diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/__init__.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..d924d05265f65f4c73f4459d0dd385aa12cf999e --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/__init__.py @@ -0,0 +1,346 @@ +""" +======================================= +Signal processing (:mod:`scipy.signal`) +======================================= + +Convolution +=========== + +.. autosummary:: + :toctree: generated/ + + convolve -- N-D convolution. + correlate -- N-D correlation. + fftconvolve -- N-D convolution using the FFT. + oaconvolve -- N-D convolution using the overlap-add method. + convolve2d -- 2-D convolution (more options). + correlate2d -- 2-D correlation (more options). + sepfir2d -- Convolve with a 2-D separable FIR filter. + choose_conv_method -- Chooses faster of FFT and direct convolution methods. + correlation_lags -- Determines lag indices for 1D cross-correlation. + +B-splines +========= + +.. autosummary:: + :toctree: generated/ + + gauss_spline -- Gaussian approximation to the B-spline basis function. + cspline1d -- Coefficients for 1-D cubic (3rd order) B-spline. + qspline1d -- Coefficients for 1-D quadratic (2nd order) B-spline. + cspline2d -- Coefficients for 2-D cubic (3rd order) B-spline. + qspline2d -- Coefficients for 2-D quadratic (2nd order) B-spline. + cspline1d_eval -- Evaluate a cubic spline at the given points. + qspline1d_eval -- Evaluate a quadratic spline at the given points. + spline_filter -- Smoothing spline (cubic) filtering of a rank-2 array. + +Filtering +========= + +.. autosummary:: + :toctree: generated/ + + order_filter -- N-D order filter. + medfilt -- N-D median filter. + medfilt2d -- 2-D median filter (faster). + wiener -- N-D Wiener filter. + + symiirorder1 -- 2nd-order IIR filter (cascade of first-order systems). + symiirorder2 -- 4th-order IIR filter (cascade of second-order systems). + lfilter -- 1-D FIR and IIR digital linear filtering. + lfiltic -- Construct initial conditions for `lfilter`. + lfilter_zi -- Compute an initial state zi for the lfilter function that + -- corresponds to the steady state of the step response. + filtfilt -- A forward-backward filter. + savgol_filter -- Filter a signal using the Savitzky-Golay filter. + + deconvolve -- 1-D deconvolution using lfilter. + + sosfilt -- 1-D IIR digital linear filtering using + -- a second-order sections filter representation. + sosfilt_zi -- Compute an initial state zi for the sosfilt function that + -- corresponds to the steady state of the step response. + sosfiltfilt -- A forward-backward filter for second-order sections. + hilbert -- Compute 1-D analytic signal, using the Hilbert transform. + hilbert2 -- Compute 2-D analytic signal, using the Hilbert transform. + + decimate -- Downsample a signal. + detrend -- Remove linear and/or constant trends from data. + resample -- Resample using Fourier method. + resample_poly -- Resample using polyphase filtering method. + upfirdn -- Upsample, apply FIR filter, downsample. + +Filter design +============= + +.. autosummary:: + :toctree: generated/ + + bilinear -- Digital filter from an analog filter using + -- the bilinear transform. + bilinear_zpk -- Digital filter from an analog filter using + -- the bilinear transform. + findfreqs -- Find array of frequencies for computing filter response. + firls -- FIR filter design using least-squares error minimization. + firwin -- Windowed FIR filter design, with frequency response + -- defined as pass and stop bands. + firwin2 -- Windowed FIR filter design, with arbitrary frequency + -- response. + freqs -- Analog filter frequency response from TF coefficients. + freqs_zpk -- Analog filter frequency response from ZPK coefficients. + freqz -- Digital filter frequency response from TF coefficients. + freqz_zpk -- Digital filter frequency response from ZPK coefficients. + sosfreqz -- Digital filter frequency response for SOS format filter. + gammatone -- FIR and IIR gammatone filter design. + group_delay -- Digital filter group delay. + iirdesign -- IIR filter design given bands and gains. + iirfilter -- IIR filter design given order and critical frequencies. + kaiser_atten -- Compute the attenuation of a Kaiser FIR filter, given + -- the number of taps and the transition width at + -- discontinuities in the frequency response. + kaiser_beta -- Compute the Kaiser parameter beta, given the desired + -- FIR filter attenuation. + kaiserord -- Design a Kaiser window to limit ripple and width of + -- transition