of data points. On the other hand, the linear search in MATLAB is
% relatively insensitive to d due to the vectorization. In this code, the
% efficiency of linear search is further improved by using the JIT
% aceeleration of MATLAB. Numerical example shows that its performance is
% comparable with kd-tree algorithm in mex.
%
% See also, kdtree, nnsearch, delaunary, dsearch
% By Yi Cao at Cranfield University on 25 March 2008
% Example 1: small data sets
%{
R=randn(100,2);
Q=randn(3,2);
idx=knnsearch(Q,R);
plot(R(:,1),R(:,2),'b.',Q(:,1),Q(:,2),'ro',R(idx,1),R(idx,2),'gx');
%}
% Example 2: ten nearest points to [0 0]
%{
R=rand(100,2);
Q=[0 0];
K=10;
idx=knnsearch(Q,R,10);
r=max(sqrt(sum(R(idx,:).^2,2)));
theta=0:0.01:pi/2;
x=r*cos(theta);
y=r*sin(theta);
plot(R(:,1),R(:,2),'b.',Q(:,1),Q(:,2),'co',R(idx,1),R(idx,2),'gx',x,y,'r-','linewidth',2);
%}
% Example 3: cputime comparion with delaunay+dsearch I, a few to look up
%{
R=randn(10000,4);
Q=randn(500,4);
t0=cputime;
idx=knnsearch(Q,R);
t1=cputime;
T=delaunayn(R);
idx1=dsearchn(R,T,Q);
t2=cputime;
fprintf('Are both indices the same? %d\n',isequal(idx,idx1));
fprintf('CPU time for knnsearch = %g\n',t1-t0);
fprintf('CPU time for delaunay = %g\n',t2-t1);
%}
% Example 4: cputime comparion with delaunay+dsearch II, lots to look up
%{
Q=randn(10000,4);
R=randn(500,4);
t0=cputime;
idx=knnsearch(Q,R);
t1=cputime;
T=delaunayn(R);
idx1=dsearchn(R,T,Q);
t2=cputime;
fprintf('Are both indices the same? %d\n',isequal(idx,idx1));
fprintf('CPU time for knnsearch = %g\n',t1-t0);
fprintf('CPU time for delaunay = %g\n',t2-t1);
%}
% Example 5: cputime comparion with kd-tree by Steven Michael (mex file)
% <a href="http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=7030&objectType=file">kd-tree by Steven Michael</a>
%{
Q=randn(10000,10);
R=randn(500,10);
t0=cputime;
idx=knnsearch(Q,R);
t1=cputime;
tree=kdtree(R);
idx1=kdtree_closestpoint(tree,Q);
t2=cputime;
fprintf('Are both indices the same? %d\n',isequal(idx,idx1));
fprintf('CPU time for knnsearch = %g\n',t1-t0);
fprintf('CPU time for delaunay = %g\n',t2-t1);
%}
% Check inputs
[Q,R,K,fident] = parseinputs(varargin{:});
% Check outputs
error(nargoutchk(0,2,nargout));
% C2 = sum(C.*C,2)';
[N,M] = size(Q);
L=size(R,1);
idx = zeros(N,K);
D = idx;
if K==1
% Loop for each query point
for k=1:N
d=zeros(L,1);
for t=1:M
d=d+(R(:,t)-Q(k,t)).^2;
end
if fident
d(k)=inf;
end
[D(k),idx(k)]=min(d);
end
else
for k=1:N
d=zeros(L,1);
for t=1:M
d=d+(R(:,t)-Q(k,t)).^2;
end
if fident
d(k)=inf;
end
[s,t]=sort(d);
idx(k,:)=t(1:K);
D(k,:)=s(1:K);
end
end
if nargout>1
D=sqrt(D);
end
function [Q,R,K,fident] = parseinputs(varargin)
% Check input and output
error(nargchk(1,3,nargin));
Q=varargin{1};
if nargin<2
R=Q;
fident = true;
else
fident = false;
R=varargin{2};
end
if isempty(R)
fident = true;
R=Q;
end
if ~fident
fident = isequal(Q,R);
end
if nargin<3
K=1;
else
K=varargin{3};
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
lorenz.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/lorentz/lorenz.m
| 1,363 |
utf_8
|
9da3a6e8b70b72c64b10f262bb879ade
|
function [x,y,z,T] = lorenz(rho, sigma, beta, initV, T, eps)
% LORENZ Function generates the lorenz attractor of the prescribed values
% of parameters rho, sigma, beta
%
% [X,Y,Z] = LORENZ(RHO,SIGMA,BETA,INITV,T,EPS)
% X, Y, Z - output vectors of the strange attactor trajectories
% RHO - Rayleigh number
% SIGMA - Prandtl number
% BETA - parameter
% INITV - initial point
% T - time interval
% EPS - ode solver precision
%
% Example.
% [X Y Z] = lorenz(28, 10, 8/3);
% plot3(X,Y,Z);
if nargin<3
error('MATLAB:lorenz:NotEnoughInputs','Not enough input arguments.');
end
if nargin<4
eps = 0.000001;
T = [0 25];
initV = [0 1 1.05];
end
options = odeset('RelTol',eps,'AbsTol',[eps eps eps/10]);
[T,X] = ode45(@(T,X) F(T, X, sigma, rho, beta), T, initV, options);
plot3(X(:,1),X(:,2),X(:,3));
axis equal;
grid;
title('Lorenz attractor');
xlabel('X'); ylabel('Y'); zlabel('Z');
x = X(:,1);
y = X(:,2);
z = X(:,3);
return
end
function dx = F(T, X, sigma, rho, beta)
% Evaluates the right hand side of the Lorenz system
% x' = sigma*(y-x)
% y' = x*(rho - z) - y
% z' = x*y - beta*z
% typical values: rho = 28; sigma = 10; beta = 8/3;
dx = zeros(3,1);
dx(1) = sigma*(X(2) - X(1));
dx(2) = X(1)*(rho - X(3)) - X(2);
dx(3) = X(1)*X(2) - beta*X(3);
return
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
demoUI.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/bilateral-filtering/bilateral-toolbox/demoUI.m
| 11,896 |
utf_8
|
66455746f1799fcc484ea751ad4eda26
|
function varargout = demoUI(varargin)
% DEMOUI MATLAB code for demoUI.fig
% DEMOUI, by itself, creates a new DEMOUI or raises the existing
% singleton*.
%
% H = DEMOUI returns the handle to a new DEMOUI or the handle to
% the existing singleton*.
%
% DEMOUI('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in DEMOUI.M with the given input arguments.
%
% DEMOUI('Property','Value',...) creates a new DEMOUI or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before demoUI_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to demoUI_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help demoUI
% Last Modified by GUIDE v2.5 05-Jul-2016 17:35:13
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @demoUI_OpeningFcn, ...
'gui_OutputFcn', @demoUI_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before demoUI is made visible.
function demoUI_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to demoUI (see VARARGIN)
% Choose default command line output for demoUI
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes demoUI wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = demoUI_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
function imagepath_Callback(hObject, eventdata, handles)
% hObject handle to imagepath (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of imagepath as text
% str2double(get(hObject,'String')) returns contents of imagepath as a double
% --- Executes during object creation, after setting all properties.
function imagepath_CreateFcn(hObject, eventdata, handles)
% hObject handle to imagepath (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in browseButton.
function browseButton_Callback(hObject, eventdata, handles)
% hObject handle to browseButton (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
CallbackFcns browse;
% --- Executes on button press in loadButton.
function loadButton_Callback(hObject, eventdata, handles)
% hObject handle to loadButton (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
CallbackFcns load;
% --- Executes on button press in filterButton.
function filterButton_Callback(hObject, eventdata, handles)
% hObject handle to filterButton (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
CallbackFcns filter;
% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- Executes on slider movement.
function sliderS_Callback(hObject, eventdata, handles)
% hObject handle to sliderS (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
CallbackFcns sigmas_slider;
% --- Executes during object creation, after setting all properties.
function sliderS_CreateFcn(hObject, eventdata, handles)
% hObject handle to sliderS (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
% --- Executes on slider movement.
function sliderR_Callback(hObject, eventdata, handles)
% hObject handle to sliderR (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
CallbackFcns sigmar_slider;
% --- Executes during object creation, after setting all properties.
function sliderR_CreateFcn(hObject, eventdata, handles)
% hObject handle to sliderR (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
% --- Executes on selection change in listbox1.
function listbox1_Callback(hObject, eventdata, handles)
% hObject handle to listbox1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: contents = cellstr(get(hObject,'String')) returns listbox1 contents as cell array
% contents{get(hObject,'Value')} returns selected item from listbox1
% --- Executes during object creation, after setting all properties.
function listbox1_CreateFcn(hObject, eventdata, handles)
% hObject handle to listbox1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: listbox controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function editS_Callback(hObject, eventdata, handles)
% hObject handle to editS (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of editS as text
% str2double(get(hObject,'String')) returns contents of editS as a double
CallbackFcns sigmas_edit;
% --- Executes during object creation, after setting all properties.
function editS_CreateFcn(hObject, eventdata, handles)
% hObject handle to editS (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
function editR_Callback(hObject, eventdata, handles)
% hObject handle to editR (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of editR as text
% str2double(get(hObject,'String')) returns contents of editR as a double
CallbackFcns sigmar_edit;
% --- Executes during object creation, after setting all properties.
function editR_CreateFcn(hObject, eventdata, handles)
% hObject handle to editR (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
% --- Executes on button press in saveButton.
function saveButton_Callback(hObject, eventdata, handles)
% hObject handle to saveButton (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
CallbackFcns save;
% --- Executes on slider movement.
function sliderEps_Callback(hObject, eventdata, handles)
% hObject handle to sliderEps (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'Value') returns position of slider
% get(hObject,'Min') and get(hObject,'Max') to determine range of slider
CallbackFcns eps_slider;
% --- Executes during object creation, after setting all properties.
function sliderEps_CreateFcn(hObject, eventdata, handles)
% hObject handle to sliderEps (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: slider controls usually have a light gray background.
if isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor',[.9 .9 .9]);
end
function editEps_Callback(hObject, eventdata, handles)
% hObject handle to editEps (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of editEps as text
% str2double(get(hObject,'String')) returns contents of editEps as a double
CallbackFcns eps_edit;
% --- Executes during object creation, after setting all properties.
function editEps_CreateFcn(hObject, eventdata, handles)
% hObject handle to editEps (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor','white');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
CallbackFcns.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/bilateral-filtering/bilateral-toolbox/CallbackFcns.m
| 3,734 |
utf_8
|
bb2767d88ebb2ec18d4b4dd2088ee8d5
|
function CallbackFcns (action)
switch (action)
case 'sigmas_slider'
sigmas = get(gcbo, 'Value');
sigmas = round(sigmas) + 1;
updatesigmas(sigmas);
case 'sigmar_slider'
sigmar = get(gcbo, 'Value');
sigmar = (round(sigmar*10))/10 + 5;
updatesigmar(sigmar);
case 'sigmas_edit'
sigmas = eval(get(gcbo, 'String'));
updatesigmas(sigmas);
case 'sigmar_edit'
sigmar = eval(get(gcbo, 'String'));
updatesigmar(sigmar);
case 'eps_slider'
eps = get(gcbo, 'Value');
eps = (round(eps) + 1)*0.001;
update_eps(eps);
case 'eps_edit'
eps = eval(get(gcbo, 'String'));
update_eps(eps);
case 'browse'
[filename, user_canceled] = imgetfile;
if (~user_canceled)
imagepath_Handle = findobj(gcbf,'Tag','imagepath');
set(imagepath_Handle,'String',filename);
end
case 'load'
imagepath_Handle = findobj(gcbf,'Tag','imagepath');
mread = imread(get(imagepath_Handle,'String'));
axes(findobj(gcbf,'Tag','input'));
cla; hold on;
imshow(mread); axis('image', 'off');
minput = double(mread);
set(gcbf,'UserData',minput);
case 'filter'
minput = get(gcbf,'UserData');
editS_Handle = findobj(gcbf,'Tag','editS');
sigmas = eval(get(editS_Handle,'String'));
editR_Handle = findobj(gcbf,'Tag','editR');
sigmar = eval(get(editR_Handle,'String'));
editEps_Handle = findobj(gcbf,'Tag','editEps');
eps = eval(get(editEps_Handle,'String'));
% [moutput,params] = shiftableBF(minput,sigmas,sigmar);
[moutput,N] = GPA(minput, sigmar, sigmas, eps, 'Gauss');
axes(findobj(gcbf,'Tag','output'));
cla; hold on;
imshow(uint8(moutput)); axis('image', 'off');
rkernel_Handle = findobj(gcbf,'Tag','rkernelplot');
axes(rkernel_Handle);
cla;
set(rkernel_Handle,'Color','White');
set(rkernel_Handle,'AmbientLightColor','White');
set(rkernel_Handle,'XColor','Black');
set(rkernel_Handle,'YColor','Black');
box on;
sigmar2 = sigmar^2;
L = -127;
U =128;
t = L : 0.01 : U;
tauList = [-50,0,50]; %center
for i=1:length(tauList)
tau=tauList(i);
g = exp(-0.5*(t-tau).^2/sigmar2);
% Gauss-polynomial
nu = 0.5*(1/sigmar2);
gapprox = zeros(size(t));
for k = 0 : N
gapprox = gapprox + (1/factorial(k)) * (1/sigmar2)^k ...
*(tau*t).^k;
end
gapprox = gapprox.*exp(-nu*t.^2).* exp(-nu*tau^2);
%g3 = (1 - nu*((t-tau).^2/N)).^N;
% display
hold on, plot(t,g, 'r','LineWidth',3);
hold on, plot(t,gapprox,'k','LineWidth',2);
axis('tight'), grid('on'),
hleg=legend('Target Gaussian', 'Gaussian-Polynomial');
set(hleg,'fontsize',8);
end
case 'save'
imsave(findobj(gcbf,'Tag','output'));
end
function updatesigmas (sigmas)
sliderS_Handle = findobj(gcbf,'Tag','sliderS');
set(sliderS_Handle,'Value',sigmas-1);
editS_Handle = findobj(gcbf,'Tag','editS');
set(editS_Handle,'String',sigmas);
function updatesigmar (sigmar)
sliderR_Handle = findobj(gcbf,'Tag','sliderR');
set(sliderR_Handle,'Value',sigmar-5);
editR_Handle = findobj(gcbf,'Tag','editR');
set(editR_Handle,'String',sigmar);
function update_eps (eps)
sliderEps_Handle = findobj(gcbf,'Tag','sliderEps');
set(sliderEps_Handle,'Value',eps*1000-1);
editEps_Handle = findobj(gcbf,'Tag','editEps');
set(editEps_Handle,'String',eps);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
perform_ar_synthesis.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/motion-clouds/perform_ar_synthesis.m
| 2,236 |
utf_8
|
b3c984def5c7d189f8756566ad7b839a
|
function F = perform_ar_synthesis(H, options)
% perform_ar_synthesis - perform motion cloud synthesis
%
% F = perform_ar_synthesis(H, options);
%
% Copyright (c) 2013 Gabriel Peyre
n = size(H,1);
synth2d = @(h)real(ifft2(fft2(randn(n,n)).*h));
extend = @(f)[f f(:,1); f(1,:) f(1)];
% movement
scale = getoptions(options, 'scale', 1);
rotation = getoptions(options, 'rotation', 0);
translation = getoptions(options, 'translation', [0 0]);
center = getoptions(options, 'center', [n/2 n/2]);
sigmat = getoptions(options, 'sigmat', 40);
p = getoptions(options, 'nbframes', 64);
pdisp = getoptions(options, 'nbframes_disp', 2*p);
%
a = fit_ar2(sigmat);
x = 1:n;
[Y,X] = meshgrid(x,x);
% moved grid
X1 = center(1) + scale*( (X-center(1))*cos(rotation) - (Y-center(2))*sin(rotation) ) + translation(1);
Y1 = center(2) + scale*( (X-center(1))*sin(rotation) + (Y-center(2))*cos(rotation) ) + translation(2);
X1 = mod(X1-1,n)+1;
Y1 = mod(Y1-1,n)+1;
% apply movement
move = @(f)interp2(1:n+1,1:n+1,extend(f),Y1,X1);
% Stop button
clf;
% Axes
ax = axes(...
'Units','Normalized',...
'OuterPosition', [0 0.2 1 0.8]);
f0 = zeros(n);
f1 = zeros(n);
Contrast = 50;
s = 0;
F = [];
EarlyStop = 0;
i = 0;
randn('state', 123);
global run;
run = 1;
while run
i = i+1;
% rotate the noise
W = synth2d(H);
X1 = center(1) + ( (X-center(1))*cos(rotation*(i-1)) - (Y-center(2))*sin(rotation*(i-1)) );
Y1 = center(2) + ( (X-center(1))*sin(rotation*(i-1)) + (Y-center(2))*cos(rotation*(i-1)) );
X1 = mod(X1-1,n)+1; Y1 = mod(Y1-1,n)+1;
W = interp2(1:n+1,1:n+1,extend(W),Y1,X1);
%
f = W + a(1)*f0 + a(2)*f1;
f1 = f0; f0 = f;
s = max(s,std(f(:)));
% scale
f0 = move(f0);
f1 = move(f1);
% display
image( 127 + Contrast*f/s );
colormap gray(256);
axis image; axis off;
if i==p
uicontrol(...
'Style','pushbutton', 'String', 'Stop',...
'Units','Normalized', 'Position', [0.4 0.1 0.2 0.1],...
'Callback', @MyCallback);
end
if i>=p
set(ax, 'ButtonDownFcn', 'get(ax, ''CurrentPoint'')');
end
drawnow;
% save
if i<p
F(:,:,end+1) = f;
end
end
end
function MyCallback(a,b,c)
global run;
run = 0;
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
movie_display.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/motion-clouds/toolbox/movie_display.m
| 766 |
utf_8
|
72007c865584bc804987e7f24d64ce47
|
function movie_display(f)
% movie_display - display a 3-D array as a movie.
%
% movie_display(f);
%
% Copyright (c) 2012 Gabriel Peyre
s = 2.5;
normalize = @(x)rescale( clamp( (x-mean(x(:)))/std(x(:)), -s,s) );
A = normalize(f)*256;
clf;
% stpo button
uicontrol(...
'Style','pushbutton', 'String', 'Stop',...
'Units','Normalized', 'Position', [0.4 0.1 0.2 0.1],...
'Callback', @MyCallback);
% Axes
ax = axes(...
'Units','Normalized',...
'OuterPosition', [0 0.2 1 0.8]);
k = 0;
global run;
run = 1;
while run
k = mod(k,size(A,3))+1;
image(A(:,:,k)); axis image; axis off;
colormap gray(256);
drawnow;
set(ax, 'ButtonDownFcn', 'get(ax, ''CurrentPoint'')');
end
end
function MyCallback(a,b,c)
global run;
run = 0;
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
demo_stepwise.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/dbscan/demo_stepwise.m
| 4,650 |
utf_8
|
9f483f576b60f8e3bc193aae38407161
|
function demo_stepwise()
%twospirals
% data=twospirals(200,360,50,1.5,15);
data = twospirals(600, 360*1.3, 30, 50);
global it;
global rep;
it = 0;
addpath('../toolbox/');
rep = MkResRep();
% generate mixtures
k0 = 20;
z0 = (.1+.1i) + .8*( rand(k0,1) + 1i*rand(k0,1) );
% mean/scale/anisotrop/orientation
p = 30; % #sample per cluster
gauss = @(m,s,a,t)m + s*exp(2i*t)*( randn(p,1) + 1i*randn(p,1)*a );
X = [];
a = .5; s = .04;
for k=1:k0
X = [X; gauss(rand+rand*1i,s,a,rand)];
end
n = length(X);
clf;
plot(X, '.');
axis equal; axis([0,1,0,1]);
box on; set(gca, 'XTick', [], 'YTick', []);
data = (2*[real(X), imag(X)]-1)*6;
% data=corners(500);
s=zeros(size(data,1),1);
clf;
for i=1:size(data,1)
hold on
s(i)=scatter(data(i,1),data(i,2),'filled','markerfacecolor',[0.8,0.8,0.8]);
end
axis equal;
% axis([0 1 0 1]);
axis([-1 1 -1 1]*8);
axis off;
drawnow
%%
%using euclidean distance
distmat=zeros(size(data,1),size(data,1));
for i=1:size(data,1)
for j=i:size(data,1)
distmat(i,j)=sqrt((data(i,1:2)-data(j,1:2))*(data(i,1:2)-data(j,1:2))');
end
end
for i=1:size(data,1)
for j=i:size(data,1)
distmat(j,i)=distmat(i,j);
end
end
% k_dist=zeros(size(data,1),1);
% figure
% for k=3:5
% for i=1:size(data,1)
% tmp=sort(distmat(:,i),'ascend');
% k_dist(i)=tmp(k);
% end
% hold on
% plot(1:size(data,1),k_dist);
% end
%%
Eps=0.5;
MinPts=4;
DBSCAN_STEPWISE(s,distmat,Eps,MinPts);
end
function Clust = DBSCAN_STEPWISE(s,DistMat,Eps,MinPts)
%A step-wise illustration of DBSCAN on 2D data
%A simple DBSCAN implementation of the original paper:
%"A Density-Based Algorithm for Discovering Clusters in Large Spatial
%Databases with Noise" -- Martin Ester et.al.
%Since no spatial access method is implemented, the run time complexity
%will be N^2 rather than N*logN
%**************************************************************************
%Input: DistMat, Eps, MinPts
%DistMat: A N*N distance matrix, the (i,j) element contains the distance
%from point-i to point-j.
%Eps: A scalar value for Epsilon-neighborhood threshold.
%MinPts: A scalar value for minimum points in Eps-neighborhood that holds
%the core-point condition.
%**************************************************************************
%Output: Clust
%Clust: A N*1 vector describes the cluster membership for each point. 0 is
%reserved for NOISE.
%**************************************************************************
%Written by Tianxiao Jiang, [email protected]
%Nov-4-2015
%**************************************************************************
%Initialize Cluster membership as -1, which means UNCLASSIFIED
Clust=zeros(size(DistMat,1),1)-1;
ClusterId=1;
ClusterColor=rand(1,3);
%randomly choose the visiting order
VisitSequence=randperm(length(Clust));
for i=1:length(Clust)
% For each point, check if it is not visited yet (unclassified)
pt=VisitSequence(i);
if Clust(pt)==-1
%Iteratively expand the cluster through density-reachability
[Clust,isnoise]=ExpandCluster(s,DistMat,pt,ClusterId,Eps,MinPts,Clust,ClusterColor);
if ~isnoise
ClusterId=ClusterId+1;
ClusterColor=rand(1,3);
end
end
end
end
function [Clust,isnoise]=ExpandCluster(s,DistMat,pt,ClusterId,Eps,MinPts,Clust,ClusterColor)
global it;
%region query
seeds=find(DistMat(:,pt)<=Eps);
if length(seeds)<MinPts
Clust(pt)=0; % 0 reserved for noise
set(s(pt),'Marker','*');
pause(0.01)
isnoise=true;
return
else
Clust(seeds)=ClusterId;
set(s(seeds),'MarkerFaceColor',ClusterColor);
pause(0.01)
%delete the core point
seeds=setxor(seeds,pt);
while ~isempty(seeds)
currentP=seeds(1);
%region query
result=find(DistMat(:,currentP)<=Eps);
if length(result)>=MinPts
for i=1:length(result)
resultP=result(i);
if Clust(resultP)==-1||Clust(resultP)==0 % unclassified or noise
set(s(resultP),'MarkerFaceColor',ClusterColor);
global it;
global rep;
it = it+1;
if mod(it,4)==0
saveas(gcf, [rep 'anim-' znum2str(it,3) '.png']);
end
if Clust(resultP)==-1 %unclassified
seeds=[seeds(:);resultP];
end
Clust(resultP)=ClusterId;
end
end
end
seeds=setxor(seeds,currentP);
end
isnoise=false;
return
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
DBSCAN.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/dbscan/DBSCAN.m
| 2,588 |
utf_8
|
232558b4366cd2668ad0f85e2185b21f
|
function Clust = DBSCAN(DistMat,Eps,MinPts)
%A simple DBSCAN implementation of the original paper:
%"A Density-Based Algorithm for Discovering Clusters in Large Spatial
%Databases with Noise" -- Martin Ester et.al.
%Since no spatial access method is implemented, the run time complexity
%will be N^2 rather than N*logN
%**************************************************************************
%Input: DistMat, Eps, MinPts
%DistMat: A N*N distance matrix, the (i,j) element contains the distance
%from point-i to point-j.
%Eps: A scalar value for Epsilon-neighborhood threshold.
%MinPts: A scalar value for minimum points in Eps-neighborhood that holds
%the core-point condition.
%**************************************************************************
%Output: Clust
%Clust: A N*1 vector describes the cluster membership for each point. 0 is
%reserved for NOISE.
%**************************************************************************
%Written by Tianxiao Jiang, [email protected]
%Nov-4-2015
%**************************************************************************
%Initialize Cluster membership as -1, which means UNCLASSIFIED
Clust=zeros(size(DistMat,1),1)-1;
ClusterId=1;
%randomly choose the visiting order
VisitSequence=randperm(length(Clust));
for i=1:length(Clust)
% For each point, check if it is not visited yet (unclassified)
pt=VisitSequence(i);
if Clust(pt)==-1
%Iteratively expand the cluster through density-reachability
[Clust,isnoise]=ExpandCluster(DistMat,pt,ClusterId,Eps,MinPts,Clust);
if ~isnoise
ClusterId=ClusterId+1;
end
end
end
end
function [Clust,isnoise]=ExpandCluster(DistMat,pt,ClusterId,Eps,MinPts,Clust)
%region query
seeds=find(DistMat(:,pt)<=Eps);
if length(seeds)<MinPts
Clust(pt)=0; % 0 reserved for noise
isnoise=true;
return
else
Clust(seeds)=ClusterId;
%delete the core point
seeds=setxor(seeds,pt);
while ~isempty(seeds)
currentP=seeds(1);
%region query
result=find(DistMat(:,currentP)<=Eps);
if length(result)>=MinPts
for i=1:length(result)
resultP=result(i);
if Clust(resultP)==-1||Clust(resultP)==0 % unclassified or noise
if Clust(resultP)==-1 %unclassified
seeds=[seeds(:);resultP];
end
Clust(resultP)=ClusterId;
end
end
end
seeds=setxor(seeds,currentP);
end
isnoise=false;
return
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_image.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/total-variation/toolbox/load_image.m
| 20,275 |
utf_8
|
c700b54853577ab37402e27e4ca061b8
|
function M = load_image(type, n, options)
% load_image - load benchmark images.
%
% M = load_image(name, n, options);
%
% name can be:
% Synthetic images:
% 'chessboard1', 'chessboard', 'square', 'squareregular', 'disk', 'diskregular', 'quaterdisk', '3contours', 'line',
% 'line_vertical', 'line_horizontal', 'line_diagonal', 'line_circle',
% 'parabola', 'sin', 'phantom', 'circ_oscil',
% 'fnoise' (1/f^alpha noise).
% Natural images:
% 'boat', 'lena', 'goldhill', 'mandrill', 'maurice', 'polygons_blurred', or your own.
%
% Copyright (c) 2004 Gabriel Peyre
if nargin<2
n = 512;
end
options.null = 0;
if iscell(type)
for i=1:length(type)
M{i} = load_image(type{i},n,options);
end
return;
end
type = lower(type);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameters for geometric objects
eta = getoptions(options, 'eta', .1);
gamma = getoptions(options, 'gamma', 1/sqrt(2));
radius = getoptions(options, 'radius', 10);
center = getoptions(options, 'center', [0 0]);
center1 = getoptions(options, 'center1', [0 0]);
w = getoptions(options, 'tube_width', 0.06);
nb_points = getoptions(options, 'nb_points', 9);
scaling = getoptions(options, 'scaling', 1);
theta = getoptions(options, 'theta', 30 * 2*pi/360);
eccentricity = getoptions(options, 'eccentricity', 1.3);
sigma = getoptions(options, 'sigma', 0);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% for the line, can be vertical / horizontal / diagonal / any
if strcmp(type, 'line_vertical')
eta = 0.5; % translation
gamma = 0; % slope
elseif strcmp(type, 'line_horizontal')
eta = 0.5; % translation
gamma = Inf; % slope
elseif strcmp(type, 'line_diagonal')
eta = 0; % translation
gamma = 1; % slope
end
if strcmp(type(1:min(12,end)), 'square-tube-')
k = str2double(type(13:end));
c1 = [.22 .5]; c2 = [1-c1(1) .5];
eta = 1.5;
r1 = [c1 c1] + .21*[-1 -eta 1 eta];
r2 = [c2 c2] + .21*[-1 -eta 1 eta];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
if mod(k,2)==0
sel = n/2-k/2+1:n/2+k/2;
else
sel = n/2-(k-1)/2:n/2+(k-1)/2;
end
M( round(.25*n:.75*n), sel ) = 1;
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
switch lower(type)
case 'constant'
M = ones(n);
case 'ramp'
x = linspace(0,1,n);
[Y,M] = meshgrid(x,x);
case 'bump'
s = getoptions(options, 'bump_size', .5);
c = getoptions(options, 'center', [0 0]);
if length(s)==1
s = [s s];
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
X = (X-c(1))/s(1); Y = (Y-c(2))/s(2);
M = exp( -(X.^2+Y.^2)/2 );
case 'periodic'
x = linspace(-pi,pi,n)/1.1;
[Y,X] = meshgrid(x,x);
f = getoptions(options, 'freq', 6);
M = (1+cos(f*X)).*(1+cos(f*Y));
case {'letter-x' 'letter-v' 'letter-z' 'letter-y'}
M = create_letter(type(8), radius, n);
case 'l'
r1 = [.1 .1 .3 .9];
r2 = [.1 .1 .9 .4];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) );
case 'ellipse'
c1 = [0.15 0.5];
c2 = [0.85 0.5];
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
d = sqrt((X-c1(1)).^2 + (Y-c1(2)).^2) + sqrt((X-c2(1)).^2 + (Y-c2(2)).^2);
M = double( d<=eccentricity*sqrt( sum((c1-c2).^2) ) );
case 'ellipse-thin'
options.eccentricity = 1.06;
M = load_image('ellipse', n, options);
case 'ellipse-fat'
options.eccentricity = 1.3;
M = load_image('ellipse', n, options);
case 'square-tube'
c1 = [.25 .5];
c2 = [.75 .5];
r1 = [c1 c1] + .18*[-1 -1 1 1];
r2 = [c2 c2] + .18*[-1 -1 1 1];
r3 = [c1(1)-w c1(2)-w c2(1)+w c2(2)+w];
M = double( draw_rectangle(r1,n) | draw_rectangle(r2,n) | draw_rectangle(r3,n) );
case 'square-tube-1'
options.tube_width = 0.03;
M = load_image('square-tube', n, options);
case 'square-tube-2'
options.tube_width = 0.06;
M = load_image('square-tube', n, options);
case 'square-tube-3'
options.im = 0.09;
M = load_image('square-tube', n, options);
case 'polygon'
theta = sort( rand(nb_points,1)*2*pi );
radius = scaling*rescale(rand(nb_points,1), 0.1, 0.93);
points = [cos(theta) sin(theta)] .* repmat(radius, 1,2);
points = (points+1)/2*(n-1)+1; points(end+1,:) = points(1,:);
M = draw_polygons(zeros(n),0.8,{points'});
[x,y] = ind2sub(size(M),find(M));
p = 100; m = length(x);
lambda = linspace(0,1,p);
X = n/2 + repmat(x-n/2, [1 p]) .* repmat(lambda, [m 1]);
Y = n/2 + repmat(y-n/2, [1 p]) .* repmat(lambda, [m 1]);
I = round(X) + (round(Y)-1)*n;
M = zeros(n); M(I) = 1;
case 'polygon-8'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-10'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'polygon-12'
options.nb_points = 8;
M = load_image('polygon', n, options);
case 'pacman'
options.radius = 0.45;
options.center = [.5 .5];
M = load_image('disk', n, options);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
T =atan2(Y,X);
M = M .* (1-(abs(T-pi/2)<theta/2));
case 'square-hole'
options.radius = 0.45;
M = load_image('disk', n, options);
options.scaling = 0.5;
M = M - load_image('polygon-10', n, options);
case 'grid-circles'
if isempty(n)
n = 256;
end
f = getoptions(options, 'frequency', 30);
eta = getoptions(options, 'width', .3);
x = linspace(-n/2,n/2,n) - round(n*0.03);
y = linspace(0,n,n);
[Y,X] = meshgrid(y,x);
R = sqrt(X.^2+Y.^2);
theta = 0.05*pi/2;
X1 = cos(theta)*X+sin(theta)*Y;
Y1 = -sin(theta)*X+cos(theta)*Y;
A1 = abs(cos(2*pi*R/f))<eta;
A2 = max( abs(cos(2*pi*X1/f))<eta, abs(cos(2*pi*Y1/f))<eta );
M = A1;
M(X1>0) = A2(X1>0);
case 'chessboard1'
x = -1:2/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (2*(Y>=0)-1).*(2*(X>=0)-1);
case 'chessboard'
width = getoptions(options, 'width', round(n/16) );
[Y,X] = meshgrid(0:n-1,0:n-1);
M = mod( floor(X/width)+floor(Y/width), 2 ) == 0;
case 'square'
if ~isfield( options, 'radius' )
radius = 0.6;
end
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M = max( abs(X),abs(Y) )<radius;
case 'squareregular'
M = rescale(load_image('square',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'regular1'
options.alpha = 1;
M = load_image('fnoise',n,options);
case 'regular2'
options.alpha = 2;
M = load_image('fnoise',n,options);
case 'regular3'
options.alpha = 3;
M = load_image('fnoise',n,options);
case 'sparsecurves'
options.alpha = 3;
M = load_image('fnoise',n,options);
M = rescale(M);
ncurves = 3;
M = cos(2*pi*ncurves);
case 'geometrical'
J = getoptions(options, 'Jgeometrical', 4);
sgeom = 100*n/256;
options.bound = 'per';
A = ones(n);
for j=0:J-1
B = A;
for k=1:2^j
I = find(B==k);
U = perform_blurring(randn(n),sgeom,options);
s = median(U(I));
I1 = find( (B==k) & (U>s) );
I2 = find( (B==k) & (U<=s) );
A(I1) = 2*k-1;
A(I2) = 2*k;
end
end
M = A;
case 'lic-texture'
disp('Computing random tensor field.');
options.sigma_tensor = getoptions(options, 'lic_regularity', 50*n/256);
T = compute_tensor_field_random(n,options);
Flow = perform_tensor_decomp(T); % extract eigenfield.
