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10,859 | burnman.classes.material | set_state |
Set the material to the given pressure and temperature.
:param pressure: The desired pressure in [Pa].
:type pressure: float
:param temperature: The desired temperature in [K].
:type temperature: float
| def set_state(self, pressure, temperature):
"""
Set the material to the given pressure and temperature.
:param pressure: The desired pressure in [Pa].
:type pressure: float
:param temperature: The desired temperature in [K].
:type temperature: float
"""
if not hasattr(self, "_pressure"):
raise Exception(
"Material.set_state() could not find class member _pressure. "
"Did you forget to call Material.__init__(self) in __init___?"
)
self.reset()
self._pressure = pressure
self._temperature = temperature
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10,860 | burnman.classes.material | set_state_with_volume |
This function acts similarly to set_state, but takes volume and
temperature as input to find the pressure. In order to ensure
self-consistency, this function does not use any pressure functions
from the material classes, but instead finds the pressure using the
brentq root-finding method.
:param volume: The desired molar volume of the mineral [m^3].
:type volume: float
:param temperature: The desired temperature of the mineral [K].
:type temperature: float
:param pressure_guesses: A list of floats denoting the initial
low and high guesses for bracketing of the pressure [Pa].
These guesses should preferably bound the correct pressure,
but do not need to do so. More importantly,
they should not lie outside the valid region of
the equation of state. Defaults to [5.e9, 10.e9].
:type pressure_guesses: list
| def set_state_with_volume(
self, volume, temperature, pressure_guesses=[0.0e9, 10.0e9]
):
"""
This function acts similarly to set_state, but takes volume and
temperature as input to find the pressure. In order to ensure
self-consistency, this function does not use any pressure functions
from the material classes, but instead finds the pressure using the
brentq root-finding method.
:param volume: The desired molar volume of the mineral [m^3].
:type volume: float
:param temperature: The desired temperature of the mineral [K].
:type temperature: float
:param pressure_guesses: A list of floats denoting the initial
low and high guesses for bracketing of the pressure [Pa].
These guesses should preferably bound the correct pressure,
but do not need to do so. More importantly,
they should not lie outside the valid region of
the equation of state. Defaults to [5.e9, 10.e9].
:type pressure_guesses: list
"""
def _delta_volume(pressure, volume, temperature):
# Try to set the state with this pressure,
# but if the pressure is too low most equations of state
# fail. In this case, treat the molar_volume as infinite
# and brentq will try a larger pressure.
try:
self.set_state(pressure, temperature)
return volume - self.molar_volume
except Exception:
return -np.inf
# we need to have a sign change in [a,b] to find a zero.
args = (volume, temperature)
try:
sol = bracket(_delta_volume, pressure_guesses[0], pressure_guesses[1], args)
except ValueError:
raise Exception(
"Cannot find a pressure, perhaps the volume or starting pressures "
"are outside the range of validity for the equation of state?"
)
pressure = brentq(_delta_volume, sol[0], sol[1], args=args)
self.set_state(pressure, temperature)
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10,861 | burnman.classes.material | to_string |
Returns a human-readable name of this material.
The default implementation will return the name of the class,
which is a reasonable default.
:returns: A human-readable name of the material.
:rtype: str
| def to_string(self):
"""
Returns a human-readable name of this material.
The default implementation will return the name of the class,
which is a reasonable default.
:returns: A human-readable name of the material.
:rtype: str
"""
return "'" + self.name + "'"
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10,862 | burnman.classes.material | unroll |
Unroll this material into a list of :class:`burnman.Mineral` and their molar
fractions. All averaging schemes then operate on this list of minerals.
Note that the return value of this function may depend on the current
state (temperature, pressure).
.. note:: Needs to be implemented in derived classes.
:returns: A list of molar fractions which should sum to 1.0,
and a list of :class:`burnman.Mineral` objects
containing the minerals in the material.
:rtype: tuple
| def unroll(self):
"""
Unroll this material into a list of :class:`burnman.Mineral` and their molar
fractions. All averaging schemes then operate on this list of minerals.
Note that the return value of this function may depend on the current
state (temperature, pressure).
.. note:: Needs to be implemented in derived classes.
:returns: A list of molar fractions which should sum to 1.0,
and a list of :class:`burnman.Mineral` objects
containing the minerals in the material.
:rtype: tuple
"""
raise NotImplementedError("need to implement unroll() in derived class!")
| (self) | [
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10,863 | burnman.classes.anisotropy | wave_velocities |
:returns: The compressional wave velocity, and two
shear wave velocities in a given propagation direction [m/s].
:rtype: list, containing the wave speeds and directions
of particle motion relative to the stiffness tensor
| def wave_velocities(self, propagation_direction):
"""
:returns: The compressional wave velocity, and two
shear wave velocities in a given propagation direction [m/s].
:rtype: list, containing the wave speeds and directions
of particle motion relative to the stiffness tensor
"""
propagation_direction = unit_normalize(propagation_direction)
Tik = self.christoffel_tensor(propagation_direction)
eigenvalues, eigenvectors = np.linalg.eig(Tik)
idx = eigenvalues.argsort()[::-1]
eigenvalues = np.real(eigenvalues[idx])
eigenvectors = eigenvectors[:, idx]
velocities = np.sqrt(eigenvalues / self.density)
return velocities, eigenvectors
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10,864 | burnman.classes.anisotropicmineral | AnisotropicMineral |
A class implementing the anisotropic mineral equation of state described
in :cite:`Myhill2022`.
This class is derived from both Mineral and AnisotropicMaterial,
and inherits most of the methods from these classes.
Instantiation of an AnisotropicMineral takes three required arguments;
a reference Mineral (i.e. a standard isotropic mineral which provides
volume as a function of pressure and temperature), cell_parameters,
which give the lengths of the molar cell vectors and the angles between
them (see :func:`~burnman.utils.unitcell.cell_parameters_to_vectors`),
and an anisotropic parameters object, which should be either a
4D array of anisotropic parameters or a dictionary of parameters which
describe the anisotropic behaviour of the mineral.
For a description of the physical meaning of the parameters in the
4D array, please refer to the code
or to the original paper.
If the user chooses to define their parameters as a dictionary,
they must also provide a function to the psi_function argument
that describes how to compute the tensors Psi, dPsidf and dPsidPth
(in Voigt form). The function arguments should be f, Pth and params,
in that order. The output variables Psi, dPsidf and dPsidth
must be returned in that order in a tuple. The user should
also explicitly state whether the material is orthotropic or not
by supplying a boolean to the orthotropic argument.
States of the mineral can only be queried after setting the
pressure and temperature using set_state().
This class is available as ``burnman.AnisotropicMineral``.
All the material parameters are expected to be in plain SI units. This
means that the elastic moduli should be in Pascals and NOT Gigapascals.
Additionally, the cell parameters should be in m/(mol formula unit)
and not in unit cell lengths. To convert unit cell lengths given in
Angstrom to molar cell parameters you should multiply by 10^(-10) *
(N_a / Z)^1/3, where N_a is Avogadro's number
and Z is the number of formula units per unit cell.
You can look up Z in many places, including www.mindat.org.
Finally, it is assumed that the unit cell of the anisotropic material
is aligned in a particular way relative to the coordinate axes
(the anisotropic_parameters are defined relative to the coordinate axes).
The crystallographic a-axis is assumed to be parallel to the first
spatial coordinate axis, and the crystallographic b-axis is assumed to
be perpendicular to the third spatial coordinate axis.
| class AnisotropicMineral(Mineral, AnisotropicMaterial):
"""
A class implementing the anisotropic mineral equation of state described
in :cite:`Myhill2022`.
This class is derived from both Mineral and AnisotropicMaterial,
and inherits most of the methods from these classes.
Instantiation of an AnisotropicMineral takes three required arguments;
a reference Mineral (i.e. a standard isotropic mineral which provides
volume as a function of pressure and temperature), cell_parameters,
which give the lengths of the molar cell vectors and the angles between
them (see :func:`~burnman.utils.unitcell.cell_parameters_to_vectors`),
and an anisotropic parameters object, which should be either a
4D array of anisotropic parameters or a dictionary of parameters which
describe the anisotropic behaviour of the mineral.
For a description of the physical meaning of the parameters in the
4D array, please refer to the code
or to the original paper.
If the user chooses to define their parameters as a dictionary,
they must also provide a function to the psi_function argument
that describes how to compute the tensors Psi, dPsidf and dPsidPth
(in Voigt form). The function arguments should be f, Pth and params,
in that order. The output variables Psi, dPsidf and dPsidth
must be returned in that order in a tuple. The user should
also explicitly state whether the material is orthotropic or not
by supplying a boolean to the orthotropic argument.
States of the mineral can only be queried after setting the
pressure and temperature using set_state().
This class is available as ``burnman.AnisotropicMineral``.
All the material parameters are expected to be in plain SI units. This
means that the elastic moduli should be in Pascals and NOT Gigapascals.
Additionally, the cell parameters should be in m/(mol formula unit)
and not in unit cell lengths. To convert unit cell lengths given in
Angstrom to molar cell parameters you should multiply by 10^(-10) *
(N_a / Z)^1/3, where N_a is Avogadro's number
and Z is the number of formula units per unit cell.
You can look up Z in many places, including www.mindat.org.
Finally, it is assumed that the unit cell of the anisotropic material
is aligned in a particular way relative to the coordinate axes
(the anisotropic_parameters are defined relative to the coordinate axes).
The crystallographic a-axis is assumed to be parallel to the first
spatial coordinate axis, and the crystallographic b-axis is assumed to
be perpendicular to the third spatial coordinate axis.
"""
def __init__(
self,
isotropic_mineral,
cell_parameters,
anisotropic_parameters,
psi_function=None,
orthotropic=None,
):
if psi_function is None:
self.check_standard_parameters(anisotropic_parameters)
self.anisotropic_params = {"c": anisotropic_parameters}
self.psi_function = self.standard_psi_function
else:
if not isinstance(orthotropic, bool):
raise Exception(
"If the Psi function is provided, "
"you must specify whether your material is "
"orthotropic as a boolean."
)
self.orthotropic = orthotropic
self.anisotropic_params = anisotropic_parameters
self.psi_function = psi_function
self.cell_vectors_0 = cell_parameters_to_vectors(cell_parameters)
if (
np.abs(np.linalg.det(self.cell_vectors_0) - isotropic_mineral.params["V_0"])
> np.finfo(float).eps
):
factor = np.cbrt(
isotropic_mineral.params["V_0"] / np.linalg.det(self.cell_vectors_0)
)
raise Exception(
"The standard state unit vectors are inconsistent "
"with the volume. Suggest multiplying each "
f"by {factor}."
)
# Note, Psi_0 may be asymmetric, in which case the Voigt contraction
# cannot be applied
self.Psi_0 = np.einsum("ij, kl", logm(self.cell_vectors_0), np.eye(3) / 3.0)
self.isotropic_mineral = isotropic_mineral
if "name" in isotropic_mineral.params:
self.name = isotropic_mineral.params["name"]
Mineral.__init__(
self, isotropic_mineral.params, isotropic_mineral.property_modifiers
)
def standard_psi_function(self, f, Pth, params):
# Compute Psi, dPsidPth, dPsidf, needed by most anisotropic properties
c = params["c"]
ns = np.arange(c.shape[-1])
x = c[:, :, 0, :] + c[:, :, 1, :] * f
dPsidf = c[:, :, 1, :]
for i in list(range(2, c.shape[2])):
# non-intuitively, the += operator doesn't simply add in-place,
# so here we overwrite the arrays with new ones
x = x + c[:, :, i, :] * np.power(f, float(i)) / float(i)
dPsidf = dPsidf + c[:, :, i, :] * np.power(f, float(i) - 1.0)
Psi = np.einsum("ikn, n->ik", x, np.power(Pth, ns))
dPsidPth = np.einsum(
"ikn, n->ik", x[:, :, 1:], ns[1:] * np.power(Pth, ns[1:] - 1)
)
dPsidf = np.einsum("ikn, n->ik", dPsidf, np.power(Pth, ns))
return (Psi, dPsidf, dPsidPth)
@copy_documentation(Material.set_state)
def set_state(self, pressure, temperature):
# 1) Compute dPthdf|T
# relatively large dP needed for accurate estimate of dPthdf
self.isotropic_mineral.set_state(pressure, temperature)
V2 = self.isotropic_mineral.V
KT2 = self.isotropic_mineral.K_T
self.isotropic_mineral.set_state_with_volume(V2, self.params["T_0"])
P1 = self.isotropic_mineral.pressure
KT1 = self.isotropic_mineral.K_T
self.dPthdf = KT1 - KT2
self.Pth = pressure - P1
self.isotropic_mineral.set_state(pressure, temperature)
Mineral.set_state(self, pressure, temperature)
# 2) Compute other properties needed for anisotropic equation of state
V = self.V
V_0 = self.params["V_0"]
Vrel = V / V_0
f = np.log(Vrel)
self._Vrel = Vrel
self._f = f
out = self.psi_function(f, self.Pth, self.anisotropic_params)
Psi_Voigt, self.dPsidf_Voigt, self.dPsidPth_Voigt = out
self.Psi = voigt_notation_to_compliance_tensor(Psi_Voigt) + self.Psi_0
# Convert to (f, T) variables
self.dPsidP_Voigt = -self.isothermal_compressibility_reuss * (
self.dPsidf_Voigt + self.dPsidPth_Voigt * self.dPthdf
)
self.dPsidT_Voigt = self.alpha * (
self.dPsidf_Voigt
+ self.dPsidPth_Voigt * (self.dPthdf + self.isothermal_bulk_modulus_reuss)
)
@material_property
def deformation_gradient_tensor(self):
"""
:returns: The deformation gradient tensor describing the deformation of the
mineral from its undeformed state
(i.e. the state at the reference pressure and temperature).
:rtype: numpy.array (2D)
"""
F = expm(np.einsum("ijkl, kl", self.Psi, np.eye(3)))
return F
@material_property
def unrotated_cell_vectors(self):
"""
:returns: The vectors of the cell [m] constructed from one mole
of formula units after deformation of the mineral from its
undeformed state (i.e. the state at the reference
pressure and temperature). See the documentation for the function
:func:`~burnman.utils.unitcell.cell_parameters_to_vectors`
for the assumed relationships between the cell vectors and
spatial coordinate axes.
:rtype: numpy.array (2D)
"""
return self.deformation_gradient_tensor
@material_property
def deformed_coordinate_frame(self):
"""
:returns: The orientations of the three spatial coordinate axes
after deformation of the mineral [m]. For orthotropic minerals,
this is equal to the | (isotropic_mineral, cell_parameters, anisotropic_parameters, psi_function=None, orthotropic=None) | [
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10,865 | burnman.classes.anisotropicmineral | __init__ | null | def __init__(
self,
isotropic_mineral,
cell_parameters,
anisotropic_parameters,
psi_function=None,
orthotropic=None,
):
if psi_function is None:
self.check_standard_parameters(anisotropic_parameters)
self.anisotropic_params = {"c": anisotropic_parameters}
self.psi_function = self.standard_psi_function
else:
if not isinstance(orthotropic, bool):
raise Exception(
"If the Psi function is provided, "
"you must specify whether your material is "
"orthotropic as a boolean."
)
self.orthotropic = orthotropic
self.anisotropic_params = anisotropic_parameters
self.psi_function = psi_function
self.cell_vectors_0 = cell_parameters_to_vectors(cell_parameters)
if (
np.abs(np.linalg.det(self.cell_vectors_0) - isotropic_mineral.params["V_0"])
> np.finfo(float).eps
):
factor = np.cbrt(
isotropic_mineral.params["V_0"] / np.linalg.det(self.cell_vectors_0)
)
raise Exception(
"The standard state unit vectors are inconsistent "
"with the volume. Suggest multiplying each "
f"by {factor}."
)
# Note, Psi_0 may be asymmetric, in which case the Voigt contraction
# cannot be applied
self.Psi_0 = np.einsum("ij, kl", logm(self.cell_vectors_0), np.eye(3) / 3.0)
self.isotropic_mineral = isotropic_mineral
if "name" in isotropic_mineral.params:
self.name = isotropic_mineral.params["name"]
Mineral.__init__(
self, isotropic_mineral.params, isotropic_mineral.property_modifiers
)
| (self, isotropic_mineral, cell_parameters, anisotropic_parameters, psi_function=None, orthotropic=None) | [
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10,866 | burnman.classes.anisotropicmineral | check_standard_parameters | null | def check_standard_parameters(self, anisotropic_parameters):
if not np.all(anisotropic_parameters[:, :, 0, 0] == 0):
raise Exception(
"anisotropic_parameters_pqmn should be set to " "zero for all m = n = 0"
)
sum_ijij_block = np.sum(anisotropic_parameters[:3, :3, :, :], axis=(0, 1))
if np.abs(sum_ijij_block[1, 0] - 1.0) > 1.0e-5:
raise Exception(
"The sum of the upper 3x3 pq-block of "
"anisotropic_parameters_pqmn must equal "
"1 for m=1, n=0 for consistency with the volume. "
f"Value is {sum_ijij_block[1, 0]}"
)
for m in range(2, len(sum_ijij_block)):
if np.abs(sum_ijij_block[m, 0]) > 1.0e-10:
raise Exception(
"The sum of the upper 3x3 pq-block of "
"anisotropic_parameters_pqmn must equal 0 for"
f"m={m}, n=0 for consistency with the volume. "
f"Value is {sum_ijij_block[m, 0]}"
)
for m in range(len(sum_ijij_block)):
for n in range(1, len(sum_ijij_block[0])):
if np.abs(sum_ijij_block[m, n]) > 1.0e-10:
raise Exception(
"The sum of the upper 3x3 pq-block of "
"anisotropic_parameters_pqmn must equal "
f"0 for m={m}, n={n} for "
"consistency with the volume. "
f"Value is {sum_ijij_block[m, n]}"
)
if cond(anisotropic_parameters[:, :, 1, 0]) > 1 / np.finfo(float).eps:
raise Exception("anisotropic_parameters[:, :, 1, 0] is singular")
sum_lower_left_block = np.sum(anisotropic_parameters[3:, :3, :, :], axis=1)
self.orthotropic = True
for i, s in enumerate(sum_lower_left_block):
if not np.all(np.abs(s) < 1.0e-10):
self.orthotropic = False
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10,869 | burnman.classes.mineral | debug_print | null | def debug_print(self, indent=""):
print("%s%s" % (indent, self.to_string()))
| (self, indent='') | [
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] |
10,877 | burnman.classes.mineral | set_method |
Set the equation of state to be used for this mineral.
Takes a string corresponding to any of the predefined
equations of state: 'bm2', 'bm3', 'mgd2', 'mgd3', 'slb2', 'slb3',
'mt', 'hp_tmt', or 'cork'. Alternatively, you can pass a user defined
class which derives from the equation_of_state base class.
After calling set_method(), any existing derived properties
(e.g., elastic parameters or thermodynamic potentials) will be out
of date, so set_state() will need to be called again.
| def set_method(self, equation_of_state):
"""
Set the equation of state to be used for this mineral.