region. + minimum_phase -- Convert a linear phase FIR filter to minimum phase. + savgol_coeffs -- Compute the FIR filter coefficients for a Savitzky-Golay + -- filter. + remez -- Optimal FIR filter design. + + unique_roots -- Unique roots and their multiplicities. + residue -- Partial fraction expansion of b(s) / a(s). + residuez -- Partial fraction expansion of b(z) / a(z). + invres -- Inverse partial fraction expansion for analog filter. + invresz -- Inverse partial fraction expansion for digital filter. + BadCoefficients -- Warning on badly conditioned filter coefficients. + +Lower-level filter design functions: + +.. autosummary:: + :toctree: generated/ + + abcd_normalize -- Check state-space matrices and ensure they are rank-2. + band_stop_obj -- Band Stop Objective Function for order minimization. + besselap -- Return (z,p,k) for analog prototype of Bessel filter. + buttap -- Return (z,p,k) for analog prototype of Butterworth filter. + cheb1ap -- Return (z,p,k) for type I Chebyshev filter. + cheb2ap -- Return (z,p,k) for type II Chebyshev filter. + cmplx_sort -- Sort roots based on magnitude. + ellipap -- Return (z,p,k) for analog prototype of elliptic filter. + lp2bp -- Transform a lowpass filter prototype to a bandpass filter. + lp2bp_zpk -- Transform a lowpass filter prototype to a bandpass filter. + lp2bs -- Transform a lowpass filter prototype to a bandstop filter. + lp2bs_zpk -- Transform a lowpass filter prototype to a bandstop filter. + lp2hp -- Transform a lowpass filter prototype to a highpass filter. + lp2hp_zpk -- Transform a lowpass filter prototype to a highpass filter. + lp2lp -- Transform a lowpass filter prototype to a lowpass filter. + lp2lp_zpk -- Transform a lowpass filter prototype to a lowpass filter. + normalize -- Normalize polynomial representation of a transfer function. + + + +Matlab-style IIR filter design +============================== + +.. autosummary:: + :toctree: generated/ + + butter -- Butterworth + buttord + cheby1 -- Chebyshev Type I + cheb1ord + cheby2 -- Chebyshev Type II + cheb2ord + ellip -- Elliptic (Cauer) + ellipord + bessel -- Bessel (no order selection available -- try butterod) + iirnotch -- Design second-order IIR notch digital filter. + iirpeak -- Design second-order IIR peak (resonant) digital filter. + iircomb -- Design IIR comb filter. + +Continuous-time linear systems +============================== + +.. autosummary:: + :toctree: generated/ + + lti -- Continuous-time linear time invariant system base class. + StateSpace -- Linear time invariant system in state space form. + TransferFunction -- Linear time invariant system in transfer function form. + ZerosPolesGain -- Linear time invariant system in zeros, poles, gain form. + lsim -- Continuous-time simulation of output to linear system. + impulse -- Impulse response of linear, time-invariant (LTI) system. + step -- Step response of continuous-time LTI system. + freqresp -- Frequency response of a continuous-time LTI system. + bode -- Bode magnitude and phase data (continuous-time LTI). + +Discrete-time linear systems +============================ + +.. autosummary:: + :toctree: generated/ + + dlti -- Discrete-time linear time invariant system base class. + StateSpace -- Linear time invariant system in state space form. + TransferFunction -- Linear time invariant system in transfer function form. + ZerosPolesGain -- Linear time invariant system in zeros, poles, gain form. + dlsim -- Simulation of output to a discrete-time linear system. + dimpulse -- Impulse response of a discrete-time LTI system. + dstep -- Step response of a discrete-time LTI system. + dfreqresp -- Frequency response of a discrete-time LTI system. + dbode -- Bode magnitude and phase data (discrete-time LTI). + +LTI representations +=================== + +.. autosummary:: + :toctree: generated/ + + tf2zpk -- Transfer function to zero-pole-gain. + tf2sos -- Transfer function to second-order sections. + tf2ss -- Transfer function to state-space. + zpk2tf -- Zero-pole-gain to transfer function. + zpk2sos -- Zero-pole-gain to second-order sections. + zpk2ss -- Zero-pole-gain to state-space. + ss2tf -- State-pace to transfer function. + ss2zpk -- State-space to pole-zero-gain. + sos2zpk -- Second-order sections to zero-pole-gain. + sos2tf -- Second-order sections to transfer function. + cont2discrete -- Continuous-time to discrete-time LTI conversion. + place_poles -- Pole placement. + +Waveforms +========= + +.. autosummary:: + :toctree: generated/ + + chirp -- Frequency swept cosine signal, with several freq functions. + gausspulse -- Gaussian modulated sinusoid. + max_len_seq -- Maximum length sequence. + sawtooth -- Periodic sawtooth. + square -- Square wave. + sweep_poly -- Frequency swept cosine signal; freq is arbitrary polynomial. + unit_impulse -- Discrete unit impulse. + +Window functions +================ + +For window functions, see the `scipy.signal.windows` namespace. + +In the `scipy.signal` namespace, there is a convenience function to +obtain these windows by name: + +.. autosummary:: + :toctree: generated/ + + get_window -- Return a window of a given length and type. + +Wavelets +======== + +.. autosummary:: + :toctree: generated/ + + cascade -- Compute scaling function and wavelet from coefficients. + daub -- Return low-pass. + morlet -- Complex Morlet wavelet. + qmf -- Return quadrature mirror filter from low-pass. + ricker -- Return ricker wavelet. + morlet2 -- Return Morlet wavelet, compatible with cwt. + cwt -- Perform continuous wavelet transform. + +Peak finding +============ + +.. autosummary:: + :toctree: generated/ + + argrelmin -- Calculate the relative minima of data. + argrelmax -- Calculate the relative maxima of data. + argrelextrema -- Calculate the relative extrema of data. + find_peaks -- Find a subset of peaks inside a signal. + find_peaks_cwt -- Find peaks in a 1-D array with wavelet transformation. + peak_prominences -- Calculate the prominence of each peak in a signal. + peak_widths -- Calculate the width of each peak in a signal. + +Spectral analysis +================= + +.. autosummary:: + :toctree: generated/ + + periodogram -- Compute a (modified) periodogram. + welch -- Compute a periodogram using Welch's method. + csd -- Compute the cross spectral density, using Welch's method. + coherence -- Compute the magnitude squared coherence, using Welch's method. + spectrogram -- Compute the spectrogram (legacy). + lombscargle -- Computes the Lomb-Scargle periodogram. + vectorstrength -- Computes the vector strength. + ShortTimeFFT -- Interface for calculating the \ + :ref:`Short Time Fourier Transform ` and \ + its inverse. + stft -- Compute the Short Time Fourier Transform (legacy). + istft -- Compute the Inverse Short Time Fourier Transform (legacy). + check_COLA -- Check the COLA constraint for iSTFT reconstruction. + check_NOLA -- Check the NOLA constraint for iSTFT reconstruction. + +Chirp Z-transform and Zoom FFT +============================================ + +.. autosummary:: + :toctree: generated/ + + czt - Chirp z-transform convenience function + zoom_fft - Zoom FFT convenience function + CZT - Chirp z-transform function generator + ZoomFFT - Zoom FFT function generator + czt_points - Output the z-plane points sampled by a chirp z-transform + +The functions are simpler to use than the classes, but are less efficient when +using the same transform on many arrays of the same length, since they +repeatedly generate the same chirp signal with every call. In these cases, +use the classes to create a reusable function instead. + +""" + +from . import _sigtools, windows +from ._waveforms import * +from ._max_len_seq import max_len_seq +from ._upfirdn import upfirdn + +from ._spline import ( + cspline2d, + qspline2d, + sepfir2d, + symiirorder1, + symiirorder2, +) + +from ._bsplines import * +from ._filter_design import * +from ._fir_filter_design import * +from ._ltisys import * +from ._lti_conversion import * +from ._signaltools import * +from ._savitzky_golay import savgol_coeffs, savgol_filter +from ._spectral_py import * +from ._short_time_fft import * +from ._wavelets import * +from ._peak_finding import * +from ._czt import * +from .windows import get_window # keep this one in signal namespace + +# Deprecated namespaces, to be removed in v2.0.0 +from . import ( + bsplines, filter_design, fir_filter_design, lti_conversion, ltisys, + spectral, signaltools, waveforms, wavelets, spline +) + +__all__ = [ + s for s in dir() if not s.startswith("_") +] + +from scipy._lib._testutils import PytestTester +test = PytestTester(__name__) +del PytestTester diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_arraytools.