options.isoriented = 0; % no orientation in streamlines
% initial texture
lic_width = getoptions(options, 'lic_width', 0);
M0 = perform_blurring(randn(n),lic_width);
M0 = perform_histogram_equalization( M0, 'linear');
options.histogram = 'linear';
options.dt = 0.4;
options.M0 = M0;
options.verb = 1;
options.flow_correction = 1;
options.niter_lic = 3;
w = 30;
M = perform_lic(Flow, w, options);
case 'square_texture'
M = load_image('square',n);
M = rescale(M);
% make a texture patch
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M(I) = M(I) + lambda * sin( x(I) * 2*pi / eta );
case 'tv-image'
M = rand(n);
tau = compute_total_variation(M);
options.niter = 400;
[M,err_tv,err_l2] = perform_tv_projection(M,tau/1000,options);
M = perform_histogram_equalization(M,'linear');
case 'oscillatory_texture'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
theta = pi/3;
x = cos(theta)*X + sin(theta)*Y;
c = [0.3,0.4]; r = 0.2;
I = find( (X-c(1)).^2 + (Y-c(2)).^2 < r^2 );
eta = 3/n; lambda = 0.3;
M = sin( x * 2*pi / eta );
case {'line', 'line_vertical', 'line_horizontal', 'line_diagonal'}
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
if gamma~=Inf
M = (X-eta) - gamma*Y < 0;
else
M = (Y-eta) < 0;
end
case 'line-windowed'
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
eta = .3;
gamma = getoptions(options, 'gamma', pi/10);
parabola = getoptions(options, 'parabola', 0);
M = (X-eta) - gamma*Y - parabola*Y.^2 < 0;
f = sin( pi*x ).^2;
M = M .* ( f'*f );
case 'grating'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
theta = getoptions(options, 'theta', .2);
freq = getoptions(options, 'freq', .2);
X = cos(theta)*X + sin(theta)*Y;
M = sin(2*pi*X/freq);
case 'disk'
if ~isfield( options, 'radius' )
radius = 0.35;
end
if ~isfield( options, 'center' )
center = [0.5, 0.5]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'twodisks'
M = zeros(n);
options.center = [.25 .25];
M = load_image('disk', n, options);
options.center = [.75 .75];
M = M + load_image('disk', n, options);
case 'diskregular'
M = rescale(load_image('disk',n,options));
if not(isfield(options, 'alpha'))
options.alpha = 3;
end
S = load_image('fnoise',n,options);
M = M + rescale(S,-0.3,0.3);
case 'quarterdisk'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
case 'fading_contour'
if ~isfield( options, 'radius' )
radius = 0.95;
end
if ~isfield( options, 'center' )
center = -[0.1, 0.1]; % center of the circle
end
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
M = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
theta = 2/pi*atan2(Y,X);
h = 0.5;
M = exp(-(1-theta).^2/h^2).*M;
case '3contours'
radius = 1.3;
center = [-1, 1];
radius1 = 0.8;
center1 = [0, 0];
x = 0:1/(n-1):1;
[Y,X] = meshgrid(x,x);
f1 = (X-center(1)).^2 + (Y-center(2)).^2 < radius^2;
f2 = (X-center1(1)).^2 + (Y-center1(2)).^2 < radius1^2;
M = f1 + 0.5*f2.*(1-f1);
case 'line_circle'
gamma = 1/sqrt(2);
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
M1 = double( X>gamma*Y+0.25 );
M2 = X.^2 + Y.^2 < 0.6^2;
M = 20 + max(0.5*M1,M2) * 216;
case 'fnoise'
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
alpha = getoptions(options, 'alpha', 1);
M = gen_noisy_image(n,alpha);
case 'gaussiannoise'
% generate an image of filtered noise with gaussian
sigma = getoptions(options, 'sigma', 10);
M = randn(n);
m = 51;
h = compute_gaussian_filter([m m],sigma/(4*n),[n n]);
M = perform_convolution(M,h);
return;
case {'bwhorizontal','bwvertical','bwcircle'}
[Y,X] = meshgrid(0:n-1,0:n-1);
if strcmp(type, 'bwhorizontal')
d = X;
elseif strcmp(type, 'bwvertical')
d = Y;
elseif strcmp(type, 'bwcircle')
d = sqrt( (X-(n-1)/2).^2 + (Y-(n-1)/2).^2 );
end
if isfield(options, 'stripe_width')
stripe_width = options.stripe_width;
else
stripe_width = 5;
end
if isfield(options, 'black_prop')
black_prop = options.black_prop;
else
black_prop = 0.5;
end
M = double( mod( d/(2*stripe_width),1 )>=black_prop );
case 'parabola'
% curvature
c = getoptions(c, 'c', .1);
% angle
theta = getoptions(options, 'theta', pi/sqrt(2));
x = -0.5:1/(n-1):0.5;
[Y,X] = meshgrid(x,x);
Xs = X*cos(theta) + Y*sin(theta);
Y =-X*sin(theta) + Y*cos(theta); X = Xs;
M = Y>c*X.^2;
case 'sin'
[Y,X] = meshgrid(-1:2/(n-1):1, -1:2/(n-1):1);
M = Y >= 0.6*cos(pi*X);
M = double(M);
case 'circ_oscil'
x = linspace(-1,1,n);
[Y,X] = meshgrid(x,x);
R = sqrt(X.^2+Y.^2);
M = cos(R.^3*50);
case 'phantom'
M = phantom(n);
case 'periodic_bumps'
nbr_periods = getoptions(options, 'nbr_periods', 8);
theta = getoptions(options, 'theta', 1/sqrt(2));
skew = getoptions(options, 'skew', 1/sqrt(2) );
A = [cos(theta), -sin(theta); sin(theta), cos(theta)];
B = [1 skew; 0 1];
T = B*A;
x = (0:n-1)*2*pi*nbr_periods/(n-1);
[Y,X] = meshgrid(x,x);
pos = [X(:)'; Y(:)'];
pos = T*pos;
X = reshape(pos(1,:), n,n);
Y = reshape(pos(2,:), n,n);
M = cos(X).*sin(Y);
case 'noise'
sigma = getoptions(options, 'sigma', 1);
M = randn(n) * sigma;
case 'disk-corner'
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
rho = .3; eta = .1;
M1 = rho*X+eta<Y;
c = [0 .2]; r = .85;
d = (X-c(1)).^2 + (Y-c(2)).^2;
M2 = d<r^2;
M = M1.*M2;
otherwise
ext = {'gif', 'png', 'jpg', 'bmp', 'tiff', 'pgm', 'ppm'};
for i=1:length(ext)
name = [type '.' ext{i}];
if( exist(name) )
M = imread( name );
M = double(M);
if not(isempty(n)) && (n~=size(M, 1) || n~=size(M, 2)) && nargin>=2
M = image_resize(M,n,n);
end
if strcmp(type, 'peppers-bw')
M(:,1) = M(:,2);
M(1,:) = M(2,:);
end
if sigma>0
M = perform_blurring(M,sigma);
end
return;
end
end
error( ['Image ' type ' does not exists.'] );
end
M = double(M);
if sigma>0
M = perform_blurring(M,sigma);
end
M = rescale(M);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = create_letter(a, r, n)
c = 0.2;
p1 = [c;c];
p2 = [c; 1-c];
p3 = [1-c; 1-c];
p4 = [1-c; c];
p4 = [1-c; c];
pc = [0.5;0.5];
pu = [0.5; c];
switch a
case 'x'
point_list = { [p1 p3] [p2 p4] };
case 'z'
point_list = { [p2 p3 p1 p4] };
case 'v'
point_list = { [p2 pu p3] };
case 'y'
point_list = { [p2 pc pu] [pc p3] };
end
% fit image
for i=1:length(point_list)
a = point_list{i}(2:-1:1,:);
a(1,:) = 1-a(1,:);
point_list{i} = round( a*(n-1)+1 );
end
M = draw_polygons(zeros(n),r,point_list);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_polygons(mask,r,point_list)
sk = mask*0;
for i=1:length(point_list)
pl = point_list{i};
for k=2:length(pl)
sk = draw_line(sk,pl(1,k-1),pl(2,k-1),pl(1,k),pl(2,k),r);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_line(sk,x1,y1,x2,y2,r)
n = size(sk,1);
[Y,X] = meshgrid(1:n,1:n);
q = 100;
t = linspace(0,1,q);
x = x1*t+x2*(1-t); y = y1*t+y2*(1-t);
if r==0
x = round( x ); y = round( y );
sk( x+(y-1)*n ) = 1;
else
for k=1:q
I = find((X-x(k)).^2 + (Y-y(k)).^2 <= r^2 );
sk(I) = 1;
end
end
function M = gen_noisy_image(n,alpha)
% gen_noisy_image - generate a noisy cloud-like image.
%
% M = gen_noisy_image(n,alpha);
%
% generate an image M whose Fourier spectrum amplitude is
% |M^(omega)| = 1/f^{omega}
%
% Copyright (c) 2004 Gabriel Peyr?
if nargin<1
n = 128;
end
if nargin<2
alpha = 1.5;
end
if mod(n(1),2)==0
x = -n/2:n/2-1;
else
x = -(n-1)/2:(n-1)/2;
end
[Y,X] = meshgrid(x,x);
d = sqrt(X.^2 + Y.^2) + 0.1;
f = rand(n)*2*pi;
M = (d.^(-alpha)) .* exp(f*1i);
% M = real(ifft2(fftshift(M)));
M = ifftshift(M);
M = real( ifft2(M) );
function y = gen_signal_2d(n,alpha)
% gen_signal_2d - generate a 2D C^\alpha signal of length n x n.
% gen_signal_2d(n,alpha) generate a 2D signal C^alpha.
%
% The signal is scale in [0,1].
%
% Copyright (c) 2003 Gabriel Peyr?
% new new method
[Y,X] = meshgrid(0:n-1, 0:n-1);
A = X+Y+1;
B = X-Y+n+1;
a = gen_signal(2*n+1, alpha);
b = gen_signal(2*n+1, alpha);
y = a(A).*b(B);
% M = a(1:n)*b(1:n)';
return;
% new method
h = (-n/2+1):(n/2); h(n/2)=1;
[X,Y] = meshgrid(h,h);
h = sqrt(X.^2+Y.^2+1).^(-alpha-1/2);
h = h .* exp( 2i*pi*rand(n,n) );
h = fftshift(h);
y = real( ifft2(h) );
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
return;
%% old code
y = rand(n,n);
y = y - mean(mean(y));
for i=1:alpha
y = cumsum(cumsum(y)')';
y = y - mean(mean(y));
end
m1 = min(min(y));
m2 = max(max(y));
y = (y-m1)/(m2-m1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function M = draw_rectangle(r,n)
x = linspace(0,1,n);
[Y,X] = meshgrid(x,x);
M = double( (X>=r(1)) & (X<=r(3)) & (Y>=r(2)) & (Y<=r(4)) ) ;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
resize_img.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/total-variation/toolbox/resize_img.m
| 4,491 |
utf_8
|
08e13146c462c4c031869291d64de7a5
|
function resize_img(imnames, Voxdim, BB, ismask)
% resize_img -- resample images to have specified voxel dims and BBox
% resize_img(imnames, voxdim, bb, ismask)
%
% Output images will be prefixed with 'r', and will have voxel dimensions
% equal to voxdim. Use NaNs to determine voxdims from transformation matrix
% of input image(s).
% If bb == nan(2,3), bounding box will include entire original image
% Origin will move appropriately. Use world_bb to compute bounding box from
% a different image.
%
% Pass ismask=true to re-round binary mask values (avoid
% growing/shrinking masks due to linear interp)
%
% See also voxdim, world_bb
% Based on John Ashburner's reorient.m
% http://www.sph.umich.edu/~nichols/JohnsGems.html#Gem7
% http://www.sph.umich.edu/~nichols/JohnsGems5.html#Gem2
% Adapted by Ged Ridgway -- email bugs to [email protected]
% This version doesn't check spm_flip_analyze_images -- the handedness of
% the output image and matrix should match those of the input.
% Check spm version:
if exist('spm_select','file') % should be true for spm5
spm5 = 1;
elseif exist('spm_get','file') % should be true for spm2
spm5 = 0;
else
error('Can''t find spm_get or spm_select; please add SPM to path')
end
spm_defaults;
% prompt for missing arguments
if ( ~exist('imnames','var') || isempty(char(imnames)) )
if spm5
imnames = spm_select(inf, 'image', 'Choose images to resize');
else
imnames = spm_get(inf, 'img', 'Choose images to resize');
end
end
% check if inter fig already open, don't close later if so...
Fint = spm_figure('FindWin', 'Interactive'); Fnew = [];
if ( ~exist('Voxdim', 'var') || isempty(Voxdim) )
Fnew = spm_figure('GetWin', 'Interactive');
Voxdim = spm_input('Vox Dims (NaN for "as input")? ',...
'+1', 'e', '[nan nan nan]', 3);
end
if ( ~exist('BB', 'var') || isempty(BB) )
Fnew = spm_figure('GetWin', 'Interactive');
BB = spm_input('Bound Box (NaN => original)? ',...
'+1', 'e', '[nan nan nan; nan nan nan]', [2 3]);
end
if ~exist('ismask', 'var')
ismask = false;
end
if isempty(ismask)
ismask = false;
end
% reslice images one-by-one
vols = spm_vol(imnames);
for V=vols'
% (copy to allow defaulting of NaNs differently for each volume)
voxdim = Voxdim;
bb = BB;
% default voxdim to current volume's voxdim, (from mat parameters)
if any(isnan(voxdim))
vprm = spm_imatrix(V.mat);
vvoxdim = vprm(7:9);
voxdim(isnan(voxdim)) = vvoxdim(isnan(voxdim));
end
voxdim = voxdim(:)';
mn = bb(1,:);
mx = bb(2,:);
% default BB to current volume's
if any(isnan(bb(:)))
vbb = world_bb(V);
vmn = vbb(1,:);
vmx = vbb(2,:);
mn(isnan(mn)) = vmn(isnan(mn));
mx(isnan(mx)) = vmx(isnan(mx));
end
% voxel [1 1 1] of output should map to BB mn
% (the combination of matrices below first maps [1 1 1] to [0 0 0])
mat = spm_matrix([mn 0 0 0 voxdim])*spm_matrix([-1 -1 -1]);
% voxel-coords of BB mx gives number of voxels required
% (round up if more than a tenth of a voxel over)
imgdim = ceil(mat \ [mx 1]' - 0.1)';
% output image
VO = V;
[pth,nam,ext] = fileparts(V.fname);
VO.fname = fullfile(pth,['r' nam ext]);
VO.dim(1:3) = imgdim(1:3);
VO.mat = mat;
VO = spm_create_vol(VO);
spm_progress_bar('Init',imgdim(3),'reslicing...','planes completed');
for i = 1:imgdim(3)
M = inv(spm_matrix([0 0 -i])*inv(VO.mat)*V.mat);
img = spm_slice_vol(V, M, imgdim(1:2), 1); % (linear interp)
if ismask
img = round(img);
end
spm_write_plane(VO, img, i);
spm_progress_bar('Set', i)
end
spm_progress_bar('Clear');
end
% call spm_close_vol if spm2
if ~spm5
spm_close_vol(VO);
end
if (isempty(Fint) && ~isempty(Fnew))
% interactive figure was opened by this script, so close it again.
close(Fnew);
end
disp('Done.')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function bb = world_bb(V)
% world-bb -- get bounding box in world (mm) coordinates
d = V.dim(1:3);
% corners in voxel-space
c = [ 1 1 1 1
1 1 d(3) 1
1 d(2) 1 1
1 d(2) d(3) 1
d(1) 1 1 1
d(1) 1 d(3) 1
d(1) d(2) 1 1
d(1) d(2) d(3) 1 ]';
% corners in world-space
tc = V.mat(1:3,1:4)*c;
% bounding box (world) min and max
mn = min(tc,[],2)';
mx = max(tc,[],2)';
bb = [mn; mx];
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
perform_wavortho_transf.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/orthobases/perform_wavortho_transf.m
| 2,736 |
utf_8
|
362bed43d951f6bdefb520003047e2ea
|
function f = perform_wavortho_transf(f,Jmin,dir,options)
% perform_wavortho_transf - compute orthogonal wavelet transform
%
% fw = perform_wavortho_transf(f,Jmin,dir,options);
%
% You can give the filter in options.h.
%
% Works in arbitrary dimension.
%
% Copyright (c) 2009 Gabriel Peyre
options.null = 0;
h = getoptions(options,'h', compute_wavelet_filter('Daubechies',4) );
g = [0 h(length(h):-1:2)] .* (-1).^(1:length(h));
n = size(f,1);
Jmax = log2(n)-1;
if dir==1
%%% FORWARD %%%
for j=Jmax:-1:Jmin
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
a = cat(d, subsampling(cconvol(a,h,d),d), subsampling(cconvol(a,g,d),d) );
end
f = subassign(f,sel,a);
end
else
%%% FORWARD %%%
for j=Jmin:Jmax
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
w = subselectdim(a,2^j+1:2^(j+1),d);
a = subselectdim(a,1:2^j,d);
a = cconvol(upsampling(a,d),reverse(h),d) + cconvol(upsampling(w,d),reverse(g),d);
end
f = subassign(f,sel,a);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselect(f,sel)
switch nb_dims(f)
case 1
f = f(sel);
case 2
f = f(sel,sel);
case 3
f = f(sel,sel,sel);
case 4
f = f(sel,sel,sel,sel);
case 5
f = f(sel,sel,sel,sel,sel);
case 6
f = f(sel,sel,sel,sel,sel,sel);
case 7
f = f(sel,sel,sel,sel,sel,sel,sel);
case 8
f = f(sel,sel,sel,sel,sel,sel,sel,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselectdim(f,sel,d)
switch d
case 1
f = f(sel,:,:,:,:,:,:,:);
case 2
f = f(:,sel,:,:,:,:,:,:);
case 3
f = f(:,:,sel,:,:,:,:,:);
case 4
f = f(:,:,:,sel,:,:,:,:);
case 5
f = f(:,:,:,:,sel,:,:,:);
case 6
f = f(:,:,:,:,:,sel,:,:);
case 7
f = f(:,:,:,:,:,:,sel,:);
case 8
f = f(:,:,:,:,:,:,:,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subassign(f,sel,g)
switch nb_dims(f)
case 1
f(sel) = g;
case 2
f(sel,sel) = g;
case 3
f(sel,sel,sel) = g;
case 4
f(sel,sel,sel,sel) = g;
case 5
f(sel,sel,sel,sel,sel) = g;
case 6
f(sel,sel,sel,sel,sel,sel) = g;
case 7
f(sel,sel,sel,sel,sel,sel,sel) = g;
case 8
f(sel,sel,sel,sel,sel,sel,sel,sel) = g;
otherwise
error('Not implemented');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
nbECGM.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/displ-interp-2d/toolbox-lsap/nbECGM.m
| 737 |
utf_8
|
12c013e9e8fa1ded80b1fdb944a77e4f
|
% -----------------------------------------------------------
% file: nbECGM.m
% -----------------------------------------------------------
% authors: Sebastien Bougleux (UNICAEN) and Luc Brun (ENSICAEN)
% institution: Normandie Univ, CNRS - ENSICAEN - UNICAEN, GREYC UMR 6072
% -----------------------------------------------------------
% This file is part of LSAPE.
% LSAPE is free software: you can redistribute it and/or modify
% it under the terms of the CeCILL-C License. See README file
% for more details.
% -----------------------------------------------------------
function nb = nbECGM(nbU,nbV)
nb = 0;
for p=0:min(nbU,nbV)
nb = nb + factorial(p) * nchoosek(nbU,p) * nchoosek(nbV,p);
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
showDecoratedTiles.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/penrose/showDecoratedTiles.m
| 2,810 |
utf_8
|
335ec04536c1ee3229b4817c7b9de25a
|
function showDecoratedTiles(T)
%showDecoratedTiles Show Penrose rhombus tiles with connecting arcs.
%
% showDecoratedTiles(T) displays the Penrose rhombus tiles constructed
% from the triangles in the input table, T. Each triangle is decorated
% with arcs so that the arcs connect smoothly from triangle to
% triangle, resulting in an interesting geometric pattern overlaid on
% the Penrose tiles.
%
% EXAMPLE
% Decompose a B triangle 4 times and display the resulting rhombus
% tiles.
%
% t = bTriangle([],-1,1);
% for k = 1:4
% t = decomposeTriangles(t);
% end
% showDecoratedTiles(t)
% Copyright 2018 The MathWorks, Inc.
showTiles(T);
[arc1,arc2] = triangleCurves(T);
arc_color = [255 255 191]/255;
line(real(arc1),imag(arc1),...
'LineWidth',0.5,...
'Color',arc_color);
line(real(arc2),imag(arc2),...
'LineWidth',3,...
'Color',arc_color);
axis equal
function [arc1,arc2] = triangleCurves(T)
arc1 = [];
arc2 = [];
for k = 1:height(T)
t_k = T(k,:);
switch t_k.Type
case 'A'
[arc1_k,arc2_k] = arcsA(t_k.Apex,t_k.Left,t_k.Right);
case 'Ap'
[arc1_k,arc2_k] = arcsAp(t_k.Apex,t_k.Left,t_k.Right);
case 'B'
[arc1_k,arc2_k] = arcsB(t_k.Apex,t_k.Left,t_k.Right);
case 'Bp'
[arc1_k,arc2_k] = arcsBp(t_k.Apex,t_k.Left,t_k.Right);
end
arc1 = [arc1 arc1_k NaN];
arc2 = [arc2 arc2_k NaN];
end
function [arc1,arc2] = arcsA(P1,P2,P3)
ray = P1 - P2;
theta1 = angle(ray);
theta2 = theta1 - deg2rad(72);
theta = linspace(theta1,theta2,10);
arc1 = P2 + 0.25 * abs(ray) * exp(1i * theta);
ray = P1 - P3;
theta1 = angle(ray);
theta2 = theta1 + deg2rad(72);
theta = linspace(theta1,theta2,10);
arc2 = P3 + 0.25 * abs(ray) * exp(1i * theta);
function [arc1,arc2] = arcsAp(P1,P2,P3)
ray = P1 - P2;
theta1 = angle(ray);
theta2 = theta1 - deg2rad(72);
theta = linspace(theta1,theta2,10);
arc2 = P2 + 0.25 * abs(ray) * exp(1i * theta);
ray = P1 - P3;
theta1 = angle(ray);
theta2 = theta1 + deg2rad(72);
theta = linspace(theta1,theta2,10);
arc1 = P3 + 0.25 * abs(ray) * exp(1i * theta);
function [arc1,arc2] = arcsB(P1,P2,P3)
ray = P1 - P2;
theta1 = angle(ray);
theta2 = theta1 - deg2rad(36);
theta = linspace(theta1,theta2,10);
arc2 = P2 + 0.75 * abs(ray) * exp(1i * theta);
ray = P1 - P3;
theta1 = angle(ray);
theta2 = theta1 + deg2rad(36);
theta = linspace(theta1,theta2,10);
arc1 = P3 + 0.25 * abs(ray) * exp(1i * theta);
function [arc1,arc2] = arcsBp(P1,P2,P3)
ray = P1 - P2;
theta1 = angle(ray);
theta2 = theta1 - deg2rad(36);
theta = linspace(theta1,theta2,10);
arc1 = P2 + 0.25 * abs(ray) * exp(1i * theta);
ray = P1 - P3;
theta1 = angle(ray);
theta2 = theta1 + deg2rad(36);
theta = linspace(theta1,theta2,10);
arc2 = P3 + 0.75 * abs(ray) * exp(1i * theta);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
isoscelesTriangle.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/penrose/isoscelesTriangle.m
| 1,580 |
utf_8
|
fb942b8fbc4f919cb973dd5524fac1be
|
function [apex,left,right] = isoscelesTriangle(apex,left,right,theta)
%isoscelesTriangle Isosceles triangle.
% [apex,left,right] = isoscelesTriangle(apex,left,right,theta) returns
% the three vertices of an isosceles triangle given any two vertices and
% the apex angle (in degrees). Triangle vertices are represented as
% points in the complex plane. Specify the unknown input vertex as [].
%
% If none of the input vertices is empty, then they are returned
% unmodified.
%
% EXAMPLE
% Compute the isosceles triangle with apex at (0,1), left base vertex at
% (0,0), and an apex angle of 36 degrees.
%
% [apex,left,right] = isoscelesTriangle(1i,0,[],36)
% v = [apex left right apex];
% plot(real(v),imag(v),'LineWidth',2)
% axis equal
% Copyright 2018 The MathWorks, Inc.
if isempty(apex)
base_to_side_ratio = sqrt(2 - 2*cos(deg2rad(theta)));
base = right - left;
apex = left + (abs(base)/base_to_side_ratio) * exp(1i * (angle(base) + deg2rad((180-theta)/2)));
apex = scrub(apex);
elseif isempty(left)
right_side = right - apex;
left = apex + abs(right_side) * exp(1i * (angle(right_side) - deg2rad(theta)));
left = scrub(left);
elseif isempty(right)
left_side = left - apex;
right = apex + abs(left_side) * exp(1i * (angle(left_side) + deg2rad(theta)));
right = scrub(right);
end
function z = scrub(z)
% z = scrub(z) removes unsightly real or imaginary part.
if abs(real(z)) < 10*eps(abs(imag(z)))
z = imag(z)*1i;
end
if abs(imag(z)) < 10*eps(abs(real(z)))
z = real(z);
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
showLabeledTriangles.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/penrose/showLabeledTriangles.m
| 2,695 |
utf_8
|
8d390c710fc92875de69726b2d36e2ea
|
function showLabeledTriangles(T)
%showLabeledTriangles Show triangles with type and side labels.
%
% showLabeledTriangles(T) shows the outline of each triangle contained
% in the input table. Each row of the input table has the form
% returned by aTriangle, apTriangle, bTriangle, or bpTriangle. Each
% displayed triangled is labeled according to type: A, A', B, or B'.
% Each triangle side is marked with a symbol that helps indicate a
% correct or incorrect tiling.
%
% EXAMPLE
%
% Show how a B triangle is decomposed into three triangles (of type A,
% B, and B') according to Penrose tiling rules.
%
% t = bTriangle([],-1,1);
% t1 = decomposeTriangles(t);
% showLabeledTriangles(t1)
% Copyright 2018 The MathWorks, Inc.
showTriangles(T);
vertices = [T.Left T.Apex T.Right];
centroids = mean(vertices,2);
cx = real(centroids);
cy = imag(centroids);
labels = cellstr(T.Type);
labels = strrep(labels,'Ap','A''');
labels = strrep(labels,'Bp','B''');
hold on
text(cx,cy,labels,...
'HorizontalAlignment','center',...
'VerticalAlignment','middle',...
'FontWeight','bold',...
'FontSize',14);
labelSides(T(T.Type == "A",:),...
0.5,{'LineStyle','none','Marker','o','Color','k','MarkerSize',15},...
0.5,{'LineStyle','none','Marker','s','Color','k','MarkerSize',12},...
0.6,{'LineStyle','none','Marker','*','Color','k','MarkerSize',14});
labelSides(T(T.Type == "Ap",:),...
0.5,{'LineStyle','none','Marker','s','Color','k','MarkerSize',12},...
0.5,{'LineStyle','none','Marker','o','Color','k','MarkerSize',15},...
0.4,{'LineStyle','none','Marker','*','Color','k','MarkerSize',14});
labelSides(T(T.Type == "B",:),...
0.5,{'LineStyle','none','Marker','s','Color','k','MarkerSize',12},...
0.5,{'LineStyle','none','Marker','o','Color','k','MarkerSize',15},...
0.6,{'LineStyle','none','Marker','p','Color','k','MarkerSize',16});
labelSides(T(T.Type == "Bp",:),...
0.5,{'LineStyle','none','Marker','o','Color','k','MarkerSize',15},...
0.5,{'LineStyle','none','Marker','s','Color','k','MarkerSize',12},...
0.4,{'LineStyle','none','Marker','p','Color','k','MarkerSize',16});
hold off
function labelSides(T,alpha_left,line_params_left,alpha_right,line_params_right,alpha_base,line_params_base)
side1_label_point = T.Apex + alpha_left*(T.Left - T.Apex);
plot(real(side1_label_point),imag(side1_label_point),line_params_left{:});
side2_label_point = T.Apex + alpha_right*(T.Right - T.Apex);
plot(real(side2_label_point),imag(side2_label_point),line_params_right{:});
base_label_point = T.Left + alpha_base*(T.Right - T.Left);
plot(real(base_label_point),imag(base_label_point),line_params_base{:});
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
solveTSP.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/tsp/solveTSP.m
| 3,663 |
utf_8
|
20479919ca2129026113b1c9c3f48ee5
|
function varargout = solveTSP( cities, display, maxIteration, order)
% cities = solveTSP( cities, maxItt, display)
%
% cities - An Nx2 matrix containing cartesian coordinates of the "cities"
% beeing visited. The initial trail is assumed from the first city to the
% scond and so on...
%
% display - bolean flag decide if to display the progress of the program (slows the running time).