Takes a string corresponding to any of the predefined
equations of state: 'bm2', 'bm3', 'mgd2', 'mgd3', 'slb2', 'slb3',
'mt', 'hp_tmt', or 'cork'. Alternatively, you can pass a user defined
class which derives from the equation_of_state base class.
After calling set_method(), any existing derived properties
(e.g., elastic parameters or thermodynamic potentials) will be out
of date, so set_state() will need to be called again.
"""
if equation_of_state is None:
self.method = None
return
new_method = eos.create(equation_of_state)
if self.method is not None and "equation_of_state" in self.params:
self.method = eos.create(self.params["equation_of_state"])
if type(new_method).__name__ == "instance":
raise Exception(
"Please derive your method from object (see python old style classes)"
)
if (
self.method is not None
and isinstance(new_method, type(self.method)) is False
):
# Warn user that they are changing the EoS
warnings.warn(
"Warning, you are changing the method to "
f"{new_method.__class__.__name__} even though the "
"material is designed to be used with the method "
f"{self.method.__class__.__name__}. "
"This does not overwrite any mineral attributes",
stacklevel=2,
)
self.reset()
self.method = new_method
# Validate the params object on the requested EOS.
try:
self.method.validate_parameters(self.params)
except Exception as e:
print(
f"Mineral {self.to_string()} failed to validate parameters "
f'with message: "{e.message}"'
)
raise
# Invalidate the cache upon resetting the method
self.reset()
| (self, equation_of_state) | [
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] |
10,878 | burnman.utils.misc | set_state | (copied from set_state):
Set the material to the given pressure and temperature.
:param pressure: The desired pressure in [Pa].
:type pressure: float
:param temperature: The desired temperature in [K].
:type temperature: float
| def copy_documentation(copy_from):
"""
Decorator @copy_documentation(another_function) will copy the documentation found in a different
function (for example from a base class). The docstring applied to some function a() will be ::
(copied from BaseClass.some_function):
<documentation from BaseClass.some_function>
<optionally the documentation found in a()>
"""
def mydecorator(func):
def wrapper(*args):
return func(*args)
old = ""
if func.__doc__:
old = "\n" + func.__doc__
copied_from = ""
if hasattr(copy_from, "__name__"):
copied_from = "(copied from " + copy_from.__name__ + "):\n"
wrapper.__doc__ = copied_from + copy_from.__doc__ + old
wrapper.__name__ = func.__name__
return wrapper
return mydecorator
| (*args) | [
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10,880 | burnman.classes.anisotropicmineral | standard_psi_function | null | def standard_psi_function(self, f, Pth, params):
# Compute Psi, dPsidPth, dPsidf, needed by most anisotropic properties
c = params["c"]
ns = np.arange(c.shape[-1])
x = c[:, :, 0, :] + c[:, :, 1, :] * f
dPsidf = c[:, :, 1, :]
for i in list(range(2, c.shape[2])):
# non-intuitively, the += operator doesn't simply add in-place,
# so here we overwrite the arrays with new ones
x = x + c[:, :, i, :] * np.power(f, float(i)) / float(i)
dPsidf = dPsidf + c[:, :, i, :] * np.power(f, float(i) - 1.0)
Psi = np.einsum("ikn, n->ik", x, np.power(Pth, ns))
dPsidPth = np.einsum(
"ikn, n->ik", x[:, :, 1:], ns[1:] * np.power(Pth, ns[1:] - 1)
)
dPsidf = np.einsum("ikn, n->ik", dPsidf, np.power(Pth, ns))
return (Psi, dPsidf, dPsidPth)
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] |
10,881 | burnman.classes.mineral | to_string |
Returns the name of the mineral class
| def to_string(self):
"""
Returns the name of the mineral class
"""
return (
"'"
+ self.__class__.__module__.replace(".minlib_", ".")
+ "."
+ self.__class__.__name__
+ "'"
)
| (self) | [
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10,882 | burnman.classes.mineral | unroll | null | def unroll(self):
return ([self], [1.0])
| (self) | [
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10,884 | burnman.classes.layer | BoundaryLayerPerturbation |
A class that implements a temperature perturbation model corresponding to a
simple thermal boundary layer.
The model takes the following form:
T = a*exp((r - r1)/(r0 - r1)*c) + b*exp((r - r0)/(r1 - r0)*c)
The relationships between the input parameters and a, b and c are
given below.
This model is a simpler version of that proposed
by :cite:`Richter1981`.
:param radius_bottom: The radius at the bottom of the layer (r0) [m].
:type radius_bottom: float
:param radius_top: The radius at the top of the layer (r1) [m].
:type radius_top: float
:param rayleigh_number: The Rayleigh number of convection within the layer. The
exponential scale factor is this number to the power of 1/4
(Ra = c^4).
:type rayleigh_number: float
:param temperature_change: The total difference in potential
temperature across the layer [K]. temperature_change = (a + b)*exp(c).
:type temperature_change: float
:param boundary_layer_ratio: The ratio of the linear scale factors (a/b)
corresponding to the thermal boundary layers at the top and bottom of
the layer. A number greater than 1 implies a larger change in
temperature across the top boundary than the bottom boundary.
:type boundary_layer_ratio: float
| class BoundaryLayerPerturbation(object):
"""
A class that implements a temperature perturbation model corresponding to a
simple thermal boundary layer.
The model takes the following form:
T = a*exp((r - r1)/(r0 - r1)*c) + b*exp((r - r0)/(r1 - r0)*c)
The relationships between the input parameters and a, b and c are
given below.
This model is a simpler version of that proposed
by :cite:`Richter1981`.
:param radius_bottom: The radius at the bottom of the layer (r0) [m].
:type radius_bottom: float
:param radius_top: The radius at the top of the layer (r1) [m].
:type radius_top: float
:param rayleigh_number: The Rayleigh number of convection within the layer. The
exponential scale factor is this number to the power of 1/4
(Ra = c^4).
:type rayleigh_number: float
:param temperature_change: The total difference in potential
temperature across the layer [K]. temperature_change = (a + b)*exp(c).
:type temperature_change: float
:param boundary_layer_ratio: The ratio of the linear scale factors (a/b)
corresponding to the thermal boundary layers at the top and bottom of
the layer. A number greater than 1 implies a larger change in
temperature across the top boundary than the bottom boundary.
:type boundary_layer_ratio: float
"""
def __init__(
self,
radius_bottom,
radius_top,
rayleigh_number,
temperature_change,
boundary_layer_ratio,
):
self.r0 = radius_bottom
self.r1 = radius_top
self.Ra = rayleigh_number
self.c = np.power(self.Ra, 1.0 / 4.0)
self.a = temperature_change / (np.exp(self.c) * (1.0 + boundary_layer_ratio))
self.b = -boundary_layer_ratio * self.a
def temperature(self, radii):
"""
Returns the temperature at one or more radii [K].
:param radii: The radii at which to evaluate the temperature.
:type radii: float or numpy.array
:returns: The temperatures at the requested radii.
:rtype: float or numpy.array
"""
return self.a * np.exp(
(radii - self.r1) / (self.r0 - self.r1) * self.c
) + self.b * np.exp((radii - self.r0) / (self.r1 - self.r0) * self.c)
def dTdr(self, radii):
"""
Returns the thermal gradient at one or more radii [K/m].
:param radii: The radii at which to evaluate the thermal gradients.
:type radii: float or numpy.array
:returns: The thermal gradient at the requested radii.
:rtype: float or numpy.array
"""
return (
self.c
/ (self.r0 - self.r1)
* (
self.a * np.exp((radii - self.r1) / (self.r0 - self.r1) * self.c)
- self.b * np.exp((radii - self.r0) / (self.r1 - self.r0) * self.c)
)
)
def set_model_thermal_gradients(self, dTdr_bottom, dTdr_top):
"""
Reparameterizes the model based on the thermal gradients
at the bottom and top of the model.
:param dTdr_bottom: The thermal gradient at the bottom of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_bottom: float
:param dTdr_top: The thermal gradient at the top of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_top: float
"""
def delta_dTdrs(args, dTdr_bottom, dTdr_top):
a, b = args
self.a = a
self.b = b
return [dTdr_bottom - self.dTdr(self.r0), dTdr_top - self.dTdr(self.r1)]
fsolve(delta_dTdrs, [self.a, self.b], args=(dTdr_bottom, dTdr_top))
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10,885 | burnman.classes.layer | __init__ | null | def __init__(
self,
radius_bottom,
radius_top,
rayleigh_number,
temperature_change,
boundary_layer_ratio,
):
self.r0 = radius_bottom
self.r1 = radius_top
self.Ra = rayleigh_number
self.c = np.power(self.Ra, 1.0 / 4.0)
self.a = temperature_change / (np.exp(self.c) * (1.0 + boundary_layer_ratio))
self.b = -boundary_layer_ratio * self.a
| (self, radius_bottom, radius_top, rayleigh_number, temperature_change, boundary_layer_ratio) | [
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10,886 | burnman.classes.layer | dTdr |
Returns the thermal gradient at one or more radii [K/m].
:param radii: The radii at which to evaluate the thermal gradients.
:type radii: float or numpy.array
:returns: The thermal gradient at the requested radii.
:rtype: float or numpy.array
| def dTdr(self, radii):
"""
Returns the thermal gradient at one or more radii [K/m].
:param radii: The radii at which to evaluate the thermal gradients.
:type radii: float or numpy.array
:returns: The thermal gradient at the requested radii.
:rtype: float or numpy.array
"""
return (
self.c
/ (self.r0 - self.r1)
* (
self.a * np.exp((radii - self.r1) / (self.r0 - self.r1) * self.c)
- self.b * np.exp((radii - self.r0) / (self.r1 - self.r0) * self.c)
)
)
| (self, radii) | [
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] |
10,887 | burnman.classes.layer | set_model_thermal_gradients |
Reparameterizes the model based on the thermal gradients
at the bottom and top of the model.
:param dTdr_bottom: The thermal gradient at the bottom of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_bottom: float
:param dTdr_top: The thermal gradient at the top of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_top: float
| def set_model_thermal_gradients(self, dTdr_bottom, dTdr_top):
"""
Reparameterizes the model based on the thermal gradients
at the bottom and top of the model.
:param dTdr_bottom: The thermal gradient at the bottom of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_bottom: float
:param dTdr_top: The thermal gradient at the top of the model [K/m].
Typically negative for a cooling planet.
:type dTdr_top: float
"""
def delta_dTdrs(args, dTdr_bottom, dTdr_top):
a, b = args
self.a = a
self.b = b
return [dTdr_bottom - self.dTdr(self.r0), dTdr_top - self.dTdr(self.r1)]
fsolve(delta_dTdrs, [self.a, self.b], args=(dTdr_bottom, dTdr_top))
| (self, dTdr_bottom, dTdr_top) | [
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] |
10,888 | burnman.classes.layer | temperature |
Returns the temperature at one or more radii [K].
:param radii: The radii at which to evaluate the temperature.
:type radii: float or numpy.array
:returns: The temperatures at the requested radii.
:rtype: float or numpy.array
| def temperature(self, radii):
"""
Returns the temperature at one or more radii [K].
:param radii: The radii at which to evaluate the temperature.
:type radii: float or numpy.array
:returns: The temperatures at the requested radii.
:rtype: float or numpy.array
"""
return self.a * np.exp(
(radii - self.r1) / (self.r0 - self.r1) * self.c
) + self.b * np.exp((radii - self.r0) / (self.r1 - self.r0) * self.c)
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10,889 | burnman.classes.calibrant | Calibrant |
The base class for a pressure calibrant material.
:param calibrant_function: A function that takes either pressure,
temperature and a params object as arguments, returning the volume,
or takes volume, temperature and a params object, returning the pressure.
:type calibrant_function: function
:param calibrant_function_return_type: The return type of the calibrant function.
Valid values are 'pressure' or 'volume'.
:type calibrant_function_return_type: str
:param params: A dictionary containing the parameters required by the
calibrant function.
:type params: dictionary
| class Calibrant(object):
"""
The base class for a pressure calibrant material.
:param calibrant_function: A function that takes either pressure,
temperature and a params object as arguments, returning the volume,
or takes volume, temperature and a params object, returning the pressure.
:type calibrant_function: function
:param calibrant_function_return_type: The return type of the calibrant function.
Valid values are 'pressure' or 'volume'.
:type calibrant_function_return_type: str
:param params: A dictionary containing the parameters required by the
calibrant function.
:type params: dictionary
"""
def __init__(self, calibrant_function, calibrant_function_return_type, params):
if calibrant_function_return_type == "pressure":
self.pressure_function = calibrant_function
self.volume_function = self._volume_using_pressure_function
elif calibrant_function_return_type == "volume":
self.volume_function = calibrant_function
self.pressure_function = self._pressure_using_volume_function
else:
raise Exception(
"calibrant function return type must either " "be pressure or volume"
)
self.calibrant_function = calibrant_function
self.params = params
def _volume_using_pressure_function(self, pressure, temperature, params):
"""
Helper function to compute volume iteratively by Brent's method using
a function of the form pressure(volume, temperature).
"""
def func(x):
return self.pressure_function(x, temperature, params) - pressure
try:
sol = bracket(func, params["V_0"], 1.0e-2 * params["V_0"])
except ValueError:
raise ValueError(
"Cannot find a volume, perhaps you are outside "
"of the range of validity for the equation "
"of state?"
)
return opt.brentq(func, sol[0], sol[1])
def _pressure_using_volume_function(self, volume, temperature, params):
"""
Helper function to compute pressure iteratively by Brent's method using
a function of the form volume(pressure, temperature).
"""
def func(x):
(self.volume_function(x, temperature, params) - volume)
try:
sol = bracket(func, 0.0, 300.0e9)
except ValueError:
raise ValueError(
"Cannot find a pressure, perhaps you are outside "
"of the range of validity for the equation "
"of state?"
)
return opt.brentq(func, sol[0], sol[1])
def pressure(self, volume, temperature, VT_covariance=None):
"""
Returns the pressure of the calibrant as a function of
volume, temperature and (optionally) a volume-temperature
variance-covariance matrix.
:param volume: The volume of the calibrant [m^3/mol].
:type volume: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param VT_covariance: The volume-temperature
variance-covariance matrix [optional].
:type VT_covariance: 2x2 numpy.array
:returns: The pressure of the calibrant [Pa] and the
pressure-volume-temperature variance-covariance matrix
if PT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
"""
if VT_covariance is None:
return self.pressure_function(volume, temperature, self.params)
else:
# Here we take the centered differences
# We could alternatively use thermodynamic properties
# but these have not yet been implemented.
dV = volume / 1.0e7
dT = 0.01
PdV0 = self.pressure_function(volume - dV / 2.0, temperature, self.params)
PdV1 = self.pressure_function(volume + dV / 2.0, temperature, self.params)
PdT0 = self.pressure_function(volume, temperature - dT / 2.0, self.params)
PdT1 = self.pressure_function(volume, temperature + dT / 2.0, self.params)
pressure = (PdV0 + PdV1 + PdT0 + PdT1) / 4.0
gradPVT = np.zeros((2, 3))
gradPVT[:, 1:] = np.eye(2)
gradPVT[:, 0] = [(PdV1 - PdV0) / dV, (PdT1 - PdT0) / dT]
PVT_covariance = gradPVT.T.dot(VT_covariance).dot(gradPVT)
return pressure, PVT_covariance
def volume(self, pressure, temperature, PT_covariance=None):
"""
Returns the volume of the calibrant as a function of
pressure, temperature and (optionally) a pressure-temperature
variance-covariance matrix.
:param pressure: The pressure of the calibrant [Pa].
:type pressure: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param PT_covariance: The pressure-temperature
variance-covariance matrix [optional].
:type PT_covariance: 2x2 numpy.array
:returns: The volume of the calibrant [m^3/mol] and
the volume-pressure-temperature variance-covariance matrix
if VT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
"""
if PT_covariance is None:
return self.volume_function(pressure, temperature, self.params)
else:
# Here we take the centered differences
# We could alternatively use thermodynamic properties
# but these have not yet been implemented.
dP = 100.0
dT = 0.01
VdP0 = self.volume_function(pressure - dP / 2.0, temperature, self.params)
VdP1 = self.volume_function(pressure + dP / 2.0, temperature, self.params)
VdT0 = self.volume_function(pressure, temperature - dT / 2.0, self.params)
VdT1 = self.volume_function(pressure, temperature + dT / 2.0, self.params)
volume = (VdP0 + VdP1 + VdT0 + VdT1) / 4.0
gradVPT = np.zeros((2, 3))
gradVPT[:, 1:] = np.eye(2)
gradVPT[:, 0] = [(VdP1 - VdP0) / dP, (VdT1 - VdT0) / dT]
VPT_covariance = gradVPT.T.dot(PT_covariance).dot(gradVPT)
return volume, VPT_covariance
| (calibrant_function, calibrant_function_return_type, params) | [
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10,890 | burnman.classes.calibrant | __init__ | null | def __init__(self, calibrant_function, calibrant_function_return_type, params):
if calibrant_function_return_type == "pressure":
self.pressure_function = calibrant_function
self.volume_function = self._volume_using_pressure_function
elif calibrant_function_return_type == "volume":
self.volume_function = calibrant_function
self.pressure_function = self._pressure_using_volume_function
else:
raise Exception(
"calibrant function return type must either " "be pressure or volume"
)
self.calibrant_function = calibrant_function
self.params = params
| (self, calibrant_function, calibrant_function_return_type, params) | [
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] |
10,891 | burnman.classes.calibrant | _pressure_using_volume_function |
Helper function to compute pressure iteratively by Brent's method using
a function of the form volume(pressure, temperature).
| def _pressure_using_volume_function(self, volume, temperature, params):
"""
Helper function to compute pressure iteratively by Brent's method using
a function of the form volume(pressure, temperature).
"""
def func(x):
(self.volume_function(x, temperature, params) - volume)
try:
sol = bracket(func, 0.0, 300.0e9)
except ValueError:
raise ValueError(
"Cannot find a pressure, perhaps you are outside "
"of the range of validity for the equation "
"of state?"
)
return opt.brentq(func, sol[0], sol[1])
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] |
10,892 | burnman.classes.calibrant | _volume_using_pressure_function |
Helper function to compute volume iteratively by Brent's method using
a function of the form pressure(volume, temperature).
| def _volume_using_pressure_function(self, pressure, temperature, params):
"""
Helper function to compute volume iteratively by Brent's method using
a function of the form pressure(volume, temperature).
"""
def func(x):
return self.pressure_function(x, temperature, params) - pressure
try:
sol = bracket(func, params["V_0"], 1.0e-2 * params["V_0"])
except ValueError:
raise ValueError(
"Cannot find a volume, perhaps you are outside "
"of the range of validity for the equation "
"of state?"
)
return opt.brentq(func, sol[0], sol[1])
| (self, pressure, temperature, params) | [
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10,893 | burnman.classes.calibrant | pressure |
Returns the pressure of the calibrant as a function of
volume, temperature and (optionally) a volume-temperature
variance-covariance matrix.
:param volume: The volume of the calibrant [m^3/mol].
:type volume: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param VT_covariance: The volume-temperature
variance-covariance matrix [optional].