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_arraytools.py new file mode 100644 index 0000000000000000000000000000000000000000..87ce75d8d892a64021da7abc5d149556c22cf983 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_arraytools.py @@ -0,0 +1,264 @@ +""" +Functions for acting on a axis of an array. +""" +import numpy as np + + +def axis_slice(a, start=None, stop=None, step=None, axis=-1): + """Take a slice along axis 'axis' from 'a'. + + Parameters + ---------- + a : numpy.ndarray + The array to be sliced. + start, stop, step : int or None + The slice parameters. + axis : int, optional + The axis of `a` to be sliced. + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal._arraytools import axis_slice + >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + >>> axis_slice(a, start=0, stop=1, axis=1) + array([[1], + [4], + [7]]) + >>> axis_slice(a, start=1, axis=0) + array([[4, 5, 6], + [7, 8, 9]]) + + Notes + ----- + The keyword arguments start, stop and step are used by calling + slice(start, stop, step). This implies axis_slice() does not + handle its arguments the exactly the same as indexing. To select + a single index k, for example, use + axis_slice(a, start=k, stop=k+1) + In this case, the length of the axis 'axis' in the result will + be 1; the trivial dimension is not removed. (Use numpy.squeeze() + to remove trivial axes.) + """ + a_slice = [slice(None)] * a.ndim + a_slice[axis] = slice(start, stop, step) + b = a[tuple(a_slice)] + return b + + +def axis_reverse(a, axis=-1): + """Reverse the 1-D slices of `a` along axis `axis`. + + Returns axis_slice(a, step=-1, axis=axis). + """ + return axis_slice(a, step=-1, axis=axis) + + +def odd_ext(x, n, axis=-1): + """ + Odd extension at the boundaries of an array + + Generate a new ndarray by making an odd extension of `x` along an axis. + + Parameters + ---------- + x : ndarray + The array to be extended. + n : int + The number of elements by which to extend `x` at each end of the axis. + axis : int, optional + The axis along which to extend `x`. Default is -1. + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal._arraytools import odd_ext + >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) + >>> odd_ext(a, 2) + array([[-1, 0, 1, 2, 3, 4, 5, 6, 7], + [-4, -1, 0, 1, 4, 9, 16, 23, 28]]) + + Odd extension is a "180 degree rotation" at the endpoints of the original + array: + + >>> t = np.linspace(0, 1.5, 100) + >>> a = 0.9 * np.sin(2 * np.pi * t**2) + >>> b = odd_ext(a, 40) + >>> import matplotlib.pyplot as plt + >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='odd extension') + >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original') + >>> plt.legend(loc='best') + >>> plt.show() + """ + if n < 1: + return x + if n > x.shape[axis] - 1: + raise ValueError(("The extension length n (%d) is too big. " + + "It must not exceed x.shape[axis]-1, which is %d.") + % (n, x.shape[axis] - 1)) + left_end = axis_slice(x, start=0, stop=1, axis=axis) + left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis) + right_end = axis_slice(x, start=-1, axis=axis) + right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis) + ext = np.concatenate((2 * left_end - left_ext, + x, + 2 * right_end - right_ext), + axis=axis) + return ext + + +def even_ext(x, n, axis=-1): + """ + Even extension at the boundaries of an array + + Generate a new ndarray by making an even extension of `x` along an axis. + + Parameters + ---------- + x : ndarray + The array to be extended. + n : int + The number of elements by which to extend `x` at each end of the axis. + axis : int, optional + The axis along which to extend `x`. Default is -1. + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal._arraytools import even_ext + >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) + >>> even_ext(a, 2) + array([[ 3, 2, 1, 2, 3, 4, 5, 4, 3], + [ 4, 1, 0, 1, 4, 9, 16, 9, 4]]) + + Even extension is a "mirror image" at the boundaries of the original array: + + >>> t = np.linspace(0, 1.5, 100) + >>> a = 0.9 * np.sin(2 * np.pi * t**2) + >>> b = even_ext(a, 40) + >>> import matplotlib.pyplot as plt + >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='even extension') + >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original') + >>> plt.legend(loc='best') + >>> plt.show() + """ + if n < 1: + return x + if n > x.shape[axis] - 1: + raise ValueError(("The extension length n (%d) is too big. " + + "It must not exceed x.shape[axis]-1, which is %d.") + % (n, x.shape[axis] - 1)) + left_ext = axis_slice(x, start=n, stop=0, step=-1, axis=axis) + right_ext = axis_slice(x, start=-2, stop=-(n + 2), step=-1, axis=axis) + ext = np.concatenate((left_ext, + x, + right_ext), + axis=axis) + return ext + + +def const_ext(x, n, axis=-1): + """ + Constant extension at the boundaries of an array + + Generate a new ndarray that is a constant extension of `x` along an axis. + + The extension repeats the values at the first and last element of + the axis. + + Parameters + ---------- + x : ndarray + The array to be extended. + n : int + The number of elements by which to extend `x` at each end of the axis. + axis : int, optional + The axis along which to extend `x`. Default is -1. + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal._arraytools import const_ext + >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) + >>> const_ext(a, 2) + array([[ 1, 1, 1, 2, 3, 4, 5, 5, 5], + [ 0, 0, 0, 1, 4, 9, 16, 16, 16]]) + + Constant extension continues with the same values as the endpoints of the + array: + + >>> t = np.linspace(0, 1.5, 100) + >>> a = 0.9 * np.sin(2 * np.pi * t**2) + >>> b = const_ext(a, 40) + >>> import matplotlib.pyplot as plt + >>> plt.plot(np.arange(-40, 140), b, 'b', lw=1, label='constant extension') + >>> plt.plot(np.arange(100), a, 'r', lw=2, label='original') + >>> plt.legend(loc='best') + >>> plt.show() + """ + if n < 1: + return x + left_end = axis_slice(x, start=0, stop=1, axis=axis) + ones_shape = [1] * x.ndim + ones_shape[axis] = n + ones = np.ones(ones_shape, dtype=x.dtype) + left_ext = ones * left_end + right_end = axis_slice(x, start=-1, axis=axis) + right_ext = ones * right_end + ext = np.concatenate((left_ext, + x, + right_ext), + axis=axis) + return ext + + +def zero_ext(x, n, axis=-1): + """ + Zero padding at the boundaries of an array + + Generate a new ndarray that is a zero-padded extension of `x` along + an axis. + + Parameters + ---------- + x : ndarray + The array to be extended. + n : int + The number of elements by which to extend `x` at each end of the + axis. + axis : int, optional + The axis along which to extend `x`. Default is -1. + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal._arraytools import zero_ext + >>> a = np.array([[1, 2, 3, 4, 5], [0, 1, 4, 9, 16]]) + >>> zero_ext(a, 2) + array([[ 0, 0, 1, 2, 3, 4, 5, 0, 0], + [ 0, 0, 0, 1, 4, 9, 16, 0, 0]]) + """ + if n < 1: + return x + zeros_shape = list(x.shape) + zeros_shape[axis] = n + zeros = np.zeros(zeros_shape, dtype=x.dtype) + ext = np.concatenate((zeros, x, zeros), axis=axis) + return ext + + +def _validate_fs(fs, allow_none=True): + """ + Check if the given sampling frequency is a scalar and raises an exception + otherwise. If allow_none is False, also raises an exception for none + sampling rates. Returns the sampling frequency as float or none if the + input is none. + """ + if fs is None: + if not allow_none: + raise ValueError("Sampling frequency can not be none.") + else: # should be float + if not np.isscalar(fs): + raise ValueError("Sampling frequency fs must be a single scalar.") + fs = float(fs) + return fs diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_bsplines.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_bsplines.py new file mode 100644 index 0000000000000000000000000000000000000000..c9b136da7c5543f517e03f09f88666290f1590d7 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_bsplines.py @@ -0,0 +1,519 @@ +from numpy import (asarray, pi, zeros_like, + array, arctan2, tan, ones, arange, floor, + r_, atleast_1d, sqrt, exp, greater, cos, add, sin) + +# From splinemodule.c +from ._spline import cspline2d, sepfir2d +from ._signaltools import lfilter, sosfilt, lfiltic + +from scipy.interpolate import BSpline + +__all__ = ['spline_filter', 'gauss_spline', + 'cspline1d', 'qspline1d', 'cspline1d_eval', 'qspline1d_eval'] + + +def spline_filter(Iin, lmbda=5.0): + """Smoothing spline (cubic) filtering of a rank-2 array. + + Filter an input data set, `Iin`, using a (cubic) smoothing spline of + fall-off `lmbda`. + + Parameters + ---------- + Iin : array_like + input data set + lmbda : float, optional + spline smooghing fall-off value, default is `5.0`. + + Returns + ------- + res : ndarray + filtered input data + + Examples + -------- + We can filter an multi dimensional signal (ex: 2D image) using cubic + B-spline filter: + + >>> import numpy as np + >>> from scipy.signal import spline_filter + >>> import matplotlib.pyplot as plt + >>> orig_img = np.eye(20) # create an image + >>> orig_img[10, :] = 1.0 + >>> sp_filter = spline_filter(orig_img, lmbda=0.1) + >>> f, ax = plt.subplots(1, 2, sharex=True) + >>> for ind, data in enumerate([[orig_img, "original image"], + ... [sp_filter, "spline filter"]]): + ... ax[ind].imshow(data[0], cmap='gray_r') + ... ax[ind].set_title(data[1]) + >>> plt.tight_layout() + >>> plt.show() + + """ + intype = Iin.dtype.char + hcol = array([1.0, 4.0, 1.0], 'f') / 6.0 + if intype in ['F', 'D']: + Iin = Iin.astype('F') + ckr = cspline2d(Iin.real, lmbda) + cki = cspline2d(Iin.imag, lmbda) + outr = sepfir2d(ckr, hcol, hcol) + outi = sepfir2d(cki, hcol, hcol) + out = (outr + 1j * outi).astype(intype) + elif intype in ['f', 'd']: + ckr = cspline2d(Iin, lmbda) + out = sepfir2d(ckr, hcol, hcol) + out = out.astype(intype) + else: + raise TypeError("Invalid data type for Iin") + return out + + +_splinefunc_cache = {} + + +def gauss_spline(x, n): + r"""Gaussian approximation to B-spline basis function of order n. + + Parameters + ---------- + x : array_like + a knot vector + n : int + The order of the spline. Must be non-negative, i.e., n >= 0 + + Returns + ------- + res : ndarray + B-spline basis function values approximated by a zero-mean Gaussian + function. + + Notes + ----- + The B-spline basis function can be approximated well by a zero-mean + Gaussian function with standard-deviation equal to :math:`\sigma=(n+1)/12` + for large `n` : + + .. math:: \frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma}) + + References + ---------- + .. [1] Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen + F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In: + Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational + Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer + Science, vol 4485. Springer, Berlin, Heidelberg + .. [2] http://folk.uio.no/inf3330/scripting/doc/python/SciPy/tutorial/old/node24.html + + Examples + -------- + We can calculate B-Spline basis functions approximated by a gaussian + distribution: + + >>> import numpy as np + >>> from scipy.signal import gauss_spline + >>> knots = np.array([-1.0, 0.0, -1.0]) + >>> gauss_spline(knots, 3) + array([0.15418033, 0.6909883, 0.15418033]) # may vary + + """ + x = asarray(x) + signsq = (n + 1) / 12.0 + return 1 / sqrt(2 * pi * signsq) * exp(-x ** 2 / 2 / signsq) + + +def _cubic(x): + x = asarray(x, dtype=float) + b = BSpline.basis_element([-2, -1, 0, 1, 2], extrapolate=False) + out = b(x) + out[(x < -2) | (x > 2)] = 0 + return out + + +def _quadratic(x): + x = abs(asarray(x, dtype=float)) + b = BSpline.basis_element([-1.5, -0.5, 0.5, 1.5], extrapolate=False) + out = b(x) + out[(x < -1.5) | (x > 1.5)] = 0 + return out + + +def _coeff_smooth(lam): + xi = 1 - 96 * lam + 24 * lam * sqrt(3 + 144 * lam) + omeg = arctan2(sqrt(144 * lam - 1), sqrt(xi)) + rho = (24 * lam - 1 - sqrt(xi)) / (24 * lam) + rho = rho * sqrt((48 * lam + 24 * lam * sqrt(3 + 144 * lam)) / xi) + return rho, omeg + + +def _hc(k, cs, rho, omega): + return (cs / sin(omega) * (rho ** k) * sin(omega * (k + 1)) * + greater(k, -1)) + + +def _hs(k, cs, rho, omega): + c0 = (cs * cs * (1 + rho * rho) / (1 - rho * rho) / + (1 - 2 * rho * rho * cos(2 * omega) + rho ** 4)) + gamma = (1 - rho * rho) / (1 + rho * rho) / tan(omega) + ak = abs(k) + return c0 * rho ** ak * (cos(omega * ak) + gamma * sin(omega * ak)) + + +def _cubic_smooth_coeff(signal, lamb): + rho, omega = _coeff_smooth(lamb) + cs = 1 - 2 * rho * cos(omega) + rho * rho + K = len(signal) + k = arange(K) + + zi_2 = (_hc(0, cs, rho, omega) * signal[0] + + add.reduce(_hc(k + 1, cs, rho, omega) * signal)) + zi_1 = (_hc(0, cs, rho, omega) * signal[0] + + _hc(1, cs, rho, omega) * signal[1] + + add.reduce(_hc(k + 2, cs, rho, omega) * signal)) + + # Forward filter: + # for n in range(2, K): + # yp[n] = (cs * signal[n] + 2 * rho * cos(omega) * yp[n - 1] - + # rho * rho * yp[n - 2]) + zi = lfiltic(cs, r_[1, -2 * rho * cos(omega), rho * rho], r_[zi_1, zi_2]) + zi = zi.reshape(1, -1) + + sos = r_[cs, 0, 0, 1, -2 * rho * cos(omega), rho * rho] + sos = sos.reshape(1, -1) + + yp, _ = sosfilt(sos, signal[2:], zi=zi) + yp = r_[zi_2, zi_1, yp] + + # Reverse filter: + # for n in range(K - 3, -1, -1): + # y[n] = (cs * yp[n] + 2 * rho * cos(omega) * y[n + 1] - + # rho * rho * y[n + 2]) + + zi_2 = add.reduce((_hs(k, cs, rho, omega) + + _hs(k + 1, cs, rho, omega)) * signal[::-1]) + zi_1 = add.reduce((_hs(k - 1, cs, rho, omega) + + _hs(k + 2, cs, rho, omega)) * signal[::-1]) + + zi = lfiltic(cs, r_[1, -2 * rho * cos(omega), rho * rho], r_[zi_1, zi_2]) + zi = zi.reshape(1, -1) + y, _ = sosfilt(sos, yp[-3::-1], zi=zi) + y = r_[y[::-1], zi_1, zi_2] + return y + + +def _cubic_coeff(signal): + zi = -2 + sqrt(3) + K = len(signal) + powers = zi ** arange(K) + + if K == 1: + yplus = signal[0] + zi * add.reduce(powers * signal) + output = zi / (zi - 1) * yplus + return atleast_1d(output) + + # Forward filter: + # yplus[0] = signal[0] + zi * add.reduce(powers * signal) + # for k in range(1, K): + # yplus[k] = signal[k] + zi * yplus[k - 1] + + state = lfiltic(1, r_[1, -zi], atleast_1d(add.reduce(powers * signal))) + + b = ones(1) + a = r_[1, -zi] + yplus, _ = lfilter(b, a, signal, zi=state) + + # Reverse filter: + # output[K - 1] = zi / (zi - 1) * yplus[K - 1] + # for k in range(K - 2, -1, -1): + # output[k] = zi * (output[k + 1] - yplus[k]) + out_last = zi / (zi - 1) * yplus[K - 1] + state = lfiltic(-zi, r_[1, -zi], atleast_1d(out_last)) + + b = asarray([-zi]) + output, _ = lfilter(b, a, yplus[-2::-1], zi=state) + output = r_[output[::-1], out_last] + return output * 6.0 + + +def _quadratic_coeff(signal): + zi = -3 + 2 * sqrt(2.0) + K = len(signal) + powers = zi ** arange(K) + + if K == 1: + yplus = signal[0] + zi * add.reduce(powers * signal) + output = zi / (zi - 1) * yplus + return atleast_1d(output) + + # Forward filter: + # yplus[0] = signal[0] + zi * add.reduce(powers * signal) + # for k in range(1, K): + # yplus[k] = signal[k] + zi * yplus[k - 1] + + state = lfiltic(1, r_[1, -zi], atleast_1d(add.reduce(powers * signal))) + + b = ones(1) + a = r_[1, -zi] + yplus, _ = lfilter(b, a, signal, zi=state) + + # Reverse filter: + # output[K - 1] = zi / (zi - 1) * yplus[K - 1] + # for k in range(K - 2, -1, -1): + # output[k] = zi * (output[k + 1] - yplus[k]) + out_last = zi / (zi - 1) * yplus[K - 1] + state = lfiltic(-zi, r_[1, -zi], atleast_1d(out_last)) + + b = asarray([-zi]) + output, _ = lfilter(b, a, yplus[-2::-1], zi=state) + output = r_[output[::-1], out_last] + return output * 8.0 + + +def cspline1d(signal, lamb=0.0): + """ + Compute cubic spline coefficients for rank-1 array. + + Find the cubic spline coefficients for a 1-D signal assuming + mirror-symmetric boundary conditions. To obtain the signal back from the + spline representation mirror-symmetric-convolve these coefficients with a + length 3 FIR window [1.0, 4.0, 1.0]/ 6.0 . + + Parameters + ---------- + signal : ndarray + A rank-1 array representing samples of a signal. + lamb : float, optional + Smoothing coefficient, default is 0.0. + + Returns + ------- + c : ndarray + Cubic spline coefficients. + + See Also + -------- + cspline1d_eval : Evaluate a cubic spline at the new set of points. + + Examples + -------- + We can filter a signal to reduce and smooth out high-frequency noise with + a cubic spline: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import cspline1d, cspline1d_eval + >>> rng = np.random.default_rng() + >>> sig = np.repeat([0., 1., 0.], 100) + >>> sig += rng.standard_normal(len(sig))*0.05 # add noise + >>> time = np.linspace(0, len(sig)) + >>> filtered = cspline1d_eval(cspline1d(sig), time) + >>> plt.plot(sig, label="signal") + >>> plt.plot(time, filtered, label="filtered") + >>> plt.legend() + >>> plt.show() + + """ + if lamb != 0.0: + return _cubic_smooth_coeff(signal, lamb) + else: + return _cubic_coeff(signal) + + +def qspline1d(signal, lamb=0.0): + """Compute quadratic spline coefficients for rank-1 array. + + Parameters + ---------- + signal : ndarray + A rank-1 array representing samples of a signal. + lamb : float, optional + Smoothing coefficient (must be zero for now). + + Returns + ------- + c : ndarray + Quadratic spline coefficients. + + See Also + -------- + qspline1d_eval : Evaluate a quadratic spline at the new set of points. + + Notes + ----- + Find the quadratic spline coefficients for a 1-D signal assuming + mirror-symmetric boundary conditions. To obtain the signal back from the + spline representation mirror-symmetric-convolve these coefficients with a + length 3 FIR window [1.0, 6.0, 1.0]/ 8.0 . + + Examples + -------- + We can filter a signal to reduce and smooth out high-frequency noise with + a quadratic spline: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import qspline1d, qspline1d_eval + >>> rng = np.random.default_rng() + >>> sig = np.repeat([0., 1., 0.], 100) + >>> sig += rng.standard_normal(len(sig))*0.05 # add noise + >>> time = np.linspace(0, len(sig)) + >>> filtered = qspline1d_eval(qspline1d(sig), time) + >>> plt.plot(sig, label="signal") + >>> plt.plot(time, filtered, label="filtered") + >>> plt.legend() + >>> plt.show() + + """ + if lamb != 0.0: + raise ValueError("Smoothing quadratic splines not supported yet.") + else: + return _quadratic_coeff(signal) + + +def cspline1d_eval(cj, newx, dx=1.0, x0=0): + """Evaluate a cubic