% default = false;
%
% maxIteration - maximum iterations for the program
% default = 10,000
%
%
% [cities ind] = solveTSP( cities, display) returns the aranged cities and
% an index vector of the visiting order
%
% [cities ind totalDist] = solveTSP( cities, display)
% totalDist is the route total distance
%
% demo1:
% cities = solveTSP( rand(100,2), true );
%
% demo2:
% t = (0:999)' /1000;
% cities = [ t.^2.*cos( t*30 ) t.^2.*sin( t*30 ) ];
% [ans ind] = sort( rand(1000,1) );
% [cities ind] = solveTSP( cities(ind,:), true );
if nargin < 2
display = false;
end
if nargin<3
%maxIteration = 1e5;
maxIteration = 1000;
end
siz = size(cities);
if siz(2) ~= 2
error( 'The program is expecting cities to be an Nx2 matix of cartesian coordinates' );
end
N = siz(1);
if nargin<4
order = (1:N)'; % initial cities visit order
end
if display
hFig = gcf; % figure;
hAx = gca;
updateRate = ceil( N/50 );
end
itt = 1;
maxItt = min(20*N,maxIteration);
noChange = 0;
while itt < maxItt && noChange < N
dist = calcDistVec( cities(order,:),1 ); % travel distance between the cities
%% ----------- Displaying current route -----------------------
if display && ~mod(itt,updateRate) && ishandle( hFig )
hold(hAx,'off');
plot( hAx, cities( order,1),cities( order,2),'r.' );
hold( hAx,'on');
plot( hAx, cities( order,1),cities( order,2) );
str = {[ 'iteration: ' num2str( itt ) ] ;
[ 'total route: ' num2str( sum( dist) ) ] };
title( hAx,str );
pause(0.02)
end
flip = mod( itt-1, N-3 )+2 ;
untie = dist(1:end-flip) + dist(flip+1:end); % the distance saved by untying a loop
shufledDist = calcDistVec( cities( order,:),flip );
connect = shufledDist(1:end-1) + shufledDist( 2:end); % the distance payed by connecting the loop (after flip)
benifit = connect - untie; % "what's the distance benifit from this loop fliping
%% --------------- Finding the optimal flips (most benficial) ----------------
localMin = imerode(benifit,ones(2*flip+1,1) );
minimasInd = find( localMin == benifit);
reqFlips = minimasInd( benifit(minimasInd) < -eps );
%% -------- fliping all loops found worth fliping --------------------
prevOrd = order;
for n=1:numel( reqFlips )
order( reqFlips(n) : reqFlips(n)+flip-1 ) = order( reqFlips(n) +flip-1: -1 :reqFlips(n) );
end
%% ------- counting how many iterations there was no improvement
if isequal( order,prevOrd )
noChange = noChange + 1;
else
noChange = 0;
end
itt = itt+1;
end % while itt < maxItt && noChange < N
output = {cities( order,:), order, sum( dist)};
varargout = output(1:nargout);
function dist = calcDistVec( cord,offset )
% dist = calcDistVec( cord,offset )
% offset is the number of cities to calculate the distence between
% the distance for the first city is allway 0
dist = zeros( size(cord,1)-offset+1,1 );
temp = cord( 1:end-offset,:) - cord( offset+1:end,:);
dist(2:end) = sqrt( sum(temp.^2,2) );
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
tsp_ga.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/tsp/tsp_ga.m
| 9,855 |
utf_8
|
d7af84e7693bc9af24e3d4164fd89ae6
|
%TSP_GA Traveling Salesman Problem (TSP) Genetic Algorithm (GA)
% Finds a (near) optimal solution to the TSP by setting up a GA to search
% for the shortest route (least distance for the salesman to travel to
% each city exactly once and return to the starting city)
%
% Summary:
% 1. A single salesman travels to each of the cities and completes the
% route by returning to the city he started from
% 2. Each city is visited by the salesman exactly once
%
% Input:
% USERCONFIG (structure) with zero or more of the following fields:
% - XY (float) is an Nx2 matrix of city locations, where N is the number of cities
% - DMAT (float) is an NxN matrix of point to point distances/costs
% - POPSIZE (scalar integer) is the size of the population (should be divisible by 4)
% - NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
% - SHOWPROG (scalar logical) shows the GA progress if true
% - SHOWRESULT (scalar logical) shows the GA results if true
% - SHOWWAITBAR (scalar logical) shows a waitbar if true
%
% Input Notes:
% 1. Rather than passing in a structure containing these fields, any/all of
% these inputs can be passed in as parameter/value pairs in any order instead.
% 2. Field/parameter names are case insensitive but must match exactly otherwise.
%
% Output:
% RESULTSTRUCT (structure) with the following fields:
% (in addition to a record of the algorithm configuration)
% - OPTROUTE (integer array) is the best route found by the algorithm
% - MINDIST (scalar float) is the cost of the best route
%
% Usage:
% tsp_ga
% -or-
% tsp_ga(userConfig)
% -or-
% resultStruct = tsp_ga;
% -or-
% resultStruct = tsp_ga(userConfig);
% -or-
% [...] = tsp_ga('Param1',Value1,'Param2',Value2, ...);
%
% Example:
% % Let the function create an example problem to solve
% tsp_ga;
%
% Example:
% % Request the output structure from the solver
% resultStruct = tsp_ga;
%
% Example:
% % Pass a random set of user-defined XY points to the solver
% userConfig = struct('xy',10*rand(50,2));
% resultStruct = tsp_ga(userConfig);
%
% Example:
% % Pass a more interesting set of XY points to the solver
% n = 100;
% phi = (sqrt(5)-1)/2;
% theta = 2*pi*phi*(0:n-1);
% rho = (1:n).^phi;
% [x,y] = pol2cart(theta(:),rho(:));
% xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
% userConfig = struct('xy',xy);
% resultStruct = tsp_ga(userConfig);
%
% Example:
% % Pass a random set of 3D (XYZ) points to the solver
% xyz = 10*rand(50,3);
% userConfig = struct('xy',xyz);
% resultStruct = tsp_ga(userConfig);
%
% Example:
% % Change the defaults for GA population size and number of iterations
% userConfig = struct('popSize',200,'numIter',1e4);
% resultStruct = tsp_ga(userConfig);
%
% Example:
% % Turn off the plots but show a waitbar
% userConfig = struct('showProg',false,'showResult',false,'showWaitbar',true);
% resultStruct = tsp_ga(userConfig);
%
% See also: mtsp_ga, tsp_nn, tspo_ga, tspof_ga, tspofs_ga, distmat
%
% Author: Joseph Kirk
% Email: [email protected]
% Release: 3.0
% Release Date: 05/01/2014
function varargout = tsp_ga(varargin)
% Initialize default configuration
defaultConfig.xy = 10*rand(50,2);
defaultConfig.dmat = [];
defaultConfig.popSize = 100;
defaultConfig.numIter = 1e4;
defaultConfig.showProg = true;
defaultConfig.showResult = true;
defaultConfig.showWaitbar = false;
% Interpret user configuration inputs
if ~nargin
userConfig = struct();
elseif isstruct(varargin{1})
userConfig = varargin{1};
else
try
userConfig = struct(varargin{:});
catch
error('Expected inputs are either a structure or parameter/value pairs');
end
end
% Override default configuration with user inputs
configStruct = get_config(defaultConfig,userConfig);
% Extract configuration
xy = configStruct.xy;
dmat = configStruct.dmat;
popSize = configStruct.popSize;
numIter = configStruct.numIter;
showProg = configStruct.showProg;
showResult = configStruct.showResult;
showWaitbar = configStruct.showWaitbar;
if isempty(dmat)
nPoints = size(xy,1);
a = meshgrid(1:nPoints);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),nPoints,nPoints);
end
% Verify Inputs
[N,dims] = size(xy);
[nr,nc] = size(dmat);
if N ~= nr || N ~= nc
error('Invalid XY or DMAT inputs!')
end
n = N;
% Sanity Checks
popSize = 4*ceil(popSize/4);
numIter = max(1,round(real(numIter(1))));
showProg = logical(showProg(1));
showResult = logical(showResult(1));
showWaitbar = logical(showWaitbar(1));
% Initialize the Population
pop = zeros(popSize,n);
pop(1,:) = (1:n);
for k = 2:popSize
pop(k,:) = randperm(n);
end
% Run the GA
globalMin = Inf;
totalDist = zeros(1,popSize);
distHistory = zeros(1,numIter);
tmpPop = zeros(4,n);
newPop = zeros(popSize,n);
if showProg
figure('Name','TSP_GA | Current Best Solution','Numbertitle','off');
hAx = gca;
end
if showWaitbar
hWait = waitbar(0,'Searching for near-optimal solution ...');
end
for iter = 1:numIter
% Evaluate Each Population Member (Calculate Total Distance)
for p = 1:popSize
d = dmat(pop(p,n),pop(p,1)); % Closed Path
for k = 2:n
d = d + dmat(pop(p,k-1),pop(p,k));
end
totalDist(p) = d;
end
% Find the Best Route in the Population
[minDist,index] = min(totalDist);
distHistory(iter) = minDist;
if minDist < globalMin
globalMin = minDist;
optRoute = pop(index,:);
if showProg
% Plot the Best Route
rte = optRoute([1:n 1]);
if dims > 2, plot3(hAx,xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
else plot(hAx,xy(rte,1),xy(rte,2),'r.-'); end
title(hAx,sprintf('Total Distance = %1.4f, Iteration = %d',minDist,iter));
drawnow;
end
end
% Genetic Algorithm Operators
randomOrder = randperm(popSize);
for p = 4:4:popSize
rtes = pop(randomOrder(p-3:p),:);
dists = totalDist(randomOrder(p-3:p));
[ignore,idx] = min(dists); %#ok
bestOf4Route = rtes(idx,:);
routeInsertionPoints = sort(ceil(n*rand(1,2)));
I = routeInsertionPoints(1);
J = routeInsertionPoints(2);
for k = 1:4 % Mutate the Best to get Three New Routes
tmpPop(k,:) = bestOf4Route;
switch k
case 2 % Flip
tmpPop(k,I:J) = tmpPop(k,J:-1:I);
case 3 % Swap
tmpPop(k,[I J]) = tmpPop(k,[J I]);
case 4 % Slide
tmpPop(k,I:J) = tmpPop(k,[I+1:J I]);
otherwise % Do Nothing
end
end
newPop(p-3:p,:) = tmpPop;
end
pop = newPop;
% Update the waitbar
if showWaitbar && ~mod(iter,ceil(numIter/325))
waitbar(iter/numIter,hWait);
end
end
if showWaitbar
close(hWait);
end
if showResult
% Plots the GA Results
figure('Name','TSP_GA | Results','Numbertitle','off');
subplot(2,2,1);
pclr = ~get(0,'DefaultAxesColor');
if dims > 2, plot3(xy(:,1),xy(:,2),xy(:,3),'.','Color',pclr);
else plot(xy(:,1),xy(:,2),'.','Color',pclr); end
title('City Locations');
subplot(2,2,2);
imagesc(dmat(optRoute,optRoute));
title('Distance Matrix');
subplot(2,2,3);
rte = optRoute([1:n 1]);
if dims > 2, plot3(xy(rte,1),xy(rte,2),xy(rte,3),'r.-');
else plot(xy(rte,1),xy(rte,2),'r.-'); end
title(sprintf('Total Distance = %1.4f',minDist));
subplot(2,2,4);
plot(distHistory,'b','LineWidth',2);
title('Best Solution History');
set(gca,'XLim',[0 numIter+1],'YLim',[0 1.1*max([1 distHistory])]);
end
% Return Output
if nargout
resultStruct = struct( ...
'xy', xy, ...
'dmat', dmat, ...
'popSize', popSize, ...
'numIter', numIter, ...
'showProg', showProg, ...
'showResult', showResult, ...
'showWaitbar', showWaitbar, ...
'optRoute', optRoute, ...
'minDist', minDist);
varargout = {resultStruct};
end
end
% Subfunction to override the default configuration with user inputs
function config = get_config(defaultConfig,userConfig)
% Initialize the configuration structure as the default
config = defaultConfig;
% Extract the field names of the default configuration structure
defaultFields = fieldnames(defaultConfig);
% Extract the field names of the user configuration structure
userFields = fieldnames(userConfig);
nUserFields = length(userFields);
% Override any default configuration fields with user values
for i = 1:nUserFields
userField = userFields{i};
isField = strcmpi(defaultFields,userField);
if nnz(isField) == 1
thisField = defaultFields{isField};
config.(thisField) = userConfig.(userField);
end
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
nbECGM.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/tsp/toolbox-lsap/nbECGM.m
| 737 |
utf_8
|
12c013e9e8fa1ded80b1fdb944a77e4f
|
% -----------------------------------------------------------
% file: nbECGM.m
% -----------------------------------------------------------
% authors: Sebastien Bougleux (UNICAEN) and Luc Brun (ENSICAEN)
% institution: Normandie Univ, CNRS - ENSICAEN - UNICAEN, GREYC UMR 6072
% -----------------------------------------------------------
% This file is part of LSAPE.
% LSAPE is free software: you can redistribute it and/or modify
% it under the terms of the CeCILL-C License. See README file
% for more details.
% -----------------------------------------------------------
function nb = nbECGM(nbU,nbV)
nb = 0;
for p=0:min(nbU,nbV)
nb = nb + factorial(p) * nchoosek(nbU,p) * nchoosek(nbV,p);
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
synth.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/texture-synthesis/synth.m
| 7,300 |
utf_8
|
63e55eb25b6cd0ff71909e7414adf4fb
|
function [Image, Mapping] = synth(rawSample, winsize, newRows, newCols, outpath)
% Non-parametric Texture Synthesis using Efros & Leung's algorithm
% Author: Alex Rubinsteyn (alex.rubinsteyn at gmail)
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
% 02110-1301 USA
% Inputs:
% 'filename': the image file containing the sample image (the texture to grow)
% 'winsize': the edge length of the window to match at each iteration (the window is (winsize x winsize) )
% (newRows, newCols): the size of the output image
% Outputs:
% 'Image': the output image (the synthesized texture)
% 'time': the amount of time it took to perform the synthesis
MaxErrThreshold = 0.1;
% rawSample = im2double(imread(filename));
rawSample = im2double(rawSample);
sample = rawSample;
[rows, cols, channels] = size(sample);
windowlessSize = [(rows - winsize + 1) (cols - winsize + 1)];
halfWindow = (winsize - 1) / 2;
npixels = newRows * newCols;
Image = zeros(newRows, newCols, 3);
Mapping = zeros(newRows, newCols,3);
red_patches = im2col(sample(:, :, 1), [winsize winsize], 'sliding');
green_patches = im2col(sample(:, :, 2), [winsize winsize], 'sliding');
blue_patches = im2col(sample(:, :, 3), [winsize winsize], 'sliding');
%initialize new texture with a random 3x3 patch from the sample
randRow = ceil(rand() * (rows - 2));
randCol = ceil(rand() * (cols - 2));
seedSize = 3;
seedRows = ceil(newRows/2):ceil(newRows/2)+seedSize-1;
seedCols = ceil(newCols/2):ceil(newCols/2)+seedSize-1;
M = sample(randRow:randRow+seedSize-1, randCol:randCol+seedSize-1, :);
if 0
k = length(seedRows);
I = randperm(k*k);
for i=1:3
m = M(:,:,i); m = reshape(m(I), size(m));
M(:,:,i) = m;
end
end
Image(seedRows, seedCols, :) = M;
Mapping(seedRows, seedCols,1) = (randRow:randRow+seedSize-1)' * ones(1,length(seedCols));
Mapping(seedRows, seedCols,2) = ones(length(seedCols),1) * (randCol:randCol+seedSize-1);
nfilled = seedSize * seedSize;
filled = repmat(false, [newRows newCols]);
filled(seedRows, seedCols) = repmat(true, [3 3]);
gaussMask = fspecial('gaussian',winsize, winsize/6.4);
nskipped = 0;
while nfilled < npixels
progress = false;
[pixelRows, pixelCols] = GetUnfilledNeighbors(filled, winsize);
for i = 1:length(pixelRows)
pixelRow = pixelRows(i);
pixelCol = pixelCols(i);
rowRange = pixelRow-halfWindow:pixelRow+halfWindow;
colRange = pixelCol - halfWindow:pixelCol + halfWindow;
deadRows = rowRange < 1 | rowRange > newRows;
deadCols = colRange < 1 | colRange > newCols;
if sum(deadRows) + sum(deadCols) > 0
safeRows = rowRange(~deadRows);
safeCols = colRange(~deadCols);
template = zeros(winsize, winsize, 3);
template(~deadRows, ~deadCols, :) = Image(safeRows, safeCols, :);
validMask = repmat(false, [winsize winsize]);
validMask(~deadRows, ~deadCols) = filled(safeRows, safeCols);
else
template = Image(rowRange, colRange, :);
validMask = filled(rowRange, colRange);
end
[bestMatches, SSD] = FindMatches(template, validMask, gaussMask, red_patches, green_patches, blue_patches);
matchIdx = RandomPick(bestMatches);
matchError = SSD(matchIdx);
if matchError < MaxErrThreshold
[matchRow, matchCol] = ind2sub(windowlessSize, matchIdx);
%match coords are at corner of window and need to be offset
matchRow = matchRow + halfWindow;
matchCol = matchCol + halfWindow;
Mapping(pixelRow, pixelCol,1) = matchRow;
Mapping(pixelRow, pixelCol,2) = matchCol;
Image(pixelRow, pixelCol, :) = sample(matchRow, matchCol, :);
filled(pixelRow, pixelCol) = true;
nfilled = nfilled + 1;
progress = true;
else
nskipped = nskipped + 1;
end
end
progressbar(nfilled,npixels);
if not(exist('k'))
k=1;
end
I = Image + (1-filled);
J = Mapping/max(rows, cols) + (1-filled);
clf;
subplot(1,2,1); image(I); axis image; axis off;
subplot(1,2,2); image(J); axis image; axis off;
drawnow;
imwrite(rescale(I), [outpath 'anim-' znum2str(k,3) '.png' ]);
imwrite(rescale(J), [outpath 'map-' znum2str(k,3) '.png' ]);
k = k+1;
% disp(sprintf('Pixels filled: %d / %d', nfilled, npixels));
%
% figure;
% subplot(2,1,1);
% imshow(filled);
% subplot(2,1,2);
% imshow(Image);
if ~progress
MaxErrThreshold = MaxErrThreshold * 1.1;
disp(sprintf('Incrementing error tolerance to %d', MaxErrThreshold));
end
end
%% Get pixels at edge of synthesized texture
function [pixelRows, pixelCols] = GetUnfilledNeighbors(filled, winsize)
border = bwmorph(filled,'dilate')-filled;
[pixelRows, pixelCols] = find(border);
len = length(pixelRows);
%randomly permute candidate pixels
randIdx = randperm(len);
pixelRows = pixelRows(randIdx);
pixelCols = pixelCols(randIdx);
%sort by number of neighbors
filledSums = colfilt(filled, [winsize winsize], 'sliding', @sum);
numFilledNeighbors = filledSums( sub2ind(size(filled), pixelRows, pixelCols) );
[sorted, sortIndex] = sort(numFilledNeighbors, 1, 'descend');
pixelRows = pixelRows(sortIndex);
pixelCols = pixelCols(sortIndex);
%% Pick a random pixel from valid patches
function idx = RandomPick(matches)
indices = find(matches);
idx = indices(ceil(rand() * length(indices)));
%% Find candidate patches that match template
function [pixelList, SSD] = FindMatches (template, validMask, gaussMask, red_patches, green_patches, blue_patches)
ErrThreshold = 0.3;
[pixels_per_patch, npatches] = size(red_patches);
totalWeight = sum(sum(gaussMask(validMask)));
mask = (gaussMask .* validMask) / totalWeight;
mask_vec = mask(:)';
red = reshape(template(:, :, 1), [pixels_per_patch 1]);
green = reshape(template(:, :, 2), [pixels_per_patch 1]);
blue = reshape(template(:, :, 3), [pixels_per_patch 1]);
red_templates = repmat(red, [1 npatches]);
green_templates = repmat(green, [1 npatches]);
blue_templates = repmat(blue, [1 npatches]);
red_dist = mask_vec * (red_templates - red_patches).^2;
green_dist = mask_vec * (green_templates - green_patches).^2 ;
blue_dist = mask_vec * (blue_templates - blue_patches).^2;
SSD = (red_dist + green_dist + blue_dist);
pixelList = SSD <= min(SSD) * (1+ErrThreshold);
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
spharm.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/spherical-harmonics/spharm.m
| 3,033 |
utf_8
|
eab2f35cc9c57041cd97499a220f93a0
|
% This function generates the Spherical Harmonics basis functions of degree
% L and order M.
%
% SYNTAX: [Ymn,THETA,PHI,X,Y,Z]=spharm4(L,M,RES,PLOT_FLAG);
%
% INPUTS:
%
% L - Spherical harmonic degree, [1x1]
% M - Spherical harmonic order, [1x1]
% RES - Vector of # of points to use [#Theta x #Phi points],[1x2] or [2x1]
% PLOT_FLAG - Binary flag to generates a figure of the spherical harmonic surfaces (DEFAULT=1)
%
%
% OUTPUTS:
%
% Ymn - Spherical harmonics coordinates, [RES(1) x RES(2)]
% THETA - Circumferential coordinates, [RES(1) x RES(2)]
% PHI - Latitudinal coordinates, [RES(1) x RES(2)]
% X,Y,Z - Cartesian coordinates of magnitude, squared, spherical harmonic surface points, [RES(1) x RES(2)]
%
%
% NOTE: It is very important to keep the various usages of THETA and PHI
% straight. For this function THETA is the Azimuthal/Longitude/Circumferential
% coordinate and is defined on the interval [0,2*pi], whereas PHI is the
% Altitude/Latitude/Elevation and is defined on the interval [0,pi]. Also note that
% the conversion to cartesian coordinates requires that PHI be offset by pi/2 so
% that the conversion is on the interval [-pi/2,pi/2].
%
% DBE 2005/09/30
function [Ymn,THETA,PHI,Xm,Ym,Zm]=spharm4(L,M,RES,PLOT_FLAG);
% Define constants (REQUIRED THAT L(DEGREE)>=M(ORDER))
if nargin==0
L=3; % DEGREE
M=2; % ORDER
RES=[55 55];
end
if nargin<3
RES=[25 25];
PLOT_FLAG=1;
end
if nargin<4
PLOT_FLAG=1;
end
if L<M, error('The ORDER (M) must be less than or eqaul to the DEGREE(L).'); end
THETA=linspace(0,2*pi,RES(1)); % Azimuthal/Longitude/Circumferential
PHI =linspace(0, pi,RES(2)); % Altitude /Latitude /Elevation
[THETA,PHI]=meshgrid(THETA,PHI);
Lmn=legendre(L,cos(PHI));
if L~=0
Lmn=squeeze(Lmn(M+1,:,:));
end
a1=((2*L+1)/(4*pi));
a2=factorial(L-M)/factorial(L+M);
C=sqrt(a1*a2);
Ymn=C*Lmn.*exp(i*M*THETA);
[Xm,Ym,Zm]=sph2cart(THETA,PHI-pi/2,abs(Ymn).^2);
[Xr,Yr,Zr]=sph2cart(THETA,PHI-pi/2,real(Ymn).^2);
[Xi,Yi,Zi]=sph2cart(THETA,PHI-pi/2,imag(Ymn).^2);
% [Xp,Yp,Zp]=sph2cart(THETA,PHI-pi/2,angle(Ymn).^2);
if PLOT_FLAG
f=figure; axis off; hold on;
axes('position',[0.0500 0 0.2666 1]);
surf(Xm,Ym,Zm);
axis equal off; %rot3d;
light; lighting phong; camzoom(1.3);
axes('position',[0.3666 0 0.2666 1]);
surf(Xr,Yr,Zr);
axis equal off; %rot3d;
light; lighting phong; camzoom(1.3);
axes('position',[0.6833 0 0.2666 1]);
surf(Xi,Yi,Zi);
axis equal off; %rot3d;
light; lighting phong; camzoom(1.3);
axes('position',[0 0.9 1 0.1]); axis off;
t(1)=text(0.50,0.25,'Spherical Harmonics','HorizontalAlignment','Center');
axes('position',[0 0 1 0.1]); axis off;
t(2)=text(0.20,0.25,['|Y^',num2str(M),'_',num2str(L),'|^2'],'HorizontalAlignment','Center');
t(3)=text(0.50,0.25,['Real(Y^',num2str(M),'_',num2str(L),')^2'],'HorizontalAlignment','Center');
t(4)=text(0.80,0.25,['Imag(Y^',num2str(M),'_',num2str(L),')^2'],'HorizontalAlignment','Center');
setfig(gcf,10,5,12);
end
return
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
check_face_vertex.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/spherical-harmonics/toolbox/check_face_vertex.m
| 669 |
utf_8
|
c940a837f5afef7c3a7f7aed3aff9f7a
|
function [vertex,face] = check_face_vertex(vertex,face, options)
% check_face_vertex - check that vertices and faces have the correct size
%
% [vertex,face] = check_face_vertex(vertex,face);
%
% Copyright (c) 2007 Gabriel Peyre
vertex = check_size(vertex,2,4);
face = check_size(face,3,4);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function a = check_size(a,vmin,vmax)
if isempty(a)
return;
end
if size(a,1)>size(a,2)
a = a';
end
if size(a,1)<3 && size(a,2)==3
a = a';
end
if size(a,1)<=3 && size(a,2)>=3 && sum(abs(a(:,3)))==0
% for flat triangles
a = a';
end
if size(a,1)<vmin || size(a,1)>vmax
error('face or vertex is not of correct size');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
perform_bfgs.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/perceptron/perform_bfgs.m
| 58,067 |
utf_8
|
91b03f91b3bec570bfdda2f700810657
|
function [f, R, info] = perform_bfgs(Grad, f, options)
% perform_bfgs - wrapper to HANSO code
%
% [f, R, info] = perform_bfgs(Grad, f, options);
%
% Grad should return (value, gradient)
% f is an initialization
% options.niter is the number of iterations.
% options.bfgs_memory is the memory for the hessian bookeeping.
% R is filled using options.report which takes as input (f,val).
%
% Copyright (c) 2011 Gabriel Peyre
n = length(f);
pars.nvar = n;
pars.fgname = @(f,pars)Grad(f);
options.x0 = f;
options.nvec = getoptions(options, 'bfgs_memory', 20); % BFGS memory
options.maxit = getoptions(options, 'niter', 1000);
options.prtlevel = 0;
options.normtol = eps;
options.tol = eps;
options.verb = 1;
% options.report = @(x,val)struct('E', val, 'timing', cputime()-t);
[f, R, energy, d, H, iter, info] = bfgs(pars,options);
%
% if (info == 7)
% disp(['Not satisfying Wolf conditions!'])
% end
function [x, R, f, d, H, iter, info, X, G, w, fevalrec, xrec, Hrec] = bfgs(pars, options)
%BFGS The BFGS quasi-Newton minimization algorithm, Version 2.0, 2010
% Basic call:[x, R, f, d] = bfgs(pars)
% Full call: [x, R, f, d, H, iter, info, X, G, w, fevalrec, xrec, Hrec] = bfgs(pars,options)
% Input parameters
% pars is a required struct, with two required fields
% pars.nvar: the number of variables
% pars.fgname: string giving the name of function (in single quotes)
% that returns the function and its gradient at a given input x,
% with call [f,g] = fgtest(x,pars) if pars.fgname is 'fgtest'.
% Any data required to compute the function and gradient may be
% encoded in other fields of pars.
% options is an optional struct, with no required fields
% options.x0: each column is a starting vector of variables
% (default: empty)
% options.nstart: number of starting vectors, generated randomly
% if needed to augment those specified in options.x0
% (default: 10 if options.x0 is not specified)
% options.maxit: max number of iterations
% (default 1000) (applies to each starting vector)
% options.nvec: 0 for full BFGS matrix update, otherwise specifies
% number of vectors to save and use in the limited memory updates
% (default: 0 if pars.nvar <= 100, otherwise 10)
% options.H0:
% for full BFGS: initial inverse Hessian approximation
% (must be positive definite, but this is not checked)
% for limited memory BFGS: same, but applied every iteration
% (must be sparse in this case)
% (default: identity matrix, sparse in limited memory case)
% options.scale:
% for full BFGS: 1 to scale H0 at first iteration, 0 otherwise
% for limited memory BFGS: 1 to scale H0 every time, 0 otherwise
% (default: 1)
% options.ngrad: number of gradients willing to save and use in
% solving QP to check optimality tolerance on smallest vector in
% their convex hull; see also next two options
% (default: min(100, 2*pars.nvar, pars.nvar + 10)
% (1 is recommended if and only if f is known to be smooth)
% options.normtol: termination tolerance on d: smallest vector in
% convex hull of up to options.ngrad gradients
% (default: 1e-6)
% options.evaldist: the gradients used in the termination test
% qualify only if they are evaluated at points approximately
% within distance options.evaldist of x
% (default: 1e-4)
% options.fvalquit: quit if f drops below this value
% (default: -inf)
% options.xnormquit: quit if norm(x) exceeds this value
% (default: inf)
% options.cpumax: quit if cpu time in secs exceeds this
% (default: inf) (applies to total running time)
% options.strongwolfe: 0 for weak Wolfe line search (default)
% 1 for strong Wolfe line search
% (strong Wolfe line search is not recommended for use with
% BFGS; it is very complicated and bad if f is nonsmooth;
% however, it can be useful to simulate an exact line search)
% options.wolfe1: first Wolfe line search parameter
% (ensuring sufficient decrease in function value, default: 0)
% (should be > 0 in theory, but 0 is fine in practice)
% options.wolfe2: second Wolfe line search parameter
% (ensuring algebraic increase (weak) or absolute decrease (strong)
% in projected gradient, default: 0.5)
% (important in theory and practice that this is not 0 or 1,
% except that it can be set to 0 if an exact line search is to be
% simulated, using options.strongwolfe = 1)
% options.quitLSfail: 1 if quit when line search fails, 0 otherwise
% (default: 1, except if options.strongwolfe = 1 and
% options.wolfe2 = 0, simulating exact line search)
% (0 is potentially useful if f is not numerically continuous)
% options.prtlevel: one of 0 (no printing), 1 (minimal), 2 (verbose)
% (default: 1)
%
% Output parameters:
% all return information on the runs for each starting vector
% x: the final iterates
% f: the final function values
% d: the final smallest vectors in the convex hull of the saved gradients
% at termination (the final gradient if options.ngrad == 1)
% H: final BFGS inverse Hessian approximation matrices
% (full BFGS update only, symmetrized so they are exactly symmetric)
% (nan if limited memory updates were used)
% iter: number of iterations
% info: reason for termination:
% 0: tolerance on smallest vector in convex hull of saved gradients met
% 1: max number of iterations reached
% 2: f reached target value
% 3: norm(x) exceeded limit
% 4: cpu time exceeded limit
% 5: f is inf or nan at initial point
% 6: direction not a descent direction due to rounding error
% 7: line search bracketed minimizer but Wolfe conditions not satisfied
% 8: line search did not bracket minimizer: f may be unbounded below
% X: iterates where saved gradients were evaluated (see below)
% G: saved gradients used for computation of smallest vector in convex hull
% of gradients at points near final x
% w: weights giving the smallest vector in the convex hull of the saved
% gradients
% fevalrec: record of all function values evaluated in all line searches,
% including the final accepted values (nans if options.strongwolfe = 1)
% xrec: record of all x iterates
% Hrec: record of all H iterates
% (not symmetrized, may not be symmetric because of rounding error)
% Note: if there is more than one starting vector, then:
% f, iter, info are vectors of length options.nstart
% x, d are matrices of size pars.nvar by options.nstart
% H, X, G, w, xrec, Hrec are cell arrays of length options.nstart, and
% fevalrec is a cell array of cell arrays
% Thus, for example, d(:,i) = G{i}*w{i}, for i = 1,...,options.nstart
%
% BFGS is normally used for optimizing smooth, not necessarily convex,
% functions, for which the convergence rate is generically superlinear.
% But it also works very well for functions that are nonsmooth at their
% minimizers, typically with a linear convergence rate and a final
% inverse Hessian approximation that is very ill conditioned, as long
% as a weak Wolfe line search is used. This version of BFGS will work
% well both for smooth and nonsmooth functions and has a stopping
% criterion that applies for both cases, described above.