:type VT_covariance: 2x2 numpy.array
:returns: The pressure of the calibrant [Pa] and the
pressure-volume-temperature variance-covariance matrix
if PT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
| def pressure(self, volume, temperature, VT_covariance=None):
"""
Returns the pressure of the calibrant as a function of
volume, temperature and (optionally) a volume-temperature
variance-covariance matrix.
:param volume: The volume of the calibrant [m^3/mol].
:type volume: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param VT_covariance: The volume-temperature
variance-covariance matrix [optional].
:type VT_covariance: 2x2 numpy.array
:returns: The pressure of the calibrant [Pa] and the
pressure-volume-temperature variance-covariance matrix
if PT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
"""
if VT_covariance is None:
return self.pressure_function(volume, temperature, self.params)
else:
# Here we take the centered differences
# We could alternatively use thermodynamic properties
# but these have not yet been implemented.
dV = volume / 1.0e7
dT = 0.01
PdV0 = self.pressure_function(volume - dV / 2.0, temperature, self.params)
PdV1 = self.pressure_function(volume + dV / 2.0, temperature, self.params)
PdT0 = self.pressure_function(volume, temperature - dT / 2.0, self.params)
PdT1 = self.pressure_function(volume, temperature + dT / 2.0, self.params)
pressure = (PdV0 + PdV1 + PdT0 + PdT1) / 4.0
gradPVT = np.zeros((2, 3))
gradPVT[:, 1:] = np.eye(2)
gradPVT[:, 0] = [(PdV1 - PdV0) / dV, (PdT1 - PdT0) / dT]
PVT_covariance = gradPVT.T.dot(VT_covariance).dot(gradPVT)
return pressure, PVT_covariance
| (self, volume, temperature, VT_covariance=None) | [
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10,894 | burnman.classes.calibrant | volume |
Returns the volume of the calibrant as a function of
pressure, temperature and (optionally) a pressure-temperature
variance-covariance matrix.
:param pressure: The pressure of the calibrant [Pa].
:type pressure: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param PT_covariance: The pressure-temperature
variance-covariance matrix [optional].
:type PT_covariance: 2x2 numpy.array
:returns: The volume of the calibrant [m^3/mol] and
the volume-pressure-temperature variance-covariance matrix
if VT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
| def volume(self, pressure, temperature, PT_covariance=None):
"""
Returns the volume of the calibrant as a function of
pressure, temperature and (optionally) a pressure-temperature
variance-covariance matrix.
:param pressure: The pressure of the calibrant [Pa].
:type pressure: float
:param temperature: The temperature of the calibrant [K].
:type temperature: float
:param PT_covariance: The pressure-temperature
variance-covariance matrix [optional].
:type PT_covariance: 2x2 numpy.array
:returns: The volume of the calibrant [m^3/mol] and
the volume-pressure-temperature variance-covariance matrix
if VT_covariance is provided.
:rtype: float, tuple of a float and a numpy.array (3x3)
"""
if PT_covariance is None:
return self.volume_function(pressure, temperature, self.params)
else:
# Here we take the centered differences
# We could alternatively use thermodynamic properties
# but these have not yet been implemented.
dP = 100.0
dT = 0.01
VdP0 = self.volume_function(pressure - dP / 2.0, temperature, self.params)
VdP1 = self.volume_function(pressure + dP / 2.0, temperature, self.params)
VdT0 = self.volume_function(pressure, temperature - dT / 2.0, self.params)
VdT1 = self.volume_function(pressure, temperature + dT / 2.0, self.params)
volume = (VdP0 + VdP1 + VdT0 + VdT1) / 4.0
gradVPT = np.zeros((2, 3))
gradVPT[:, 1:] = np.eye(2)
gradVPT[:, 0] = [(VdP1 - VdP0) / dP, (VdT1 - VdT0) / dT]
VPT_covariance = gradVPT.T.dot(PT_covariance).dot(gradVPT)
return volume, VPT_covariance
| (self, pressure, temperature, PT_covariance=None) | [
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10,895 | burnman.classes.combinedmineral | CombinedMineral |
This is the base class for endmembers constructed from a
linear combination of other minerals.
Instances of this class should be initialised with a
list of Mineral instances, a second list containing the
number of moles of each mineral, and (optionally) a
third list containing three floats describing a
free energy adjustment which is linear in pressure and temperature
(i.e. a constant energy [J/mol], entropy [J/K/mol]
and volume adjustment [J/Pa/mol or m^3/mol]).
For example, a crude approximation to a bridgmanite model might be
bdg = CombinedMineral([per, stv], [1.0, 1.0], [-15.e3, 0., 0.])
This class is available as :class:`burnman.CombinedMineral`.
| class CombinedMineral(Mineral):
"""
This is the base class for endmembers constructed from a
linear combination of other minerals.
Instances of this class should be initialised with a
list of Mineral instances, a second list containing the
number of moles of each mineral, and (optionally) a
third list containing three floats describing a
free energy adjustment which is linear in pressure and temperature
(i.e. a constant energy [J/mol], entropy [J/K/mol]
and volume adjustment [J/Pa/mol or m^3/mol]).
For example, a crude approximation to a bridgmanite model might be
bdg = CombinedMineral([per, stv], [1.0, 1.0], [-15.e3, 0., 0.])
This class is available as :class:`burnman.CombinedMineral`.
"""
def __init__(
self,
mineral_list,
molar_amounts,
free_energy_adjustment=[],
name="User-created endmember",
):
model = MechanicalSolution(endmembers=[[m, ""] for m in mineral_list])
self.mixture = Solution(solution_model=model, molar_fractions=molar_amounts)
# Remove elements from the chemical formula if they have
# negligible concentrations
for key, value in list(self.mixture.formula.items()):
if np.abs(value) < 1.0e-10:
self.mixture.formula.pop(key)
self.params = {
"name": name,
"formula": self.mixture.formula,
"equation_of_state": "combined",
"molar_mass": self.mixture.molar_mass,
"n": sum(self.mixture.formula.values()),
}
if free_energy_adjustment != []:
assert len(free_energy_adjustment) == 3
dE, dS, dV = free_energy_adjustment
self.property_modifiers = [
["linear", {"delta_E": dE, "delta_S": dS, "delta_V": dV}]
]
Mineral.__init__(self)
def set_state(self, pressure, temperature):
self.mixture.set_state(pressure, temperature)
Mineral.set_state(self, pressure, temperature)
@material_property
def molar_gibbs(self):
"""
Returns Gibbs free energy of the mineral [J]
Aliased with self.gibbs
"""
return self.mixture.molar_gibbs + self._property_modifiers["G"]
@material_property
def _molar_volume_unmodified(self):
return self.mixture.molar_volume
@material_property
def molar_volume(self):
"""
Returns molar volume of the mineral [m^3/mol]
Aliased with self.V
"""
return self.mixture.molar_volume + self._property_modifiers["dGdP"]
@material_property
def molar_entropy(self):
"""
Returns entropy of the mineral [J]
Aliased with self.S
"""
return self.mixture.molar_entropy - self._property_modifiers["dGdT"]
@material_property
def isothermal_bulk_modulus(self):
"""
Returns isothermal bulk modulus of the mineral [Pa]
Aliased with self.K_T
"""
K_T_orig = self.mixture.isothermal_bulk_modulus
return self.molar_volume / (
(self._molar_volume_unmodified / K_T_orig)
- self._property_modifiers["d2GdP2"]
)
@material_property
def shear_modulus(self):
"""
Returns shear modulus of the mineral [Pa]
Aliased with self.G
"""
return self.mixture.shear_modulus
@material_property
def thermal_expansivity(self):
"""
Returns thermal expansion coefficient (alpha) of the mineral [1/K]
Aliased with self.alpha
"""
return (
(self.mixture.thermal_expansivity * self._molar_volume_unmodified)
+ self._property_modifiers["d2GdPdT"]
) / self.molar_volume
@material_property
def molar_heat_capacity_p(self):
"""
Returns heat capacity at constant pressure of the mineral [J/K/mol]
Aliased with self.C_p
"""
return (
self.mixture.molar_heat_capacity_p
- self.temperature * self._property_modifiers["d2GdT2"]
)
"""
Properties from mineral parameters,
Legendre transformations
or Maxwell relations
"""
@material_property
def molar_mass(self):
"""
Returns molar mass of the mineral [kg/mol]
"""
return self.mixture.molar_mass
@material_property
def formula(self):
"""
Returns molar chemical formula of the mineral
"""
return self.mixture.formula
@material_property
def density(self):
"""
Returns density of the mineral [kg/m^3]
Aliased with self.rho
"""
return self.molar_mass / self.molar_volume
@material_property
def molar_internal_energy(self):
"""
Returns molar internal energy of the mineral [J/mol]
Aliased with self.energy
"""
return (
self.molar_gibbs
- self.pressure * self.molar_volume
+ self.temperature * self.molar_entropy
)
@material_property
def molar_helmholtz(self):
"""
Returns molar Helmholtz free energy of the mineral [J/mol]
Aliased with self.helmholtz
"""
return self.molar_gibbs - self.pressure * self.molar_volume
@material_property
def molar_enthalpy(self):
"""
Returns molar enthalpy of the mineral [J/mol]
Aliased with self.H
"""
return self.molar_gibbs + self.temperature * self.molar_entropy
@material_property
def adiabatic_bulk_modulus(self):
"""
Returns adiabatic bulk modulus of the mineral [Pa]
Aliased with self.K_S
"""
if self.temperature < 1.0e-10:
return self.isothermal_bulk_modulus
else:
return (
self.isothermal_bulk_modulus
* self.molar_heat_capacity_p
/ self.molar_heat_capacity_v
)
@material_property
def isothermal_compressibility(self):
"""
Returns isothermal compressibility of the mineral
(or inverse isothermal bulk modulus) [1/Pa]
Aliased with self.K_T
"""
return 1.0 / self.isothermal_bulk_modulus
@material_property
def adiabatic_compressibility(self):
"""
Returns adiabatic compressibility of the mineral
(or inverse adiabatic bulk modulus) [1/Pa]
Aliased with self.K_S
"""
return 1.0 / self.adiabatic_bulk_modulus
@material_property
def p_wave_velocity(self):
"""
Returns P wave speed of the mineral [m/s]
Aliased with self.v_p
"""
return np.sqrt(
(self.adiabatic_bulk_modulus + 4.0 / 3.0 * self.shear_modulus)
/ self.density
)
@material_property
def bulk_sound_velocity(self):
"""
Returns bulk sound speed of the mineral [m/s]
Aliased with self.v_phi
"""
return np.sqrt(self.adiabatic_bulk_modulus / self.density)
@material_property
def shear_wave_velocity(self):
"""
Returns shear wave speed of the mineral [m/s]
Aliased with self.v_s
"""
return np.sqrt(self.shear_modulus / self.density)
@material_property
def grueneisen_parameter(self):
"""
Returns grueneisen parameter of the mineral [unitless]
Aliased with self.gr
"""
if self.temperature < 1.0e-12:
return 0.0
else:
return (
self.thermal_expansivity
* self.isothermal_bulk_modulus
* self.molar_volume
/ self.molar_heat_capacity_v
)
@material_property
def molar_heat_capacity_v(self):
"""
Returns molar heat capacity at constant volume of the mineral [J/K/mol]
Aliased with self.C_v
"""
return (
self.molar_heat_capacity_p
- self.molar_volume
* self.temperature
* self.thermal_expansivity
* self.thermal_expansivity
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10,896 | burnman.classes.combinedmineral | __init__ | null | def __init__(
self,
mineral_list,
molar_amounts,
free_energy_adjustment=[],
name="User-created endmember",
):
model = MechanicalSolution(endmembers=[[m, ""] for m in mineral_list])
self.mixture = Solution(solution_model=model, molar_fractions=molar_amounts)
# Remove elements from the chemical formula if they have
# negligible concentrations
for key, value in list(self.mixture.formula.items()):
if np.abs(value) < 1.0e-10:
self.mixture.formula.pop(key)
self.params = {
"name": name,
"formula": self.mixture.formula,
"equation_of_state": "combined",
"molar_mass": self.mixture.molar_mass,
"n": sum(self.mixture.formula.values()),
}
if free_energy_adjustment != []:
assert len(free_energy_adjustment) == 3
dE, dS, dV = free_energy_adjustment
self.property_modifiers = [
["linear", {"delta_E": dE, "delta_S": dS, "delta_V": dV}]
]
Mineral.__init__(self)
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10,903 | burnman.classes.combinedmineral | set_state | null | def set_state(self, pressure, temperature):
self.mixture.set_state(pressure, temperature)
Mineral.set_state(self, pressure, temperature)
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10,907 | burnman.classes.composite | Composite |
Base class for a composite material.
The static phases can be minerals or materials,
meaning composite can be nested arbitrarily.
The fractions of the phases can be input
as either 'molar' or 'mass' during instantiation,
and modified (or initialised) after this point by
using set_fractions.
This class is available as ``burnman.Composite``.
| class Composite(Material):
"""
Base class for a composite material.
The static phases can be minerals or materials,
meaning composite can be nested arbitrarily.
The fractions of the phases can be input
as either 'molar' or 'mass' during instantiation,
and modified (or initialised) after this point by
using set_fractions.
This class is available as ``burnman.Composite``.
"""
def __init__(
self, phases, fractions=None, fraction_type="molar", name="Unnamed composite"
):
"""
Create a composite using a list of phases and their fractions (adding to 1.0).
:param phases: List of phases.
:type phases: list of :class:`burnman.Material`
:param fractions: molar or mass fraction for each phase.
:type fractions: list of floats
:param fraction_type: 'molar' or 'mass' (optional, 'molar' as standard)
specify whether molar or mass fractions are specified.
:type fraction_type: str
"""
Material.__init__(self)
assert len(phases) > 0
self.phases = phases
if fractions is not None:
self.set_fractions(fractions, fraction_type)
else:
self.molar_fractions = None
self.set_averaging_scheme("VoigtReussHill")
self.name = name
self.equilibrium_tolerance = 1.0e-3 # J/reaction
self.print_precision = 4 # number of significant figures used by self.__str__
def __str__(self):
string = "Composite: {0}".format(self.name)
try:
string += "\n P, T: {0:.{sf}g} Pa, {1:.{sf}g} K".format(
self.pressure, self.temperature, sf=self.print_precision
)
except:
pass
string += "\nPhase and endmember fractions:"
for phase, fraction in zip(*self.unroll()):
string += "\n {0}: {1:0.{sf}f}".format(
phase.name, fraction, sf=self.print_precision
)
if isinstance(phase, Solution):
for i in range(phase.n_endmembers):
string += "\n {0}: {1:0.{sf}f}".format(
phase.endmember_names[i],
phase.molar_fractions[i],
sf=self.print_precision,
)
return string
def set_fractions(self, fractions, fraction_type="molar"):
"""
Change the fractions of the phases of this Composite.
Resets cached properties
:param fractions: list or numpy array of floats
molar or mass fraction for each phase.
:param fraction_type: 'molar' or 'mass'
specify whether molar or mass fractions are specified.
"""
assert len(self.phases) == len(fractions)
if isinstance(fractions, list):
fractions = np.array(fractions)
try:
total = sum(fractions)
except TypeError:
raise Exception(
"Since v0.8, burnman.Composite takes an array of Materials, "
"then an array of fractions"
)
assert np.all(fractions >= -1e-12)
self.reset()
if abs(total - 1.0) > 1e-12:
warnings.warn(
"Warning: list of fractions does not add "
f"up to one but {total:g}. Normalizing."
)
fractions /= total
if fraction_type == "molar":
molar_fractions = fractions
elif fraction_type == "mass":
molar_fractions = self._mass_to_molar_fractions(self.phases, fractions)
else:
raise Exception(
"Fraction type not recognised. " "Please use 'molar' or mass"
)
# Set minimum value of a molar fraction at 0.0 (rather than -1.e-12)
self.molar_fractions = molar_fractions.clip(0.0)
def set_method(self, method):
"""
set the same equation of state method for all the phases in the composite
"""
for phase in self.phases:
phase.set_method(method)
# Clear the cache on resetting method
self.reset()
def set_averaging_scheme(self, averaging_scheme):
"""
Set the averaging scheme for the moduli in the composite.
Default is set to VoigtReussHill, when Composite is initialized.
"""
if type(averaging_scheme) == str:
self.averaging_scheme = getattr(averaging_schemes, averaging_scheme)()
else:
self.averaging_scheme = averaging_scheme
# Clear the cache on resetting averaging scheme
self.reset()
def set_state(self, pressure, temperature):
"""
Update the material to the given pressure [Pa] and temperature [K].
"""
Material.set_state(self, pressure, temperature)
for phase in self.phases:
phase.set_state(pressure, temperature)
def debug_print(self, indent=""):
print("{0}Composite: {1}".format(indent, self.name))
indent += " "
if self.molar_fractions is None:
for i, phase in enumerate(self.phases):
phase.debug_print(indent + " ")
else:
for i, phase in enumerate(self.phases):
print("%s%g of" % (indent, self.molar_fractions[i]))
phase.debug_print(indent + " ")
def unroll(self):
if self.molar_fractions is None:
raise Exception("Unroll only works if the composite has defined fractions.")
phases = []
fractions = []
for i, phase in enumerate(self.phases):
p_mineral, p_fraction = phase.unroll()
check_pairs(p_mineral, p_fraction)
fractions.extend([f * self.molar_fractions[i] for f in p_fraction])
phases.extend(p_mineral)
return phases, fractions
def to_string(self):
"""
return the name of the composite
"""
return "{0}: {1}".format(self.__class__.__name__, self.name)
@material_property
def formula(self):
"""
Returns molar chemical formula of the composite
"""
return sum_formulae([ph.formula for ph in self.phases], self.molar_fractions)
@material_property
def molar_internal_energy(self):
"""
Returns molar internal energy of the mineral [J/mol]
Aliased with self.energy
"""
U = sum(
phase.molar_internal_energy * molar_fraction
for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)
)
return U
@material_property
def molar_gibbs(self):
"""
Returns molar Gibbs free energy of the composite [J/mol]
Aliased with self.gibbs
"""
G = sum(
phase.molar_gibbs * molar_fraction
for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)
)
return G
@material_property
def molar_helmholtz(self):
"""
Returns molar Helmholtz free energy of the mineral [J/mol]
Aliased with self.helmholtz
"""
F = sum(
phase.molar_helmholtz * molar_fraction
for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)
)
return F
@material_property
def molar_volume(self):
"""
Returns molar volume of the composite [m^3/mol]
Aliased with self.V
"""
volumes = np.array(
[
phase.molar_volume * molar_fraction
for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)
]
)
return np.sum(volumes)
@material_property
def molar_mass(self):
"""
Returns molar mass of the composite [kg/mol]
"""
return sum(
[
phase.molar_mass * molar_fraction
for (phase, molar_fraction) in zip(self.phases, self.molar_fractions)
]
)
@material_property
def density(self):
"""
Compute the density of the composite based on the molar volumes and masses
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10,908 | burnman.classes.composite | __init__ |
Create a composite using a list of phases and their fractions (adding to 1.0).
:param phases: List of phases.
:type phases: list of :class:`burnman.Material`
:param fractions: molar or mass fraction for each phase.
:type fractions: list of floats
:param fraction_type: 'molar' or 'mass' (optional, 'molar' as standard)
specify whether molar or mass fractions are specified.