% See A.S. Lewis and M.L. Overton, Nonsmooth Optimization via BFGS, 2008.
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% parameter defaults
if nargin == 0
error('bfgs: "pars" is a required input parameter')
end
if nargin == 1
options = [];
end
options = setdefaults(pars, options); % set most default options
options = setx0(pars, options); % augment options.x0 randomly
x0 = options.x0;
nstart = size(x0,2);
cpufinish = cputime + options.cpumax;
fvalquit = options.fvalquit;
xnormquit = options.xnormquit;
prtlevel = options.prtlevel;
% set other options
options = setdefaultsbfgs(pars, options);
for run = 1:nstart
if prtlevel > 0 & nstart > 1
fprintf('bfgs: starting point %d\n', run)
end
options.cpumax = cpufinish - cputime; % time left
if nargout > 10
[x(:,run), R, f(run), d(:,run), HH, iter(run), info(run), X{run}, G{run}, w{run}, ...
fevalrec{run}, xrec{run}, Hrec{run}] = bfgs1run(x0(:,run), pars, options);
elseif nargout > 7 % avoid computing fevalrec, xrec, Hrec which are expensive as they grow inside the main loop
[x(:,run), R, f(run), d(:,run), HH, iter(run), info(run), X{run}, G{run}, w{run}] = bfgs1run(x0(:,run), pars, options);
else % avoid computing unnecessary cell arrays
[x(:,run), R, f(run), d(:,run), HH, iter(run), info(run)] = bfgs1run(x0(:,run), pars, options);
end
% make exactly symmetric (too expensive to do inside optimization loop}
H{run} = (HH + HH')/2;
if cputime > cpufinish | f < fvalquit | norm(x) > xnormquit
break
end
end
if nstart == 1 % no point returning cell arrays of length 1
H = H{1};
if nargout > 10
fevalrec = fevalrec{1};
xrec = xrec{1};
Hrec = Hrec{1}; % don't symmetrize
end
if nargout > 7
X = X{1};
G = G{1};
w = w{1};
end
end
function [x, R, f, d, H, iter, info, X, G, w, fevalrec, xrec, Hrec] = bfgs1run(x0, pars, options)
% Version 2.0, 2010
% make a single run of BFGS from one starting point
% intended to be called by bfgs.m
% outputs:
% x: final iterate
% f: final function value
% d: final smallest vector in convex hull of saved gradients
% H: final inverse Hessian approximation
% iter: number of iterations
% info: reason for termination
% 0: tolerance on smallest vector in convex hull of saved gradients met
% 1: max number of iterations reached
% 2: f reached target value
% 3: norm(x) exceeded limit
% 4: cpu time exceeded limit
% 5: f or g is inf or nan at initial point
% 6: direction not a descent direction (because of rounding)
% 7: line search bracketed minimizer but Wolfe conditions not satisfied
% 8: line search did not bracket minimizer: f may be unbounded below
% X: iterates where saved gradients were evaluated
% G: gradients evaluated at these points
% w: weights defining convex combination d = G*w
% fevalrec: record of all function evaluations in the line searches
% xrec: record of x iterates
% Hrec: record of H iterates
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n = pars.nvar;
fgname = pars.fgname;
normtol = options.normtol;
fvalquit = options.fvalquit;
xnormquit = options.xnormquit;
cpufinish = cputime + options.cpumax;
maxit = options.maxit;
nvec = options.nvec;
prtlevel = options.prtlevel;
strongwolfe = options.strongwolfe;
wolfe1 = options.wolfe1;
wolfe2 = options.wolfe2;
quitLSfail = options.quitLSfail;
ngrad = options.ngrad;
evaldist = options.evaldist;
verb = getoptions(options, 'verb', 1);
report = getoptions(options, 'report', @(x,v)v);
H0 = options.H0;
H = H0; % sparse for limited memory BFGS
scale = options.scale;
x = x0;
if isstr(fgname)
[f,g] = feval(fgname, x, pars);
else
[f,g] = fgname(x, pars);
end
d = g;
G = g;
X = x;
nG = 1;
w = 1;
dnorm = norm(g);
if nvec > 0 % limited memory BFGS
S = [];
Y = [];
end
iter = 0;
if nargout > 9
% so outputs defined if quit immediately
fevalrec{1} = nan; % cell array
xrec = nan*ones(n,1); % not cell array
Hrec{1} = nan; % cell array
end
if isnaninf(f) % better not to generate an error return
if prtlevel > 0
fprintf('bfgs: f is infinite or nan at initial iterate\n')
end
info = 5;
return
elseif isnaninf(g)
if prtlevel > 0
fprintf('bfgs: gradient is infinite or nan at initial iterate\n')
end
info = 5;
return
elseif dnorm < normtol
if prtlevel > 0
fprintf('bfgs: tolerance on gradient satisfied at initial iterate\n')
end
info = 0;
return
elseif f < fvalquit
if prtlevel > 0
fprintf('bfgs: below target objective at initial iterate\n')
end
info = 2;
return
elseif norm(x) > xnormquit
if prtlevel > 0
keyboard
fprintf('bfgs: norm(x) exceeds specified limit at initial iterate\n')
end
info = 3;
return
end
clear R;
for iter = 1:maxit
if verb
progressbar(iter,maxit);
end
R(iter) = report(x,f);
if nvec == 0 % full BFGS
p = -H*g;
else % limited memory BFGS
p = -hgprod(H, g, S, Y); % not H0, as in previous version
end
gtp = g'*p;
if gtp >= 0 | isnan(gtp) % in rare cases, H could contain nans
if prtlevel > 0
fprintf('bfgs: not descent direction, quit at iteration %d, f = %g, dnorm = %5.1e\n',...
iter, f, dnorm)
end
info = 6;
return
end
gprev = g; % for BFGS update
if strongwolfe
% strong Wolfe line search is not recommended
% except to simulate an exact line search
% function values are not returned, so set fevalrecline to nan
fevalrecline = nan;
[alpha, x, f, g, fail] = ...
linesch_sw(x, f, g, p, pars, wolfe1, wolfe2, fvalquit, prtlevel);
if wolfe2 == 0 % exact line search: increase alpha slightly to get
% to other side of any discontinuity in nonsmooth case
increase = 1e-8*(1 + alpha); % positive if alpha = 0
x = x + increase*p;
if prtlevel > 1
fprintf(' exact line sch simulation: slightly increasing step from %g to %g\n', alpha, alpha + increase)
end
[f,g] = feval(pars.fgname, x, pars);
end
else % weak Wolfe line search is the default
[alpha, x, f, g, fail, notused, notused2, fevalrecline] = ...
linesch_ww(x, f, g, p, pars, wolfe1, wolfe2, fvalquit, prtlevel);
end
% for the optimality check:
% discard the saved gradients iff the new point x is not sufficiently
% close to the previous point and replace them by new gradient
if alpha*norm(p) > evaldist
nG = 1;
G = g;
X = x;
% otherwise add new gradient to set of saved gradients,
% discarding oldest if already have ngrad saved gradients
elseif nG < ngrad
nG = nG + 1;
G = [g G];
X = [x X];
else % nG = ngrad
G = [g G(:,1:ngrad-1)];
X = [x X(:,1:ngrad-1)];
end
% optimality check: compute smallest vector in convex hull of qualifying
% gradients: reduces to norm of latest gradient if ngrad == 1, and the
% set must always have at least one gradient: could gain efficiency
% here by updating previous QP solution
if nG > 1
[w,d] = qpspecial(G); % Anders Skajaa code for this special QP
else
w = 1;
d = g;
end
dnorm = norm(d);
if nargout > 9
xrec(:,iter) = x;
fevalrec{iter} = fevalrecline; % function vals computed in line search
Hrec{iter} = H;
end
if prtlevel > 1
nfeval = length(fevalrecline);
fprintf('bfgs: iter %d: nfevals = %d, step = %5.1e, f = %g, nG = %d, dnorm = %5.1e\n', ...
iter, nfeval, alpha, f, nG, dnorm)
end
if f < fvalquit % this is checked inside the line search
if prtlevel > 0
fprintf('bfgs: reached target objective, quit at iteration %d \n', iter)
end
info = 2;
return
elseif norm(x) > xnormquit % this is not checked inside the line search
if prtlevel > 0
fprintf('bfgs: norm(x) exceeds specified limit, quit at iteration %d \n', iter)
end
info = 3;
return
end
if fail == 1 % line search failed (Wolfe conditions not both satisfied)
if ~quitLSfail
if prtlevel > 1
fprintf('bfgs: continue although line search failed\n')
end
else % quit since line search failed
if prtlevel > 0
fprintf('bfgs: quit at iteration %d, f = %g, dnorm = %5.1e\n', iter, f, dnorm)
end
info = 7;
return
end
elseif fail == -1 % function apparently unbounded below
if prtlevel > 0
fprintf('bfgs: f may be unbounded below, quit at iteration %d, f = %g\n', iter, f)
end
info = 8;
return
end
if dnorm <= normtol
if prtlevel > 0
if nG == 1
fprintf('bfgs: gradient norm below tolerance, quit at iteration %d, f = %g\n', iter, f')
else
fprintf('bfgs: norm of smallest vector in convex hull of gradients below tolerance, quit at iteration %d, f = %g\n', iter, f')
end
end
info = 0;
return
end
if cputime > cpufinish
if prtlevel > 0
fprintf('bfgs: cpu time limit exceeded, quit at iteration %d\n', iter)
end
info = 4;
return
end
s = alpha*p;
y = g - gprev;
sty = s'*y; % successful line search ensures this is positive
if nvec == 0 % perform rank two BFGS update to the inverse Hessian H
if sty > 0
if iter == 1 & scale
% for full BFGS, Nocedal and Wright recommend scaling I before
% the first update only
H = (sty/(y'*y))*H;
end
% for formula, see Nocedal and Wright's book
rho = 1/sty;
rhoHyst = rho*(H*y)*s'; % M = I - rho*s*y';
H = H - rhoHyst' - rhoHyst + rho*s*(y'*rhoHyst) + rho*s*s'; % H = M*H*M' + rho*s*s';
else % should not happen unless line search fails, and in that case should normally have quit
if prtlevel > 1
fprintf('bfgs: sty <= 0, skipping BFGS update at iteration %d \n', iter)
end
end
else % save s and y vectors for limited memory update
s = alpha*p;
y = g - gprev;
if iter <= nvec
S = [S s];
Y = [Y y];
else % could be more efficient here by avoiding moving the columns
S = [S(:,2:nvec) s];
Y = [Y(:,2:nvec) y];
end
if scale
H = ((s'*y)/(y'*y))*H0; % recommended by Nocedal-Wright
end
end
end % for loop
if prtlevel > 0
fprintf('bfgs: %d iterations reached, f = %g, dnorm = %5.1e\n', maxit, f, dnorm)
end
info = 1; % quit since max iterations reached
function [xbundle, gbundle] = getbundle(x, g, samprad, N, pars);
% get bundle of N-1 gradients at points near x, in addition to g,
% which is gradient at x and goes in first column
% intended to be called by gradsampfixed
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "gradsamp".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
m = length(x);
xbundle(:,1) = x;
gbundle(:,1) = g;
for k = 2:N % note the 2
xpert = x + samprad*(rand(m,1) - 0.5); % uniform distribution
[f,grad] = feval(pars.fgname, xpert, pars);
count = 0;
while isnaninf(f) | isnaninf(grad) % in particular, disallow infinite function values
xpert = (x + xpert)/2; % contract back until feasible
[f,grad] = feval(pars.fgname, xpert, pars);
count = count + 1;
if count > 100 % should never happen, but just in case
error('too many contractions needed to find finite f and grad values')
end
end; % discard function values
xbundle(:,k) = xpert;
gbundle(:,k) = grad;
end
function options = setdefaults(pars,options)
% call: options = setdefaults(pars,options)
% check that fields of pars and options are set correctly and
% set basic default values for options that are common to various
% optimization methods, including bfgs and gradsamp
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargin < 2
options = [];
end
if ~isfield(pars, 'nvar')
error('setdefaults: input "pars" must have a field "nvar" (number of variables)')
elseif ~isposint(pars.nvar)
error('setdefaults: input "pars.nvar" (number of variables) must be a positive integer')
end
if ~isfield(pars, 'fgname')
error('setdefaults: input "pars" must have a field "fgname" (name of m-file computing function and gradient)')
end
if isfield(options, 'maxit')
if ~isnonnegint(options.maxit)
error('setdefaults: input "options.maxit" must be a nonnegative integer')
end
else
options.maxit = 1000;
end
if isfield(options, 'normtol')
if ~isposreal(options.normtol)
error('setdefaults: input "options.normtol" must be a positive real scalar')
end
else
options.normtol = 1.0e-6;
end
if isfield(options, 'fvalquit')
if ~isreal(options.fvalquit)|~isscalar(options.fvalquit)
error('setdefaults: input "options.fvalquit" must be a real scalar')
end
else
options.fvalquit = -inf;
end
if isfield(options, 'xnormquit')
if ~isreal(options.xnormquit)|~isscalar(options.xnormquit)
error('setdefaults: input "options.fvalquit" must be a real scalar')
end
else
options.xnormquit = inf;
end
if ~isfield(options, 'cpumax')
options.cpumax = inf;
end
if ~isfield(options, 'prtlevel')
options.prtlevel = 1;
end
function ipi = isposint(x)
% return true if x is a positive integer, false otherwise
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~isscalar(x)
ipi = 0;
else % following is OK since x is scalar
ipi = isreal(x) & round(x) == x & x > 0;
end
function inni = isnonnegint(x)
% return true if x is a nonnegative integer, false otherwise
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~isscalar(x)
inni = 0;
else % following is OK since x is scalar
inni = (isreal(x) & round(x) == x & x >= 0);
end
function ipr = isposreal(x)
% return true if x is a positive real scalar, false otherwise
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~isscalar(x)
ipr = 0;
else % following is OK since x is scalar
ipr = isreal(x) & x > 0;
end
function options = setx0(pars,options)
% set columns of options.x0 randomly if not provided by user
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nvar = pars.nvar;
if ~isfield(options, 'x0')
options.x0 = [];
end
if isempty(options.x0)
if isfield(options, 'nstart')
if ~isposint(options.nstart)
error('setx0: input "options.nstart" must be a positive integer when "options.x0" is not provided')
else
options.x0 = randn(nvar, options.nstart);
end
else
options.x0 = randn(nvar, 10);
end
else
if size(options.x0,1) ~= nvar
error('setx0: input "options.x0" must have "pars.nvar" rows')
end
if isfield(options, 'nstart')
if ~isnonnegint(options.nstart)
error('setx0: input "options.nstart" must be a nonnegative integer')
elseif options.nstart < size(options.x0,2)
error('setx0: "options.nstart" is less than number of columns of "options.x0"')
else % augment vectors in options.x0 with randomly generated ones
nrand = options.nstart - size(options.x0,2);
options.x0 = [options.x0 randn(nvar, nrand)];
end
end % no else part, options.x0 is as provided
end
function options = setdefaultsbfgs(pars, options)
% set defaults for BFGS (in addition to those already set by setdefaults)
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% line search options
if isfield(options, 'strongwolfe')
if options.strongwolfe ~= 0 & options.strongwolfe ~= 1
error('setdefaultsbfgs: input "options.strongwolfe" must be 0 or 1')
end
else
% strong Wolfe is very complicated and is bad for nonsmooth functions
options.strongwolfe = 0;
end
if isfield(options, 'wolfe1') % conventionally anything in (0,1), but 0 is OK while close to 1 is not
if ~isreal(options.wolfe1) | options.wolfe1 < 0 | options.wolfe1 > 0.5
error('setdefaultsbfgs: input "options.wolfe1" must be between 0 and 0.5')
end
else
options.wolfe1 = 1e-4; % conventionally this should be positive, and although
% zero is usually fine in practice, there are exceptions
end
if isfield(options, 'wolfe2') % conventionally should be > wolfe1, but both 0 OK for e.g. Shor
if ~isreal(options.wolfe2) | options.wolfe2 < options.wolfe1 | options.wolfe2 >= 1
error('setdefaultsbfgs: input "options.wolfe2" must be between max(0,options.wolfe1) and 1')
end
else
options.wolfe2 = 0.5; % 0 and 1 are both bad choices
end
if options.strongwolfe
if options.prtlevel > 0
if options.wolfe2 > 0
fprintf('setdefaultsbfgs: strong Wolfe line search selected, but weak Wolfe is usually preferable\n')
fprintf('(especially if f is nonsmooth)\n')
else
fprintf('setdefaultsbfgs: simulating exact line search\n')
end
end
if ~exist('linesch_sw')
error('"linesch_sw" is not in path: it can be obtained from the NLCG distribution')
end
else
if ~exist('linesch_ww')
error('"linesch_ww" is not in path: it is required for weak Wolfe line search')
end
end
if isfield(options, 'quitLSfail')
if options.quitLSfail ~= 0 & options.quitLSfail ~= 1
error('setdefaultsbfgs: input "options.quitLSfail" must be 0 or 1')
end
else
if options.strongwolfe == 1 & options.wolfe2 == 0
% simulated exact line search, so don't quit if it fails
options.quitLSfail = 0;
else % quit if line search fails
options.quitLSfail = 1;
end
end
% other default options
n = pars.nvar;
if isfield(options, 'nvec')
if ~isnonnegint(options.nvec)
error('setdefaultsbfgs: input "options.nvec" must be a nonnegative integer')
end
elseif n <= 100
options.nvec = 0; % full BFGS
else
options.nvec = 10; % limited memory BFGS
end
if isfield(options,'H0')
% H0 should be positive definite but too expensive to check
if any(size(options.H0) ~= [n n])
error('bfgs: input options.H0 must be matrix with order pars.nvar')
end
if options.nvec > 0 & ~issparse(options.H0)
error('bfgs: input "options.H0" must be a sparse matrix when "options.nvec" is positive')
end
else
if options.nvec == 0
options.H0 = eye(n); % identity for full BFGS
else
options.H0 = speye(n); % sparse identity for limited memory BFGS
end
end
if isfield(options, 'scale')
if options.scale ~= 0 & options.scale ~= 1
error('setdefaultsbfgs: input "options.scale" must be 0 or 1')
end
else
options.scale = 1;
end
% note: if f is smooth, superlinear convergence will ensure that termination
% takes place before too many gradients are used in the QP optimality check
% so the optimality check will not be expensive in the smooth case
if isfield(options,'ngrad')
if ~isnonnegint(options.ngrad)
error('setdefaultsbfgs: input "options.ngrad" must be a nonnegative integer')
end
else % note this could be more than options.nvec
% rationale: it is only towards the end that we start accumulating
% many gradients, and then they may be needed to veryify optimality
options.ngrad = min([100, 2*pars.nvar, pars.nvar + 10]);
end
if isfield(options,'evaldist')
if ~isposreal(options.ngrad)
error('setdefaultsbfgs: input "options.evaldist" must be a positive real scalar')
end
else
options.evaldist = 1e-4;
end
function [alpha, xalpha, falpha, gradalpha, fail, beta, gradbeta, fevalrec] = ...
linesch_ww(x0, f0, grad0, d, pars, c1, c2, fvalquit, prtlevel)
% LINESCH_WW Line search enforcing weak Wolfe conditions, suitable
% for minimizing both smooth and nonsmooth functions
% Version 2.0 for HANSO 2.0
% call: [alpha, xalpha, falpha, gradalpha, fail, beta, gradbeta, fevalrec] = ...
% linesch_ww_mod(x0, f0, grad0, d, pars, c1, c2, fvalquit, prtlevel);
% Input
% x0: intial point
% f0: function value at x0
% grad0: gradient at x0
% d: search direction
% pars: a structure that specifies the function name as well
% anything else that the user needs to access in programming the
% function and gradient values
% pars.fgname: name of function that returns function and gradient
% it expects as input only x and pars, a parameter structure
% it is invoked by: [f,g] = feval(fgname, x, pars)
% c1: Wolfe parameter for the sufficient decrease condition
% f(x0 + t d) ** < ** f0 + c1*t*grad0'*d (DEFAULT 0)
% c2: Wolfe parameter for the WEAK condition on directional derivative
% (grad f)(x0 + t d)'*d ** > ** c2*grad0'*d (DEFAULT 0.5)
% where 0 <= c1 <= c2 <= 1.
% For usual convergence theory for smooth functions, normally one
% requires 0 < c1 < c2 < 1, but c1=0 is fine in practice.
% May want c1 = c2 = 0 for some nonsmooth optimization
% algorithms such as Shor or bundle, but not BFGS.
% Setting c2=0 may interfere with superlinear convergence of
% BFGS in smooth case.
% fvalquit: quit immediately if f drops below this value, regardless
% of the Wolfe conditions (default -inf)
% prtlevel: 0 for no printing, 1 minimal (default), 2 verbose
%
% Output:
% alpha: steplength satisfying weak Wolfe conditions if one was found,
% otherwise left end point of interval bracketing such a point
% (possibly 0)
% xalpha: x0 + alpha*d
% falpha: f(x0 + alpha d)
% gradalpha:(grad f)(x0 + alpha d)
% fail: 0 if both Wolfe conditions satisfied, or falpha < fvalquit
% 1 if one or both Wolfe conditions not satisfied but an
% interval was found bracketing a point where both satisfied
% -1 if no such interval was found, function may be unbounded below
% beta: same as alpha if it satisfies weak Wolfe conditions,
% otherwise right end point of interval bracketing such a point
% (inf if no such finite interval found)
% gradbeta: (grad f)(x0 + beta d) (this is important for bundle methods)
% (vector of nans if beta is inf)
%
% fevalrec: record of function evaluations
% The weak Wolfe line search is far less complicated that the standard
% strong Wolfe line search that is discussed in many texts. It appears
% to have no disadvantages compared to strong Wolfe when used with
% Newton or BFGS methods on smooth functions, and it is essential for
% the application of BFGS or bundle to nonsmooth functions as done in HANSO.
% However, it is NOT recommended for use with conjugate gradient methods,
% which require a strong Wolfe line search for convergence guarantees.
% Weak Wolfe requires two conditions to be satisfied: sufficient decrease
% in the objective, and sufficient increase in the directional derivative
% (not reduction in its absolute value, as required by strong Wolfe).
%
% There are some subtleties for nonsmooth functions. In the typical case
% that the directional derivative changes sign somewhere along d, it is
% no problem to satisfy the 2nd condition, but descent may not be possible
% if the change of sign takes place even when the step is tiny. In this
% case it is important to return the gradient corresponding to the positive
% directional derivative even though descent was not obtained. On the other
% hand, for some nonsmooth functions the function decrease is steady
% along the line until at some point it jumps to infinity, because an
% implicit constraint is violated. In this case, the first condition is
% satisfied but the second is not. All cases are covered by returning
% the end points of an interval [alpha, beta] and returning the function
% value at alpha, but the gradients at both alpha and beta.
%
% The assertion that [alpha,beta] brackets a point satisfying the
% weak Wolfe conditions depends on an assumption that the function
% f(x + td) is a continuous and piecewise continuously differentiable
% function of t, and that in the unlikely event that f is evaluated at
% a point of discontinuity of the derivative, g'*d, where g is the
% computed gradient, is either the left or right derivative at the point
% of discontinuity, or something in between these two values.
%
% For functions that are known to be nonsmooth, setting the second Wolfe
% parameter to zero makes sense, especially for a bundle method, and for
% the Shor R-algorithm, for which it is essential. However, it's not
% a good idea for BFGS, as for smooth functions this may prevent superlinear
% convergence, and it can even make trouble for BFGS on, e.g.,
% f(x) = x_1^2 + eps |x_2|, when eps is small.
%
% Line search quits immediately if f drops below fvalquit.
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "bfgs".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if nargin < 6 % check if the optional Wolfe parameters were passed
c1 = 0; % not conventional, but seems OK. See note at top.
end
if nargin < 7
c2 = 0.5; % see note at top
end
if nargin < 8
fvalquit = -inf;
end
if nargin < 9
prtlevel = 1;
end
if (c1 < 0 | c1 > c2 | c2 > 1) & prtlevel > 0 % allows c1 = 0, c2 = 0 and c2 = 1
fprintf('linesch_ww_mod: Wolfe parameters do not satisfy 0 <= c1 <= c2 <= 1\n')
end
fgname = pars.fgname;
alpha = 0; % lower bound on steplength conditions
xalpha = x0;
falpha = f0;
gradalpha = grad0; % need to pass grad0, not grad0'*d, in case line search fails
beta = inf; % upper bound on steplength satisfying weak Wolfe conditions
gradbeta = nan*ones(size(x0));
g0 = grad0'*d;
if g0 >= 0
% error('linesch_ww_mod: g0 is nonnegative, indicating d not a descent direction')
fprintf('linesch_ww_mod: WARNING, not a descent direction\n')
end
dnorm = norm(d);
if dnorm == 0
error('linesch_ww_mod: d is zero')
end
t = 1; % important to try steplength one first
nfeval = 0;
nbisect = 0;
nexpand = 0;
% the following limits are rather arbitrary
% nbisectmax = 30; % 50 is TOO BIG, because of rounding errors
nbisectmax = max(30, round(log2(1e5*dnorm))); % allows more if ||d|| big
nexpandmax = max(10, round(log2(1e5/dnorm))); % allows more if ||d|| small
done = 0;
while ~done
x = x0 + t*d;
nfeval = nfeval + 1;
[f,grad] = feval(fgname, x, pars);
fevalrec(nfeval) = f;
if f < fvalquit % nothing more to do, quit
fail = 0;
alpha = t; % normally beta is inf
xalpha = x;
falpha = f;
gradalpha = grad;
return
end
gtd = grad'*d;
% the first condition must be checked first. NOTE THE >=.
if f >= f0 + c1*t*g0 | isnan(f) % first condition violated, gone too far
beta = t;
gradbeta = grad; % discard f
% now the second condition. NOTE THE <=
elseif gtd <= c2*g0 | isnan(gtd) % second condition violated, not gone far enough
alpha = t;
xalpha = x;
falpha = f;
gradalpha = grad;
else % quit, both conditions are satisfied
fail = 0;
alpha = t;
xalpha = x;
falpha = f;
gradalpha = grad;
beta = t;
gradbeta = grad;
return
end
% setup next function evaluation
if beta < inf
if nbisect < nbisectmax
nbisect = nbisect + 1;
t = (alpha + beta)/2; % bisection
else
done = 1;
end
else
if nexpand < nexpandmax
nexpand = nexpand + 1;
t = 2*alpha; % still in expansion mode
else
done = 1;
end
end
end % loop
% Wolfe conditions not satisfied: there are two cases
if beta == inf % minimizer never bracketed
fail = -1;
if prtlevel > 1
fprintf('Line search failed to bracket point satisfying weak ');
fprintf('Wolfe conditions, function may be unbounded below\n')
end
else % point satisfying Wolfe conditions was bracketed
fail = 1;
if prtlevel > 1
fprintf('Line search failed to satisfy weak Wolfe conditions')
fprintf(' although point satisfying conditions was bracketed\n')
end
end
function ini = isnaninf(M)
% returns the scalar 1 if ANY entry of M is nan or inf; 0 otherwise
% note: isnan and isinf return matrices if M is a matrix, and
% if treats [0 1] as false, not true.
% ini = sum(sum(isnan(M))) > 0 | sum(sum(isinf(M))) > 0;
ini = any(any(isnan(M))) | any(any(isinf(M)));
%
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function r = hgprod(H0, g, S, Y)
% compute the product required by the LM-BFGS method
% see Nocedal and Wright
% Send comments/bug reports to Michael Overton, [email protected],
% with a subject header containing the string "hanso" or "gradsamp".
% Version 2.0, 2010, see GPL license info below.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Michael Overton
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N = size(S,2); % number of saved vector pairs (s,y)
q = g;
for i = N:-1:1
s = S(:,i);
y = Y(:,i);
rho(i) = 1/(s'*y);
alpha(i) = rho(i)*(s'*q);
q = q - alpha(i)*y;
end
r = H0*q;
for i=1:N
s = S(:,i);
y = Y(:,i);
beta = rho(i)*(y'*r);
r = r + (alpha(i)-beta)*s;
end
function [x,d,q,info] = qpspecial(G,varargin)
% Call:
% [x,d,q,info] = qpspecial(G,varargin)
%
% Solves the QP
%
% min q(x) = || G*x ||_2^2 = x'*(G'*G)*x
% s.t. sum(x) = 1
% x >= 0
%
% The problem corresponds to finding the smallest vector
% (2-norm) in the convex hull of the columns of G
%
% Inputs:
% G -- (M x n double) matrix G, see problem above
% varargin{1} -- (int) maximum number of iterates allowed
% If not present, maxit = 100 is used
% varargin{2} -- (n x 1 double) vector x0 with initial (FEASIBLE) iterate.
% If not present, (or requirements on x0 not met) a
% useable default x0 will be used
%
% Outputs:
% x -- Optimal point attaining optimal value
% d = G*x -- Smallest vector in the convex hull
% q -- Optimal value found = d'*d
% info -- Run data:
% info(1) =
% 0 = everything went well, q is optimal
% 1 = maxit reached and final x is feasible. so q
% might not be optimal, but it is better than q(x0)
% 2 = something went wrong
% info(2) = #iterations used
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% HANSO 2.0 Copyright (C) 2010 Anders Skajaa
%% This program is free software: you can redistribute it and/or modify
%% it under the terms of the GNU General Public License as published by
%% the Free Software Foundation, either version 3 of the License, or
%% (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program. If not, see <http://www.gnu.org/licenses/>.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
echo = 0; % set echo = 1 for printing
% (for debugging). Otherwise 0.
%
[m,n] = size(G); % size of problem
if ~(m*n>0) % in this case
fprintf(['qpspecial:',... % G is empty, so nothing we can do
' G is empty.\n']); % exit with warning
info = [2,0]; % info(1) = 2;
x = []; d = []; q = inf; % and empty structs
return; % and optimal value is inf
end %
%
e = ones(n,1); % vector of ones
%
if nargin > 1 % set defauls
maxit = varargin{1}; % maximal # iterations
maxit = ceil(maxit); % in case of a non-integer input
maxit = max(maxit,5); % always allow at least 5 iterations
else %
maxit = 100; % default is 100
end % which is always plenty
if nargin > 2 %
x = varargin{2}; % if x0 is specified
x = x(:); % if given as row instead of col
nx = size(x,1); % check that size is right
if any(x<0) || nx~=n % use it, unless it is
x = e; % infeasible in the ineq
end % constraints.
else % use it, otherwise
x = e; % use (1,1,...,1)
end % which is an interior point
%
idx = (1:(n+1):(n^2))'; % needed many times
Q = G'*G; % Hessian in QP
z = x; % intialize z
y = 0; % intialize y
eta = 0.9995; % step size dampening
delta = 3; % for the sigma heuristic
mu0 = (x'*z) / n; % first my
tolmu = 1e-5; % relative stopping tolerance, mu
tolrs = 1e-5; % and residual norm
kmu = tolmu*mu0; % constant for stopping, mu
nQ = norm(Q,inf)+2; % norm of [Q,I,e]
krs = tolrs*nQ; % constant for stopping, residuals
ap = 0; ad = 0; % init steps just for printing
if echo > 0 % print first line
fprintf(['k mu ',... %
' stpsz res\n',... %
'-----------------',... %
'-----------------\n']); %
end %
%
for k = 1:maxit %
%
r1 = -Q*x + e*y + z; % residual
r2 = -1 + sum(x); % residual
r3 = -x.*z; % slacks
rs = norm([r1;r2],inf); % residual norm
mu = -sum(r3)/n; % current mu
%
% printing (for debugging)
if echo > 0
fprintf('%-3.1i %9.2e %9.2e %9.2e \n',...
k,mu/mu0,max(ap,ad),rs/nQ);
end
% stopping
if mu < kmu % mu must be small
if rs < krs % primal feas res must be small
info = [0,k-1]; % in this case, all went well
break; % so exit with info = 0
end % so exit loop
end %
%
zdx = z./x; % factorization
QD = Q; %
QD(idx) = QD(idx) + zdx; %
[C,ef] = chol(QD); % C'*C = QD
if ef > 0 % safety to catch possible
info = [2,k]; % problems in the choleschy
break; % in this case,
end % break with info = 2
KT = C'\e; % K' = (C')^(-1) * e
M = KT'*KT; % M = K*K'
%
r4 = r1+r3./x; % compute approx
r5 = KT'*(C'\r4); % tangent direction
r6 = r2+r5; % using factorization
dy = -r6/M; % from above
r7 = r4 + e*dy; %
dx = C\(C'\r7); %
dz = (r3 - z.*dx)./x; %
%
p = -x ./ dx; % Determine maximal step
ap = min(min(p(p>0)),1); % possible in the
if isempty(ap) % approx tangent direction
ap = 1; % here primal step size
end %
p = -z ./ dz; % here dual step size
ad = min(min(p(p>0)),1); %
if isempty(ad) % using different step sizes
ad = 1; % in primal and dual improves
end % performance a bit
%
muaff = ((x + ap*dx)'*... % heuristic for
(z + ad*dz))/n; % the centering parameter
sig = (muaff/mu)^delta; %
%
r3 = r3 + sig*mu; % compute the new corrected
r3 = r3 - dx.*dz; % search direction that now
r4 = r1+r3./x; % includes the appropriate
r5 = KT'*(C'\r4); % amount of centering and
r6 = r2+r5; % mehrotras second order
dy = -r6/M; % correction term (see r3).
r7 = r4 + e*dy; % we of course reuse the
dx = C\(C'\r7); % factorization from above
dz = (r3 - z.*dx)./x; %
%
p = -x ./ dx; % Determine maximal step
ap = min(min(p(p>0)),1); % possible in the
if isempty(ap) % new direction
ap = 1; % here primal step size
end %
p = -z ./ dz; % here dual step size
ad = min(min(p(p>0)),1); %
if isempty(ad) %
ad = 1; %
end %
% update variables
x = x + eta * ap * dx; % primal
y = y + eta * ad * dy; % dual multipliers
z = z + eta * ad * dz; % dual slacks
%
end % end main loop
%
if k == maxit % if reached maxit
info = [1,k]; % set info(1) = 1
end %
x = max(x,0); % project x onto R+
x = x/sum(x); % so that sum(x) = 1 exactly
d = G*x; % and set other output
q = d'*d; % variables using best
% found x
%
if echo > 0 % printing
str = 'optimal'; % status string to print
if info(1)==1 % in the last line
str = 'maxit reached';%
elseif info(1)==2 %
str = 'failed'; %
end %
fprintf(['---------',... % print last line
'-------------------',... %
'------\n',... %
' result: %s \n',... %
'-------------------',... %
'---------------\n'],str);%
end %
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
distinguishable_colors.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/pocs/toolbox/distinguishable_colors.m
| 5,753 |
utf_8
|
57960cf5d13cead2f1e291d1288bccb2
|
function colors = distinguishable_colors(n_colors,bg,func)
% DISTINGUISHABLE_COLORS: pick colors that are maximally perceptually distinct
%
% When plotting a set of lines, you may want to distinguish them by color.
% By default, Matlab chooses a small set of colors and cycles among them,
% and so if you have more than a few lines there will be confusion about
% which line is which. To fix this problem, one would want to be able to
% pick a much larger set of distinct colors, where the number of colors
% equals or exceeds the number of lines you want to plot. Because our
% ability to distinguish among colors has limits, one should choose these
% colors to be "maximally perceptually distinguishable."
%
% This function generates a set of colors which are distinguishable
% by reference to the "Lab" color space, which more closely matches
% human color perception than RGB. Given an initial large list of possible
% colors, it iteratively chooses the entry in the list that is farthest (in
% Lab space) from all previously-chosen entries. While this "greedy"
% algorithm does not yield a global maximum, it is simple and efficient.
% Moreover, the sequence of colors is consistent no matter how many you
% request, which facilitates the users' ability to learn the color order
% and avoids major changes in the appearance of plots when adding or
% removing lines.
%
% Syntax:
% colors = distinguishable_colors(n_colors)
% Specify the number of colors you want as a scalar, n_colors. This will
% generate an n_colors-by-3 matrix, each row representing an RGB
% color triple. If you don't precisely know how many you will need in
% advance, there is no harm (other than execution time) in specifying
% slightly more than you think you will need.
%
% colors = distinguishable_colors(n_colors,bg)
% This syntax allows you to specify the background color, to make sure that
% your colors are also distinguishable from the background. Default value
% is white. bg may be specified as an RGB triple or as one of the standard
% "ColorSpec" strings. You can even specify multiple colors:
% bg = {'w','k'}
% or
% bg = [1 1 1; 0 0 0]
% will only produce colors that are distinguishable from both white and
% black.
%
% colors = distinguishable_colors(n_colors,bg,rgb2labfunc)
% By default, distinguishable_colors uses the image processing toolbox's
% color conversion functions makecform and applycform. Alternatively, you
% can supply your own color conversion function.
%
% Example:
% c = distinguishable_colors(25);
% figure
% image(reshape(c,[1 size(c)]))
%
% Example using the file exchange's 'colorspace':
% func = @(x) colorspace('RGB->Lab',x);
% c = distinguishable_colors(25,'w',func);
% Copyright 2010-2011 by Timothy E. Holy
% Parse the inputs
if (nargin < 2)
bg = [1 1 1]; % default white background
else
if iscell(bg)
% User specified a list of colors as a cell aray
bgc = bg;
for i = 1:length(bgc)
bgc{i} = parsecolor(bgc{i});
end
bg = cat(1,bgc{:});
else
% User specified a numeric array of colors (n-by-3)
bg = parsecolor(bg);
end
end
% Generate a sizable number of RGB triples. This represents our space of
% possible choices. By starting in RGB space, we ensure that all of the
% colors can be generated by the monitor.
n_grid = 30; % number of grid divisions along each axis in RGB space
x = linspace(0,1,n_grid);
[R,G,B] = ndgrid(x,x,x);
rgb = [R(:) G(:) B(:)];
if (n_colors > size(rgb,1)/3)
error('You can''t readily distinguish that many colors');
end
% Convert to Lab color space, which more closely represents human
% perception
if (nargin > 2)
lab = func(rgb);
bglab = func(bg);
else
C = makecform('srgb2lab');
lab = applycform(rgb,C);
bglab = applycform(bg,C);
end
% If the user specified multiple background colors, compute distances
% from the candidate colors to the background colors
mindist2 = inf(size(rgb,1),1);
for i = 1:size(bglab,1)-1
dX = bsxfun(@minus,lab,bglab(i,:)); % displacement all colors from bg
dist2 = sum(dX.^2,2); % square distance
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color
end
% Iteratively pick the color that maximizes the distance to the nearest
% already-picked color
colors = zeros(n_colors,3);
lastlab = bglab(end,:); % initialize by making the "previous" color equal to background
for i = 1:n_colors
dX = bsxfun(@minus,lab,lastlab); % displacement of last from all colors on list
dist2 = sum(dX.^2,2); % square distance
mindist2 = min(dist2,mindist2); % dist2 to closest previously-chosen color
[~,index] = max(mindist2); % find the entry farthest from all previously-chosen colors
colors(i,:) = rgb(index,:); % save for output
lastlab = lab(index,:); % prepare for next iteration
end
end
function c = parsecolor(s)
if ischar(s)
c = colorstr2rgb(s);
elseif isnumeric(s) && size(s,2) == 3
c = s;
else
error('MATLAB:InvalidColorSpec','Color specification cannot be parsed.');
end
end
function c = colorstr2rgb(c)
% Convert a color string to an RGB value.
% This is cribbed from Matlab's whitebg function.
% Why don't they make this a stand-alone function?
rgbspec = [1 0 0;0 1 0;0 0 1;1 1 1;0 1 1;1 0 1;1 1 0;0 0 0];
cspec = 'rgbwcmyk';
k = find(cspec==c(1));
if isempty(k)
error('MATLAB:InvalidColorString','Unknown color string.');
end
if k~=3 || length(c)==1,
c = rgbspec(k,:);
elseif length(c)>2,
if strcmpi(c(1:3),'bla')
c = [0 0 0];
elseif strcmpi(c(1:3),'blu')
c = [0 0 1];
else
error('MATLAB:UnknownColorString', 'Unknown color string.');
end
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
plot_mesh.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/spherical-wavelets/toolbox_multires/plot_mesh.m
| 11,185 |
utf_8
|
f48aac5032a78db13e31a0504dde8ce4
|
function h = plot_mesh(vertex,face,options)
% plot_mesh - plot a 3D mesh.
%
% plot_mesh(vertex,face, options);
%
% 'options' is a structure that may contains:
% - 'normal' : a (nvertx x 3) array specifying the normals at each vertex.
% - 'edge_color' : a float specifying the color of the edges.
% - 'face_color' : a float specifying the color of the faces.
% - 'face_vertex_color' : a color per vertex or face.
% - 'vertex'
% - 'texture' : a 2-D image to be mapped on the surface
% - 'texture_coords' : a (nvertx x 2) array specifying the texture
% coordinates in [0,1] of the vertices in the texture.
% - 'tmesh' : set it to 1 if this corresponds to a volumetric tet mesh.
%
% See also: mesh_previewer.
%
% Copyright (c) 2004 Gabriel Peyr?
if nargin<2
error('Not enough arguments.');
end
options.null = 0;
name = getoptions(options, 'name', '');
normal = getoptions(options, 'normal', []);
face_color = getoptions(options, 'face_color', .7);
edge_color = getoptions(options, 'edge_color', 0);
normal_scaling = getoptions(options, 'normal_scaling', .8);
sanity_check = getoptions(options, 'sanity_check', 1);
view_param = getoptions(options, 'view_param', []);
texture = getoptions(options, 'texture', []);
texture_coords = getoptions(options, 'texture_coords', []);
tmesh = getoptions(options, 'tmesh', 0);
if size(vertex,1)==2
% 2D triangulation
% vertex = cat(1,vertex, zeros(1,size(vertex,2)));
plot_graph(triangulation2adjacency(face),vertex);
return;
end
% can flip to accept data in correct ordering
[vertex,face] = check_face_vertex(vertex,face);
if size(face,1)==4 && tmesh==1
%%%% tet mesh %%%%
% normal to the plane <x,w><=a
w = getoptions(options, 'cutting_plane', [0.2 0 1]');
w = w(:)/sqrt(sum(w.^2));
t = sum(vertex.*repmat(w,[1 size(vertex,2)]));
a = getoptions(options, 'cutting_offs', median(t(:)) );
b = getoptions(options, 'cutting_interactive', 0);
plot_points = getoptions(options, 'plot_points', 0);
while true;
% in/out
I = ( t<=a );
% trim
e = sum(I(face));
J = find(e==4);
facetrim = face(:,J);
% convert to triangular mesh
hold on;
if not(isempty(facetrim))
face1 = tet2tri(facetrim, vertex, 1);
% options.method = 'slow';
face1 = perform_faces_reorientation(vertex,face1, options);
h{1} = plot_mesh(vertex,face1, options);
end
view(3); % camlight;
shading faceted;
if plot_points
K = find(e==0);
K = face(:,K); K = unique(K(:));
h{2} = plot3(vertex(1,K), vertex(2,K), vertex(3,K), 'k.');
end
hold off;
if b==0
break;
end
[x,y,b] = ginput(1);
if b==1
a = a+.03;
elseif b==3
a = a-.03;
else
break;
end
end
return;
end
vertex = vertex';
face = face';
if strcmp(name, 'bunny') || strcmp(name, 'pieta')
% vertex = -vertex;
end
if strcmp(name, 'armadillo')
vertex(:,3) = -vertex(:,3);
end
if sanity_check && ( (size(face,2)~=3 && size(face,2)~=4) || (size(vertex,2)~=3 && size(vertex,2)~=2))
error('face or vertex does not have correct format.');
end
if ~isfield(options, 'face_vertex_color') || isempty(options.face_vertex_color)
options.face_vertex_color = zeros(size(vertex,1),1);
end
face_vertex_color = options.face_vertex_color;
if not(isempty(texture))
%%% textured mesh %%%
if isempty(texture_coords)
error('You need to provide texture_coord.');
end
if size(texture_coords,2)~=2
texture_coords = texture_coords';
end
opts.EdgeColor = 'none';
patcht(face,vertex,face,texture_coords,texture',opts);
if size(texture,3)==1
colormap gray(256);
else
colormap jet(256);
end
set_view(name, view_param);
axis off; axis equal;
% camlight; % problem with pithon notebook
shading faceted;
return;
end
shading_type = 'interp';
if isempty(face_vertex_color)
h = patch('vertices',vertex,'faces',face,'facecolor',[face_color face_color face_color],'edgecolor',[edge_color edge_color edge_color]);
else
nverts = size(vertex,1);
% vertex_color = rand(nverts,1);
if size(face_vertex_color,1)==size(vertex,1)
shading_type = 'interp';
else
shading_type = 'flat';
end
h = patch('vertices',vertex,'faces',face,'FaceVertexCData',face_vertex_color, 'FaceColor',shading_type);
end
colormap gray(256);
lighting phong;
% camlight infinite;
camproj('perspective');
axis square;
axis off;
if ~isempty(normal)
%%% plot the normals %%%
n = size(vertex,1);
subsample_normal = getoptions(options, 'subsample_normal', min(4000/n,1) );
sel = randperm(n); sel = sel(1:floor(end*subsample_normal));
hold on;
quiver3(vertex(sel,1),vertex(sel,2),vertex(sel,3),normal(1,sel)',normal(2,sel)',normal(3,sel)',normal_scaling);
hold off;
end
% cameramenu;
set_view(name, view_param);
shading(shading_type);
% camlight; %% BUG WITH PYTHON
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function set_view(name, view_param)
switch lower(name)
case 'hammerheadtriang'
view(150,-45);
case 'horse'
view(134,-61);
case 'skull'
view(21.5,-12);
case 'mushroom'
view(160,-75);
case 'bunny'
% view(0,-55);
view(0,90);
case 'david_head'
view(-100,10);
case 'screwdriver'
view(-10,25);
case 'pieta'
view(15,31);
case 'mannequin'
view(25,15);
view(27,6);
case 'david-low'
view(40,3);
case 'david-head'
view(-150,5);
case 'brain'
view(30,40);
case 'pelvis'
view(5,-15);
case 'fandisk'
view(36,-34);
case 'earth'
view(125,35);
case 'camel'
view(-123,-5);
camroll(-90);
case 'beetle'
view(-117,-5);
camroll(-90);
zoom(.85);
case 'cat'
view(-60,15);
case 'nefertiti'
view(-20,65);
end
if not(isempty(view_param))
view(view_param(1),view_param(2));
end
axis tight;
axis equal;
if strcmp(name, 'david50kf') || strcmp(name, 'hand')
zoom(.85);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function patcht(FF,VV,TF,VT,I,Options)
% This function PATCHT, will show a triangulated mesh like Matlab function
% Patch but then with a texture.
%
% patcht(FF,VV,TF,VT,I,Options);
%
% inputs,
% FF : Face list 3 x N with vertex indices
% VV : Vertices 3 x M
% TF : Texture list 3 x N with texture vertex indices
% VT : Texture Coordinates s 2 x K, range must be [0..1] or real pixel postions
% I : The texture-image RGB [O x P x 3] or Grayscale [O x P]
% Options : Structure with options for the textured patch such as
% EdgeColor, EdgeAlpha see help "Surface Properties :: Functions"
%
% Options.PSize : Special option, defines the image texturesize for each
% individual polygon, a low number gives a more block
% like texture, defaults to 64;
%
% note:
% On a normal PC displaying 10,000 faces will take about 6 sec.
%
% Example,
%
% % Load Data;
% load testdata;
% % Show the textured patch
% figure, patcht(FF,VV,TF,VT,I);
% % Allow Camera Control (with left, right and center mouse button)
% mouse3d
%
% Function is written by D.Kroon University of Twente (July 2010)
% FaceColor is a texture
Options.FaceColor='texturemap';
% Size of texture image used for every triangle
if(isfield(Options,'PSize'))
sizep=round(Options.PSize(1));
Options=rmfield(Options,'PSize');
else
sizep=64;
end
% Check input sizes
if(size(FF,2)~=size(TF,2))
error('patcht:inputs','Face list must be equal in size to texture-index list');
end
if((ndims(I)~=2)&&(ndims(I)~=3))
error('patcht:inputs','No valid Input texture image');
end
% Detect if grayscale or color image
switch(size(I,3))
case 1
iscolor=false;
case 3
iscolor=true;
otherwise
error('patcht:inputs','No valid Input texture image');
end
if(max(VT(:))<2)
% Remap texture coordinates to image coordinates
VT2(:,1)=(size(I,1)-1)*(VT(:,1))+1;
VT2(:,2)=(size(I,2)-1)*(VT(:,2))+1;
else
VT2=VT;
end
% Calculate the texture interpolation values
[lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep);
% Split texture-image in r,g,b to allow fast 1D index
Ir=I(:,:,1); if(iscolor), Ig=I(:,:,2); Ib=I(:,:,3); end
% The Patch used for every triangle (rgb)
Jr=zeros([(sizep+1) (sizep+1) 1],class(I));
if(iscolor)
Jg=zeros([(sizep+1) (sizep+1) 1],class(I));
Jb=zeros([(sizep+1) (sizep+1) 1],class(I));
end
hold on;
% Loop through all triangles of the mesh
for i=1:size(FF,1)
% Get current triangle vertices and current texture-vertices
V=VV(FF(i,:),:);
Vt=VT2(TF(i,:),:);
% Define the triangle as a surface
x=[V(1,1) V(2,1); V(3,1) V(3,1)];
y=[V(1,2) V(2,2); V(3,2) V(3,2)];
z=[V(1,3) V(2,3); V(3,3) V(3,3)];
% Define the texture coordinates of the surface
tx=[Vt(1,1) Vt(2,1) Vt(3,1) Vt(3,1)];
ty=[Vt(1,2) Vt(2,2) Vt(3,2) Vt(3,2)] ;
xy=[tx(1) ty(1); tx(2) ty(2); tx(3) ty(3); tx(3) ty(3)];
% Calculate texture interpolation coordinates
pos(:,1)=xy(1,1)*lambda1+xy(2,1)*lambda2+xy(3,1)*lambda3;
pos(:,2)=xy(1,2)*lambda1+xy(2,2)*lambda2+xy(3,2)*lambda3;
pos=round(pos); pos=max(pos,1); pos(:,1)=min(pos(:,1),size(I,1)); pos(:,2)=min(pos(:,2),size(I,2));
posind=(pos(:,1)-1)+(pos(:,2)-1)*size(I,1)+1;
% Map texture to surface image
Jr(jind)=Ir(posind);
J(:,:,1)=Jr;
if(iscolor)
Jg(jind)=Ig(posind);
Jb(jind)=Ib(posind);
J(:,:,2)=Jg;
J(:,:,3)=Jb;
end
% Show the surface
surface(x,y,z,J,Options);
end
hold off;
function [lambda1 lambda2 lambda3 jind]=calculateBarycentricInterpolationValues(sizep)
% Define a triangle in the upperpart of an square, because only that
% part is used by the surface function
x1=sizep; y1=sizep; x2=sizep; y2=0; x3=0 ;y3=0;
% Calculate the bary centric coordinates (instead of creating a 2D image
% with the interpolation values, we map them directly to an 1D vector)
detT = (x1-x3)*(y2-y3) - (x2-x3)*(y1-y3);
[x,y]=ndgrid(0:sizep,0:sizep); x=x(:); y=y(:);
lambda1=((y2-y3).*(x-x3)+(x3-x2).*(y-y3))/detT;
lambda2=((y3-y1).*(x-x3)+(x1-x3).*(y-y3))/detT;
lambda3=1-lambda1-lambda2;
% Make from 2D (surface)image indices 1D image indices
[jx jy]=ndgrid(sizep-(0:sizep)+1,sizep-(0:sizep)+1);
jind=(jx(:)-1)+(jy(:)-1)*(sizep+1)+1;
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
load_spherical_function.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/spherical-wavelets/toolbox_multires/load_spherical_function.m
| 2,090 |
utf_8
|
e9c44feb124e0a5925b9c201378082dc
|
function f = load_spherical_function(name, pos, options)
% load_spherical_function - load a function on the sphere
%
% f = load_spherical_function(name, pos, options);
%
% Copyright (c) 2007 Gabriel Peyre
if iscell(pos)
pos = pos{end};
end
if size(pos,1)>size(pos,2)
pos = pos';
end
x = pos(1,:); x = x(:);
M = [];
if not(isstr(name))
M = name;
name = 'image';
end
switch name
case 'linear'
f = x;
case 'cos'
f = cos(6*pi*x);
case 'singular'
f = abs(x).^.4;
case 'image'
name = getoptions(options, 'image_name', 'lena');
if isempty(M)
M = load_image(name);
q = size(M,1);
q = min(q,512);
M = crop(M,q);
M = perform_blurring(M,4);
end
f = perform_spherical_interpolation(pos,M);
case 'etopo'
resol = 15;
fname = ['ETOPO' num2str(resol)];
fid = fopen(fname, 'rb');
if fid<0
error('Unable to read ETOPO file');
end
s = [360*(60/resol), 180*(60/resol)];
M = fread(fid, Inf, 'short');
M = reshape(M, s(1),s(2) );
fclose(fid);
f = perform_spherical_interpolation(pos,M, 0);
case {'earth' 'earth-grad'}
filename = 'earth-bw';
M = double( load_image(filename) );
M = perform_blurring(M,4);
if strcmp(name, 'earth-grad')
G = grad(M);
M = sqrt(sum(G.^2,3));
M = perform_blurring(M,15);
end
f = perform_spherical_interpolation(pos,M,0);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = perform_spherical_interpolation(pos,M,center)
if nargin<3
center = 0;
end
qx = size(M,1);
qy = size(M,2);
Y = atan2(pos(2,:),pos(1,:))/(2*pi) + 1/2;
if center
X = acos(pos(3,:))/(2*pi) + 1/4;
else
X = acos(pos(3,:))/(pi);
end
x = linspace(0,1,qx);
y = linspace(0,1,qy);
f = interp2( y,x,M, Y(:),X(:) );
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
perform_haar_transf.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/spherical-wavelets/toolbox_multires/perform_haar_transf.m
| 3,170 |
utf_8
|
14b7d7fd610eca05949ef196c55d7b83
|
function f = perform_haar_transf(f, Jmin, dir, options)
% perform_haar_transf - peform fast Haar transform
%
% y = perform_haar_transf(x, Jmin, dir);
%
% Implement a Haar wavelets.
% Works in any dimension.
%
% Copyright (c) 2008 Gabriel Peyre
n = size(f,1);
Jmax = log2(n)-1;
if dir==1
%%% FORWARD %%%
for j=Jmax:-1:Jmin
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
Coarse = ( subselectdim(a,1:2:size(a,d),d) + subselectdim(a,2:2:size(a,d),d) )/sqrt(2);
Detail = ( subselectdim(a,1:2:size(a,d),d) - subselectdim(a,2:2:size(a,d),d) )/sqrt(2);
a = cat(d, Coarse, Detail );
end
f = subassign(f,sel,a);
end
else
%%% BACKWARD %%%
for j=Jmin:Jmax
sel = 1:2^(j+1);
a = subselect(f,sel);
for d=1:nb_dims(f)
Detail = subselectdim(a,2^j+1:2^(j+1),d);
Coarse = subselectdim(a,1:2^j,d);
a = subassigndim(a, 1:2:2^(j+1), ( Coarse + Detail )/sqrt(2),d );
a = subassigndim(a, 2:2:2^(j+1), ( Coarse - Detail )/sqrt(2),d );
end
f = subassign(f,sel,a);
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselect(f,sel)
switch nb_dims(f)
case 1
f = f(sel);
case 2
f = f(sel,sel);
case 3
f = f(sel,sel,sel);
case 4
f = f(sel,sel,sel,sel);
case 5
f = f(sel,sel,sel,sel,sel);
case 6
f = f(sel,sel,sel,sel,sel,sel);
case 7
f = f(sel,sel,sel,sel,sel,sel,sel);
case 8
f = f(sel,sel,sel,sel,sel,sel,sel,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subselectdim(f,sel,d)
switch d
case 1
f = f(sel,:,:,:,:,:,:,:);
case 2
f = f(:,sel,:,:,:,:,:,:);
case 3
f = f(:,:,sel,:,:,:,:,:);
case 4
f = f(:,:,:,sel,:,:,:,:);
case 5
f = f(:,:,:,:,sel,:,:,:);
case 6
f = f(:,:,:,:,:,sel,:,:);
case 7
f = f(:,:,:,:,:,:,sel,:);
case 8
f = f(:,:,:,:,:,:,:,sel);
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subassign(f,sel,g)
switch nb_dims(f)
case 1
f(sel) = g;
case 2
f(sel,sel) = g;
case 3
f(sel,sel,sel) = g;
case 4
f(sel,sel,sel,sel) = g;
case 5
f(sel,sel,sel,sel,sel) = g;
case 6
f(sel,sel,sel,sel,sel,sel) = g;
case 7
f(sel,sel,sel,sel,sel,sel,sel) = g;
case 8
f(sel,sel,sel,sel,sel,sel,sel,sel) = g;
otherwise
error('Not implemented');
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function f = subassigndim(f,sel,g,d)
switch d
case 1
f(sel,:,:,:,:,:,:,:) = g;
case 2
f(:,sel,:,:,:,:,:,:) = g;
case 3
f(:,:,sel,:,:,:,:,:) = g;
case 4
f(:,:,:,sel,:,:,:,:) = g;
case 5
f(:,:,:,:,sel,:,:,:) = g;
case 6
f(:,:,:,:,:,sel,:,:) = g;
case 7
f(:,:,:,:,:,:,sel,:) = g;
case 8
f(:,:,:,:,:,:,:,sel) = g;
otherwise
error('Not implemented');
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
refine2.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-2d/refine2.m
| 40,907 |
utf_8
|
18e116aff5e1105226be34049478e95d
|
function [vert,conn,tria,tnum] = refine2(varargin)
%REFINE2 (Frontal)-Delaunay-refinement for two-dimensional,
%polygonal geometries.
% [VERT,EDGE,TRIA,TNUM] = REFINE2(NODE,EDGE) returns a co-
% nstrained Delaunay triangulation of the polygonal region
% {NODE,EDGE}. NODE is an N-by-2 array of polygonal verti-
% ces and EDGE is an E-by-2 array of edge indexing. Each
% row in EDGE represents an edge of the polygon, such that
% NODE(EDGE(JJ,1),:) and NODE(EDGE(JJ,2),:) are the coord-
% inates of the endpoints of the JJ-TH edge. If the argum-
% ent EDGE is omitted it assumed that the vertices in NODE
% are connected in ascending order.
%
% [...] = REFINE2(NODE,EDGE,PART) computes a triangulation
% for a multiply-connected geometry. PART is a cell-array
% of polygonal "parts", where each element PART{KK} is an
% array of edge indices defining a given polygonal region.
% EDGE(PART{KK}, :) is the set of edges in the KK-TH part.
%
% VERT is a V-by-2 array of XY coordinates in the triangu-
% lation, EDGE is an array of constrained edges, TRIA is a
% T-by-3 array of triangles, and TNUM is a T-by-1 array of
% part indices. Each row of TRIA and EDGE define an eleme-
% nt. VERT(TRIA(II,1),:), VERT(TRIA(II,2),:) and VERT(TRIA
% (II,3),:) are the coordinates of the II-TH triangle. The
% edges in EDGE are defined in a similar manner. NUM is an
% array of part indexing, such that TNUM(II) is the index
% of the part in which the II-TH triangle resides.
%
% [...] = REFINE2(..., OPTS) passes an additional options
% structure OPTS, containing various user-defined paramet-
% ers, including:
%
% - OPTS.KIND = {'DELFRONT'}, 'DELAUNAY' -- the type of ref-
% inement employed. The 'DELFRONT' algorithm is typically
% slower, but produces higher quality output.
%
% - OPTS.RHO2 = {1.025} -- the maximum allowable radius-edge
% ratio. Refinement proceeds until all interior triangles
% satisfy the radius-edge threshold. Smaller radius-edge
% ratios lead to improved triangle shape, with RHO2=1 req-
% uiring that all angles exceed 30 degrees. Setting RHO2<1
% may lead to non-convergence.
%
% - OPTS.REF1 = {'REFINE'}, 'PRESERVE' -- refinement 'flag'
% for 1-dimensional faces (i.e. edges). The 'PRESERVE' op-
% tion results in minimal refinement, attempting to retain
% the initial edges without further subdivision. Edges are
% split only to satisfy basic geomertical conformance.
%
% - OPTS.REF2 = {'REFINE'}, 'PRESERVE' -- refinement 'flag'
% for 2-dimensional faces (i.e. trias). The 'PRESERVE' op-
% tion results in minimal refinement, attempting to retain
% the initial trias without further subdivision. Trias are
% split only to satisfy basic geomertical conformance.
%
% - OPTS.SIZ1 = {1.333} -- the normalised rel.-length th-
% reshold for edge-elements. Each exterior edge is refined
% until LL/HH<SIZ1, where LL is the edge-length, HH is the
% edge-centred mesh-size value.
%
% - OPTS.SIZ2 = {1.300} -- the normalised rel.-length th-
% reshold for tria-elements. Each interior tria is refined
% until RE/HH<SIZ2, where RE is an effective tria length,
% based on the circumradius, HH is the tria-centred mesh-
% size value.
%
% - OPTS.DISP = { +10 } -- refinement verbosity. Set to INF
% for quiet execution.
%
% [...] = REFINE2(..., HFUN,ARGS) also passes an optional
% mesh-size function argument. Setting HFUN = HMAX, where
% HMAX is a scalar value, imposes a constant size constra-
% int over the full domain. HFUN can also be defined as a
% general function handle [HH] = HFUN(PP), where PP is an
% N-by-2 array of XY coordinates and HH is the associated
% vector of mesh-size values. User-defined HFUN must be
% fully vectorised. Additional arguments {A1,A2,...AN} for
% HFUN can be passed as trailing parameters to REFINE2. In
% such cases, HFUN must adopt a signature [HH] = HFUN(PP,
% A1,A2,...,AN). HFUN must return positive values.
%
% See also SMOOTH2, TRIDIV2, TRICOST, TRIDEMO
% This routine implements a "multi-refinement" variant of
% Delaunay-refinement type mesh-generation. Both standard
% Delaunay-refinement and Frontal-Delaunay type algorithms
% are available. The Frontal-Delaunay approach is a simpl-
% ified version of the JIGSAW algorithm, described in:
%
% * D. Engwirda, (2014): "Locally-optimal Delaunay-refineme-
% nt and optimisation-based mesh generation", Ph.D. Thesis
% School of Mathematics and Statistics, Univ. of Sydney.
% http://hdl.handle.net/2123/13148
%
% * D. Engwirda & D. Ivers, (2016): "Off-centre Steiner poi-
% nts for Delaunay-refinement on curved surfaces", Comput-
% er-Aided Design, (72), 157--171.
% http://dx.doi.org/10.1016/j.cad.2015.10.007
% This work is an extension of the "off-centre" type tech-
% niques introduced in:
%
% * H. Erten & A. Ungor, (2009): "Quality triangulation with
% locally optimal Steiner points", SIAM Journal on Scient-
% ific Comp. 31(3), 2103--2130.
% http://doi.org/10.1137/080716748
%
% * S. Rebay, (1993): "Efficient Unstructured Mesh Generati-
% on by Means of Delaunay Triangulation and Bowyer-Watson
% Algorithm, J. Comp. Physics 106(1), 125--138.
% http://dx.doi.org/10.1006/jcph.1993.1097
% Generally speaking, the Delaunay-refinement method impl-
% emented here is a variantion of the "classical" algorit-
% hm introduced in:
%
% * J. Ruppert, (1995): "A Delaunay refinement algorithm for
% quality 2-dimensional mesh generation." Journal of Algo-
% rithms 18(3), 548--585.