:type fraction_type: str
| def __init__(
self, phases, fractions=None, fraction_type="molar", name="Unnamed composite"
):
"""
Create a composite using a list of phases and their fractions (adding to 1.0).
:param phases: List of phases.
:type phases: list of :class:`burnman.Material`
:param fractions: molar or mass fraction for each phase.
:type fractions: list of floats
:param fraction_type: 'molar' or 'mass' (optional, 'molar' as standard)
specify whether molar or mass fractions are specified.
:type fraction_type: str
"""
Material.__init__(self)
assert len(phases) > 0
self.phases = phases
if fractions is not None:
self.set_fractions(fractions, fraction_type)
else:
self.molar_fractions = None
self.set_averaging_scheme("VoigtReussHill")
self.name = name
self.equilibrium_tolerance = 1.0e-3 # J/reaction
self.print_precision = 4 # number of significant figures used by self.__str__
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10,909 | burnman.classes.composite | __str__ | null | def __str__(self):
string = "Composite: {0}".format(self.name)
try:
string += "\n P, T: {0:.{sf}g} Pa, {1:.{sf}g} K".format(
self.pressure, self.temperature, sf=self.print_precision
)
except:
pass
string += "\nPhase and endmember fractions:"
for phase, fraction in zip(*self.unroll()):
string += "\n {0}: {1:0.{sf}f}".format(
phase.name, fraction, sf=self.print_precision
)
if isinstance(phase, Solution):
for i in range(phase.n_endmembers):
string += "\n {0}: {1:0.{sf}f}".format(
phase.endmember_names[i],
phase.molar_fractions[i],
sf=self.print_precision,
)
return string
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10,910 | burnman.classes.composite | _mass_to_molar_fractions |
Converts a set of mass fractions for phases into a set of molar fractions.
:param phases: The list of phases for which fractions should be converted.
:type phases: list of :class:`burnman.Material`
:param mass_fractions: An array of mass fractions of the input phases.
:type mass_fractions: numpy.array of floats
:returns: An array of molar fractions corresponding to the
input molar fractions.
:rtype: numpy.array of floats
| def _mass_to_molar_fractions(self, phases, mass_fractions):
"""
Converts a set of mass fractions for phases into a set of molar fractions.
:param phases: The list of phases for which fractions should be converted.
:type phases: list of :class:`burnman.Material`
:param mass_fractions: An array of mass fractions of the input phases.
:type mass_fractions: numpy.array of floats
:returns: An array of molar fractions corresponding to the
input molar fractions.
:rtype: numpy.array of floats
"""
molar_masses = np.array([phase.molar_mass for phase in phases])
moles = mass_fractions / molar_masses
return moles / sum(moles)
| (self, phases, mass_fractions) | [
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] |
10,911 | burnman.classes.composite | _set_endmember_properties |
Sets endmember_formulae, endmember_names, endmembers_per_phase and
elements as properties of the Composite. This helper function
is used to set all properties at the same time while still allowing
the properties to be stored and documented as individual
cached_properties.
| def _set_endmember_properties(self):
"""
Sets endmember_formulae, endmember_names, endmembers_per_phase and
elements as properties of the Composite. This helper function
is used to set all properties at the same time while still allowing
the properties to be stored and documented as individual
cached_properties.
"""
endmember_formulae = []
endmember_names = []
endmembers_per_phase = []
for ph_idx, ph in enumerate(self.phases):
if isinstance(ph, Solution):
endmember_formulae.extend(ph.endmember_formulae)
endmember_names.extend(
[name + " in " + ph.name for name in ph.endmember_names]
)
endmembers_per_phase.append(ph.n_endmembers)
elif isinstance(ph, Mineral):
endmember_formulae.append(ph.formula)
endmember_names.append(ph.name)
endmembers_per_phase.append(1)
else:
raise Exception(
"Unsupported Material type, can only read"
"burnman.Mineral or burnman.Solution"
)
# Populate the stoichiometric matrix
keys = []
for f in endmember_formulae:
keys.extend(f.keys())
# Save to dict so that we only need to do this once
self.__dict__["endmember_formulae"] = endmember_formulae
self.__dict__["endmember_names"] = endmember_names
self.__dict__["endmembers_per_phase"] = endmembers_per_phase
self.__dict__["elements"] = sort_element_list_to_IUPAC_order(set(keys))
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10,912 | burnman.classes.composite | chemical_potential |
Returns the chemical potentials of the currently defined components
in the composite. Raises an exception if
the assemblage is not equilibrated.
:param components: List of formulae of the desired components.
If not specified, the method uses the components specified
by a previous call to set_components.
:type components: list of dictionaries
:returns: The chemical potentials of the desired components in the
equilibrium composite.
:rtype: numpy.array of floats
| def chemical_potential(self, components=None):
"""
Returns the chemical potentials of the currently defined components
in the composite. Raises an exception if
the assemblage is not equilibrated.
:param components: List of formulae of the desired components.
If not specified, the method uses the components specified
by a previous call to set_components.
:type components: list of dictionaries
:returns: The chemical potentials of the desired components in the
equilibrium composite.
:rtype: numpy.array of floats
"""
if not self.equilibrated:
raise Exception(
"This composite is not equilibrated, so "
"it cannot have a defined chemical potential."
)
if components is not None:
self.set_components(components)
# Return the chemical potential of each component
return np.dot(self.component_array.T, self.endmember_partial_gibbs)
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10,914 | burnman.classes.composite | debug_print | null | def debug_print(self, indent=""):
print("{0}Composite: {1}".format(indent, self.name))
indent += " "
if self.molar_fractions is None:
for i, phase in enumerate(self.phases):
phase.debug_print(indent + " ")
else:
for i, phase in enumerate(self.phases):
print("%s%g of" % (indent, self.molar_fractions[i]))
phase.debug_print(indent + " ")
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] |
10,918 | burnman.classes.composite | set_averaging_scheme |
Set the averaging scheme for the moduli in the composite.
Default is set to VoigtReussHill, when Composite is initialized.
| def set_averaging_scheme(self, averaging_scheme):
"""
Set the averaging scheme for the moduli in the composite.
Default is set to VoigtReussHill, when Composite is initialized.
"""
if type(averaging_scheme) == str:
self.averaging_scheme = getattr(averaging_schemes, averaging_scheme)()
else:
self.averaging_scheme = averaging_scheme
# Clear the cache on resetting averaging scheme
self.reset()
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] |
10,919 | burnman.classes.composite | set_components |
Sets the components and components_array attributes of the
composite material. The components attribute is a list of dictionaries
containing the chemical formulae of the components.
The components_array attribute is a 2D numpy array describing the
linear transformation between endmember amounts and component amounts.
The components do not need to be linearly independent, not do they need
to form a complete basis set for the composite.
However, it must be possible to obtain the composition of each
component from a linear sum of the endmember compositions of
the composite. For example, if the composite was composed of
MgSiO3 and Mg2SiO4, SiO2 would be a valid component, but Si would not.
The method raises an exception if any of the chemical potentials are
not defined by the assemblage.
:param components: List of formulae of the components.
:type components: list of dictionaries
| def set_components(self, components):
"""
Sets the components and components_array attributes of the
composite material. The components attribute is a list of dictionaries
containing the chemical formulae of the components.
The components_array attribute is a 2D numpy array describing the
linear transformation between endmember amounts and component amounts.
The components do not need to be linearly independent, not do they need
to form a complete basis set for the composite.
However, it must be possible to obtain the composition of each
component from a linear sum of the endmember compositions of
the composite. For example, if the composite was composed of
MgSiO3 and Mg2SiO4, SiO2 would be a valid component, but Si would not.
The method raises an exception if any of the chemical potentials are
not defined by the assemblage.
:param components: List of formulae of the components.
:type components: list of dictionaries
"""
# Convert components into array form
b = np.array(
[
[component[el] if el in component else 0.0 for component in components]
for el in self.elements
]
)
# Solve to find a set of endmember proportions that
# satisfy each of the component formulae
p = np.linalg.lstsq(self.stoichiometric_array.T, b, rcond=None)
res = np.abs((self.stoichiometric_array.T.dot(p[0]) - b).T)
res = np.sum(res, axis=1)
# Check that all components can be described by linear sums of
# the endmembers
if not np.all(res < 1.0e-12):
bad_indices = np.argwhere(res > 1.0e-12)
raise Exception(
f"Components {bad_indices} not defined by " "prescribed assemblage"
)
self.components = components
self.component_array = p[0]
| (self, components) | [
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10,920 | burnman.classes.composite | set_fractions |
Change the fractions of the phases of this Composite.
Resets cached properties
:param fractions: list or numpy array of floats
molar or mass fraction for each phase.
:param fraction_type: 'molar' or 'mass'
specify whether molar or mass fractions are specified.
| def set_fractions(self, fractions, fraction_type="molar"):
"""
Change the fractions of the phases of this Composite.
Resets cached properties
:param fractions: list or numpy array of floats
molar or mass fraction for each phase.
:param fraction_type: 'molar' or 'mass'
specify whether molar or mass fractions are specified.
"""
assert len(self.phases) == len(fractions)
if isinstance(fractions, list):
fractions = np.array(fractions)
try:
total = sum(fractions)
except TypeError:
raise Exception(
"Since v0.8, burnman.Composite takes an array of Materials, "
"then an array of fractions"
)
assert np.all(fractions >= -1e-12)
self.reset()
if abs(total - 1.0) > 1e-12:
warnings.warn(
"Warning: list of fractions does not add "
f"up to one but {total:g}. Normalizing."
)
fractions /= total
if fraction_type == "molar":
molar_fractions = fractions
elif fraction_type == "mass":
molar_fractions = self._mass_to_molar_fractions(self.phases, fractions)
else:
raise Exception(
"Fraction type not recognised. " "Please use 'molar' or mass"
)
# Set minimum value of a molar fraction at 0.0 (rather than -1.e-12)
self.molar_fractions = molar_fractions.clip(0.0)
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10,921 | burnman.classes.composite | set_method |
set the same equation of state method for all the phases in the composite
| def set_method(self, method):
"""
set the same equation of state method for all the phases in the composite
"""
for phase in self.phases:
phase.set_method(method)
# Clear the cache on resetting method
self.reset()
| (self, method) | [
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] |
10,922 | burnman.classes.composite | set_state |
Update the material to the given pressure [Pa] and temperature [K].
| def set_state(self, pressure, temperature):
"""
Update the material to the given pressure [Pa] and temperature [K].
"""
Material.set_state(self, pressure, temperature)
for phase in self.phases:
phase.set_state(pressure, temperature)
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10,924 | burnman.classes.composite | to_string |
return the name of the composite
| def to_string(self):
"""
return the name of the composite
"""
return "{0}: {1}".format(self.__class__.__name__, self.name)
| (self) | [
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10,925 | burnman.classes.composite | unroll | null | def unroll(self):
if self.molar_fractions is None:
raise Exception("Unroll only works if the composite has defined fractions.")
phases = []
fractions = []
for i, phase in enumerate(self.phases):
p_mineral, p_fraction = phase.unroll()
check_pairs(p_mineral, p_fraction)
fractions.extend([f * self.molar_fractions[i] for f in p_fraction])
phases.extend(p_mineral)
return phases, fractions
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] |
10,926 | burnman.classes.composition | Composition |
Class for a composition object, which can be used
to store, modify and renormalize compositions,
and also convert between mass, molar
and atomic amounts. Weight is provided as an alias
for mass, as we assume that only Earthlings
will use this software.
This class is available as ``burnman.Composition``.
| class Composition(object):
"""
Class for a composition object, which can be used
to store, modify and renormalize compositions,
and also convert between mass, molar
and atomic amounts. Weight is provided as an alias
for mass, as we assume that only Earthlings
will use this software.
This class is available as ``burnman.Composition``.
"""
def __init__(self, composition_dictionary, unit_type="mass", normalize=False):
"""
Create a composition using a dictionary and unit type.
:param composition_dictionary: Dictionary of components
(given as a string) and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar' (optional, 'mass' as default)
Specify whether the input composition is given as mass or
molar amounts.
:type unit_type: str
:param normalize: If False, absolute numbers of kilograms/moles of component are
stored, otherwise the component amounts of returned compositions
will sum to one (until Composition.renormalize() is used).
:type normalize: bool
"""
self._cached = {}
n_total = float(sum(composition_dictionary.values()))
# Create the input dictionary, normalize if requested
input_dictionary = OrderedCounter(deepcopy(composition_dictionary))
if normalize:
for k in composition_dictionary.keys():
input_dictionary[k] = composition_dictionary[k] / n_total
# Break component formulae into atomic dictionaries
self.component_formulae = {
c: dictionarize_formula(c) for c in composition_dictionary.keys()
}
# Create lists of elemental compositions of components
self.element_list = OrderedCounter()
for component in self.component_formulae.values():
self.element_list += OrderedCounter(
{element: n_atoms for (element, n_atoms) in component.items()}
)
self.element_list = list(self.element_list.keys())
if unit_type == "mass" or unit_type == "weight":
self.mass_composition = input_dictionary
elif unit_type == "molar":
self.mass_composition = self._mole_to_mass_composition(input_dictionary)
else:
raise Exception(
"Unit type not yet implemented. "
"Should be either mass, weight or molar."
)
def renormalize(self, unit_type, normalization_component, normalization_amount):
"""
Change the total amount of material in the composition
to satisfy a given normalization condition
(mass, weight, molar, or atomic)
:param unit_type: 'mass', 'weight', 'molar' or 'atomic'
Unit type with which to normalize the composition
:type unit_type: str
:param normalization_component: Component/element on which to renormalize.
String must either be one of the components/elements
already in the composition, or have the value 'total'.
:type normalization_component: str
:param normalization_amount: Amount of component in the
renormalised composition.
:type normalization_amount: float
"""
if unit_type not in ["mass", "weight", "molar", "atomic"]:
raise Exception(
"unit_type not yet implemented."
"Should be either mass, weight, molar or atomic."
)
c = self.composition(unit_type)
if normalization_component == "total":
f = normalization_amount / float(sum(c.values()))
else:
f = normalization_amount / c[normalization_component]
new_mass_composition = OrderedCounter()
for k in self.mass_composition.keys():
new_mass_composition[k] = self.mass_composition[k] * f
self.mass_composition = new_mass_composition
def add_components(self, composition_dictionary, unit_type):
"""
Add (or remove) components from the composition.
The components are added to the current state of the
(mass, weight or molar) composition; if the composition has
been renormalised, then this should be taken into account.
:param composition_dictionary: Components to add, and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar'.
Unit type of the components to be added.
:type unit_type: str
"""
if unit_type == "mass" or unit_type == "weight":
composition = self.mass_composition
elif unit_type == "molar":
composition = self.molar_composition
else:
raise Exception(
"Unit type not recognised. " "Should be either mass, weight or molar."
)
composition += OrderedCounter(composition_dictionary)
# Reinitialize composition object
self.__init__(composition, unit_type)
def change_component_set(self, new_component_list):
"""
Change the set of basis components without
changing the bulk composition.
Will raise an exception if the new component set is
invalid for the given composition.
:param new_component_list: New set of basis components.
:type new_component_list: list of strings
"""
composition = np.array(
[self.atomic_composition[element] for element in self.element_list]
)
component_matrix = np.zeros((len(new_component_list), len(self.element_list)))
for i, component in enumerate(new_component_list):
formula = dictionarize_formula(component)
for element, n_atoms in formula.items():
component_matrix[i][self.element_list.index(element)] = n_atoms
sol = nnls(component_matrix.T, composition)
if sol[1] < 1.0e-12:
component_amounts = sol[0]
else:
raise Exception(
"Failed to change component set. "
"Could not find a non-negative "
"least squares solution. "
"Can the bulk composition be described "
"with this set of components?"
)
composition = OrderedCounter(dict(zip(new_component_list, component_amounts)))
# Reinitialize the object
self.__init__(composition, "molar")
def _mole_to_mass_composition(self, molar_comp):
"""
Hidden function to returns the mass composition as a counter [kg]
"""
cf = self.component_formulae
mass_composition = OrderedCounter(
{c: molar_comp[c] * formula_mass(cf[c]) for c in molar_comp.keys()}
)
return mass_composition
@property
def weight_composition(self):
"""
An alias for mass composition [kg].
"""
return self.mass_composition
@property
def molar_composition(self):
"""
Returns the molar composition as a counter [moles]
"""
mass_comp = self.mass_composition
cf = self.component_formulae
return OrderedCounter(
{c: mass_comp[c] / formula_mass(cf[c]) for c in mass_comp.keys()}
)
@property
def atomic_composition(self):
"""
Returns the atomic composition as a counter [moles]
"""
return self._moles_to_atoms(self.molar_composition)
def composition(self, unit_type):
"""
Helper function to return the composition in the
desired type.
:param unit_type: One of 'mass', 'weight', 'molar' and 'atomic'.
:type unit_type: str
:returns: Mass (weight), molar or atomic composition.
:rtype: OrderedCounter
"""
return getattr(self, f"{unit_type}_composition")
def _moles_to_atoms(self, molar_comp_dictionary):
"""
Hidden function that converts a molar component
dictionary into an atomic (elemental) dictionary
"""
component_matrix = | (composition_dictionary, unit_type='mass', normalize=False) | [
0.06760840862989426,
-0.0030329555738717318,
-0.025107767432928085,
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0.057400401681661606,
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0.006659742444753647,
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0.017255455255508423,
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0.03325454145669937,
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0.03172333911061287,
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0.014271576888859272,
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0.010247266851365566,
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0.0036071559879928827,
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10,927 | burnman.classes.composition | __init__ |
Create a composition using a dictionary and unit type.
:param composition_dictionary: Dictionary of components
(given as a string) and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar' (optional, 'mass' as default)
Specify whether the input composition is given as mass or
molar amounts.
:type unit_type: str
:param normalize: If False, absolute numbers of kilograms/moles of component are
stored, otherwise the component amounts of returned compositions
will sum to one (until Composition.renormalize() is used).
:type normalize: bool
| def __init__(self, composition_dictionary, unit_type="mass", normalize=False):
"""
Create a composition using a dictionary and unit type.
:param composition_dictionary: Dictionary of components
(given as a string) and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar' (optional, 'mass' as default)
Specify whether the input composition is given as mass or
molar amounts.
:type unit_type: str
:param normalize: If False, absolute numbers of kilograms/moles of component are
stored, otherwise the component amounts of returned compositions
will sum to one (until Composition.renormalize() is used).
:type normalize: bool
"""
self._cached = {}
n_total = float(sum(composition_dictionary.values()))
# Create the input dictionary, normalize if requested
input_dictionary = OrderedCounter(deepcopy(composition_dictionary))
if normalize:
for k in composition_dictionary.keys():
input_dictionary[k] = composition_dictionary[k] / n_total
# Break component formulae into atomic dictionaries
self.component_formulae = {
c: dictionarize_formula(c) for c in composition_dictionary.keys()
}
# Create lists of elemental compositions of components
self.element_list = OrderedCounter()
for component in self.component_formulae.values():
self.element_list += OrderedCounter(
{element: n_atoms for (element, n_atoms) in component.items()}
)
self.element_list = list(self.element_list.keys())
if unit_type == "mass" or unit_type == "weight":
self.mass_composition = input_dictionary
elif unit_type == "molar":
self.mass_composition = self._mole_to_mass_composition(input_dictionary)
else:
raise Exception(
"Unit type not yet implemented. "
"Should be either mass, weight or molar."