% http://dx.doi.org/10.1006/jagm.1995.1021
%
% See also: S. Cheng, T. Dey & J. Shewchuk, (2012): "Dela-
% unay mesh generation", CRC Press, for comprehensive cov-
% erage of Delaunay-based meshing techniques.
% A much more advanced, and fully three-dimensional imple-
% mentation is available in the JIGSAW library. For addit-
% ional information, see:
% https://github.com/dengwirda/jigsaw-matlab
%-----------------------------------------------------------
% Darren Engwirda : 2017 --
% Email : [email protected]
% Last updated : 09/07/2018
%-----------------------------------------------------------
node = []; PSLG = []; part = {}; opts = [] ;
hfun = []; harg = {};
%---------------------------------------------- extract args
if (nargin>=+1), node = varargin{1}; end
if (nargin>=+2), PSLG = varargin{2}; end
if (nargin>=+3), part = varargin{3}; end
if (nargin>=+4), opts = varargin{4}; end
if (nargin>=+5), hfun = varargin{5}; end
if (nargin>=+6), harg = varargin(6:end); end
[opts] = makeopt(opts) ;
%---------------------------------------------- default EDGE
nnod = size(node,1) ;
if (isempty(PSLG))
PSLG = [(1:nnod-1)',(2:nnod)'; nnod,1] ;
end
%---------------------------------------------- default PART
ncon = size(PSLG,1) ;
if (isempty(part)), part{1} = (1:ncon)'; end
%---------------------------------------------- basic checks
if (~isnumeric(node) || ~isnumeric(PSLG) || ...
~iscell (part) || ~isstruct (opts) )
error('refine2:incorrectInputClass' , ...
'Incorrect input class.') ;
end
%---------------------------------------------- basic checks
if (ndims(node) ~= +2 || ndims(PSLG) ~= +2)
error('refine2:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
if (size(node,2) < +2 || size(PSLG,2) < +2)
error('refine2:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
%---------------------------------------------- basic checks
if (min([PSLG(:)])<+1 || max([PSLG(:)])>nnod)
error('refine2:invalidInputs', ...
'Invalid EDGE input array.') ;
end
pmin = cellfun(@min,part);
pmax = cellfun(@max,part);
if (min([pmin(:)])<+1 || max([pmax(:)])>ncon)
error('refine2:invalidInputs', ...
'Invalid PART input array.') ;
end
%-------------------------------- prune any non-unique topo.
[ivec,ivec,jvec] = ...
unique(sort(PSLG,+2),'rows') ;
PSLG = PSLG(ivec,:) ;
for ppos = +1:length(part)
if ( ~isnumeric(part{ppos}) )
error ( ...
'refine2:incorrectInputClass', ...
'Incorrect input class. ') ;
end
part{ppos} = ...
unique(jvec(part{ppos})) ;
end
%-------------------------------- check part "manifold-ness"
for ppos = +1:length(part)
eloc = PSLG(part{ppos},:) ;
nadj = ...
accumarray(eloc(:),1) ;
if (any(mod(nadj,2) ~= 0) )
error('refine2:nonmanifoldInputs', ...
'Non-manifold PART detected.') ;
end
end
%---------------------------------------------- output title
if (~isinf(opts.disp))
fprintf(1,'\n') ;
fprintf(1,' Refine triangulation...\n') ;
fprintf(1,'\n') ;
fprintf(1,[...
' -------------------------------------------------------\n', ...
' |ITER.| |CDT1(X)| |CDT2(X)| \n', ...
' -------------------------------------------------------\n', ...
] ) ;
end
%-------------------------------- PASS 0: inflate box bounds
vert = node; tria = []; tnum = []; iter = 0 ;
conn = PSLG;
vmin = min(vert,[],1); % inflate bbox for stability
vmax = max(vert,[],1);
vdel = vmax - 1.*vmin;
vmin = vmin - .5*vdel;
vmax = vmax + .5*vdel;
vbox = [
vmin(1), vmin(2)
vmax(1), vmin(2)
vmax(1), vmax(2)
vmin(1), vmax(2)
] ;
vert = [vert ; vbox] ;
%-------------------------------- PASS 0: shield sharp feat.
[vert,conn,tria,tnum,iter] = ...
cdtbal0(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter);
%-------------------------------- PASS 1: refine 1-simplexes
[vert,conn,tria,tnum,iter] = ...
cdtref1(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter);
%-------------------------------- PASS 2: refine 2-simplexes
[vert,conn,tria,tnum,iter] = ...
cdtref2(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter);
if (~isinf(opts.disp)), fprintf(1,'\n'); end
%-------------------------------- trim extra adjacency info.
tria = tria( :,1:3) ;
%-------------------------------- trim vert. - deflate bbox.
keep = false(size(vert,1),1);
keep(tria(:)) = true;
keep(conn(:)) = true;
redo = zeros(size(vert,1),1);
redo(keep) = ...
(+1:length(find(keep)))';
conn = redo(conn);
tria = redo(tria);
vert = vert(keep,:) ;
end
function [vert,conn,tria,tnum,iter] = ...
cdtbal0(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter)
%CDTBAL0 constrained Delaunay-refinement for "sharp" 0-dim.
%features at PSLG vertices.
% [...] = CDTBAL0(...) refines the set of 1-simplex eleme-
% nts incident to "sharp" features in the PSLG. Specifica-
% lly, edges that subtend "small" angles are split about a
% set of new "collar" vertices, equi-distributed about the
% centre of "sharp" features. Collar size is computed as a
% min. of the incident edge-len. and local mesh-size cons-
% traints.
if (iter <= opts.iter)
%------------------------------------- build current CDT
[vert,conn, ...
tria,tnum] = deltri2(vert,conn, ...
node,PSLG, ...
part, ...
opts.dtri) ;
%------------------------------------- build current adj
[edge,tria] = tricon2(tria,conn) ;
[feat,ftri] = isfeat2(vert, ...
edge,tria) ;
apex = false(size(vert,1), 1) ;
apex(tria(ftri)) = true ;
%------------------------------------- eval. length-fun.
if (~isempty(hfun))
if (isnumeric(hfun))
vlen = hfun * ...
ones(size(vert,1),1) ;
else
vlen = feval( ...
hfun,vert,harg{:}) ;
vlen = vlen(:) ;
end
else
vlen = +inf * ...
ones(size(vert,1),1) ;
end
%------------------------------------- form edge vectors
evec = vert(conn(:,2),:) ...
- vert(conn(:,1),:) ;
elen = sqrt(sum(evec.^2,2));
evec = evec./[elen,elen] ;
%------------------------------------- min. adj. lengths
for epos = +1 : size(conn,1)
ivrt = conn(epos,1) ;
jvrt = conn(epos,2) ;
vlen(ivrt) = min( ...
vlen(ivrt), .67*elen(epos)) ;
vlen(jvrt) = min( ...
vlen(jvrt), .67*elen(epos)) ;
end
%------------------------------------- mark feature edge
iref = apex(conn(:,1)) ... %- refine at vert. 1
& ~apex(conn(:,2)) ;
jref = apex(conn(:,2)) ... %- refine at vert. 2
& ~apex(conn(:,1)) ;
dref = apex(conn(:,1)) ... %- refine at both!
& apex(conn(:,2)) ;
keep =~apex(conn(:,1)) ... %- refine at neither
& ~apex(conn(:,2)) ;
%------------------------------------- protecting collar
ilen = vlen(conn(iref,1)) ;
inew = vert(conn(iref,1),:) ...
+ [ilen,ilen].*evec(iref,:) ;
jlen = vlen(conn(jref,2)) ;
jnew = vert(conn(jref,2),:) ...
- [jlen,jlen].*evec(jref,:) ;
Ilen = vlen(conn(dref,1)) ;
Inew = vert(conn(dref,1),:) ...
+ [Ilen,Ilen].*evec(dref,:) ;
Jlen = vlen(conn(dref,2)) ;
Jnew = vert(conn(dref,2),:) ...
- [Jlen,Jlen].*evec(dref,:) ;
vnew = [inew; jnew; Inew; Jnew] ;
%------------------------------------- add new vert/edge
iset = (1:size(inew,1))' ...
+ size(vert,1) ;
jset = (1:size(jnew,1))' ...
+ size(inew,1) + ...
+ size(vert,1) ;
Iset = (1:size(Inew,1))' ...
+ size(inew,1) + ...
+ size(jnew,1) + ...
+ size(vert,1) ;
Jset = (1:size(Jnew,1))' ...
+ size(inew,1) + ...
+ size(jnew,1) + ...
+ size(Inew,1) + ...
+ size(vert,1) ;
vert = [vert ; vnew] ;
cnew = [conn(iref,1), iset ;
conn(iref,2), iset ;
conn(jref,2), jset ;
conn(jref,1), jset ;
conn(dref,1), Iset ;
conn(dref,2), Jset ;
Iset, Jset] ;
conn = [conn(keep,:); cnew ] ;
end
end
function [vert,conn,tria,tnum,iter] = ...
cdtref1(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter)
%CDTREF1 constrained Delaunay-refinement for 1-simplex elem-
%nts embedded in R^2.
% [...] = CDTREF1(...) refines the set of 1-simplex eleme-
% nts embedded in the triangulation until all constraints
% are satisfied. Specifically, edges are refined until all
% local mesh-spacing and encroachment conditions are met.
% Refinement proceeds according to either a Delaunay-refi-
% nement or Frontal-Delaunay type approach, depending on
% user-settings. In either case, new steiner vertices are
% introduced to split "bad" edges - those that violate the
% set of prescribed constraints. In the "-DR" type process
% edges are split about their circumballs (midpoints). In
% the "-FD" approach, new vertices are positioned such th-
% at mesh-spacing constraints are satisfied in a "locally-
% optimal" fashion.
tcpu.full = +0. ;
tcpu.ball = +0. ;
tcpu.hfun = +0. ;
tcpu.encr = +0. ;
tcpu.offc = +0. ;
vidx = (1:size(vert,1))'; %- "new" vert list to test
tnow = tic ;
ntol = +1.55;
while (strcmpi(opts.ref1,'refine'))
iter = iter + 1 ;
if (iter>=opts.iter),break; end
%------------------------------------- calc. circumballs
ttic = tic ;
bal1 = cdtbal1(vert,conn) ;
tcpu.ball = ...
tcpu.ball + toc(ttic) ;
%------------------------------------- eval. length-fun.
ttic = tic ;
if (~isempty(hfun))
if (isnumeric(hfun))
fun0 = hfun * ...
ones(size(vert,1),1);
fun1 = hfun ;
else
fun0(vidx) = ...
feval(hfun, ...
vert(vidx,:), harg{:});
fun0 = fun0(:) ;
fun1 = fun0(conn(:,1))...
+ fun0(conn(:,2));
fun1 = fun1 / +2. ;
end
else
fun0 = +inf * ...
ones(size(vert,1),1);
fun1 = +inf ;
end
siz1 = ...
+4. * bal1(:,3)./(fun1.*fun1) ;
tcpu.hfun = ...
tcpu.hfun + toc(ttic) ;
%------------------------------------- test encroachment
ttic = tic ;
bal1(:,3) = ...
(1.-eps^.75) * bal1(:,3) ;
[vp,vi] = ...
findball(bal1,vert(:,1:2));
%------------------------------------- near=>[vert,edge]
next = +0;
ebad = false(size(conn,1),1) ;
near = zeros(size(conn,1),1) ;
for ii = +1 : size(vp,1)
for ip = vp(ii,1):vp(ii,2)
jj = vi(ip);
if (ii ~= conn(jj,1) ...
&& ii ~= conn(jj,2) )
next = next + 1;
near(next,1) = ii;
near(next,2) = jj;
end
end
end
near = near(1:next-0,:);
if (~isempty(near))
%-- mark edge "encroached" if there is a vert within its
%-- dia.-ball that is not joined to either of its vert's
%-- via an existing edge...
ivrt = conn(near(:,2),1);
jvrt = conn(near(:,2),2);
pair = [near(:,1), ivrt];
ivec = setset2(pair,conn) ;
pair = [near(:,1), jvrt];
jvec = setset2(pair,conn) ;
okay = ~ivec & ~jvec ;
ebad(near(okay,2))=true ;
end
tcpu.encr = ...
tcpu.encr + toc(ttic);
%------------------------------------- refinement queues
ref1 = false(size(conn,1),1);
ref1(ebad) = true ; %- edge encroachment
ref1(siz1>opts.siz1* ... %- bad equiv. length
opts.siz1) = true ;
num1 = find(ref1) ;
%------------------------------------- dump-out progess!
if (mod(iter,opts.disp)==0)
numc = size(conn,1) ;
numt = size(tria,1) ;
fprintf(+1, ...
'%11i %18i %18i\n', ...
[iter,numc,numt]) ;
end
%------------------------------------- nothing to refine
if (isempty(num1)), break; end
%------------------------------------- refine "bad" tria
switch (lower(opts.kind))
case 'delaunay'
%------------------------------------- do circ-ball pt's
new1 = bal1(ref1, 1:2) ;
vidx = (1:size(new1,1))' ...
+ size(vert,1) ;
cnew = [conn( ref1,1), vidx
conn( ref1,2), vidx];
conn = [conn(~ref1,:); cnew];
%------------------------------------- update vertex set
vert = [vert; new1(:,1:2)];
case 'delfront'
%-- symmetric off-centre scheme:- refine edges from both
%-- ends simultaneously, placing new vertices to satisfy
%-- the worst of mesh-spacing and local voronoi constra-
%-- ints.
ttic = tic ;
evec = vert(conn(ref1,2),:) ...
- vert(conn(ref1,1),:) ;
elen = sqrt(sum(evec.^2,2)) ;
evec = evec ./ [elen, elen] ;
%------------------------------------- "voro"-type dist.
vlen = sqrt(bal1(ref1,3));
%------------------------------------- "size"-type dist.
ihfn = fun0(conn(ref1,1));
jhfn = fun0(conn(ref1,2));
%------------------------------------- bind "safe" dist.
ilen = min(vlen,ihfn) ;
jlen = min(vlen,jhfn) ;
%------------------------------------- locate offcentres
inew = vert(conn(ref1,1),:) ...
+ [ilen,ilen].*evec ;
jnew = vert(conn(ref1,2),:) ...
- [jlen,jlen].*evec ;
%------------------------------------- iter. "size"-type
for ioff = +1 : +3
%------------------------------------- eval. length-fun.
if (~isempty(hfun))
if (isnumeric(hfun))
iprj = hfun * ...
ones(size(inew,1),1);
jprj = hfun * ...
ones(size(jnew,1),1);
else
iprj = feval( ...
hfun,inew,harg{:});
jprj = feval( ...
hfun,jnew,harg{:});
iprj = iprj(:);
jprj = jprj(:);
end
else
iprj = +inf * ...
ones(size(inew,1),1);
jprj = +inf * ...
ones(size(jnew,1),1);
end
iprj = 0.5*ihfn + 0.5*iprj;
jprj = 0.5*jhfn + 0.5*jprj;
%------------------------------------- bind "safe" dist.
ilen = min(vlen,iprj) ;
jlen = min(vlen,jprj) ;
%------------------------------------- locate offcentres
inew = vert(conn(ref1,1),:) ...
+ [ilen,ilen].*evec ;
jnew = vert(conn(ref1,2),:) ...
- [jlen,jlen].*evec ;
end
%------------------------------------- merge i,j if near
near = ...
ilen+jlen>=vlen*ntol ;
znew = inew(near,:) * .5 ...
+ jnew(near,:) * .5 ;
inew = inew(~near,1:2) ;
jnew = jnew(~near,1:2) ;
%------------------------------------- split constraints
zset = (1:size(znew,1))' ...
+ size(vert,1) ;
iset = (1:size(inew,1))' ...
+ size(znew,1) + ...
+ size(vert,1) ;
jset = (1:size(jnew,1))' ...
+ size(znew,1) + ...
+ size(inew,1) + ...
+ size(vert,1) ;
set1 = num1( near);
set2 = num1(~near);
cnew = [conn( set1,1), zset
conn( set1,2), zset
conn( set2,1), iset
conn( set2,2), jset
iset, jset ] ;
conn = [conn(~ref1,:); cnew];
%------------------------------------- update vertex set
vert = [vert; znew(:,1:2)];
vert = [vert; inew(:,1:2)];
vert = [vert; jnew(:,1:2)];
vidx = [zset; iset; jset] ;
tcpu.offc = ...
tcpu.offc + toc(ttic) ;
end % switch(lower(opts.kind))
end
tcpu.full = ...
tcpu.full + toc(tnow) ;
if (~isinf(opts.disp) )
%------------------------------------- print final stats
numc = size(conn,1) ;
numt = size(tria,1) ;
fprintf(+1, ...
'%11i %18i %18i\n', ...
[iter,numc,numt]) ;
end
if (opts.dbug)
%------------------------------------- print debug timer
fprintf(1,'\n') ;
fprintf(1,' 1-simplex REF. timer...\n');
fprintf(1,'\n') ;
fprintf(1, ...
' FULL: %f \n', tcpu.full);
fprintf(1, ...
' BALL: %f \n', tcpu.ball);
fprintf(1, ...
' HFUN: %f \n', tcpu.hfun);
fprintf(1, ...
' ENCR: %f \n', tcpu.encr);
fprintf(1, ...
' OFFC: %f \n', tcpu.offc);
fprintf(1,'\n') ;
end
end
function [vert,conn,tria,tnum,iter] = ...
cdtref2(vert,conn,tria,tnum, ...
node,PSLG,part,opts,hfun,harg,iter)
%CDTREF2 constrained Delaunay-refinement for 2-simplex elem-
%nts embedded in R^2.
% [...] = CDTREF2(...) refines the set of 2-simplex eleme-
% nts embedded in the triangulation until all constraints
% are satisfied. Specifically, triangles are refined until
% all local mesh-spacing and element-shape conditions are
% met. Refinement proceeds according to either a Delaunay-
% refinement or Frontal-Delaunay type approach, depending
% on user-settings. In either case, new steiner points are
% introduced to split "bad" triangles - those that violate
% the set of prescribed constraints. In the "-DR" type pr-
% ocess triangles are split about their circumballs. In
% the "-FD" approach, new vertices are positioned such th-
% at mesh-spacing and element-shape constraints are satis-
% fied in a "locally-optimal" fashion.
tcpu.full = +0. ;
tcpu.dtri = +0. ;
tcpu.tcon = +0. ;
tcpu.ball = +0. ;
tcpu.hfun = +0. ;
tcpu.offc = +0. ;
tcpu.filt = +0. ;
vidx = (1:size(vert,1))'; %- "new" vert list to test
tnow = tic ;
near = +.775;
while (strcmpi(opts.ref2,'refine'))
iter = iter + 1 ;
%------------------------------------- build current CDT
ttic = tic ;
nold = size(vert,1) ;
[vert,conn, ...
tria,tnum]= deltri2(vert,conn, ...
node,PSLG, ...
part, ....
opts.dtri) ;
nnew = size(vert,1) ;
vidx = ...
[vidx; (nold:nnew)'] ;
tcpu.dtri = ...
tcpu.dtri + toc(ttic) ;
%------------------------------------- build current adj
ttic = tic ;
[edge,tria]= tricon2(tria,conn) ;
tcpu.tcon = ...
tcpu.tcon + toc(ttic) ;
if (iter>=opts.iter),break; end
%------------------------------------- calc. circumballs
ttic = tic ;
bal1 = cdtbal1(vert,conn) ;
bal2 = cdtbal2(vert, ...
edge,tria) ;
len2 = minlen2(vert,tria) ;
rho2 = bal2(:,+3) ./ len2 ;
%------------------------------------- refinement scores
scr2 = rho2 .* bal2(:,+3) ;
tcpu.ball = ...
tcpu.ball + toc(ttic) ;
%------------------------------------- eval. length-fun.
ttic = tic ;
if (~isempty(hfun))
if (isnumeric(hfun))
fun0 = hfun * ...
ones(size(vert,1),1);
fun2 = hfun ;
else
fun0(vidx) = ...
feval(hfun, ...
vert(vidx,:), harg{:});
fun0 = fun0(:) ;
fun2 = fun0(tria(:,1))...
+ fun0(tria(:,2))...
+ fun0(tria(:,3));
fun2 = fun2 / +3. ;
end
else
fun0 = +inf * ...
ones(size(vert,1),1);
fun2 = +inf ;
end
siz2 = ...
+3. * bal2(:,3)./(fun2.*fun2) ;
tcpu.hfun = ...
tcpu.hfun + toc(ttic) ;
%------------------------------------- refinement queues
ref1 = false(size(conn,1),1);
ref2 = false(size(tria,1),1);
stri = isfeat2(vert,edge,tria) ;
ref2(rho2>opts.rho2* ... %- bad rad-edge len.
opts.rho2) = true ;
ref2(stri) = false ;
ref2(siz2>opts.siz2* ... %- bad equiv. length
opts.siz2) = true ;
num2 = find(ref2);
%------------------------------------- dump-out progess!
if (mod(iter,opts.disp)==0)
numc = size(conn,1) ;
numt = size(tria,1) ;
fprintf(+1, ...
'%11i %18i %18i\n', ...
[iter,numc,numt]) ;
end
%------------------------------------- nothing to refine
if (isempty(num2)), break; end
[scr2,idx2] = sort( ...
scr2(num2),'descend');
num2 = num2(idx2);
%------------------------------------- refine "bad" tria
switch (lower(opts.kind))
case 'delaunay'
%------------------------------------- do circ-ball pt's
new2 = zeros(length(num2),3);
new2(:,1:2) = bal2(num2,1:2);
rmin = ... %- min. insert radii
len2(num2)*(1.-eps^.75)^2 ;
new2(:, 3) = max( ...
bal2(num2,3)*near^2,rmin) ;
case 'delfront'
%-- off-centre scheme -- refine triangles by positioning
%-- new vertices along a local segment of the voronoi
%-- diagram, bounded by assoc. circmballs. New points
%-- are placed to satisfy the worst of local mesh-length
%-- and element-shape constraints.
ttic = tic ;
%------------------------------------- find frontal edge
[lmin,emin] = ...
minlen2(vert,tria(num2,:)) ;
ftri = false(length(num2),1) ;
epos = zeros(length(num2),1) ;
tadj = zeros(length(num2),1) ;
for ii = +1 : length(epos)
epos(ii) = tria( ...
num2(ii),emin(ii)+3) ;
end
%------------------------------------- find frontal tria
for enum = +1 : +3
eidx = tria(num2,enum+3) ;
ftri = ...
ftri | edge(eidx,5) > +0 ;
ione = ...
num2 ~= edge(eidx,3) ;
itwo = ~ione ;
tadj(ione) = ...
edge(eidx(ione),3);
tadj(itwo) = ...
edge(eidx(itwo),4);
okay = tadj > +0 ;
tidx = tadj(okay);
ftri(okay) = ...
ftri(okay) | ~ref2(tidx) ;
end
if (~any(ftri)) %- can this happen!?
ftri = true(length(num2),+1) ;
end
%------------------------------------- locate offcentres
emid = vert(edge(epos,+1),:) ...
+ vert(edge(epos,+2),:) ;
emid = emid * +0.50 ;
elen = sqrt(lmin(:));
%------------------------------------- "voro"-type dist.
vvec = bal2(num2,1:2)-emid ;
vlen = sqrt(sum(vvec.^2,2));
vvec = vvec ./ [vlen,vlen] ;
hmid = fun0(edge(epos,+1),:) ...
+ fun0(edge(epos,+2),:) ;
hmid = hmid * +0.50 ;
%------------------------------------- "ball"-type dist.
rtri = elen * opts.off2 ;
rfac = elen * +0.50 ;
dsqr = rtri.^2 - rfac.^2;
doff = rtri + ...
sqrt(max(+0.,dsqr)) ;
%------------------------------------- "size"-type dist.
dsiz = +sqrt(3.)/2. * hmid ;
%------------------------------------- bind "safe" dist.
[dist,ioff] = ...
min([dsiz,doff,vlen],[],2) ;
%------------------------------------- locate offcentres
off2 = ...
emid + [dist,dist] .* vvec ;
%------------------------------------- iter. "size"-type
for isub = +1 : +3
%------------------------------------- eval. length-fun.
if (~isempty(hfun))
if (isnumeric(hfun))
hprj = hfun * ...
ones(size(off2,1),1) ;
else
hprj = feval( ...
hfun,off2,harg{:}) ;
hprj = hprj(:) ;
end
else
hprj = +inf * ...
ones(size(off2,1),1) ;
end
%------------------------------------- "size"-type dist.
hprj = .33*hmid + .67*hprj ;
dsiz = +sqrt(3.)/2. * hprj ;
dsiz(dsiz<elen*.50) = +inf ; %- edge-ball limiter
dsiz(dsiz>vlen*.95) = +inf ; %- circ-ball limiter
%------------------------------------- bind "safe" dist.
[dist,ioff] = ...
min([dsiz,doff,vlen],[],2) ;
%------------------------------------- locate offcentres
off2 = ...
emid + [dist,dist] .* vvec ;
end
orad = ...
sqrt((elen*.5).^2 + dist.^2) ;
%------------------------------------- do offcentre pt's
new2 = ...
zeros(length(find(ftri)),+3) ;
new2(:,1:2) = off2(ftri,1:2) ;
rmin = ... %- min. insert radii
lmin(ftri)*(1.-eps^.75)^2 ;
new2(:, 3) = max( ...
(orad(ftri)*near).^2,rmin);
tcpu.offc = ...
tcpu.offc + toc (ttic) ;
end % switch(lower(opts.kind))
%------------------------------------- inter.-ball dist.
ttic = tic ;
%------------------------------------- proximity filters
[vp,vi] = ...
findball(new2,new2(:,1:2)) ;
keep = true (size(new2,1),1) ;
for ii = size(vp,1):-1:+1
for ip = vp(ii,1) ...
: vp(ii,2)
jj = vi(ip);
if (keep(jj) && ...
keep(ii) && ...
jj < ii )
keep(ii) = false ;
break;
end
end
end
new2 = new2(keep,:);
%------------------------------------- test encroachment
bal1(:,3) = ...
(1.-eps^.75) * bal1(:,3);
[vp,vi] = ...
findball(bal1,new2(:,1:2));
keep = true (size(new2,1),1);
for ii = +1:+1:size(vp,1)
for ip = vp(ii,1) ...
: vp(ii,2)
jj = vi(ip);
ref1(jj) = true ;
keep(ii) = false ;
end
end
%------------------------------------- leave sharp edges
ebnd = false(size(edge,1),1);
ebnd(tria(stri,4:6)) = true ;
enot = ...
setset2(conn,edge(ebnd,1:2));
ref1(enot) = false ;
%------------------------------------- preserve boundary
if (strcmp(lower(opts.ref1),...
'preserve'))
ref1(:) = false ;
end
%------------------------------------- refinement points
new2 = new2(keep,:);
new1 = bal1(ref1,:);
tcpu.filt = ...
tcpu.filt + toc(ttic) ;
%------------------------------------- split constraints
idx1 = ...
(1:size(new1))'+size(vert,1) ;
idx2 = ...
(1:size(new2))'+size(new1,1) ...
+size(vert,1) ;
cnew = [conn( ref1,1), idx1
conn( ref1,2), idx1];
conn = [conn(~ref1,:); cnew];
vidx = [idx1; idx2];
%------------------------------------- update vertex set
nold = size(vert,1);
vert = [vert; new1(:,1:2)];
vert = [vert; new2(:,1:2)];
nnew = size(vert,1);
if (nnew == nold), break; end %- we *must* be done
end
tcpu.full = ...
tcpu.full + toc(tnow) ;
if (~isinf(opts.disp) )
%------------------------------------- print final stats
numc = size(conn,1) ;
numt = size(tria,1) ;
fprintf(+1, ...
'%11i %18i %18i\n', ...
[iter,numc,numt]) ;
end
if (opts.dbug)
%------------------------------------- print debug timer
fprintf(1,'\n') ;
fprintf(1,' 2-simplex REF. timer...\n');
fprintf(1,'\n') ;
fprintf(1, ...
' FULL: %f \n', tcpu.full);
fprintf(1, ...
' DTRI: %f \n', tcpu.dtri);
fprintf(1, ...
' TCON: %f \n', tcpu.tcon);
fprintf(1, ...
' BALL: %f \n', tcpu.ball);
fprintf(1, ...
' HFUN: %f \n', tcpu.hfun);
fprintf(1, ...
' OFFC: %f \n', tcpu.offc);
fprintf(1, ...
' FILT: %f \n', tcpu.filt);
fprintf(1,'\n') ;
end
end
function [opts] = makeopt(opts)
%MAKEOPT setup the options structure for REFINE2.
if (~isfield(opts,'dtri'))
opts.dtri = 'constrained';
else
if (~strcmpi(opts.dtri, 'conforming') && ...
~strcmpi(opts.dtri,'constrained') )
error( ...
'refine2:invalidOption','Invalid constraint DTRI.');
end
end
if (~isfield(opts,'kind'))
opts.kind = 'delfront';
else
if (~strcmpi(opts.kind, 'delfront') && ...
~strcmpi(opts.kind, 'delaunay') )
error( ...
'refine2:invalidOption','Invalid refinement KIND.');
end
end
if (~isfield(opts,'ref1'))
opts.ref1 = 'refine';
else
if (~strcmpi(opts.ref1, 'refine') && ...
~strcmpi(opts.ref1, 'preserve') )
error( ...
'refine2:invalidOption','Invalid refinement REF1.');
end
end
if (~isfield(opts,'ref2'))
opts.ref2 = 'refine';
else
if (~strcmpi(opts.ref2, 'refine') && ...
~strcmpi(opts.ref2, 'preserve') )
error( ...
'refine2:invalidOption','Invalid refinement REF2.');
end
end
if (~isfield(opts,'iter'))
opts.iter = +inf;
else
if (~isnumeric(opts.iter))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.iter)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.iter <= +0)
error('refine2:invalidOptionValues', ...
'Invalid OPT.ITER selection.') ;
end
end
if (~isfield(opts,'disp'))
opts.disp = +10 ;
else
if (~isnumeric(opts.disp))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.disp)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.disp <= +0)
error('refine2:invalidOptionValues', ...
'Invalid OPT.DISP selection.') ;
end
end
if (~isfield(opts,'rho2'))
opts.rho2 = 1.025;
else
if (~isnumeric(opts.rho2))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.rho2)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.rho2 < +1.)
error('refine2:invalidOptionValues', ...
'Invalid OPT.RHO2 selection.') ;
end
end
if (~isfield(opts,'off2'))
opts.off2 = 0.933;
else
if (~isnumeric(opts.off2))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.off2)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.off2 < +.7)
error('refine2:invalidOptionValues', ...
'Invalid OPT.OFF2 selection.') ;
end
end
if (~isfield(opts,'siz1'))
opts.siz1 = 1.333;
else
if (~isnumeric(opts.siz1))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.siz1)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.siz1 <= 0.)
error('refine2:invalidOptionValues', ...
'Invalid OPT.SIZ1 selection.') ;
end
end
if (~isfield(opts,'siz2'))
opts.siz2 = 1.300;
else
if (~isnumeric(opts.siz2))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.siz2)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.siz2 <= 0.)
error('refine2:invalidOptionValues', ...
'Invalid OPT.SIZ2 selection.') ;
end
end
if (~isfield(opts,'dbug'))
opts.dbug = false;
else
if (~islogical(opts.dbug))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.dbug)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
tridemo.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-2d/tridemo.m
| 27,638 |
utf_8
|
0d592600bfff8aa51497b1c6ea94a5a3
|
function tridemo(demo)
%TRIDEMO run various triangulation demos for MESH2D.
% TRIDEMO(N) runs the N-TH demo problem. The following de-
% mo problems are currently available:
%
% - DEMO-0: very simple example to start with -- construct a
% mesh for a square domain with a square hold cut from its
% centre.
%
% - DEMO-1: explore the impact of the "radius-edge" thresho-
% ld (RHO2) on mesh density/quality.
%
% - DEMO-2: explore the impact of the "Frontal-Delaunay" vs.
% "Delaunay-refinement " algorithms.
%
% - DEMO-3: explore impact of user-defined mesh-size constr-
% aints.
%
% - DEMO-4: explore impact of "hill-climbing" mesh optimisa-
% tions.
%
% - DEMO-5: assemble triangulations for multi-part geometry
% definitions.
%
% - DEMO-6: assemble triangulations for geometries with int-
% ernal constraints.
%
% - DEMO-7: investigate the use of quadtree-type refinement.
%
% - DEMO-8: explore impact of user-defined mesh-size constr-
% aints.
%
% - DEMO-9: larger-scale problem, mesh refinement + optimis-
% ation.
%
% - DEMO10: medium-scale problem, mesh refinement + optimis-
% ation.
%
% See also REFINE2, SMOOTH2, TRIDIV2, FIXGEO2
%-----------------------------------------------------------
% Darren Engwirda : 2017 --
% Email : [email protected]
% Last updated : 09/07/2018
%-----------------------------------------------------------
close all;
libpath();
switch (demo)
case 0, demo0 ();
case 1, demo1 ();
case 2, demo2 ();
case 3, demo3 ();
case 4, demo4 ();
case 5, demo5 ();
case 6, demo6 ();
case 7, demo7 ();
case 8, demo8 ();
case 9, demo9 ();
case 10, demo10();
otherwise
error('tridemo:invalidSelection', 'Invalid selection!') ;
end
end
function demo0
%DEMO0 a very simple example to start with -- mesh a square
%domain with a square hold cut from its centre.
fprintf(1, [ ...
' A very simple example to start with -- construct a mesh for \n', ...
' a simple square domain with a square hole cut from its cen- \n', ...
' tre. The geometry is specified as a Planar Straight-Line \n', ...
' Graph (PSLG) -- a list of xy coordinates, or "nodes", and a \n', ...
' list of straight-line connections between nodes, or "edges".\n', ...
' The REFINE2 routine is used to build a triangulation of the \n', ...
' domain that: (a) conforms to the geometry, and (b) contains \n', ...
' only "nicely" shaped triangles. In the second panel, a mesh \n', ...
' that additionally satisfies "mesh-size" constrains is cons- \n', ...
' structed -- '
] ) ;
%------------------------------------------- setup geometry
node = [ % list of xy "node" coordinates
0, 0 % outer square
9, 0
9, 9
0, 9
4, 4 % inner square
5, 4
5, 5
4, 5 ] ;
edge = [ % list of "edges" between nodes
1, 2 % outer square
2, 3
3, 4
4, 1
5, 6 % inner square
6, 7
7, 8
8, 5 ] ;
%------------------------------------------- call mesh-gen.
[vert,etri, ...
tria,tnum] = refine2(node,edge) ;
%------------------------------------------- draw tria-mesh
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
%------------------------------------------- call mesh-gen.
hfun = +.5 ; % uniform "target" edge-lengths
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun) ;
%------------------------------------------- draw tria-mesh
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
end
function demo1
%DEMO1 explore impact of RHO2 threshold on mesh density/qua-
%lity.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/lake.msh'];
[node,edge] = triread( meshfile );
fprintf(1, [ ...
' The REFINE2 routine can be used to build guaranteed-quality \n', ...
' Delaunay triangulations for general polygonal geometries in \n', ...
' the two-dimensional plane. The "quality" of elements in the \n', ...
' triangulation can be controlled using the "radius-edge" bo- \n', ...
' und RHO2. \n', ...
] ) ;
%---------------------------------------------- RHO2 = +1.50
fprintf(1, ' \n') ;
fprintf(1, [ ...
' Setting large values for RHO2, (RHO2 = 1.50 here) generates \n', ...
' sparse triangulations with poor worst-case angle bounds. \n', ...
] ) ;
opts.kind = 'delaunay';
opts.rho2 = +1.50 ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[] ,opts) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['TRIA-MESH: RHO2<=+1.50, |TRIA|=' , ...
num2str(size(tria,1))]) ;
%---------------------------------------------- RHO2 = +1.00
fprintf(1, [ ...
' Setting small values for RHO2, (RHO2 = 1.00 here) generates \n', ...
' dense triangulations with good worst-case angle bounds. \n', ...
] ) ;
opts.kind = 'delaunay';
opts.rho2 = +1.00 ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[] ,opts) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['TRIA-MESH: RHO2<=+1.00, |TRIA|=' , ...
num2str(size(tria,1))]) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
end
function demo2
%DEMO2 explore impact of refinement "KIND" on mesh quality/-
%density.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/lake.msh'];
[node,edge] = triread( meshfile );
fprintf(1, [ ...
' The REFINE2 routine supports two Delaunay-based refinement \n', ...
' algorithms: a "standard" Delaunay-refinement type approach, \n', ...
' and a "Frontal-Delaunay" technique. For problems constrain- \n', ...
' ed by element "quality" alone, the Frontal-Delaunay approa- \n', ...
' ch typically produces sigificantly sparser meshes. in both \n', ...
' cases, the same worst-case element quality bounds are sati- \n', ...
' fied in a guaranteed manner. \n', ...
] ) ;
%---------------------------------------------- = "DELAUNAY"
opts.kind = 'delaunay';
opts.rho2 = +1.00 ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[] ,opts) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
hold on; axis image off;
title(['TRIA-MESH: KIND=DELAUNAY, |TRIA|=', ...
num2str(size(tria,1))]) ;
%---------------------------------------------- = "DELFRONT"
opts.kind = 'delfront';
opts.rho2 = +1.00 ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[] ,opts) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['TRIA-MESH: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
end
function demo3
%DEMO3 explore impact of user-defined mesh-size constraints.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/airfoil.msh'];
[node,edge] = triread( meshfile );
fprintf(1, [ ...
' Additionally, the REFINE2 routine supports size-driven ref- \n', ...
' inement, producing meshes that satisfy constraints on elem- \n', ...
' ent edge-lengths. The LFSHFN2 routine can be used to create \n', ...
' mesh-size functions based on an estimate of the "local-fea- \n', ...
' ture-size" associated with a polygonal domain. The Frontal- \n', ...
' Delaunay refinement algorithm discussed in DEMO-2 is espec- \n', ...
' ially good at generating high-quality triangulations in the \n', ...
' presence of mesh-size constraints. \n', ...
] ) ;
%---------------------------------------------- do size-fun.
olfs.dhdx = +0.15;
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge, ...
[] ,olfs) ;
[slfs] = idxtri2(vlfs,tlfs) ;
figure;
patch('faces',tlfs(:,1:3),'vertices',vlfs , ...
'facevertexcdata' , hlfs, ...
'facecolor','interp', ...
'edgecolor','none') ;
hold on; axis image off;
title(['MESH-SIZE: KIND=DELAUNAY, |TRIA|=', ...
num2str(size(tlfs,1))]) ;
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun , ...
vlfs,tlfs,slfs,hlfs);
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['TRIA-MESH: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
end
function demo4
%DEMO4 explore impact of "hill-climbing" mesh optimisations.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/airfoil.msh'];
[node,edge] = triread( meshfile );
fprintf(1, [ ...
' The SMOOTH2 routine provides iterative mesh "smoothing" ca- \n', ...
' pabilities, seeking to improve triangulation quality by ad- \n', ...
' justing the vertex positions and mesh topology. Specifical- \n', ...
' ly, a "hill-climbing" type optimisation is implemented, gu- \n', ...
' aranteeing that mesh-quality is improved monotonically. The \n', ...
' DRAWSCR routine provides detailed analysis of triangulation \n', ...
' quality, plotting histograms of various quality metrics. \n', ...
] ) ;
%---------------------------------------------- do size-fun.
olfs.dhdx = +0.15;
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge, ...
[] ,olfs) ;
[slfs] = idxtri2(vlfs,tlfs) ;
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun , ...
vlfs,tlfs,slfs,hlfs);
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-REF.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
%---------------------------------------------- do mesh-opt.
[vnew,enew, ...
tnew,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tnew(:,1:3),'vertices',vnew, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tnew,1))]) ;
hvrt = trihfn2(vert,vlfs,tlfs,slfs,hlfs) ;
hnew = trihfn2(vnew,vlfs,tlfs,slfs,hlfs) ;
tricost(vert,etri,tria,tnum,hvrt) ;
tricost(vnew,enew,tnew,tnum,hnew) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
set(figure(3),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
set(figure(4),'units','normalized', ...
'position',[.35,.05,.30,.35]) ;
end
function demo5
%DEMO5 assemble triangulations for multi-part geometry defi-
%nitions.
fprintf(1, [ ...
' Both the REFINE2 and SMOOTH2 routines also support "multi- \n', ...
' part" geometry definitions -- generating conforming triang- \n', ...
' ulations that conform to internal and external constraints. \n', ...
] ) ;
%---------------------------------------------- create geom.
nod1 = [
-1., -1.; +1., -1.
+1., +1.; -1., +1.
] ;
edg1 = [
1 , 2 ; 2 , 3
3 , 4 ; 4 , 1
] ;
edg1(:,3) = +0;
nod2 = [
+.1, +0.; +.8, +0.
+.8, +.8; +.1, +.8
] ;
edg2 = [
1 , 2 ; 2 , 3
3 , 4 ; 4 , 1
] ;
edg2(:,3) = +1;
adel = 2.*pi / +64 ;
amin = 0.*pi ;
amax = 2.*pi - adel;
xcir = +.33 * ...
cos(amin:adel:amax)';
ycir = +.33 * ...
sin(amin:adel:amax)';
xcir = xcir - .33;
ycir = ycir - .25;
ncir = [xcir,ycir] ;
numc = size(ncir,1);
ecir(:,1) = ...
[(1:numc-1)'; numc] ;
ecir(:,2) = ...
[(2:numc-0)'; +1 ] ;
ecir(:,3) = +2;
edg2(:,1:2) = ...
edg2(:,1:2)+size(nod1,1);
edge = [edg1; edg2];
node = [nod1; nod2];
ecir(:,1:2) = ...
ecir(:,1:2)+size(node,1);
edge = [edge; ecir];
node = [node; ncir];
%-- the PART argument is a cell array that defines individu-
%-- al polygonal "parts" of the overall geometry. Each elem-
%-- ent PART{I} is a list of edge indexes, indicating which
%-- edges make up the boundary of each region.
part{1} = [ ...
find(edge(:,3) == 0)
find(edge(:,3) == 1)
find(edge(:,3) == 2)
] ;
part{2} = [ ...
find(edge(:,3) == 1)
] ;
part{3} = [ ...
find(edge(:,3) == 2)
] ;
edge = edge(:,1:2) ;
%---------------------------------------------- do size-fun.
hmax = +0.045 ;
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge, ...
part) ;
hlfs = min(hmax,hlfs) ;
[slfs] = idxtri2(vlfs,tlfs) ;
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,part, [], ...
hfun, ...
vlfs,tlfs,slfs,hlfs) ;
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tria(tnum==1,1:3),'vertices',vert, ...
'facecolor',[1.,1.,1.], ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',tria(tnum==2,1:3),'vertices',vert, ...
'facecolor',[.9,.9,.9], ...
'edgecolor',[.2,.2,.2]) ;
patch('faces',tria(tnum==3,1:3),'vertices',vert, ...
'facecolor',[.8,.8,.8], ...
'edgecolor',[.2,.2,.2]) ;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
figure;
patch('faces',tlfs(:,1:3),'vertices',vlfs , ...
'facevertexcdata' , hlfs, ...
'facecolor','interp', ...
'edgecolor','none') ;
hold on; axis image off;
title(['MESH-SIZE: KIND=DELAUNAY, |TRIA|=', ...
num2str(size(tlfs,1))]) ;
tricost(vert,etri,tria,tnum);
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
set(figure(3),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
end
function demo6
%DEMO6 build triangulations for geometries with internal co-
%nstraints.
fprintf(1, [ ...
' Both the REFINE2 and SMOOTH2 routines also support geometr- \n', ...
' ies containing "internal" constraints. \n', ...
] ) ;
%---------------------------------------------- create geom.
node = [
-1., -1.; +1., -1.
+1., +1.; -1., +1.
+.0, +.0; +.2, +.7
+.6, +.2; +.4, +.8
+0., +.5; -.7, +.3
-.1, +.1; -.6, +.5
-.9, -.8; -.6, -.7
-.3, -.6; +.0, -.5
+.3, -.4; -.3, +.4
-.1, +.3
] ;
edge = [
1 , 2 ; 2 , 3
3 , 4 ; 4 , 1
5 , 6 ; 5 , 7
5 , 8 ; 5 , 9
5 , 10 ; 5 , 11
5 , 12 ; 5 , 13
5 , 14 ; 5 , 15
5 , 16 ; 5 , 17
5 , 18 ; 5 , 19
] ;
%-- the geometry must be split into its "exterior" and "int-
%-- erior" components using the optional PART argument. Each
%-- PART{I} specified should define the "exterior" boundary
%-- of a polygonal region. "Interior" constraints should not
%-- be referenced by any polygon in PART -- they are imposed
%-- as isolated edge constraints.
part{1} = [1,2,3,4] ;
%---------------------------------------------- do size-fun.
hmax = +0.175 ;
%---------------------------------------------- do mesh-gen.
opts.kind = 'delaunay' ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,part,opts, ...
hmax) ;
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',2.0) ;
title(['MESH-OPT.: KIND=DELAUNAY, |TRIA|=', ...
num2str(size(tria,1))]) ;
tricost(vert,etri,tria,tnum);
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
end
function demo7
%DEMO7 investigate the use of quadtree-type mesh refinement.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/channel.msh'];
[node,edge] = triread( meshfile );
fprintf(1, [ ...
' The TRIDIV2 routine can also be used to refine existing tr- \n', ...
' angulations. Each triangle is split into four new sub-tria- \n', ...
' ngles, such that element shape is preserved. Combining the \n', ...
' TRIDIV2 and SMOOTH2 routines allows for hierarchies of high \n', ...
' quality triangulations to be generated. \n', ...
] ) ;
%---------------------------------------------- do size-fun.
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge) ;
[slfs] = idxtri2(vlfs,tlfs) ;
pmax = max(node,[],1);
pmin = min(node,[],1);
hmax = mean(pmax-pmin)/+17 ;
hlfs = min(hmax,hlfs);
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun , ...
vlfs,tlfs,slfs,hlfs);
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
[vnew,enew, ...
tnew,tnum] = tridiv2(vert,etri,tria,tnum) ;
[vnew,enew, ...
tnew,tnum] = smooth2(vnew,enew,tnew,tnum) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
figure;
patch('faces',tnew(:,1:3),'vertices',vnew, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',etri(:,1:2),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tnew,1))]) ;
tricost(vert,etri,tria,tnum);
tricost(vnew,enew,tnew,tnum);
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
set(figure(3),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
set(figure(4),'units','normalized', ...
'position',[.35,.05,.30,.35]) ;
end
function demo8
%DEMO8 explore impact of "hill-climbing" mesh optimisations.
%---------------------------------------------- create geom.
node = [
-1., -1.; +3., -1.
+3., +1.; -1., +1.
] ;
edge = [
1 , 2 ; 2 , 3
3 , 4 ; 4 , 1
] ;
adel = 2.*pi / +64 ;
amin = 0.*pi ;
amax = 2.*pi - adel;
xcir = +.20 * ...
cos(amin:adel:amax)';
ycir = +.20 * ...
sin(amin:adel:amax)';
ncir = [xcir,ycir] ;
numc = size(ncir,1);
ecir(:,1) = ...
[(1:numc-1)'; numc] ;
ecir(:,2) = ...
[(2:numc-0)'; +1 ] ;
ecir = ecir+size(node,1);
edge = [edge; ecir];
node = [node; ncir];
%---------------------------------------------- do mesh-gen.
hfun = @hfun8 ;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun);
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert , ...
'facevertexcdata' , hfun8(vert), ...
'facecolor','interp', ...
'edgecolor','none') ;
hold on; axis image off;
title('MESH-SIZE function.');
hvrt = feval(hfun,vert) ;
tricost(vert,etri,tria,tnum,hvrt) ;
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.35,.50,.30,.35]) ;
set(figure(3),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
end
function [hfun] = hfun8(test)
%HFUN8 user-defined mesh-size function for DEMO-8.
hmax = +.05 ;
hmin = +.01 ;
xmid = +0.0 ;
ymid = +0.0 ;
hcir = exp( -.5*(test(:,1)-xmid).^2 ...
-2.*(test(:,2)-ymid).^2 ) ;
hfun = hmax - (hmax-hmin) * hcir ;
end
function demo9
%DEMO9 larger-scale problem, mesh refinement + optimisation.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/islands.msh'];
[node,edge] = triread( meshfile );
%---------------------------------------------- do size-fun.
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge) ;
[slfs] = idxtri2(vlfs,tlfs) ;
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun , ...
vlfs,tlfs,slfs,hlfs);
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
tricost(vert,etri,tria,tnum);
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
end
function demo10
%DEMO10 medium-scale problem mesh refinement + optimisation.
filename = mfilename('fullpath');
filepath = fileparts( filename );
meshfile = ...
[filepath,'/poly-data/river.msh'];
[node,edge] = triread( meshfile );
%---------------------------------------------- do size-fun.
[vlfs,tlfs, ...
hlfs] = lfshfn2(node,edge) ;
[slfs] = idxtri2(vlfs,tlfs) ;
%---------------------------------------------- do mesh-gen.
hfun = @trihfn2;
[vert,etri, ...
tria,tnum] = refine2(node,edge,[],[],hfun , ...
vlfs,tlfs,slfs,hlfs);
%---------------------------------------------- do mesh-opt.
[vert,etri, ...
tria,tnum] = smooth2(vert,etri,tria,tnum) ;
figure;
patch('faces',tria(:,1:3),'vertices',vert, ...
'facecolor','w', ...
'edgecolor',[.2,.2,.2]) ;
hold on; axis image off;
patch('faces',edge(:,1:2),'vertices',node, ...
'facecolor','w', ...
'edgecolor',[.1,.1,.1], ...
'linewidth',1.5) ;
title(['MESH-OPT.: KIND=DELFRONT, |TRIA|=', ...
num2str(size(tria,1))]) ;
tricost(vert,etri,tria,tnum);
drawnow;
set(figure(1),'units','normalized', ...
'position',[.05,.50,.30,.35]) ;
set(figure(2),'units','normalized', ...
'position',[.05,.05,.30,.35]) ;
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
tricost.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-2d/tricost.m
| 15,234 |
utf_8
|
7da2993c7253435846c34a8b1244bc43
|
function tricost(varargin)
%TRICOST draw quality-metrics for a 2-simplex triangulation
%embedded in the two-dimensional plane.
% TRICOST(VERT,EDGE,TRIA,TNUM) draws histograms of quality
% metrics for the triangulation.
% VERT is a V-by-2 array of XY coordinates in the triangu-
% lation, EDGE is an array of constrained edges, TRIA is a
% T-by-3 array of triangles, and TNUM is a T-by-1 array of
% part indices. Each row of TRIA and EDGE define an eleme-
% nt. VERT(TRIA(II,1),:), VERT(TRIA(II,2),:) and VERT(TRIA
% (II,3),:) are the coordinates of the II-TH triangle. The
% edges in EDGE are defined in a similar manner. NUM is an
% array of part indexing, such that TNUM(II) is the index
% of the part in which the II-TH triangle resides.
%
% TRICOST(...,HVRT) additionally draws histograms of rela-
% tive edge-length, indicating conformance to the spacing
% constraints. HVRT is a V-by-1 array of spacing informat-
% ion, per an evaluation of the mesh-size function at the
% mesh vertices VERT.
%
% See also REFINE2, SMOOTH2
%-----------------------------------------------------------
% Darren Engwirda : 2017 --
% Email : [email protected]
% Last updated : 09/07/2018
%-----------------------------------------------------------
vert = [] ; conn = [] ; tria = [] ;
tnum = [] ; hvrt = [] ;
%---------------------------------------------- extract args
if (nargin>=+1), vert = varargin{1}; end
if (nargin>=+2), conn = varargin{2}; end
if (nargin>=+3), tria = varargin{3}; end
if (nargin>=+4), tnum = varargin{4}; end
if (nargin>=+5), hvrt = varargin{5}; end
%---------------------------------------------- basic checks
if ( ~isnumeric(vert) || ...
~isnumeric(conn) || ...
~isnumeric(tria) || ...
~isnumeric(tnum) || ...
~isnumeric(hvrt) )
error('tricost:incorrectInputClass' , ...
'Incorrect input class.') ;
end
%---------------------------------------------- basic checks
if (ndims(vert) ~= +2 || ...
ndims(conn) ~= +2 || ...
ndims(tria) ~= +2 )
error('tricost:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
if (size(vert,2)~= +2 || ...
size(conn,2) < +2 || ...
size(tria,2) < +3 )
error('tricost:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
nvrt = size(vert,1) ;
ntri = size(tria,1) ;
%---------------------------------------------- basic checks
if (min(min(conn(:,1:2))) < +1 || ...
max(max(conn(:,1:2))) > nvrt )
error('tricost:invalidInputs', ...
'Invalid EDGE input array.') ;
end
if (min(min(tria(:,1:3))) < +1 || ...
max(max(tria(:,1:3))) > nvrt )
error('tricost:invalidInputs', ...
'Invalid TRIA input array.') ;
end
%-- borrowed from the JIGSAW library!
%-- draw sub-axes directly -- sub-plot gives
%-- silly inconsistent ax spacing...!
axpos31 = [.125,.750,.800,.150] ;
axpos32 = [.125,.450,.800,.150] ;
axpos33 = [.125,.150,.800,.150] ;
axpos41 = [.125,.835,.800,.135] ;
axpos42 = [.125,.590,.800,.135] ;
axpos43 = [.125,.345,.800,.135] ;
axpos44 = [.125,.100,.800,.135] ;
%-- draw cost histograms for 2-tria elements
figure;
set(gcf,'color','w','units','normalized', ...
'position',[.05,.10,.30,.30]);
if (~isempty(hvrt))
%-- have size-func data
axes('position',axpos41); hold on;
scrhist(triscr2(vert,tria),'tria3');
axes('position',axpos42); hold on;
anghist(triang2(vert,tria),'tria3');
axes('position',axpos43); hold on;
hfnhist(relhfn2(vert, ...
tria,hvrt),'tria3');
axes('position',axpos44); hold on;
deghist(trideg2(vert,tria),'tria3');
else
%-- null size-func data
axes('position',axpos31); hold on;
scrhist(triscr2(vert,tria),'tria3');
axes('position',axpos32); hold on;
anghist(triang2(vert,tria),'tria3');
axes('position',axpos33); hold on;
deghist(trideg2(vert,tria),'tria3');
end
end
function [mf] = mad(ff)
%MAD return mean absolute deviation (from the mean).
mf = mean(abs(ff-mean(ff))) ;
end
function deghist(dd,ty)
%DEGHIST draw histogram for "degree" quality-metric.
dd = dd(:);
be = 1:max(dd);
hc = histc(dd,be);
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(be,hc,1.05,'facecolor',k,'edgecolor',k);
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',2:2:12,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0,12]);
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.225,0,'$|d|_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.225,0, '|d|_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.225,0,'$|d|_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.225,0, '|d|_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function anghist(ad,ty)
%ANGHIST draw histogram for "angle" quality-metric.
ad = ad(:);
be = linspace(0.,180.,91);
bm =(be(1:end-1)+be(2:end))/2.;
hc = histc(ad,be);
switch (ty)
case 'tria4'
poor = bm < 10. | bm >= 160. ;
okay =(bm >= 10. & bm < 20. )| ...
(bm >= 140. & bm < 160.);
good =(bm >= 20. & bm < 30. )| ...
(bm >= 120. & bm < 140.);
best = bm >= 30. & bm < 120. ;
case 'tria3'
poor = bm < 15. | bm >= 150. ;
okay =(bm >= 15. & bm < 30. )| ...
(bm >= 120. & bm < 150.);
good =(bm >= 30. & bm < 45. )| ...
(bm >= 90. & bm < 120.);
best = bm >= 45. & bm < 90. ;
end
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',0:30:180,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,180.]) ;
mina = max(1.000,min(ad)); %%!! so that axes don't obscure!
maxa = min(179.0,max(ad));
bara = mean(ad(:));
mada = mad (ad(:));
line([ mina, mina],...
[0,max(hc)],'color','r','linewidth',1.5);
line([ maxa, maxa],...
[0,max(hc)],'color','r','linewidth',1.5);
if ( mina > 25.0)
text(mina-1.8,.90*max(hc),num2str(min(ad),'%16.1f'),...
'horizontalalignment',...
'right','fontsize',15) ;
else
text(mina+1.8,.90*max(hc),num2str(min(ad),'%16.1f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
if ( maxa < 140.)
text(maxa+1.8,.90*max(hc),num2str(max(ad),'%16.1f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
else
text(maxa-1.8,.90*max(hc),num2str(max(ad),'%16.1f'),...
'horizontalalignment',...
'right','fontsize',15) ;
end
if ( maxa < 100.)
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(maxa-16.,.45*max(hc),...
'$\bar{\sigma}_{\theta}\!= $',...
'horizontalalignment', 'left',...
'fontsize',16,'interpreter','latex') ;
text(maxa+1.8,.45*max(hc),num2str(mad(ad),'%16.2f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
else
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(maxa-16.,.45*max(hc),...
'$\bar{\sigma}_{\theta}\!= $',...
'horizontalalignment', 'left',...
'fontsize',16,'interpreter','latex') ;
text(maxa+1.8,.45*max(hc),num2str(mad(ad),'%16.3f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
end
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-9.0,0.0,'$\theta_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-9.0,0.0, '\theta_{\tau}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-9.0,0.0,'$\theta_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-9.0,0.0, '\theta_{f}' ,...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function scrhist(sc,ty)
%SCRHIST draw histogram for "score" quality-metric.
sc = sc(:);
be = linspace(0.,1.,101);
bm = (be(1:end-1)+be(2:end)) / 2.;
hc = histc(sc,be);
switch (ty)
case{'tria4','dual4'}
poor = bm < .25 ;
okay = bm >= .25 & bm < .50 ;
good = bm >= .50 & bm < .75 ;
best = bm >= .75 ;
case{'tria3','dual3'}
poor = bm < .30 ;
okay = bm >= .30 & bm < .60 ;
good = bm >= .60 & bm < .90 ;
best = bm >= .90 ;
end
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',.0:.2:1.,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,1.]) ;
mins = max(0.010,min(sc)); %%!! so that axes don't obscure!
maxs = min(0.990,max(sc));
line([ mins, mins],...
[0,max(hc)],'color','r','linewidth',1.5);
line([mean(sc),mean(sc)],...
[0,max(hc)],'color','r','linewidth',1.5);
if ( mins > .4)
text(mins-.01,.9*max(hc),num2str(min(sc),'%16.3f'),...
'horizontalalignment',...
'right','fontsize',15) ;
else
text(mins+.01,.9*max(hc),num2str(min(sc),'%16.3f'),...
'horizontalalignment',...
'left' ,'fontsize',15) ;
end
if ( mean(sc) > mins + .150)
text(mean(sc)-.01,.9*max(hc),num2str(mean(sc),'%16.3f'),...
'horizontalalignment','right','fontsize',15) ;
end
switch (ty)
case 'tria4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{T}}_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{t}_{\tau}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'tria3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{T}}_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{t}_{f}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'dual4'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{D}}_{\tau}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{d}_{\tau}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
case 'dual3'
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-.04,0.0, ...
'$\mathcal{Q}^{\mathcal{D}}_{f}$',...
'horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-.04,0.0,'Q^{d}_{f}',...
'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
end
function hfnhist(hf,ty)
%HFNHIST draw histogram for "hfunc" quality-metric.
be = linspace(0.,2.,101);
bm = (be(1:end-1)+be(2:end)) / 2.;
hc = histc(hf,be);
poor = bm < .40 | bm >= 1.6 ;
okay =(bm >= .40 & bm < .60 )| ...
(bm >= 1.4 & bm < 1.6 );
good =(bm >= .60 & bm < .80 )| ...
(bm >= 1.2 & bm < 1.4 );
best = bm >= .80 & bm < 1.2 ;
r = [.85,.00,.00] ; y = [1.0,.95,.00] ;
g = [.00,.90,.00] ; k = [.60,.60,.60] ;
bar(bm(poor),hc(poor),1.05,...
'facecolor',r,'edgecolor',r) ;
bar(bm(okay),hc(okay),1.05,...
'facecolor',y,'edgecolor',y) ;
bar(bm(good),hc(good),1.05,...
'facecolor',g,'edgecolor',g) ;
bar(bm(best),hc(best),1.05,...
'facecolor',k,'edgecolor',k) ;
axis tight;
set(gca,'ycolor', get(gca,'color'),'ytick',[],...
'xtick',.0:.5:2.,'layer','top','fontsize',...
14,'linewidth',2.,'ticklength',[.025,.025],...
'box','off','xlim',[0.,2.]);
line([max(hf),max(hf)],...
[0,max(hc)],'color','r','linewidth',1.5);
text(max(hf)+.02,.90*max(hc),num2str(max(hf),'%16.2f'),...
'horizontalalignment','left','fontsize',15) ;
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(max(hf)-.18,.45*max(hc),'$\bar{\sigma}_{h}\! = $',...
'horizontalalignment','left',...
'fontsize',16,'interpreter','latex') ;
text(max(hf)+.02,.45*max(hc),num2str(mad(hf),'%16.2f'),...
'horizontalalignment','left','fontsize',15) ;
end
if ( ~(exist('OCTAVE_VERSION','builtin') > +0) )
text(-0.10,0.0,'$h_{r}$','horizontalalignment','right',...
'fontsize',22,'interpreter','latex') ;
else
text(-0.10,0.0, 'h_{r}' ,'horizontalalignment','right',...
'fontsize',22,'interpreter', 'tex') ;
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
smooth2.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-2d/smooth2.m
| 18,053 |
utf_8
|
f11e4a411ca1d0f078610452258c13e9
|
function [vert,conn,tria,tnum] = smooth2(varargin)
%SMOOTH2 "hill-climbing" mesh-smoothing for two-dimensional,
%2-simplex triangulations.
% [VERT,EDGE,TRIA,TNUM] = SMOOTH2(VERT,EDGE,TRIA,TNUM) re-
% turns a "smoothed" triangulation {VERT,TRIA}, incorpora-
% ting "optimised" vertex coordinates and mesh topology.
%
% VERT is a V-by-2 array of XY coordinates in the triangu-
% lation, EDGE is an array of constrained edges, TRIA is a
% T-by-3 array of triangles, and TNUM is a T-by-1 array of
% part indices. Each row of TRIA and EDGE define an eleme-
% nt. VERT(TRIA(II,1),:), VERT(TRIA(II,2),:) and VERT(TRIA
% (II,3),:) are the coordinates of the II-TH triangle. The
% edges in EDGE are defined in a similar manner. NUM is an
% array of part indexing, such that TNUM(II) is the index
% of the part in which the II-TH triangle resides.
%
% [VERT,EDGE,TRIA,TNUM] = SMOOTH2(... ,OPTS) passes an ad-
% ditional options structure OPTS, containing user-defined
% parameters, including:
%
% - OPTS.VTOL = {+1.0E-02} -- relative vertex movement tole-
% rance, smoothing is converged when (VNEW-VERT) <= VTOL *
% VLEN, where VLEN is a local effective length-scale.
%
% - OPTS.ITER = {+32} -- max. number of smoothing iterations
%
% - OPTS.DISP = {+ 4} -- smoothing verbosity. Set to INF for
% quiet execution.
%
% See also REFINE2, TRICOST, TRIDEMO
% This routine is loosely based on the DISTMESH algorithm,
% employing a "spring-based" analogy to redistribute mesh
% vertices. Such an approach is described in: P.O. Persson
% and Gilbert Strang. "A simple mesh generator in MATLAB."