)
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] |
10,928 | burnman.classes.composition | _mole_to_mass_composition |
Hidden function to returns the mass composition as a counter [kg]
| def _mole_to_mass_composition(self, molar_comp):
"""
Hidden function to returns the mass composition as a counter [kg]
"""
cf = self.component_formulae
mass_composition = OrderedCounter(
{c: molar_comp[c] * formula_mass(cf[c]) for c in molar_comp.keys()}
)
return mass_composition
| (self, molar_comp) | [
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] |
10,929 | burnman.classes.composition | _moles_to_atoms |
Hidden function that converts a molar component
dictionary into an atomic (elemental) dictionary
| def _moles_to_atoms(self, molar_comp_dictionary):
"""
Hidden function that converts a molar component
dictionary into an atomic (elemental) dictionary
"""
component_matrix = np.zeros(
(len(self.component_formulae), len(self.element_list))
)
cf = self.component_formulae
molar_composition_vector = np.zeros(len(cf))
for i, (component, formula) in enumerate(cf.items()):
molar_composition_vector[i] = molar_comp_dictionary[component]
for element, n_atoms in formula.items():
component_matrix[i][self.element_list.index(element)] = n_atoms
atom_compositions = np.dot(molar_composition_vector, component_matrix)
return OrderedCounter(dict(zip(self.element_list, atom_compositions)))
| (self, molar_comp_dictionary) | [
0.06013798341155052,
0.028746308758854866,
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] |
10,930 | burnman.classes.composition | add_components |
Add (or remove) components from the composition.
The components are added to the current state of the
(mass, weight or molar) composition; if the composition has
been renormalised, then this should be taken into account.
:param composition_dictionary: Components to add, and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar'.
Unit type of the components to be added.
:type unit_type: str
| def add_components(self, composition_dictionary, unit_type):
"""
Add (or remove) components from the composition.
The components are added to the current state of the
(mass, weight or molar) composition; if the composition has
been renormalised, then this should be taken into account.
:param composition_dictionary: Components to add, and their amounts.
:type composition_dictionary: dictionary
:param unit_type: 'mass', 'weight' or 'molar'.
Unit type of the components to be added.
:type unit_type: str
"""
if unit_type == "mass" or unit_type == "weight":
composition = self.mass_composition
elif unit_type == "molar":
composition = self.molar_composition
else:
raise Exception(
"Unit type not recognised. " "Should be either mass, weight or molar."
)
composition += OrderedCounter(composition_dictionary)
# Reinitialize composition object
self.__init__(composition, unit_type)
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] |
10,931 | burnman.classes.composition | change_component_set |
Change the set of basis components without
changing the bulk composition.
Will raise an exception if the new component set is
invalid for the given composition.
:param new_component_list: New set of basis components.
:type new_component_list: list of strings
| def change_component_set(self, new_component_list):
"""
Change the set of basis components without
changing the bulk composition.
Will raise an exception if the new component set is
invalid for the given composition.
:param new_component_list: New set of basis components.
:type new_component_list: list of strings
"""
composition = np.array(
[self.atomic_composition[element] for element in self.element_list]
)
component_matrix = np.zeros((len(new_component_list), len(self.element_list)))
for i, component in enumerate(new_component_list):
formula = dictionarize_formula(component)
for element, n_atoms in formula.items():
component_matrix[i][self.element_list.index(element)] = n_atoms
sol = nnls(component_matrix.T, composition)
if sol[1] < 1.0e-12:
component_amounts = sol[0]
else:
raise Exception(
"Failed to change component set. "
"Could not find a non-negative "
"least squares solution. "
"Can the bulk composition be described "
"with this set of components?"
)
composition = OrderedCounter(dict(zip(new_component_list, component_amounts)))
# Reinitialize the object
self.__init__(composition, "molar")
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] |
10,932 | burnman.classes.composition | composition |
Helper function to return the composition in the
desired type.
:param unit_type: One of 'mass', 'weight', 'molar' and 'atomic'.
:type unit_type: str
:returns: Mass (weight), molar or atomic composition.
:rtype: OrderedCounter
| def composition(self, unit_type):
"""
Helper function to return the composition in the
desired type.
:param unit_type: One of 'mass', 'weight', 'molar' and 'atomic'.
:type unit_type: str
:returns: Mass (weight), molar or atomic composition.
:rtype: OrderedCounter
"""
return getattr(self, f"{unit_type}_composition")
| (self, unit_type) | [
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] |
10,933 | burnman.classes.composition | print |
Pretty-print function for the composition
This does not renormalize the Composition object itself,
only the printed values.
:param unit_type: 'mass', 'weight', 'molar' or 'atomic'
Unit type in which to print the composition.
:type unit_type: str
:param significant_figures: Number of significant figures
for each amount.
:type significant_figures: int
:param normalization_component: Component/element on which to renormalize.
String must either be one of the components/elements
already in composite, or have the value 'total'.
(default = 'total')
:type normalization_component: str
:param normalization_amount: Amount of component in the
renormalised composition. If not explicitly set,
no renormalization will be applied.
:type normalization_amount: float
| def print(
self,
unit_type,
significant_figures=1,
normalization_component="total",
normalization_amount=None,
):
"""
Pretty-print function for the composition
This does not renormalize the Composition object itself,
only the printed values.
:param unit_type: 'mass', 'weight', 'molar' or 'atomic'
Unit type in which to print the composition.
:type unit_type: str
:param significant_figures: Number of significant figures
for each amount.
:type significant_figures: int
:param normalization_component: Component/element on which to renormalize.
String must either be one of the components/elements
already in composite, or have the value 'total'.
(default = 'total')
:type normalization_component: str
:param normalization_amount: Amount of component in the
renormalised composition. If not explicitly set,
no renormalization will be applied.
:type normalization_amount: float
"""
if unit_type not in ["mass", "weight", "molar", "atomic"]:
raise Exception(
"unit_type not yet implemented."
"Should be either mass, weight, molar or atomic."
)
c = self.composition(unit_type)
print(f"{unit_type.capitalize()} composition")
if normalization_amount is None:
f = 1
elif normalization_component == "total":
f = normalization_amount / float(sum(c.values()))
else:
f = normalization_amount / c[normalization_component]
for key, value in sorted(c.items()):
print(f"{key}: {value*f:0.{significant_figures}f}")
| (self, unit_type, significant_figures=1, normalization_component='total', normalization_amount=None) | [
-0.021939080208539963,
0.020311977714300156,
0.006262561772018671,
0.002702154451981187,
0.07967444509267807,
-0.04470065236091614,
-0.03304272145032883,
-0.08382266759872437,
-0.025068126618862152,
0.004528176039457321,
-0.005073524080216885,
-0.004599697422236204,
-0.011193043552339077,
-0.00013410196697805077,
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10,934 | burnman.classes.composition | renormalize |
Change the total amount of material in the composition
to satisfy a given normalization condition
(mass, weight, molar, or atomic)
:param unit_type: 'mass', 'weight', 'molar' or 'atomic'
Unit type with which to normalize the composition
:type unit_type: str
:param normalization_component: Component/element on which to renormalize.
String must either be one of the components/elements
already in the composition, or have the value 'total'.
:type normalization_component: str
:param normalization_amount: Amount of component in the
renormalised composition.
:type normalization_amount: float
| def renormalize(self, unit_type, normalization_component, normalization_amount):
"""
Change the total amount of material in the composition
to satisfy a given normalization condition
(mass, weight, molar, or atomic)
:param unit_type: 'mass', 'weight', 'molar' or 'atomic'
Unit type with which to normalize the composition
:type unit_type: str
:param normalization_component: Component/element on which to renormalize.
String must either be one of the components/elements
already in the composition, or have the value 'total'.
:type normalization_component: str
:param normalization_amount: Amount of component in the
renormalised composition.
:type normalization_amount: float
"""
if unit_type not in ["mass", "weight", "molar", "atomic"]:
raise Exception(
"unit_type not yet implemented."
"Should be either mass, weight, molar or atomic."
)
c = self.composition(unit_type)
if normalization_component == "total":
f = normalization_amount / float(sum(c.values()))
else:
f = normalization_amount / c[normalization_component]
new_mass_composition = OrderedCounter()
for k in self.mass_composition.keys():
new_mass_composition[k] = self.mass_composition[k] * f
self.mass_composition = new_mass_composition
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10,935 | burnman.classes.elasticsolution | ElasticSolution |
This is the base class for all Elastic solutions.
Site occupancies, endmember activities and the constant
and volume and temperature dependencies of the excess
properties can be queried after using set_composition().
States of the solution can only be queried after setting
the pressure, temperature and composition using set_state()
and set_composition.
This class is available as :class:`burnman.ElasticSolution`.
It uses an instance of :class:`burnman.ElasticSolutionModel` to
calculate interaction terms between endmembers.
All the solution parameters are expected to be in SI units. This
means that the interaction parameters should be in J/mol, with the T
and V derivatives in J/K/mol and Pa/mol.
The parameters are relevant to all Elastic solution models. Please
see the documentation for individual models for details about
other parameters.
:param name: Name of the solution.
:type name: string
:param solution_model: The ElasticSolutionModel object defining the
properties of the solution.
:type solution_model: :class:`burnman.ElasticSolutionModel`
:param molar_fractions: The molar fractions of each endmember in the solution.
Can be reset using the set_composition() method.
:type molar_fractions: numpy.array
| class ElasticSolution(Mineral):
"""
This is the base class for all Elastic solutions.
Site occupancies, endmember activities and the constant
and volume and temperature dependencies of the excess
properties can be queried after using set_composition().
States of the solution can only be queried after setting
the pressure, temperature and composition using set_state()
and set_composition.
This class is available as :class:`burnman.ElasticSolution`.
It uses an instance of :class:`burnman.ElasticSolutionModel` to
calculate interaction terms between endmembers.
All the solution parameters are expected to be in SI units. This
means that the interaction parameters should be in J/mol, with the T
and V derivatives in J/K/mol and Pa/mol.
The parameters are relevant to all Elastic solution models. Please
see the documentation for individual models for details about
other parameters.
:param name: Name of the solution.
:type name: string
:param solution_model: The ElasticSolutionModel object defining the
properties of the solution.
:type solution_model: :class:`burnman.ElasticSolutionModel`
:param molar_fractions: The molar fractions of each endmember in the solution.
Can be reset using the set_composition() method.
:type molar_fractions: numpy.array
"""
def __init__(self, name=None, solution_model=None, molar_fractions=None):
"""
Set up matrices to speed up calculations for when P, T, X is defined.
"""
Mineral.__init__(self)
# Solution needs a method attribute to call Mineral.set_state().
# Note that set_method() below will not change self.method
self.method = "ElasticSolutionMethod"
if name is not None:
self.name = name
if solution_model is not None:
self.solution_model = solution_model
if isinstance(solution_model, ElasticMechanicalSolution):
self.solution_type = "mechanical"
else:
self.solution_type = "chemical"
# Starting guess and delta for pressure iteration
self.min_V0 = min(
[mbr[0].params["V_0"] for mbr in self.solution_model.endmembers]
)
self.dV = 0.01 * self.min_V0
# Equation of state
for i in range(self.n_endmembers):
self.solution_model.endmembers[i][0].set_method(
self.solution_model.endmembers[i][0].params["equation_of_state"]
)
# Molar fractions
if molar_fractions is not None:
self.set_composition(molar_fractions)
@cached_property
def endmembers(self):
return self.solution_model.endmembers
def set_composition(self, molar_fractions):
"""
Set the composition for this solution.
Resets cached properties.
:param molar_fractions: Molar abundance for each endmember,
needs to sum to one.
:type molar_fractions: list of float
"""
assert len(self.solution_model.endmembers) == len(molar_fractions)
if self.solution_type != "mechanical":
assert sum(molar_fractions) > 0.9999
assert sum(molar_fractions) < 1.0001
self.reset()
self.molar_fractions = np.array(molar_fractions)
if self.temperature is not None:
_ = self.molar_volume
def set_method(self, method):
for i in range(self.n_endmembers):
self.solution_model.endmembers[i][0].set_method(method)
# note: do not set self.method here!
self.reset()
def set_state(self, pressure, temperature):
Mineral.set_state(self, pressure, temperature)
try:
_ = self.molar_volume
except AttributeError:
pass
@material_property
def formula(self):
"""
Returns molar chemical formula of the solution.
"""
return sum_formulae(self.endmember_formulae, self.molar_fractions)
@material_property
def activities(self):
"""
Returns a list of endmember activities [unitless].
"""
volumes = [
self.solution_model.endmembers[i][0].method.volume(
self.pressure,
self.temperature,
self.solution_model.endmembers[i][0].params,
)
for i in range(self.n_endmembers)
]
gibbs_pure = [
self.solution_model.endmembers[i][0].method.gibbs_free_energy(
self.pressure,
self.temperature,
volumes[i],
self.solution_model.endmembers[i][0].params,
)
for i in range(self.n_endmembers)
]
acts = np.exp(
(self.partial_gibbs - np.array(gibbs_pure))
/ (gas_constant * self.temperature)
)
return acts
@material_property
def activity_coefficients(self):
"""
Returns a list of endmember activity coefficients
(gamma = activity / ideal activity) [unitless].
"""
return np.exp(
np.log(self.activities)
- IdealSolution._log_ideal_activities(
self.solution_model, self.molar_fractions
)
)
@material_property
def molar_internal_energy(self):
"""
Returns molar internal energy of the mineral [J/mol].
Aliased with self.energy
"""
return self.molar_helmholtz + self.temperature * self.molar_entropy
@material_property
def _excess_partial_helmholtz(self):
"""
Returns excess partial molar helmholtz energy
at constant volume [J/mol].
Property specific to solutions.
"""
return self.solution_model.excess_partial_helmholtz_energies(
self.molar_volume, self.temperature, self.molar_fractions
)
@material_property
def _excess_partial_pressures(self):
"""
Returns excess partial pressures at constant volume [Pa].
Property specific to solutions.
"""
return self.solution_model.excess_partial_pressures(
self.molar_volume, self.temperature, self.molar_fractions
)
@material_property
def _excess_partial_entropies(self):
"""
Returns excess partial entropies at constant volume [J/K].
Property specific to solutions.
"""
return self.solution_model.excess_partial_entropies(
self.molar_volume, self.temperature, self.molar_fractions
)
@material_property
def _partial_helmholtz(self):
"""
Returns endmember partial molar Helmholtz energy at constant volume [J/mol].
Property specific to solutions.
"""
return (
np.array(
[
self.solution_model.endmembers[i][0].helmholtz
for i in range(self.n_endmembers)
]
)
+ self._excess_partial_helmholtz
)
@material_property
def _partial_pressures(self):
"""
Returns endmember partial pressures at constant volume [Pa].
Property specific to solutions.
"""
return (
np.array(
[
self.solution_model.endmembers[i][0].pressure
for i in range(self.n_endmembers)
]
)
+ self._excess_partial_pressures
)
@material_property
def _partial_entropies(self):
"""
Returns endmember partial entropies at constant volume [J/K].
Property specific to solutions.
"""
return (
np.array(
[
self.solution_model.endmembers[i][0].molar_entropy
for i in range(self.n_endmembers)
]
)
+ self._excess_partial_entropies
)
@material_property
def partial_gibbs(self):
"""
Returns endmember partial molar Gibbs energy
at constant pressure [J/mol].
Property specific to | (name=None, solution_model=None, molar_fractions=None) | [
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] |
10,936 | burnman.classes.elasticsolution | __init__ |
Set up matrices to speed up calculations for when P, T, X is defined.
| def __init__(self, name=None, solution_model=None, molar_fractions=None):
"""
Set up matrices to speed up calculations for when P, T, X is defined.
"""
Mineral.__init__(self)
# Solution needs a method attribute to call Mineral.set_state().
# Note that set_method() below will not change self.method
self.method = "ElasticSolutionMethod"
if name is not None:
self.name = name
if solution_model is not None:
self.solution_model = solution_model
if isinstance(solution_model, ElasticMechanicalSolution):
self.solution_type = "mechanical"
else:
self.solution_type = "chemical"
# Starting guess and delta for pressure iteration
self.min_V0 = min(
[mbr[0].params["V_0"] for mbr in self.solution_model.endmembers]
)
self.dV = 0.01 * self.min_V0
# Equation of state
for i in range(self.n_endmembers):
self.solution_model.endmembers[i][0].set_method(
self.solution_model.endmembers[i][0].params["equation_of_state"]
)
# Molar fractions
if molar_fractions is not None:
self.set_composition(molar_fractions)
| (self, name=None, solution_model=None, molar_fractions=None) | [
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] |
10,942 | burnman.classes.elasticsolution | set_composition |
Set the composition for this solution.
Resets cached properties.
:param molar_fractions: Molar abundance for each endmember,
needs to sum to one.
:type molar_fractions: list of float
| def set_composition(self, molar_fractions):
"""
Set the composition for this solution.
Resets cached properties.
:param molar_fractions: Molar abundance for each endmember,
needs to sum to one.
:type molar_fractions: list of float
"""
assert len(self.solution_model.endmembers) == len(molar_fractions)
if self.solution_type != "mechanical":
assert sum(molar_fractions) > 0.9999
assert sum(molar_fractions) < 1.0001
self.reset()
self.molar_fractions = np.array(molar_fractions)
if self.temperature is not None:
_ = self.molar_volume
| (self, molar_fractions) | [
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10,943 | burnman.classes.elasticsolution | set_method | null | def set_method(self, method):
for i in range(self.n_endmembers):
self.solution_model.endmembers[i][0].set_method(method)
# note: do not set self.method here!
self.reset()
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10,944 | burnman.classes.elasticsolution | set_state | null | def set_state(self, pressure, temperature):
Mineral.set_state(self, pressure, temperature)
try:
_ = self.molar_volume
except AttributeError:
pass
| (self, pressure, temperature) | [
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10,961 | burnman.classes.elasticsolutionmodel | ElasticSolutionModel |
This is the base class for an Elastic solution model, intended for use
in defining solutions and performing thermodynamic calculations
on them. All minerals of type :class:`burnman.Solution` use
a solution model for defining how the endmembers in the solution
interact.
A user wanting a new solution model should define the functions included
in the base class. All of the functions in the base class return zero,
so if the user-defined solution model does not implement them,
they essentially have no effect, and the Helmholtz energy and
pressure of a solution will be equal to the weighted arithmetic
averages of the different endmember values.
| class ElasticSolutionModel(object):
"""
This is the base class for an Elastic solution model, intended for use
in defining solutions and performing thermodynamic calculations
on them. All minerals of type :class:`burnman.Solution` use
a solution model for defining how the endmembers in the solution
interact.
A user wanting a new solution model should define the functions included
in the base class. All of the functions in the base class return zero,
so if the user-defined solution model does not implement them,
they essentially have no effect, and the Helmholtz energy and
pressure of a solution will be equal to the weighted arithmetic
averages of the different endmember values.