% SIAM review 46(2) 2004, pp: 329--345. Details of the al-
% gorithm used here are somewhat different, with an alter-
% ative spring-based update employed, in addition to hill-
% climbing element quality guarantees, and vertex density
% controls.
%-----------------------------------------------------------
% Darren Engwirda : 2017 --
% Email : [email protected]
% Last updated : 21/07/2017
%-----------------------------------------------------------
vert = []; conn = []; tria = [] ;
tnum = [];
opts = []; hfun = []; harg = {} ;
%---------------------------------------------- extract args
if (nargin>=+1), vert = varargin{1}; end
if (nargin>=+2), conn = varargin{2}; end
if (nargin>=+3), tria = varargin{3}; end
if (nargin>=+4), tnum = varargin{4}; end
if (nargin>=+5), opts = varargin{5}; end
[opts] = makeopt(opts) ;
%---------------------------------------------- default CONN
if (isempty(conn))
[edge] = tricon2(tria);
ebnd = edge(:,4) < +1; %-- use bnd edge
conn = edge(ebnd,1:2);
end
%---------------------------------------------- default TNUM
if (isempty(tnum))
tnum = ones(size(tria, 1), 1) ;
end
%---------------------------------------------- basic checks
if ( ~isnumeric(vert) || ...
~isnumeric(conn) || ...
~isnumeric(tria) || ...
~isnumeric(tnum) || ...
~isstruct (opts) )
error('smooth2:incorrectInputClass' , ...
'Incorrect input class.') ;
end
%---------------------------------------------- basic checks
if (ndims(vert) ~= +2 || ...
ndims(conn) ~= +2 || ...
ndims(tria) ~= +2 || ...
ndims(tnum) ~= +2 )
error('smooth2:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
if (size(vert,2)~= +2 || ...
size(conn,2)~= +2 || ...
size(tria,2)~= +3 || ...
size(tnum,2)~= +1 || ...
size(tria,1)~= size(tnum,1) )
error('smooth2:incorrectDimensions' , ...
'Incorrect input dimensions.');
end
nvrt = size(vert,1) ;
%---------------------------------------------- basic checks
if (min(min(conn(:,1:2))) < +1 || ...
max(max(conn(:,1:2))) > nvrt )
error('smooth2:invalidInputs', ...
'Invalid EDGE input array.') ;
end
if (min(min(tria(:,1:3))) < +1 || ...
max(max(tria(:,1:3))) > nvrt )
error('smooth2:invalidInputs', ...
'Invalid TRIA input array.') ;
end
%---------------------------------------------- output title
if (~isinf(opts.disp))
fprintf(1,'\n') ;
fprintf(1,' Smooth triangulation...\n') ;
fprintf(1,'\n') ;
fprintf(1,[...
' -------------------------------------------------------\n', ...
' |ITER.| |MOVE(X)| |DTRI(X)| \n', ...
' -------------------------------------------------------\n', ...
] ) ;
end
%---------------------------------------------- polygon bnds
node = vert; PSLG = conn; part = {};
pmax = max(tnum(:));
for ppos = +1 : pmax
tsel = tnum == ppos ;
tcur = tria(tsel,:) ;
[ecur,tcur] ...
= tricon2 (tcur) ;
ebnd = ecur(:,4)==0 ;
same = setset2( ...
PSLG,ecur(ebnd,1:2));
part{ppos} = find(same) ;
end
%---------------------------------------------- inflate bbox
vmin = min(vert,[],1);
vmax = max(vert,[],1);
vdel = vmax - 1.*vmin;
vmin = vmin - .5*vdel;
vmax = vmax + .5*vdel;
vbox = [
vmin(1), vmin(2)
vmax(1), vmin(2)
vmax(1), vmax(2)
vmin(1), vmax(2)
] ;
vert = [vert ; vbox] ;
%---------------------------------------------- DO MESH ITER
tnow = tic ;
tcpu = struct('full',0.,'dtri',0., ...
'tcon',0.,'iter',0.,'undo',0., ...
'keep',0.) ;
for iter = +1 : opts.iter
%------------------------------------------ inflate adj.
ttic = tic ;
[edge,tria] = tricon2(tria,conn) ;
tcpu.tcon = ...
tcpu.tcon + toc(ttic) ;
%------------------------------------------ compute scr.
oscr = triscr2(vert,tria) ;
%------------------------------------------ vert. iter's
ttic = tic ;
nvrt = size(vert,1);
nedg = size(edge,1);
IMAT = sparse( ...
edge(:,1),(1:nedg)',+1,nvrt,nedg) ;
JMAT = sparse( ...
edge(:,2),(1:nedg)',+1,nvrt,nedg) ;
EMAT = IMAT + JMAT ;
vdeg = sum(EMAT,2) ; %-- vertex |deg|
free = (vdeg == 0) ;
vold = vert ;
for isub = +1 : max(+2,min(+8,iter))
%-- compute HFUN at vert/midpoints
hvrt = evalhfn(vert, ...
edge,EMAT,hfun,harg) ;
hmid = hvrt(edge(:,1),:) ...
+ hvrt(edge(:,2),:) ;
hmid = hmid * +.5 ;
%-- calc. relative edge extensions
evec = vert(edge(:,2),:) ...
- vert(edge(:,1),:) ;
elen = ...
sqrt(sum(evec.^2,2)) ;
scal = +1.0-elen./hmid ;
scal = min (+1.0, scal);
scal = max (-1.0, scal);
%-- projected points from each end
ipos = vert(edge(:,1),:) ...
-.67*[scal,scal].*evec;
jpos = vert(edge(:,2),:) ...
+.67*[scal,scal].*evec;
%scal = ... %-- nlin. weight
% max(abs(scal).^.5,eps^.75);
scal = ...
max(abs(scal).^ 1,eps^.75);
%-- sum contributions edge-to-vert
vnew = ...
IMAT*([scal,scal] .* ipos) ...
+ JMAT*([scal,scal] .* jpos) ;
vsum = max(EMAT*scal,eps^.75);
vnew = vnew ./ [vsum,vsum] ;
%-- fixed points. edge projection?
vnew(conn(:),1:2) = ...
vert(conn(:),1:2) ;
vnew(vdeg==0,1:2) = ...
vert(vdeg==0,1:2) ;
%-- reset for the next local iter.
vert = vnew ;
end
tcpu.iter = ...
tcpu.iter + toc(ttic) ;
%------------------------------------------ hill-climber
ttic = tic ;
%-- unwind vert. upadte if score lower
nscr = ones(size(tria,1),1);
btri = true(size(tria,1),1);
umax = + 8 ;
for undo = +1 : umax
nscr(btri) = triscr2( ...
vert,tria(btri,:)) ;
%-- TRUE if tria needs "unwinding"
smin = +.70 ;
smax = +.90 ;
sdel = .025 ;
stol = smin+iter*sdel;
stol = min (smax,stol) ;
btri = nscr <= stol ...
& nscr < oscr ;
if (~any(btri)), break; end
%-- relax toward old vert. coord's
ivrt = ...
unique(tria(btri,1:3));
bvrt = ...
false(size(vert,1),1) ;
bvrt(ivrt) = true;
if (undo ~= umax)
bnew = +.75 ^ undo ;
bold = +1.0 - bnew ;
else
bnew = +0.0 ;
bold = +1.0 - bnew ;
end
vert(bvrt,:) = ...
bold * vold(bvrt,:) ...
+ bnew * vert(bvrt,:) ;
btri = any( ...
bvrt(tria(:,1:3)),2) ;
end
oscr = nscr ;
tcpu.undo = ...
tcpu.undo + toc(ttic) ;
%------------------------------------- test convergence!
ttic = tic ;
vdel = ...
sum((vert-vold).^2,2) ;
evec = vert(edge(:,2),:) ...
- vert(edge(:,1),:) ;
elen = ...
sqrt(sum(evec.^2,2)) ;
hvrt = evalhfn(vert, ...
edge,EMAT,hfun,harg) ;
hmid = hvrt(edge(:,1),:) ...
+ hvrt(edge(:,2),:) ;
hmid = hmid * 0.5 ;
scal = elen./hmid ;
emid = vert(edge(:,1),:) ...
+ vert(edge(:,2),:) ;
emid = emid * 0.5 ;
%------------------------------------- |deg|-based prune
keep = false(size(vert,1),1);
keep(vdeg>+4) = true ;
keep(conn(:)) = true ;
keep(free(:)) = true ;
%------------------------------------- 'density' control
lmax = +5. / +4. ;
lmin = +1. / lmax ;
less = scal<=lmin ;
more = scal>=lmax ;
vbnd = false(size(vert,1),1);
vbnd(conn(:,1)) = true ;
vbnd(conn(:,2)) = true ;
ebad = vbnd(edge(:,1)) ... %-- not at boundaries
| vbnd(edge(:,2)) ;
less(ebad(:)) = false;
more(ebad(:)) = false;
%------------------------------------- force as disjoint
lidx = find (less) ;
for lpos = 1 : length(lidx)
epos = lidx(lpos,1);
inod = edge(epos,1);
jnod = edge(epos,2);
%--------------------------------- if still disjoint
if (keep(inod) && ...
keep(jnod) )
keep(inod) = false ;
keep(jnod) = false ;
else
less(epos) = false ;
end
end
ebad = ...
keep(edge(less,1)) ...
& keep(edge(less,2)) ;
more(ebad(:)) = false ;
%------------------------------------- reindex vert/tria
redo = ...
zeros(size(vert,1),1);
itop = ...
length(find(keep));
iend = ...
length(find(less));
redo(keep) = (1:itop)';
redo(edge(less,1)) = ... %-- to new midpoints
(itop+1 : itop+iend)';
redo(edge(less,2)) = ...
(itop+1 : itop+iend)';
vnew =[vert(keep,:) ;
emid(less,:) ;
] ;
tnew = redo(tria(:,1:3)) ;
ttmp = sort(tnew,2) ; %-- filter collapsed
okay = all( ...
diff(ttmp,1,2)~=0,2) ;
okay = ...
okay & ttmp(:,1) > 0 ;
tnew = tnew(okay,:) ;
%------------------------------------- quality preserver
nscr = ...
triscr2 (vnew,tnew) ;
stol = +0.80 ;
tbad = nscr < stol ...
& nscr < oscr(okay) ;
vbad = ...
false(size(vnew,1),1);
vbad(tnew(tbad,:)) = true;
%------------------------------------- filter edge merge
lidx = find (less) ;
ebad = ...
vbad(redo(edge(lidx,1))) | ...
vbad(redo(edge(lidx,2))) ;
less(lidx(ebad)) = false ;
keep(edge(...
lidx(ebad),1:2)) = true ;
%------------------------------------- reindex vert/conn
redo = ...
zeros(size(vert,1),1);
itop = ...
length(find(keep));
iend = ...
length(find(less));
redo(keep) = (1:itop)';
redo(edge(less,1)) = ...
(itop+1 : itop+iend)';
redo(edge(less,2)) = ...
(itop+1 : itop+iend)';
vert =[vert(keep,:);
emid(less,:);
emid(more,:);
] ;
conn = redo(conn(:,1:2)) ;
tcpu.keep = ...
tcpu.keep + toc(ttic) ;
%------------------------------------- build current CDT
ttic = tic ;
[vert,conn,tria,tnum] = ...
deltri2 (vert, ...
conn,node,PSLG,part) ;
tcpu.dtri = ...
tcpu.dtri + toc(ttic) ;
%------------------------------------- dump-out progess!
vdel = vdel./(hvrt.*hvrt) ;
move = vdel > opts.vtol^2 ;
nmov = ...
length(find(move));
ntri = size(tria,1) ;
if (mod(iter,opts.disp)==+0)
fprintf(+1, ...
'%11i %18i %18i\n', ...
[iter,nmov,ntri]) ;
end
%------------------------------------- loop convergence!
if (nmov == +0), break; end
end
tria = tria( :,1:3);
%----------------------------------------- prune unused vert
keep = false(size(vert,1),1);
keep(tria(:)) = true ;
keep(conn(:)) = true ;
redo = zeros(size(vert,1),1);
redo(keep) = ...
(+1:length(find(keep)))';
conn = redo(conn);
tria = redo(tria);
vert = vert(keep,:);
tcpu.full = ...
tcpu.full + toc(tnow) ;
if (opts.dbug)
%----------------------------------------- print debug timer
fprintf(1,'\n') ;
fprintf(1,' Mesh smoothing timer...\n');
fprintf(1,'\n') ;
fprintf(1, ...
' FULL: %f \n', tcpu.full);
fprintf(1, ...
' DTRI: %f \n', tcpu.dtri);
fprintf(1, ...
' TCON: %f \n', tcpu.tcon);
fprintf(1, ...
' ITER: %f \n', tcpu.iter);
fprintf(1, ...
' UNDO: %f \n', tcpu.undo);
fprintf(1, ...
' KEEP: %f \n', tcpu.keep);
fprintf(1,'\n') ;
end
if (~isinf(opts.disp)), fprintf(1,'\n'); end
end
function [hvrt] = evalhfn(vert,edge,EMAT,hfun,harg)
%EVALHFN eval. the spacing-fun. at mesh vertices.
if (~isempty (hfun))
if (isnumeric(hfun))
hvrt = hfun * ...
ones(size(vert,1),1) ;
else
hvrt = feval( ...
hfun,vert,harg{:}) ;
end
else
%-- no HFUN - HVRT is mean edge-len. at vertices!
evec = vert(edge(:,2),:) - ...
vert(edge(:,1),:) ;
elen = sqrt(sum(evec.^2,2)) ;
hvrt = (EMAT*elen) ...
./ max(sum(EMAT,2),eps) ;
free = true(size(vert,1),1) ;
free(edge(:,1)) = false;
free(edge(:,2)) = false;
hvrt(free) = +inf;
end
end
function [opts] = makeopt(opts)
%MAKEOPT setup the options structure for SMOOTH2.
if (~isfield(opts,'iter'))
opts.iter = +32;
else
if (~isnumeric(opts.iter))
error('smooth2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.iter)~= +1)
error('smooth2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.iter <= +0)
error('smooth2:invalidOptionValues', ...
'Invalid OPT.ITER selection.') ;
end
end
if (~isfield(opts,'disp'))
opts.disp = + 4;
else
if (~isnumeric(opts.disp))
error('smooth2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.disp)~= +1)
error('smooth2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.disp <= +0)
error('smooth2:invalidOptionValues', ...
'Invalid OPT.DISP selection.') ;
end
end
if (~isfield(opts,'vtol'))
opts.vtol = +1.0E-02;
else
if (~isnumeric(opts.vtol))
error('smooth2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.vtol)~= +1)
error('smooth2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
if (opts.vtol <= 0.)
error('smooth2:invalidOptionValues', ...
'Invalid OPT.VTOL selection.') ;
end
end
if (~isfield(opts,'dbug'))
opts.dbug = false;
else
if (~islogical(opts.dbug))
error('refine2:incorrectInputClass', ...
'Incorrect input class.');
end
if (numel(opts.dbug)~= +1)
error('refine2:incorrectDimensions', ...
'Incorrect input dimensions.') ;
end
end
end
|
github
|
mathematical-tours/mathematical-tours.github.io-master
|
savemsh.m
|
.m
|
mathematical-tours.github.io-master/tweets-sources/codes/mesh-2d/mesh-file/savemsh.m
| 16,535 |
utf_8
|
dfee52330f9c2c724696cbf905df56bb
|
function savemsh(name,mesh)
%SAVEMSH save a *.MSH file for JIGSAW.
%
% SAVEMSH(NAME,MESH);
%
% The following are optionally written to "NAME.MSH". Ent-
% ities are written if they are present in MESH:
%
% .IF. MESH.MSHID == 'EUCLIDEAN-MESH':
% -----------------------------------
%
% MESH.POINT.COORD - [NPxND+1] array of point coordinates,
% where ND is the number of spatial dimenions.
% COORD(K,ND+1) is an ID tag for the K-TH point.
%
% MESH.POINT.POWER - [NPx 1] array of vertex "weights",
% associated with the dual "power" tessellation.
%
% MESH.EDGE2.INDEX - [N2x 3] array of indexing for EDGE-2
% elements, where INDEX(K,1:2) is an array of
% "point-indices" associated with the K-TH edge, and
% INDEX(K,3) is an ID tag for the K-TH edge.
%
% MESH.TRIA3.INDEX - [N3x 4] array of indexing for TRIA-3
% elements, where INDEX(K,1:3) is an array of
% "point-indices" associated with the K-TH tria, and
% INDEX(K,4) is an ID tag for the K-TH tria.
%
% MESH.QUAD4.INDEX - [N4x 5] array of indexing for QUAD-4
% elements, where INDEX(K,1:4) is an array of
% "point-indices" associated with the K-TH quad, and
% INDEX(K,5) is an ID tag for the K-TH quad.
%
% MESH.TRIA4.INDEX - [M4x 5] array of indexing for TRIA-4
% elements, where INDEX(K,1:4) is an array of
% "point-indices" associated with the K-TH tria, and
% INDEX(K,5) is an ID tag for the K-TH tria.
%
% MESH.HEXA8.INDEX - [M8x 9] array of indexing for HEXA-8
% elements, where INDEX(K,1:8) is an array of
% "point-indices" associated with the K-TH hexa, and
% INDEX(K,9) is an ID tag for the K-TH hexa.
%
% MESH.WEDG6.INDEX - [M6x 7] array of indexing for WEDG-6
% elements, where INDEX(K,1:6) is an array of
% "point-indices" associated with the K-TH wedg, and
% INDEX(K,7) is an ID tag for the K-TH wedg.
%
% MESH.PYRA5.INDEX - [M5x 6] array of indexing for PYRA-5
% elements, where INDEX(K,1:5) is an array of
% "point-indices" associated with the K-TH pyra, and
% INDEX(K,6) is an ID tag for the K-TH pyra.
%
% MESH.VALUE - [NPxNV] array of "values" associated with
% the vertices of the mesh. NV values are associated
% with each vertex.
%
%
% .IF. MESH.MSHID == 'ELLIPSOID-MESH':
% -----------------------------------
%
% MESH.RADII - [ 3x 1] array of principle ellipsoid radii.
%
%
% .IF. MESH.MSHID == 'EUCLIDEAN-GRID':
% .OR. MESH.MSHID == 'ELLIPSOID-GRID':
% -----------------------------------
%
% MESH.POINT.COORD - [NDx1] cell array of grid coordinates
% where ND is the number of spatial dimenions. Each
% array COORD{ID} should be a vector of grid coord.'s,
% increasing or decreasing monotonically.
%
% MESH.VALUE - [NMxNV] array of "values" associated with
% the vertices of the grid, where NM is the product of
% the dimensions of the grid. NV values are associated
% with each vertex.
%
% See also JIGSAW, LOADMSH
%
%-----------------------------------------------------------
% Darren Engwirda
% github.com/dengwirda/jigsaw/
% 03-Dec-2017
% [email protected]
%-----------------------------------------------------------
%
if (~ischar (name))
error('NAME must be a valid file-name!') ;
end
if (~isstruct(mesh))
error('MESH must be a valid structure!') ;
end
[path,file,fext] = fileparts(name) ;
if(~strcmp(lower(fext),'.msh'))
name = [name,'.msh'];
end
try
%-- try to write data to file
ffid = fopen(name, 'w') ;
nver = +3;
if (exist('OCTAVE_VERSION','builtin') > 0)
fprintf(ffid,[ ...
'# %s.msh; created by JIGSAW''s OCTAVE interface\n'],file) ;
else
fprintf(ffid,[ ...
'# %s.msh; created by JIGSAW''s MATLAB interface\n'],file) ;
end
if (isfield(mesh,'mshID'))
mshID = mesh.mshID ;
else
mshID = 'EUCLIDEAN-MESH';
end
switch (upper(mshID))
case 'EUCLIDEAN-MESH'
save_euclidean_mesh(ffid,nver,mesh) ;
case 'EUCLIDEAN-GRID'
save_euclidean_grid(ffid,nver,mesh) ;
case 'EUCLIDEAN-DUAL'
%save_euclidean_dual(ffid,nver,mesh) ;
case 'ELLIPSOID-MESH'
save_ellipsoid_mesh(ffid,nver,mesh) ;
case 'ELLIPSOID-GRID'
save_ellipsoid_grid(ffid,nver,mesh) ;
case 'ELLISPOID-DUAL'
%save_ellipsoid_dual(ffid,nver,mesh) ;
otherwise
error('Invalid mshID!') ;
end
fclose(ffid);
catch err
%-- ensure that we close the file regardless!
if (ffid>-1)
fclose(ffid) ;
end
rethrow(err) ;
end
end
function save_euclidean_mesh(ffid,nver,mesh)
%SAVE-EUCLIDEAN-MESH save mesh data in EUCLDIEAN-MESH format
fprintf(ffid,'MSHID=%u;EUCLIDEAN-MESH \n',nver);
npts = +0;
if (isfield(mesh,'point') && ...
isfield(mesh.point,'coord') && ...
~isempty(mesh.point.coord) )
%-- write "POINT" data
if (~isnumeric(mesh.point.coord))
error('Incorrect input types');
end
if (ndims(mesh.point.coord) ~= 2)
error('Incorrect dimensions!');
end
ndim = size(mesh.point.coord,2) - 1 ;
npts = size(mesh.point.coord,1) - 0 ;
fprintf(ffid,['NDIMS=%u','\n'],ndim);
fprintf(ffid, ...
['POINT=%u','\n'],size(mesh.point.coord,1));
if (isa(mesh.point.coord,'double'))
vstr = sprintf('%%1.%ug;',+16);
else
vstr = sprintf('%%1.%ug;',+ 8);
end
fprintf(ffid, ...
[repmat(vstr,1,ndim),'%i\n'],mesh.point.coord');
end
if (isfield(mesh,'point') && ...
isfield(mesh.point,'power') && ...
~isempty(mesh.point.power) )
%-- write "POWER" data
if (~isnumeric(mesh.point.power))
error('Incorrect input types');
end
if (ndims(mesh.point.power) ~= 2)
error('Incorrect dimensions!');
end
npwr = size(mesh.point.power,2) - 0 ;
nrow = size(mesh.point.power,1) - 0 ;
if (isa(mesh.point.power,'double'))
vstr = sprintf('%%1.%ug;',+16) ;
else
vstr = sprintf('%%1.%ug;',+ 8) ;
end
vstr = repmat(vstr,+1,npwr) ;
fprintf(ffid,['POWER=%u;%u','\n'],[nrow,npwr]);
fprintf(ffid, ...
[vstr(+1:end-1), '\n'], mesh.point.power');
end
if (isfield(mesh,'value'))
%-- write "VALUE" data
if (~isnumeric(mesh.value))
error('Incorrect input types');
end
if (ndims(mesh.value) ~= 2)
error('Incorrect dimensions!');
end
if (size(mesh.value,1) ~= npts)
error('Incorrect dimensions!');
end
nrow = size(mesh.value,1);
nval = size(mesh.value,2);
if (isa(mesh.value, 'double'))
vstr = sprintf('%%1.%ug;',+16) ;
else
vstr = sprintf('%%1.%ug;',+ 8) ;
end
vstr = repmat(vstr,+1,nval) ;
fprintf(ffid,['VALUE=%u;%u','\n'],[nrow,nval]);
fprintf(ffid,[vstr(1:end-1),'\n'],mesh.value');
end
if (isfield(mesh,'edge2') && ...
isfield(mesh.edge2,'index') && ...
~isempty(mesh.edge2.index) )
%-- write "EDGE2" data
if (~isnumeric(mesh.edge2.index))
error('Incorrect input types');
end
if (ndims(mesh.edge2.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.edge2.index(:,1:2))) < +1 || ...
max(max(mesh.edge2.index(:,1:2))) > npts)
error('Invalid EDGE-2 indexing!') ;
end
index = mesh.edge2.index;
index(:,1:2) = index(:,1:2)-1 ; % file is zero-indexed!
fprintf(ffid,['EDGE2=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,2),'%i','\n'],index');
end
if (isfield(mesh,'tria3') && ...
isfield(mesh.tria3,'index') && ...
~isempty(mesh.tria3.index) )
%-- write "TRIA3" data
if (~isnumeric(mesh.tria3.index))
error('Incorrect input types');
end
if (ndims(mesh.tria3.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.tria3.index(:,1:3))) < +1 || ...
max(max(mesh.tria3.index(:,1:3))) > npts)
error('Invalid TRIA-3 indexing!') ;
end
index = mesh.tria3.index;
index(:,1:3) = index(:,1:3)-1 ; % file is zero-indexed!
fprintf(ffid,['TRIA3=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,3),'%i','\n'],index');
end
if (isfield(mesh,'quad4') && ...
isfield(mesh.quad4,'index') && ...
~isempty(mesh.quad4.index) )
%-- write "QUAD4" data
if (~isnumeric(mesh.quad4.index))
error('Incorrect input types');
end
if (ndims(mesh.quad4.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.quad4.index(:,1:4))) < +1 || ...
max(max(mesh.quad4.index(:,1:4))) > npts)
error('Invalid QUAD-4 indexing!') ;
end
index = mesh.quad4.index;
index(:,1:4) = index(:,1:4)-1 ; % file is zero-indexed!
fprintf(ffid,['QUAD4=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,4),'%i','\n'],index');
end
if (isfield(mesh,'tria4') && ...
isfield(mesh.tria4,'index') && ...
~isempty(mesh.tria4.index) )
%-- write "TRIA4" data
if (~isnumeric(mesh.tria4.index))
error('Incorrect input types');
end
if (ndims(mesh.tria4.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.tria4.index(:,1:4))) < +1 || ...
max(max(mesh.tria4.index(:,1:4))) > npts)
error('Invalid TRIA-4 indexing!') ;
end
index = mesh.tria4.index;
index(:,1:4) = index(:,1:4)-1 ; % file is zero-indexed!
fprintf(ffid,['TRIA4=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,4),'%i','\n'],index');
end
if (isfield(mesh,'hexa8') && ...
isfield(mesh.hexa8,'index') && ...
~isempty(mesh.hexa8.index) )
%-- write "HEXA8" data
if (~isnumeric(mesh.hexa8.index))
error('Incorrect input types');
end
if (ndims(mesh.hexa8.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.hexa8.index(:,1:8))) < +1 || ...
max(max(mesh.hexa8.index(:,1:8))) > npts)
error('Invalid HEXA-8 indexing!') ;
end
index = mesh.hexa8.index;
index(:,1:8) = index(:,1:8)-1 ; % file is zero-indexed!
fprintf(ffid,['HEXA8=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,8),'%i','\n'],index');
end
if (isfield(mesh,'wedg6') && ...
isfield(mesh.wedg6,'index') && ...
~isempty(mesh.wedg6.index) )
%-- write "WEDG6" data
if (~isnumeric(mesh.wedg6.index))
error('Incorrect input types');
end
if (ndims(mesh.wedg6.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.wedg6.index(:,1:6))) < +1 || ...
max(max(mesh.wedg6.index(:,1:6))) > npts)
error('Invalid WEDG-6 indexing!') ;
end
index = mesh.wedg6.index;
index(:,1:6) = index(:,1:6)-1 ; % file is zero-indexed!
fprintf(ffid,['WEDG6=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,6),'%i','\n'],index');
end
if (isfield(mesh,'pyra5') && ...
isfield(mesh.pyra5,'index') && ...
~isempty(mesh.pyra5.index) )
%-- write "PYRA5" data
if (~isnumeric(mesh.pyra5.index))
error('Incorrect input types');
end
if (ndims(mesh.pyra5.index) ~= 2)
error('Incorrect dimensions!');
end
if (min(min(mesh.pyra5.index(:,1:5))) < +1 || ...
max(max(mesh.pyra5.index(:,1:5))) > npts)
error('Invalid PYRA-5 indexing!') ;
end
index = mesh.pyra5.index;
index(:,1:5) = index(:,1:5)-1 ; % file is zero-indexed!
fprintf(ffid,['PYRA5=%u','\n'],size(index,1));
fprintf( ...
ffid,[repmat('%u;',1,6),'%i','\n'],index');
end
end
function save_ellipsoid_mesh(ffid,nver,mesh)
%SAVE-ELLIPSOID-MESH save mesh data in ELLIPSOID-MESH format
fprintf(ffid,'MSHID=%u;ELLIPSOID-MESH \n',nver);
npts = +0;
if (isfield(mesh,'radii') && ...
~isempty(mesh.radii) )
%-- write "RADII" data
if (~isnumeric(mesh.radii))
error('Incorrect input types');
end
if (ndims(mesh.radii) ~= 2)
error('Incorrect dimensions!');
end
if (numel(mesh.radii) ~= 3)
error('Incorrect dimensions!');
end
fprintf(ffid,'RADII=%f;%f;%f\n',mesh.radii');
end
%-- to-do: coast edges...
end
function save_euclidean_grid(ffid,nver,mesh)
%SAVE-EUCLIDEAN-GRID save mesh data in EUCLIDEAN-GRID format
save_monotonic_grid(ffid,nver,mesh, ...
'EUCLIDEAN-GRID') ;
end
function save_ellipsoid_grid(ffid,nver,mesh)
%SAVE-ELLIPSOID-GRID save mesh data in ELLIPSOID-GRID format
save_monotonic_grid(ffid,nver,mesh, ...
'ELLIPSOID-GRID') ;
end
function save_monotonic_grid(ffid,nver,mesh, ...
kind)
%SAVE-MONOTONIC-GRID save mesh data in MONOTONIC-GRID format
% ==> EUCLIDEAN-GRID, ELLIPSOID-GRID, etc...
switch (upper(kind))
case 'EUCLIDEAN-GRID'
fprintf( ...
ffid,'MSHID=%u;EUCLIDEAN-GRID\n',nver) ;
case 'ELLIPSOID-GRID'
fprintf( ...
ffid,'MSHID=%u;ELLIPSOID-GRID\n',nver) ;
end
dims = [] ;
if (isfield(mesh,'point') && ...
isfield(mesh.point,'coord') && ...
~isempty(mesh.point.coord) )
%-- write "COORD" data
if(~iscell(mesh.point.coord) )
error('Incorrect input types') ;
end
if ( numel(mesh.point.coord) ~= ...
length(mesh.point.coord) )
error('Incorrect dimensions!') ;
end
ndim = length(mesh.point.coord);
dims = zeros(1,ndim);
fprintf(ffid, ...
['NDIMS=%u \n'],length(mesh.point.coord)) ;
for idim = +1 : length(mesh.point.coord)
if ( numel(mesh.point.coord{idim}) ~= ...
length(mesh.point.coord{idim}) )
error('Incorrect dimensions!') ;
end
dims(ndim-idim+1) = ...
length(mesh.point.coord{idim}) ;
if (isa(mesh.point.coord{idim}, 'double'))
vstr = sprintf('%%1.%ug\n',+16);
else
vstr = sprintf('%%1.%ug\n',+ 8);
end
fprintf(ffid,...
'COORD=%u;%u\n',[idim,dims(ndim-idim+1)]);
fprintf(ffid,vstr,mesh.point.coord{idim});
end
end
if (isfield(mesh,'value'))
%-- write "VALUE" data
if (~isnumeric(mesh.value))
error('Incorrect input types') ;
end
if (ndims(mesh.value) ~= length(dims)+0 && ...
ndims(mesh.value) ~= length(dims)+1 )
error('Incorrect dimensions!') ;
end
if (ndims(mesh.value) == length(dims))
nval = size(mesh.value);
nval = [nval, +1] ;
else
nval = size(mesh.value);
end
if (~all(nval(1:end-1) == dims))
error('Incorrect dimensions!') ;
end
if (isa(mesh.value, 'double'))
vstr = sprintf('%%1.%ug;',+16) ;
else
vstr = sprintf('%%1.%ug;',+ 8) ;
end
vstr = repmat(vstr,+1,nval(end)) ;
vals = ...
reshape(mesh.value,[],nval(end)) ;
fprintf(ffid, ...
'VALUE=%u;%u\n',[prod(dims),nval(end)]);
fprintf(ffid,[vstr(+1:end-1),'\n'],vals');
end
end
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