"""
def __init__(self):
"""
Does nothing.
"""
pass
def excess_helmholtz_energy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess Helmholtz free energy of the solution.
The base class implementation assumes that the excess Helmholtz
energy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy.
:rtype: float
"""
return np.dot(
np.array(molar_fractions),
self.excess_partial_helmholtz_energies(
volume, temperature, molar_fractions
),
)
def excess_pressure(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess pressure of the solution.
The base class implementation assumes that the excess pressure is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of the solution.
:rtype: float
"""
return np.dot(
molar_fractions,
self.excess_partial_pressures(volume, temperature, molar_fractions),
)
def excess_entropy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess entropy of the solution.
The base class implementation assumes that the excess entropy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of the solution.
:rtype: float
"""
return np.dot(
molar_fractions,
self.excess_partial_entropies(volume, temperature, molar_fractions),
)
def excess_enthalpy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess enthalpy of the solution.
The base class implementation assumes that the excess enthalpy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess enthalpy of the solution.
:rtype: float
"""
return (
self.excess_helmholtz_energy(volume, temperature, molar_fractions)
+ temperature * self.excess_entropy(volume, temperature, molar_fractions)
- volume * self.excess_pressure(volume, temperature, molar_fractions)
)
def excess_partial_helmholtz_energies(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess Helmholtz energy for each endmember of the solution.
The base class implementation assumes that the excess Helmholtz energy
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy of each endmember
:rtype: numpy.array
"""
return np.zeros_like(molar_fractions)
def excess_partial_entropies(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess entropy for each endmember of the solution.
The base class implementation assumes that the excess entropy
is zero (true for mechanical solutions).
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of each endmember.
:rtype: numpy.array
"""
return np.zeros_like(molar_fractions)
def excess_partial_pressures(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess pressure for each endmember of the solution.
The base class implementation assumes that the excess pressure
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of each endmember.
:rtype: numpy.array
"""
return np.zeros_like(np.array(molar_fractions))
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10,962 | burnman.classes.elasticsolutionmodel | __init__ |
Does nothing.
| def __init__(self):
"""
Does nothing.
"""
pass
| (self) | [
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10,963 | burnman.classes.elasticsolutionmodel | excess_enthalpy |
Given a list of molar fractions of different phases,
compute the excess enthalpy of the solution.
The base class implementation assumes that the excess enthalpy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess enthalpy of the solution.
:rtype: float
| def excess_enthalpy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess enthalpy of the solution.
The base class implementation assumes that the excess enthalpy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess enthalpy of the solution.
:rtype: float
"""
return (
self.excess_helmholtz_energy(volume, temperature, molar_fractions)
+ temperature * self.excess_entropy(volume, temperature, molar_fractions)
- volume * self.excess_pressure(volume, temperature, molar_fractions)
)
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] |
10,964 | burnman.classes.elasticsolutionmodel | excess_entropy |
Given a list of molar fractions of different phases,
compute the excess entropy of the solution.
The base class implementation assumes that the excess entropy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of the solution.
:rtype: float
| def excess_entropy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess entropy of the solution.
The base class implementation assumes that the excess entropy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of the solution.
:rtype: float
"""
return np.dot(
molar_fractions,
self.excess_partial_entropies(volume, temperature, molar_fractions),
)
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10,965 | burnman.classes.elasticsolutionmodel | excess_helmholtz_energy |
Given a list of molar fractions of different phases,
compute the excess Helmholtz free energy of the solution.
The base class implementation assumes that the excess Helmholtz
energy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy.
:rtype: float
| def excess_helmholtz_energy(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess Helmholtz free energy of the solution.
The base class implementation assumes that the excess Helmholtz
energy is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy.
:rtype: float
"""
return np.dot(
np.array(molar_fractions),
self.excess_partial_helmholtz_energies(
volume, temperature, molar_fractions
),
)
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10,966 | burnman.classes.elasticsolutionmodel | excess_partial_entropies |
Given a list of molar fractions of different phases,
compute the excess entropy for each endmember of the solution.
The base class implementation assumes that the excess entropy
is zero (true for mechanical solutions).
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of each endmember.
:rtype: numpy.array
| def excess_partial_entropies(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess entropy for each endmember of the solution.
The base class implementation assumes that the excess entropy
is zero (true for mechanical solutions).
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess entropy of each endmember.
:rtype: numpy.array
"""
return np.zeros_like(molar_fractions)
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10,967 | burnman.classes.elasticsolutionmodel | excess_partial_helmholtz_energies |
Given a list of molar fractions of different phases,
compute the excess Helmholtz energy for each endmember of the solution.
The base class implementation assumes that the excess Helmholtz energy
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy of each endmember
:rtype: numpy.array
| def excess_partial_helmholtz_energies(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess Helmholtz energy for each endmember of the solution.
The base class implementation assumes that the excess Helmholtz energy
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess Helmholtz energy of each endmember
:rtype: numpy.array
"""
return np.zeros_like(molar_fractions)
| (self, volume, temperature, molar_fractions) | [
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] |
10,968 | burnman.classes.elasticsolutionmodel | excess_partial_pressures |
Given a list of molar fractions of different phases,
compute the excess pressure for each endmember of the solution.
The base class implementation assumes that the excess pressure
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of each endmember.
:rtype: numpy.array
| def excess_partial_pressures(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess pressure for each endmember of the solution.
The base class implementation assumes that the excess pressure
is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of each endmember.
:rtype: numpy.array
"""
return np.zeros_like(np.array(molar_fractions))
| (self, volume, temperature, molar_fractions) | [
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10,969 | burnman.classes.elasticsolutionmodel | excess_pressure |
Given a list of molar fractions of different phases,
compute the excess pressure of the solution.
The base class implementation assumes that the excess pressure is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of the solution.
:rtype: float
| def excess_pressure(self, volume, temperature, molar_fractions):
"""
Given a list of molar fractions of different phases,
compute the excess pressure of the solution.
The base class implementation assumes that the excess pressure is zero.
:param volume: Volume at which to evaluate the solution model. [m^3/mol]
:type volume: float
:param temperature: Temperature at which to evaluate the solution. [K]
:type temperature: float
:param molar_fractions: List of molar fractions of the different
endmembers in solution.
:type molar_fractions: list of floats
:returns: The excess pressure of the solution.
:rtype: float
"""
return np.dot(
molar_fractions,
self.excess_partial_pressures(volume, temperature, molar_fractions),
)
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] |
10,970 | burnman.classes.mineral_helpers | HelperLowHighPressureRockTransition |
A Helper that represents a Material that switches between two given rocks based
on a given transition pressure.
| class HelperLowHighPressureRockTransition(HelperRockSwitcher):
"""
A Helper that represents a Material that switches between two given rocks based
on a given transition pressure.
"""
def __init__(self, transition_pressure, low_pressure_rock, high_pressure_rock):
self.transition_pressure = transition_pressure
self.rocks = [low_pressure_rock, high_pressure_rock]
HelperRockSwitcher.__init__(self)
self._name = (
"HelperLowHighPressureRockTransition("
+ str(self.transition_pressure)
+ " GPa, "
+ self.rocks[0].name
+ ", "
+ self.rocks[1].name
+ ")"
)
def select_rock(self):
if self._pressure < self.transition_pressure:
return self.rocks[0]
else:
return self.rocks[1]
def set_method(self, method):
for r in self.rocks:
r.set_method(method)
def debug_print(self, indent=""):
print(
"%sHelperLowHighPressureRockTransition (%f GPa):"
% (indent, self.transition_pressure)
)
indent += " "
for r in self.rocks:
r.debug_print(indent)
| (transition_pressure, low_pressure_rock, high_pressure_rock) | [
0.010263877920806408,
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0.03069055825471878,
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-0.06446854770183563,
-0.04278300702571869,
0.06226323917508125,
-0.008302072063088417,
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0.03208725526928902,
0.06174866855144501,
0.06527716666460037,
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10,971 | burnman.classes.mineral_helpers | __init__ | null | def __init__(self, transition_pressure, low_pressure_rock, high_pressure_rock):
self.transition_pressure = transition_pressure
self.rocks = [low_pressure_rock, high_pressure_rock]
HelperRockSwitcher.__init__(self)
self._name = (
"HelperLowHighPressureRockTransition("
+ str(self.transition_pressure)
+ " GPa, "
+ self.rocks[0].name
+ ", "
+ self.rocks[1].name
+ ")"
)
| (self, transition_pressure, low_pressure_rock, high_pressure_rock) | [
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10,973 | burnman.classes.mineral_helpers | debug_print | null | def debug_print(self, indent=""):
print(
"%sHelperLowHighPressureRockTransition (%f GPa):"
% (indent, self.transition_pressure)
)
indent += " "
for r in self.rocks:
r.debug_print(indent)
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] |
10,977 | burnman.classes.mineral_helpers | select_rock | null | def select_rock(self):
if self._pressure < self.transition_pressure:
return self.rocks[0]
else:
return self.rocks[1]
| (self) | [
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10,978 | burnman.classes.mineral_helpers | set_method | null | def set_method(self, method):
for r in self.rocks:
r.set_method(method)
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10,979 | burnman.classes.mineral_helpers | set_state | null | def set_state(self, pressure, temperature):
Material.set_state(self, pressure, temperature)
self.current_rock = self.select_rock()
self.current_rock.set_state(pressure, temperature)
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] |
10,982 | burnman.classes.mineral_helpers | unroll | null | def unroll(self):
return self.current_rock.unroll()
| (self) | [
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10,983 | burnman.classes.mineral_helpers | HelperRockSwitcher |
A Helper that represents a Material that switches between different rocks
based on a user specified select_rock() function based on current temperature
and pressure. This class can be used in several ways:
1. By creating an instance and setting select_rock to a lambda that returns a rock
2. By deriving from this class and implementing select_rock.
| class HelperRockSwitcher(Material):
"""
A Helper that represents a Material that switches between different rocks
based on a user specified select_rock() function based on current temperature
and pressure. This class can be used in several ways:
1. By creating an instance and setting select_rock to a lambda that returns a rock
2. By deriving from this class and implementing select_rock.
"""
def __init__(self):
self.current_rock = None
Material.__init__(self)
def select_rock(self):
raise NotImplementedError("Need to implement select_rock() in derived class!")
def set_method(self, method):
raise NotImplementedError("Need to implement select_rock() in derived class!")
def debug_print(self, indent=""):
print("%sHelperRockSwitcher" % (indent))
def set_state(self, pressure, temperature):
Material.set_state(self, pressure, temperature)
self.current_rock = self.select_rock()
self.current_rock.set_state(pressure, temperature)
def unroll(self):
return self.current_rock.unroll()
@material_property
def molar_internal_energy(self):
return self.current_rock.molar_internal_energy
@material_property
def molar_gibbs(self):
return self.current_rock.molar_gibbs
@material_property
def molar_helmholtz(self):
return self.current_rock.molar_helmholtz
@material_property
def molar_mass(self):
return self.current_rock.molar_mass
@material_property
def molar_volume(self):
return self.current_rock.molar_volume
@material_property
def density(self):
return self.current_rock.density
@material_property
def molar_entropy(self):
return self.current_rock.molar_entropy
@material_property
def molar_enthalpy(self):
return self.current_rock.molar_enthalpy
@material_property
def isothermal_bulk_modulus(self):
return self.current_rock.isothermal_bulk_modulus
@material_property
def adiabatic_bulk_modulus(self):
return self.current_rock.adiabatic_bulk_modulus
@material_property
def isothermal_compressibility(self):
return self.current_rock.isothermal_compressibility
@material_property
def adiabatic_compressibility(self):
return self.current_rock.adiabatic_compressibility
@material_property
def shear_modulus(self):
return self.current_rock.shear_modulus
@material_property
def p_wave_velocity(self):
return self.current_rock.p_wave_velocity
@material_property
def bulk_sound_velocity(self):
return self.current_rock.bulk_sound_velocity
@material_property
def shear_wave_velocity(self):
return self.current_rock.shear_wave_velocity
@material_property
def grueneisen_parameter(self):
return self.current_rock.grueneisen_parameter
@material_property
def thermal_expansivity(self):
return self.current_rock.thermal_expansivity
@material_property
def molar_heat_capacity_v(self):
return self.current_rock.molar_heat_capacity_v
@material_property
def molar_heat_capacity_p(self):
return self.current_rock.molar_heat_capacity_p
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10,984 | burnman.classes.mineral_helpers | __init__ | null | def __init__(self):
self.current_rock = None
Material.__init__(self)
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] |
10,986 | burnman.classes.mineral_helpers | debug_print | null | def debug_print(self, indent=""):
print("%sHelperRockSwitcher" % (indent))
| (self, indent='') | [
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10,990 | burnman.classes.mineral_helpers | select_rock | null | def select_rock(self):
raise NotImplementedError("Need to implement select_rock() in derived class!")
| (self) | [
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10,991 | burnman.classes.mineral_helpers | set_method | null | def set_method(self, method):
raise NotImplementedError("Need to implement select_rock() in derived class!")
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10,996 | burnman.classes.mineral_helpers | HelperSpinTransition |
Helper class that makes a mineral that switches between two materials
(for low and high spin) based on some transition pressure [Pa]
| class HelperSpinTransition(Composite):
"""
Helper class that makes a mineral that switches between two materials
(for low and high spin) based on some transition pressure [Pa]
"""
def __init__(self, transition_pressure, ls_mat, hs_mat):
"""
Takes a transition pressure, and two minerals. Use the
thermoelastic parameters for ls_mat below the transition
pressure, and the thermoelastic parameters for hs_mat
above the transition pressure
"""
Material.__init__(self)
self.transition_pressure = transition_pressure
self.ls_mat = ls_mat
self.hs_mat = hs_mat
Composite.__init__(self, [ls_mat, hs_mat])
def debug_print(self, indent=""):
print("%sHelperSpinTransition:" % indent)
self.ls_mat.debug_print(indent + " ")
self.hs_mat.debug_print(indent + " ")
def set_state(self, pressure, temperature):
if pressure >= self.transition_pressure:
Composite.set_fractions(self, [1.0, 0.0])
else:
Composite.set_fractions(self, [0.0, 1.0])
Composite.set_state(self, pressure, temperature)
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10,997 | burnman.classes.mineral_helpers | __init__ |
Takes a transition pressure, and two minerals. Use the
thermoelastic parameters for ls_mat below the transition
pressure, and the thermoelastic parameters for hs_mat
above the transition pressure
| def __init__(self, transition_pressure, ls_mat, hs_mat):
"""
Takes a transition pressure, and two minerals. Use the
thermoelastic parameters for ls_mat below the transition
pressure, and the thermoelastic parameters for hs_mat
above the transition pressure
"""
Material.__init__(self)
self.transition_pressure = transition_pressure
self.ls_mat = ls_mat
self.hs_mat = hs_mat
Composite.__init__(self, [ls_mat, hs_mat])
| (self, transition_pressure, ls_mat, hs_mat) | [
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11,003 | burnman.classes.mineral_helpers | debug_print | null | def debug_print(self, indent=""):
print("%sHelperSpinTransition:" % indent)
self.ls_mat.debug_print(indent + " ")
self.hs_mat.debug_print(indent + " ")
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11,011 | burnman.classes.mineral_helpers | set_state | null | def set_state(self, pressure, temperature):
if pressure >= self.transition_pressure:
Composite.set_fractions(self, [1.0, 0.0])
else:
Composite.set_fractions(self, [0.0, 1.0])
Composite.set_state(self, pressure, temperature)
| (self, pressure, temperature) | [
-0.021169649437069893,
0.012333095073699951,
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] |
11,015 | burnman.classes.layer | Layer |
The base class for a planetary layer.
The user needs to set the following before properties can be computed:
- set_material(), which sets the material of the layer,
e.g. a mineral, solid_solution, or composite
- set_temperature_mode(), either predefine, or set to an adiabatic profile
- set_pressure_mode(), to set the self-consistent pressure
(with user-defined option the pressures can be overwritten).
To set the self-consistent pressure the pressure at the top and the
gravity at the bottom of the layer need to be set.
- make(), computes the self-consistent part of the layer and starts the
settings to compute properties within the layer
Note that the entire planet this layer sits in is not necessarily
self-consistent, as the pressure at the top of the layer is a
function of the density within the layer (through the gravity).
Entire planets can be computed self-consistently with the planet class.
Properties will be returned at the pre-defined radius array,
although the evaluate() function can take a newly defined depthlist
and values are interpolated between these (sufficient sampling of the layer
is needed for this to be accurate).
| class Layer(object):
"""
The base class for a planetary layer.
The user needs to set the following before properties can be computed:
- set_material(), which sets the material of the layer,
e.g. a mineral, solid_solution, or composite
- set_temperature_mode(), either predefine, or set to an adiabatic profile
- set_pressure_mode(), to set the self-consistent pressure
(with user-defined option the pressures can be overwritten).
To set the self-consistent pressure the pressure at the top and the
gravity at the bottom of the layer need to be set.
- make(), computes the self-consistent part of the layer and starts the
settings to compute properties within the layer
Note that the entire planet this layer sits in is not necessarily
self-consistent, as the pressure at the top of the layer is a
function of the density within the layer (through the gravity).
Entire planets can be computed self-consistently with the planet class.
Properties will be returned at the pre-defined radius array,
although the evaluate() function can take a newly defined depthlist
and values are interpolated between these (sufficient sampling of the layer
is needed for this to be accurate).
"""
def __init__(self, name=None, radii=None, verbose=False):
self.name = name
assert np.all(np.diff(radii) > 0)
self.radii = radii
self.outer_radius = max(self.radii)
self.inner_radius = min(self.radii)
self.thickness = self.outer_radius - self.inner_radius
self.n_slices = len(self.radii)
self.verbose = verbose
self._cached = {}
self._pressures = None
self._temperatures = None
self.sublayers = None
self.material = None
self.pressure_mode = "self-consistent"
self.temperature_mode = None
def __str__(self):
"""
Prints details of the layer
"""
writing = (
f"The {self.name} is made of {self.material.name}"
f" with {self.temperature_mode} temperatures and "
f"{self.pressure_mode} pressures\n"
)
return writing
def reset(self):
"""
Resets all cached material properties.
It is typically not required for the user to call this function.
"""
self._cached = {}
self._pressures = None
self._temperatures = None
self.sublayers = None
def set_material(self, material):
"""
Set the material of a Layer with a Material
"""
assert isinstance(material, Material)
self.material = material
self.reset()
def set_temperature_mode(
self, temperature_mode="adiabatic", temperatures=None, temperature_top=None
):
"""
Sets temperatures within the layer as user-defined values or as
a (potentially perturbed) adiabat.
:param temperature_mode: This can be set to 'user-defined', 'adiabatic',
or 'perturbed-adiabatic'. 'user-defined' fixes the temperature
with the profile input by the user. 'adiabatic' self-consistently
computes the adiabat when setting the state of the layer.
'perturbed-adiabatic' adds the user input array to the adiabat.
This allows the user to apply boundary layers (for example).
:type temperature_mode: string
:param temperatures: The desired fixed temperatures in [K].
Should have same length as defined radii in layer.
:type temperatures: array of float
:param temperature_top: Temperature at the top of the layer.
Used if the temperature mode is chosen to be 'adiabatic' or
'perturbed-adiabatic'. If 'perturbed-adiabatic' is chosen as the
temperature mode, temperature_top corresponds to the true temperature
at the top of the layer, and the reference isentrope at this radius
is defined to lie at a temperature of
temperature_top - temperatures[-1].
:type temperature_top: float
"""
self.reset()
assert (
temperature_mode == "user-defined"
or temperature_mode == "adiabatic"
or temperature_mode == "perturbed-adiabatic"
)
self.temperature_mode = temperature_mode
if (
temperature_mode == "user-defined"
or temperature_mode == "perturbed-adiabatic"
):
assert len(temperatures) == len(self.radii)
self.usertemperatures = temperatures
else:
self.usertemperatures = np.zeros_like(self.radii)
if temperature_mode == "adiabatic" or temperature_mode == "perturbed-adiabatic":
self.temperature_top = temperature_top
else:
self.temperature_top = None
def set_pressure_mode(
self,
pressure_mode="self-consistent",
pressures=None,
gravity_bottom=None,
pressure_top=None,
n_max_iterations=50,
max_delta=1.0e-5,
):
"""
Sets the pressure mode of the layer,
which can either be 'user-defined', or 'self-consistent'.
:param pressure_mode: This can be set to 'user-defined' or 'self-consistent'.
'user-defined' fixes the pressures with the profile input
by the user in the 'pressures' argument.
'self-consistent' forces Layer to calculate pressures
self-consistently. If this is selected, the user will need
to supply values for the gravity_bottom [m/s^2]
and pressure_top [Pa] arguments.
:type pressure_mode: string
:param pressures: Pressures [Pa] to set layer to
(if the 'user-defined' pressure_mode has been selected).
The array should be the same length as
the layers user-defined radii array.
:type pressures: array of floats
:param pressure_top: Pressure [Pa] at the top of the layer.
:type pressure_top: float
:param gravity_bottom: Gravity [m/s^2] at the bottom of the layer.
:type gravity_bottom: float
:param n_max_iterations: Maximum number of iterations to reach
self-consistent pressures.
:type n_max_iterations: integer
:param max_delta: Relative update to the highest pressure in the layer between
iterations to stop iterations.
:type max_delta: float
"""
self.reset()
assert pressure_mode == "user-defined" or pressure_mode == "self-consistent"
self.pressure_mode = pressure_mode
assert gravity_bottom is not None
self.gravity_bottom = gravity_bottom
if pressure_mode == "user-defined":
assert pressures is not None
assert len(pressures) == len(self.radii)
self.pressures = pressures
warnings.warn(
"By setting the pressures in Layer they "
"are unlikely to be self-consistent"
)
elif pressure_mode == "self-consistent":
self.pressure_top = pressure_top
self.n_max_iterations = n_max_iterations
self.max_delta = max_delta
else:
raise NotImplementedError(
f"pressure mode {pressure_mode} " "not recognised"
)
def make(self):
"""
This routine needs to be called before evaluating any properties.
If pressures and temperatures are not user-defined, they
are computed here. This method also initializes an array of copied
materials from which properties can be computed.
"""
self.reset()
if not hasattr(self, "material"):
raise AttributeError(
"You must set_material() for the layer " "before running make()."
)
if not hasattr(self, "temperature_mode"):
raise AttributeError(
"You must set_temperature_mode() for the "
"layer before running make()."
)
if not hasattr(self, "pressure_mode"):
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11,016 | burnman.classes.layer | __init__ | null | def __init__(self, name=None, radii=None, verbose=False):
self.name = name
assert np.all(np.diff(radii) > 0)
self.radii = radii
self.outer_radius = max(self.radii)
self.inner_radius = min(self.radii)
self.thickness = self.outer_radius - self.inner_radius
self.n_slices = len(self.radii)
self.verbose = verbose
self._cached = {}
self._pressures = None
self._temperatures = None
self.sublayers = None
self.material = None
self.pressure_mode = "self-consistent"
self.temperature_mode = None
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] |
11,017 | burnman.classes.layer | __str__ |
Prints details of the layer
| def __str__(self):
"""
Prints details of the layer
"""
writing = (
f"The {self.name} is made of {self.material.name}"
f" with {self.temperature_mode} temperatures and "
f"{self.pressure_mode} pressures\n"
)
return writing
| (self) | [
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] |
11,018 | burnman.classes.layer | _compute_gravity |
Computes the gravity of a layer
Used by _evaluate_eos()
| def _compute_gravity(self, density, gravity_bottom):
"""
Computes the gravity of a layer
Used by _evaluate_eos()
"""
# Create a spline fit of density as a function of radius
rhofunc = UnivariateSpline(self.radii, density)
# Numerically integrate Poisson's equation
def poisson(p, x):
return 4.0 * np.pi * constants.G * rhofunc(x) * x * x
grav = np.ravel(
odeint(poisson, gravity_bottom * self.radii[0] * self.radii[0], self.radii)
)
if self.radii[0] == 0:
grav[0] = 0
grav[1:] = grav[1:] / self.radii[1:] / self.radii[1:]
else:
grav[:] = grav[:] / self.radii[:] / self.radii[:]
return grav
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11,019 | burnman.classes.layer | _compute_pressure |
Calculate the pressure profile based on density and gravity.
This integrates the equation for hydrostatic equilibrium P = rho g z.
Used by _evaluate_eos()
| def _compute_pressure(self, density, gravity, pressure_top):
"""
Calculate the pressure profile based on density and gravity.
This integrates the equation for hydrostatic equilibrium P = rho g z.
Used by _evaluate_eos()
"""
# flip radius, density and gravity to increasing pressure
depthfromtop = -self.radii[::-1] + max(self.radii)
density = density[::-1]
gravity = gravity[::-1]
# Make a spline fit of density as a function of depth
rhofunc = UnivariateSpline(depthfromtop, density)
# Make a spline fit of gravity as a function of depth
gfunc = UnivariateSpline(depthfromtop, gravity)
# integrate the hydrostatic equation
pressure = np.ravel(
odeint((lambda p, x: gfunc(x) * rhofunc(x)), pressure_top, depthfromtop)
)
return pressure[::-1]
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11,020 | burnman.classes.layer | _evaluate_eos |
Returns updated gravity and pressure
make() loops over this until consistency is achieved.
| def _evaluate_eos(self, pressures, temperatures, gravity_bottom, pressure_top):
"""
Returns updated gravity and pressure
make() loops over this until consistency is achieved.
"""
[density] = self.material.evaluate(["density"], pressures, temperatures)
grav = self._compute_gravity(density, gravity_bottom)
press = self._compute_pressure(density, grav, pressure_top)
return grav, press
| (self, pressures, temperatures, gravity_bottom, pressure_top) | [
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] |
11,021 | burnman.classes.layer | _evaluate_temperature |
Returns the temperatures of the layer for given pressures.
Used by make()
| def _evaluate_temperature(self, pressures=None, temperature_top=None):
"""
Returns the temperatures of the layer for given pressures.
Used by make()
"""
if (
self.temperature_mode == "adiabatic"
or self.temperature_mode == "perturbed-adiabatic"
):
adiabat = geotherm.adiabatic(
pressures[::-1],
temperature_top - self.usertemperatures[-1],
self.material,
)[::-1]
else:
adiabat = np.zeros_like(self.radii)
return adiabat + self.usertemperatures
| (self, pressures=None, temperature_top=None) | [
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] |
11,022 | burnman.classes.layer | evaluate |
Function that is used to evaluate properties
across the layer. If radlist is not defined, values are
returned at the internal radlist.
If asking for different radii than the internal radlist,
pressure and temperature values are interpolated and the
layer material evaluated at those pressures and
temperatures.
:param properties: List of properties to evaluate.
:type properties: list of strings
:param radlist: Radii to evaluate properties at. If left empty,
internal radii list is used.
:type radlist: array of floats
:param planet_radius: Planet outer radius. Used only to calculate depth.
:type planet_radius: float
:returns: 1D or 2D array of requested properties
(1D if only one property was requested)
:rtype: numpy.array
| def evaluate(self, properties, radlist=None, radius_planet=None):
"""
Function that is used to evaluate properties
across the layer. If radlist is not defined, values are
returned at the internal radlist.
If asking for different radii than the internal radlist,
pressure and temperature values are interpolated and the
layer material evaluated at those pressures and
temperatures.
:param properties: List of properties to evaluate.
:type properties: list of strings
:param radlist: Radii to evaluate properties at. If left empty,
internal radii list is used.
:type radlist: array of floats
:param planet_radius: Planet outer radius. Used only to calculate depth.
:type planet_radius: float
:returns: 1D or 2D array of requested properties
(1D if only one property was requested)
:rtype: numpy.array
"""
if radlist is None:
values = np.empty([len(properties), len(self.radii)])
for i, prop in enumerate(properties):
if prop == "depth":
values[i] = radius_planet - self.radii
else:
try:
values[i] = getattr(self, prop)
except:
values[i] = np.array(
[
getattr(self.sublayers[i], prop)
for i in range(len(self.sublayers))
]
)
else:
func_p = interp1d(self.radii, self.pressures)
pressures = func_p(radlist)
func_t = interp1d(self.radii, self.temperatures)
temperatures = func_t(radlist)
values = np.empty([len(properties), len(radlist)])
for i, prop in enumerate(properties):
if prop == "depth":
values[i] = radius_planet - radlist
else:
try:
values[i] = self.material.evaluate(
[prop], pressures, temperatures
)
except:
func_prop = interp1d(self.radii, getattr(self, prop))
values[i] = func_prop(radlist)
if values.shape[0] == 1:
values = values[0]
return values
| (self, properties, radlist=None, radius_planet=None) | [
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] |
11,023 | burnman.classes.layer | make |
This routine needs to be called before evaluating any properties.
If pressures and temperatures are not user-defined, they
are computed here. This method also initializes an array of copied
materials from which properties can be computed.
| def make(self):
"""
This routine needs to be called before evaluating any properties.
If pressures and temperatures are not user-defined, they
are computed here. This method also initializes an array of copied
materials from which properties can be computed.
"""
self.reset()
if not hasattr(self, "material"):
raise AttributeError(
"You must set_material() for the layer " "before running make()."
)
if not hasattr(self, "temperature_mode"):
raise AttributeError(
"You must set_temperature_mode() for the "
"layer before running make()."
)
if not hasattr(self, "pressure_mode"):
raise AttributeError(
"You must set_pressure_mode() for the layer " "before running make()."
)
if self.pressure_mode == "user-defined":
self.temperatures = self._evaluate_temperature(
self.pressures, self.temperature_top
)
elif self.pressure_mode == "self-consistent":
new_press = (
self.pressure_top + (-self.radii + max(self.radii)) * 1.0e3
) # initial pressure curve guess
temperatures = self._evaluate_temperature(new_press, self.temperature_top)
# Make it self-consistent!!!
i = 0
while i < self.n_max_iterations:
i += 1
ref_press = new_press
new_grav, new_press = self._evaluate_eos(
new_press, temperatures, self.gravity_bottom, self.pressure_top
)
temperatures = self._evaluate_temperature(
new_press, self.temperature_top
)
rel_err = abs((max(ref_press) - max(new_press)) / max(new_press))
if self.verbose:
print(
f"Iteration {i:0d} maximum relative pressure error: "
f"{rel_err:.1f}"
)
if rel_err < self.max_delta:
break
self.pressures = new_press
self.temperatures = temperatures
else:
raise NotImplementedError("pressure mode not recognised")
self.sublayers = []
for r in range(len(self.radii)):
self.sublayers.append(self.material.copy())
self.sublayers[r].set_state(self.pressures[r], self.temperatures[r])
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11,024 | burnman.classes.layer | reset |
Resets all cached material properties.
It is typically not required for the user to call this function.
| def reset(self):
"""
Resets all cached material properties.
It is typically not required for the user to call this function.
"""
self._cached = {}
self._pressures = None
self._temperatures = None
self.sublayers = None
| (self) | [
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] |
11,025 | burnman.classes.layer | set_material |
Set the material of a Layer with a Material
| def set_material(self, material):
"""
Set the material of a Layer with a Material
"""
assert isinstance(material, Material)
self.material = material
self.reset()
| (self, material) | [
0.04193508252501488,
0.0010410487884655595,
0.03162374347448349,
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11,026 | burnman.classes.layer | set_pressure_mode |
Sets the pressure mode of the layer,
which can either be 'user-defined', or 'self-consistent'.
:param pressure_mode: This can be set to 'user-defined' or 'self-consistent'.
'user-defined' fixes the pressures with the profile input
by the user in the 'pressures' argument.
'self-consistent' forces Layer to calculate pressures
self-consistently. If this is selected, the user will need
to supply values for the gravity_bottom [m/s^2]
and pressure_top [Pa] arguments.
:type pressure_mode: string
:param pressures: Pressures [Pa] to set layer to
(if the 'user-defined' pressure_mode has been selected).
The array should be the same length as
the layers user-defined radii array.
:type pressures: array of floats
:param pressure_top: Pressure [Pa] at the top of the layer.
:type pressure_top: float
:param gravity_bottom: Gravity [m/s^2] at the bottom of the layer.
:type gravity_bottom: float
:param n_max_iterations: Maximum number of iterations to reach
self-consistent pressures.
:type n_max_iterations: integer
:param max_delta: Relative update to the highest pressure in the layer between
iterations to stop iterations.
:type max_delta: float
| def set_pressure_mode(
self,
pressure_mode="self-consistent",
pressures=None,
gravity_bottom=None,
pressure_top=None,
n_max_iterations=50,
max_delta=1.0e-5,
):
"""
Sets the pressure mode of the layer,
which can either be 'user-defined', or 'self-consistent'.
:param pressure_mode: This can be set to 'user-defined' or 'self-consistent'.
'user-defined' fixes the pressures with the profile input
by the user in the 'pressures' argument.
'self-consistent' forces Layer to calculate pressures
self-consistently. If this is selected, the user will need
to supply values for the gravity_bottom [m/s^2]
and pressure_top [Pa] arguments.
:type pressure_mode: string
:param pressures: Pressures [Pa] to set layer to
(if the 'user-defined' pressure_mode has been selected).
The array should be the same length as
the layers user-defined radii array.
:type pressures: array of floats
:param pressure_top: Pressure [Pa] at the top of the layer.
:type pressure_top: float
:param gravity_bottom: Gravity [m/s^2] at the bottom of the layer.
:type gravity_bottom: float
:param n_max_iterations: Maximum number of iterations to reach
self-consistent pressures.
:type n_max_iterations: integer
:param max_delta: Relative update to the highest pressure in the layer between
iterations to stop iterations.
:type max_delta: float
"""
self.reset()
assert pressure_mode == "user-defined" or pressure_mode == "self-consistent"
self.pressure_mode = pressure_mode
assert gravity_bottom is not None
self.gravity_bottom = gravity_bottom
if pressure_mode == "user-defined":
assert pressures is not None
assert len(pressures) == len(self.radii)
self.pressures = pressures
warnings.warn(
"By setting the pressures in Layer they "
"are unlikely to be self-consistent"
)
elif pressure_mode == "self-consistent":
self.pressure_top = pressure_top
self.n_max_iterations = n_max_iterations
self.max_delta = max_delta
else:
raise NotImplementedError(
f"pressure mode {pressure_mode} " "not recognised"
)
| (self, pressure_mode='self-consistent', pressures=None, gravity_bottom=None, pressure_top=None, n_max_iterations=50, max_delta=1e-05) | [
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11,027 | burnman.classes.layer | set_temperature_mode |
Sets temperatures within the layer as user-defined values or as
a (potentially perturbed) adiabat.
:param temperature_mode: This can be set to 'user-defined', 'adiabatic',
or 'perturbed-adiabatic'. 'user-defined' fixes the temperature
with the profile input by the user. 'adiabatic' self-consistently
computes the adiabat when setting the state of the layer.
'perturbed-adiabatic' adds the user input array to the adiabat.
This allows the user to apply boundary layers (for example).
:type temperature_mode: string
:param temperatures: The desired fixed temperatures in [K].
Should have same length as defined radii in layer.
:type temperatures: array of float
:param temperature_top: Temperature at the top of the layer.
Used if the temperature mode is chosen to be 'adiabatic' or
'perturbed-adiabatic'. If 'perturbed-adiabatic' is chosen as the
temperature mode, temperature_top corresponds to the true temperature
at the top of the layer, and the reference isentrope at this radius
is defined to lie at a temperature of
temperature_top - temperatures[-1].
:type temperature_top: float
| def set_temperature_mode(
self, temperature_mode="adiabatic", temperatures=None, temperature_top=None
):
"""
Sets temperatures within the layer as user-defined values or as
a (potentially perturbed) adiabat.
:param temperature_mode: This can be set to 'user-defined', 'adiabatic',
or 'perturbed-adiabatic'. 'user-defined' fixes the temperature
with the profile input by the user. 'adiabatic' self-consistently
computes the adiabat when setting the state of the layer.
'perturbed-adiabatic' adds the user input array to the adiabat.
This allows the user to apply boundary layers (for example).
:type temperature_mode: string
:param temperatures: The desired fixed temperatures in [K].
Should have same length as defined radii in layer.
:type temperatures: array of float
:param temperature_top: Temperature at the top of the layer.
Used if the temperature mode is chosen to be 'adiabatic' or
'perturbed-adiabatic'. If 'perturbed-adiabatic' is chosen as the
temperature mode, temperature_top corresponds to the true temperature
at the top of the layer, and the reference isentrope at this radius
is defined to lie at a temperature of
temperature_top - temperatures[-1].
:type temperature_top: float
"""
self.reset()
assert (
temperature_mode == "user-defined"
or temperature_mode == "adiabatic"
or temperature_mode == "perturbed-adiabatic"
)
self.temperature_mode = temperature_mode
if (
temperature_mode == "user-defined"
or temperature_mode == "perturbed-adiabatic"
):
assert len(temperatures) == len(self.radii)
self.usertemperatures = temperatures
else:
self.usertemperatures = np.zeros_like(self.radii)
if temperature_mode == "adiabatic" or temperature_mode == "perturbed-adiabatic":
self.temperature_top = temperature_top
else:
self.temperature_top = None
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11,028 | burnman.classes.material | Material |
Base class for all materials. The main functionality is unroll() which
returns a list of objects of type :class:`~burnman.Mineral` and their molar
fractions. This class is available as ``burnman.Material``.
The user needs to call set_method() (once in the beginning) and set_state()
before querying the material with unroll() or density().
| class Material(object):
"""
Base class for all materials. The main functionality is unroll() which
returns a list of objects of type :class:`~burnman.Mineral` and their molar
fractions. This class is available as ``burnman.Material``.
The user needs to call set_method() (once in the beginning) and set_state()
before querying the material with unroll() or density().
"""
def __init__(self):
self._pressure = None
self._temperature = None
if not hasattr(self, "name"):
# if a derived class decides to set .name before calling this
# constructor (I am looking at you, SLB_2011.py!), do not
# overwrite the name here.
self._name = self.__class__.__name__
self._cached = {}
@property
def name(self):
"""Human-readable name of this material.
By default this will return the name of the class, but it can be set
to an arbitrary string. Overriden in Mineral.
"""
return self._name
@name.setter
def name(self, value):
self._name = value
def set_method(self, method):
"""
Set the averaging method. See :doc:`averaging` for details.
.. note:: Needs to be implemented in derived classes.
"""
raise NotImplementedError("need to implement set_method() in derived class!")
def to_string(self):
"""
Returns a human-readable name of this material.
The default implementation will return the name of the class,
which is a reasonable default.
:returns: A human-readable name of the material.
:rtype: str
"""
return "'" + self.name + "'"
def debug_print(self, indent=""):
"""
Print a human-readable representation of this Material.
"""
raise NotImplementedError(
"Derived classes need to implement debug_print(). This is '"
+ self.__class__.__name__
+ "'"
)
def print_minerals_of_current_state(self):
"""
Print a human-readable representation of this Material at the current
P, T as a list of minerals.
This requires set_state() has been called before.
"""
(minerals, fractions) = self.unroll()
if len(minerals) == 1:
print(minerals[0].to_string())
else:
print("Material %s:" % self.to_string())
for mineral, fraction in zip(minerals, fractions):
print(" %g of phase %s" % (fraction, mineral.to_string()))
def set_state(self, pressure, temperature):
"""
Set the material to the given pressure and temperature.
:param pressure: The desired pressure in [Pa].
:type pressure: float
:param temperature: The desired temperature in [K].
:type temperature: float
"""
if not hasattr(self, "_pressure"):
raise Exception(
"Material.set_state() could not find class member _pressure. "
"Did you forget to call Material.__init__(self) in __init___?"
)
self.reset()
self._pressure = pressure
self._temperature = temperature
def set_state_with_volume(
self, volume, temperature, pressure_guesses=[0.0e9, 10.0e9]
):
"""
This function acts similarly to set_state, but takes volume and
temperature as input to find the pressure. In order to ensure
self-consistency, this function does not use any pressure functions
from the material classes, but instead finds the pressure using the
brentq root-finding method.
:param volume: The desired molar volume of the mineral [m^3].
:type volume: float
:param temperature: The desired temperature of the mineral [K].
:type temperature: float
:param pressure_guesses: A list of floats denoting the initial
low and high guesses for bracketing of the pressure [Pa].
These guesses should preferably bound the correct pressure,
but do not need to do so. More importantly,
they should not lie outside the valid region of
the equation of state. Defaults to [5.e9, 10.e9].
:type pressure_guesses: list
"""
def _delta_volume(pressure, volume, temperature):
# Try to set the state with this pressure,
# but if the pressure is too low most equations of state
# fail. In this case, treat the molar_volume as infinite
# and brentq will try a larger pressure.
try:
self.set_state(pressure, temperature)
return volume - self.molar_volume
except Exception:
return -np.inf
# we need to have a sign change in [a,b] to find a zero.
args = (volume, temperature)
try:
sol = bracket(_delta_volume, pressure_guesses[0], pressure_guesses[1], args)
except ValueError:
raise Exception(
"Cannot find a pressure, perhaps the volume or starting pressures "
"are outside the range of validity for the equation of state?"
)
pressure = brentq(_delta_volume, sol[0], sol[1], args=args)
self.set_state(pressure, temperature)
def reset(self):
"""
Resets all cached material properties.
It is typically not required for the user to call this function.
"""
self._cached = {}
def copy(self):
return deepcopy(self)
def unroll(self):
"""
Unroll this material into a list of :class:`burnman.Mineral` and their molar
fractions. All averaging schemes then operate on this list of minerals.
Note that the return value of this function may depend on the current
state (temperature, pressure).
.. note:: Needs to be implemented in derived classes.
:returns: A list of molar fractions which should sum to 1.0,
and a list of :class:`burnman.Mineral` objects
containing the minerals in the material.
:rtype: tuple
"""
raise NotImplementedError("need to implement unroll() in derived class!")
def evaluate(self, vars_list, pressures, temperatures):
"""
Returns an array of material properties requested through a list of strings
at given pressure and temperature conditions.
At the end it resets the set_state to the original values.
The user needs to call set_method() before.
:param vars_list: Variables to be returned for given conditions
:type vars_list: list of strings
:param pressures: ndlist or ndarray of float of pressures in [Pa].
:type pressures: :class:`numpy.array`, n-dimensional
:param temperatures: ndlist or ndarray of float of temperatures in [K].
:type temperatures: :class:`numpy.array`, n-dimensional
:returns: Array returning all variables at given pressure/temperature values.
output[i][j] is property vars_list[j] for temperatures[i] and pressures[i].
:rtype: :class:`numpy.array`, n-dimensional
"""
old_pressure = self.pressure
old_temperature = self.temperature
pressures = np.array(pressures)
temperatures = np.array(temperatures)
assert pressures.shape == temperatures.shape
output = np.empty((len(vars_list),) + pressures.shape)
for i, p in np.ndenumerate(pressures):
self.set_state(p, temperatures[i])
for j in range(len(vars_list)):
output[(j,) + i] = getattr(self, vars_list[j])
if old_pressure is None or old_temperature is None:
# do not set_state if old values were None. Just reset to None
# manually
self._pressure = self._temperature = None
self.reset()
else:
self.set_state(old_pressure, old_temperature)
return output
@property
def pressure(self):
"""
Returns current pressure that was set with :func: | () | [
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11,029 | burnman.classes.material | __init__ | null | def __init__(self):
self._pressure = None
self._temperature = None
if not hasattr(self, "name"):
# if a derived class decides to set .name before calling this
# constructor (I am looking at you, SLB_2011.py!), do not
# overwrite the name here.
self._name = self.__class__.__name__
self._cached = {}
| (self) | [
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11,040 | burnman.classes.polytope | MaterialPolytope |
A class that can be instantiated to create pycddlib polytope objects.
These objects can be interrogated to provide the vertices satisfying the
input constraints.
This class is available as :class:`burnman.polytope.MaterialPolytope`.
| class MaterialPolytope(object):
"""
A class that can be instantiated to create pycddlib polytope objects.
These objects can be interrogated to provide the vertices satisfying the
input constraints.
This class is available as :class:`burnman.polytope.MaterialPolytope`.
"""
def __init__(
self,
equalities,
inequalities,
number_type="fraction",
return_fractions=False,
independent_endmember_occupancies=None,
):
"""
Initialization function for the MaterialPolytope class.
Declares basis attributes of the class.
:param equalities: A numpy array containing all the
equalities defining the polytope. Each row should evaluate to 0.
:type equalities: numpy.array (2D)
:param inequalities: A numpy array containing all the inequalities
defining the polytope. Each row should evaluate to <= 0.
:type inequalities: numpy.array (2D)
:param number_type: Whether pycddlib should read the input arrays as
fractions or floats. Valid options are 'fraction' or 'float'.
:type number_type: str
:param return_fractions: Choose whether the generated polytope object
should return fractions or floats.
:type return_fractions: bool
:param independent_endmember_occupancies: If specified, this array provides
the independent endmember set against which the dependent endmembers
are defined.
:type independent_endmember_occupancies: numpy.array (2D) or None
"""
self.set_return_type(return_fractions)
self.equality_matrix = equalities[:, 1:]
self.equality_vector = -equalities[:, 0]
self.polytope_matrix = cdd.Matrix(
equalities, linear=True, number_type=number_type
)
self.polytope_matrix.rep_type = cdd.RepType.INEQUALITY
self.polytope_matrix.extend(inequalities, linear=False)
self.polytope = cdd.Polyhedron(self.polytope_matrix)
if independent_endmember_occupancies is not None:
self.independent_endmember_occupancies = independent_endmember_occupancies
def set_return_type(self, return_fractions=False):
"""
Sets the return_type for the polytope object. Also deletes the cached
endmember_occupancies property.
:param return_fractions: Choose whether the generated polytope object
should return fractions or floats.
:type return_fractions: bool
"""
try:
del self.__dict__["endmember_occupancies"]
except KeyError:
pass
self.return_fractions = return_fractions
@cached_property
def raw_vertices(self):
"""
Returns a list of the vertices of the polytope without any
postprocessing. See also endmember_occupancies.
"""
return self.polytope.get_generators()[:]
@cached_property
def limits(self):
"""
Return the limits of the polytope (the set of bounding inequalities).
"""
return np.array(self.polytope.get_inequalities(), dtype=float)
@cached_property
def n_endmembers(self):
"""
Return the number of endmembers
(the number of vertices of the polytope).
"""
return len(self.raw_vertices)
@cached_property
def endmember_occupancies(self):
"""
Return the endmember occupancies
(a processed list of all of the vertex locations).
"""
if self.return_fractions:
if self.polytope.number_type == "fraction":
v = np.array(
[[Fraction(value) for value in v] for v in self.raw_vertices]
)
else:
v = np.array(
[
[Rational(value).limit_denominator(1000000) for value in v]
for v in self.raw_vertices
]
)
else:
v = np.array([[float(value) for value in v] for v in self.raw_vertices])
if len(v.shape) == 1:
raise ValueError(
"The combined equality and positivity "
"constraints result in a null polytope."
)
return v[:, 1:] / v[:, 0, np.newaxis]
@cached_property
def independent_endmember_occupancies(self):
"""
Return an independent set of endmember occupancies
(a linearly-independent set of vertex locations)
"""
arr = self.endmember_occupancies
return arr[independent_row_indices(arr)]
@cached_property
def endmembers_as_independent_endmember_amounts(self):
"""
Return a list of all the endmembers as a linear sum of
the independent endmembers.
"""
ind = self.independent_endmember_occupancies
sol = (
np.linalg.lstsq(
np.array(ind.T).astype(float),
np.array(self.endmember_occupancies.T).astype(float),
rcond=0,
)[0]
.round(decimals=12)
.T
)
return sol
def _decompose_vertices_into_simplices(self, vertices):
"""
Decomposes a set of vertices into simplices by Delaunay triangulation.
"""
# Delaunay triangulation only works in dimensions > 1
# and we remove the nullspace (sum(fractions) = 1)
if len(vertices) > 2:
nulls = np.repeat(vertices[:, -1], vertices.shape[1]).reshape(
vertices.shape
)
tri = Delaunay((vertices - nulls)[:, :-1])
return tri.simplices
else:
return [[0, 1]]
@cached_property
def independent_endmember_polytope(self):
"""
Returns the polytope expressed in terms of proportions of the
independent endmembers. The polytope involves the first
n-1 independent endmembers. The last endmember proportion makes
the sum equal to one.
"""
arr = self.endmembers_as_independent_endmember_amounts
arr = np.hstack((np.ones((len(arr), 1)), arr[:, :-1]))
M = cdd.Matrix(arr, number_type="fraction")
M.rep_type = cdd.RepType.GENERATOR
return cdd.Polyhedron(M)
@cached_property
def independent_endmember_limits(self):
"""
Gets the limits of the polytope as a function of the independent
endmembers.
"""
return np.array(
self.independent_endmember_polytope.get_inequalities(), dtype=float
)
def subpolytope_from_independent_endmember_limits(self, limits):
"""
Returns a smaller polytope by applying additional limits to the amounts
of the independent endmembers.
"""
modified_limits = self.independent_endmember_polytope.get_inequalities().copy()
modified_limits.extend(limits, linear=False)
return cdd.Polyhedron(modified_limits)
def subpolytope_from_site_occupancy_limits(self, limits):
"""
Returns a smaller polytope by applying additional limits to the
individual site occupancies.
"""
modified_limits = self.polytope_matrix.copy()
modified_limits.extend(limits, linear=False)
return cdd.Polyhedron(modified_limits)
def grid(
self,
points_per_edge=2,
unique_sorted=True,
grid_type="independent endmember proportions",
limits=None,
):
"""
Create a grid of points which span the polytope.
:param points_per_edge: Number of points per edge of the polytope.
:type points_per_edge: int
:param unique_sorted: The gridding is done by splitting the polytope into
a set of simplices. This means that points will be duplicated along
vertices, faces etc. If unique_sorted is True, this function
will sort and make the points unique. This is an expensive
operation for large polytopes, and may not always be necessary.
:type unique_sorted: bool
:param grid_type: W | (equalities, inequalities, number_type='fraction', return_fractions=False, independent_endmember_occupancies=None) | [
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11,041 | burnman.classes.polytope | __init__ |
Initialization function for the MaterialPolytope class.
Declares basis attributes of the class.
:param equalities: A numpy array containing all the
equalities defining the polytope. Each row should evaluate to 0.
:type equalities: numpy.array (2D)
:param inequalities: A numpy array containing all the inequalities
defining the polytope. Each row should evaluate to <= 0.
:type inequalities: numpy.array (2D)
:param number_type: Whether pycddlib should read the input arrays as
fractions or floats. Valid options are 'fraction' or 'float'.
:type number_type: str
:param return_fractions: Choose whether the generated polytope object
should return fractions or floats.
:type return_fractions: bool
:param independent_endmember_occupancies: If specified, this array provides
the independent endmember set against which the dependent endmembers
are defined.
:type independent_endmember_occupancies: numpy.array (2D) or None
| def __init__(
self,
equalities,
inequalities,
number_type="fraction",
return_fractions=False,
independent_endmember_occupancies=None,
):
"""
Initialization function for the MaterialPolytope class.
Declares basis attributes of the class.
:param equalities: A numpy array containing all the
equalities defining the polytope. Each row should evaluate to 0.
:type equalities: numpy.array (2D)
:param inequalities: A numpy array containing all the inequalities
defining the polytope. Each row should evaluate to <= 0.
:type inequalities: numpy.array (2D)
:param number_type: Whether pycddlib should read the input arrays as
fractions or floats. Valid options are 'fraction' or 'float'.
:type number_type: str
:param return_fractions: Choose whether the generated polytope object
should return fractions or floats.
:type return_fractions: bool
:param independent_endmember_occupancies: If specified, this array provides
the independent endmember set against which the dependent endmembers
are defined.
:type independent_endmember_occupancies: numpy.array (2D) or None
"""
self.set_return_type(return_fractions)
self.equality_matrix = equalities[:, 1:]
self.equality_vector = -equalities[:, 0]
self.polytope_matrix = cdd.Matrix(
equalities, linear=True, number_type=number_type
)
self.polytope_matrix.rep_type = cdd.RepType.INEQUALITY
self.polytope_matrix.extend(inequalities, linear=False)
self.polytope = cdd.Polyhedron(self.polytope_matrix)
if independent_endmember_occupancies is not None:
self.independent_endmember_occupancies = independent_endmember_occupancies
| (self, equalities, inequalities, number_type='fraction', return_fractions=False, independent_endmember_occupancies=None) | [
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11,042 | burnman.classes.polytope | _decompose_vertices_into_simplices |
Decomposes a set of vertices into simplices by Delaunay triangulation.
| def _decompose_vertices_into_simplices(self, vertices):
"""
Decomposes a set of vertices into simplices by Delaunay triangulation.
"""
# Delaunay triangulation only works in dimensions > 1
# and we remove the nullspace (sum(fractions) = 1)
if len(vertices) > 2:
nulls = np.repeat(vertices[:, -1], vertices.shape[1]).reshape(
vertices.shape
)
tri = Delaunay((vertices - nulls)[:, :-1])
return tri.simplices
else:
return [[0, 1]]
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11,043 | burnman.classes.polytope | grid |
Create a grid of points which span the polytope.
:param points_per_edge: Number of points per edge of the polytope.
:type points_per_edge: int
:param unique_sorted: The gridding is done by splitting the polytope into
a set of simplices. This means that points will be duplicated along
vertices, faces etc. If unique_sorted is True, this function
will sort and make the points unique. This is an expensive
operation for large polytopes, and may not always be necessary.
:type unique_sorted: bool
:param grid_type: Whether to grid the polytope in terms of
independent endmember proportions or site occupancies.
Choices are 'independent endmember proportions' or 'site occupancies'
:type grid_type: str
:param limits: Additional inequalities restricting the
gridded area of the polytope.
:type limits: numpy.array (2D)
:returns: A list of points gridding the polytope.
:rtype: numpy.array (2D)
| def grid(
self,
points_per_edge=2,
unique_sorted=True,
grid_type="independent endmember proportions",
limits=None,
):
"""
Create a grid of points which span the polytope.
:param points_per_edge: Number of points per edge of the polytope.
:type points_per_edge: int
:param unique_sorted: The gridding is done by splitting the polytope into
a set of simplices. This means that points will be duplicated along
vertices, faces etc. If unique_sorted is True, this function
will sort and make the points unique. This is an expensive
operation for large polytopes, and may not always be necessary.
:type unique_sorted: bool
:param grid_type: Whether to grid the polytope in terms of
independent endmember proportions or site occupancies.
Choices are 'independent endmember proportions' or 'site occupancies'
:type grid_type: str
:param limits: Additional inequalities restricting the
gridded area of the polytope.
:type limits: numpy.array (2D)
:returns: A list of points gridding the polytope.
:rtype: numpy.array (2D)
"""
if limits is None:
if grid_type == "independent endmember proportions":
f_occ = self.endmembers_as_independent_endmember_amounts / (
points_per_edge - 1
)
elif grid_type == "site occupancies":
f_occ = self.endmember_occupancies / (points_per_edge - 1)
else:
raise Exception(
"grid type not recognised. Should be one of "
"independent endmember proportions "
"or site occupancies"
)
simplices = self._decompose_vertices_into_simplices(
self.endmembers_as_independent_endmember_amounts
)
else:
if grid_type == "independent endmember proportions":
ppns = np.array(
self.subpolytope_from_independent_endmember_limits(
limits
).get_generators()[:]
)[:, 1:]
last_ppn = np.array([1.0 - sum(p) for p in ppns]).reshape(
(len(ppns), 1)
)
vertices_as_independent_endmember_proportions = np.hstack(
(ppns, last_ppn)
)
f_occ = vertices_as_independent_endmember_proportions / (
points_per_edge - 1
)
elif grid_type == "site occupancies":
occ = np.array(
self.subpolytope_from_site_occupancy_limits(
limits
).get_generators()[:]
)[:, 1:]
f_occ = occ / (points_per_edge - 1)
ind = self.independent_endmember_occupancies
vertices_as_independent_endmember_proportions = (
np.linalg.lstsq(
np.array(ind.T).astype(float),
np.array(occ.T).astype(float),
rcond=None,
)[0]
.round(decimals=12)
.T
)
else:
raise Exception(
"grid_type not recognised. "
"Should be one of "
"independent endmember proportions "
"or site occupancies"
)
simplices = self._decompose_vertices_into_simplices(
vertices_as_independent_endmember_proportions
)
n_ind = f_occ.shape[1]
n_simplices = len(simplices)
dim = len(simplices[0])
simplex_grid = SimplexGrid(dim, points_per_edge)
grid = simplex_grid.grid("array")
points_per_simplex = simplex_grid.n_points()
n_points = n_simplices * points_per_simplex
points = np.empty((n_points, n_ind))
idx = 0
for i in range(0, n_simplices):
points[idx : idx + points_per_simplex] = grid.dot(f_occ[simplices[i]])
idx += points_per_simplex
if unique_sorted:
points = np.unique(points, axis=0)
return points
| (self, points_per_edge=2, unique_sorted=True, grid_type='independent endmember proportions', limits=None) | [
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