spline at the new set of points. + + `dx` is the old sample-spacing while `x0` was the old origin. In + other-words the old-sample points (knot-points) for which the `cj` + represent spline coefficients were at equally-spaced points of: + + oldx = x0 + j*dx j=0...N-1, with N=len(cj) + + Edges are handled using mirror-symmetric boundary conditions. + + Parameters + ---------- + cj : ndarray + cublic spline coefficients + newx : ndarray + New set of points. + dx : float, optional + Old sample-spacing, the default value is 1.0. + x0 : int, optional + Old origin, the default value is 0. + + Returns + ------- + res : ndarray + Evaluated a cubic spline points. + + See Also + -------- + cspline1d : Compute cubic spline coefficients for rank-1 array. + + Examples + -------- + We can filter a signal to reduce and smooth out high-frequency noise with + a cubic spline: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import cspline1d, cspline1d_eval + >>> rng = np.random.default_rng() + >>> sig = np.repeat([0., 1., 0.], 100) + >>> sig += rng.standard_normal(len(sig))*0.05 # add noise + >>> time = np.linspace(0, len(sig)) + >>> filtered = cspline1d_eval(cspline1d(sig), time) + >>> plt.plot(sig, label="signal") + >>> plt.plot(time, filtered, label="filtered") + >>> plt.legend() + >>> plt.show() + + """ + newx = (asarray(newx) - x0) / float(dx) + res = zeros_like(newx, dtype=cj.dtype) + if res.size == 0: + return res + N = len(cj) + cond1 = newx < 0 + cond2 = newx > (N - 1) + cond3 = ~(cond1 | cond2) + # handle general mirror-symmetry + res[cond1] = cspline1d_eval(cj, -newx[cond1]) + res[cond2] = cspline1d_eval(cj, 2 * (N - 1) - newx[cond2]) + newx = newx[cond3] + if newx.size == 0: + return res + result = zeros_like(newx, dtype=cj.dtype) + jlower = floor(newx - 2).astype(int) + 1 + for i in range(4): + thisj = jlower + i + indj = thisj.clip(0, N - 1) # handle edge cases + result += cj[indj] * _cubic(newx - thisj) + res[cond3] = result + return res + + +def qspline1d_eval(cj, newx, dx=1.0, x0=0): + """Evaluate a quadratic spline at the new set of points. + + Parameters + ---------- + cj : ndarray + Quadratic spline coefficients + newx : ndarray + New set of points. + dx : float, optional + Old sample-spacing, the default value is 1.0. + x0 : int, optional + Old origin, the default value is 0. + + Returns + ------- + res : ndarray + Evaluated a quadratic spline points. + + See Also + -------- + qspline1d : Compute quadratic spline coefficients for rank-1 array. + + Notes + ----- + `dx` is the old sample-spacing while `x0` was the old origin. In + other-words the old-sample points (knot-points) for which the `cj` + represent spline coefficients were at equally-spaced points of:: + + oldx = x0 + j*dx j=0...N-1, with N=len(cj) + + Edges are handled using mirror-symmetric boundary conditions. + + Examples + -------- + We can filter a signal to reduce and smooth out high-frequency noise with + a quadratic spline: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import qspline1d, qspline1d_eval + >>> rng = np.random.default_rng() + >>> sig = np.repeat([0., 1., 0.], 100) + >>> sig += rng.standard_normal(len(sig))*0.05 # add noise + >>> time = np.linspace(0, len(sig)) + >>> filtered = qspline1d_eval(qspline1d(sig), time) + >>> plt.plot(sig, label="signal") + >>> plt.plot(time, filtered, label="filtered") + >>> plt.legend() + >>> plt.show() + + """ + newx = (asarray(newx) - x0) / dx + res = zeros_like(newx) + if res.size == 0: + return res + N = len(cj) + cond1 = newx < 0 + cond2 = newx > (N - 1) + cond3 = ~(cond1 | cond2) + # handle general mirror-symmetry + res[cond1] = qspline1d_eval(cj, -newx[cond1]) + res[cond2] = qspline1d_eval(cj, 2 * (N - 1) - newx[cond2]) + newx = newx[cond3] + if newx.size == 0: + return res + result = zeros_like(newx) + jlower = floor(newx - 1.5).astype(int) + 1 + for i in range(3): + thisj = jlower + i + indj = thisj.clip(0, N - 1) # handle edge cases + result += cj[indj] * _quadratic(newx - thisj) + res[cond3] = result + return res diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq.py new file mode 100644 index 0000000000000000000000000000000000000000..4d64beaca86d1da50b563668679b6fc52c954ab0 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq.py @@ -0,0 +1,139 @@ +# Author: Eric Larson +# 2014 + +"""Tools for MLS generation""" + +import numpy as np + +from ._max_len_seq_inner import _max_len_seq_inner + +__all__ = ['max_len_seq'] + + +# These are definitions of linear shift register taps for use in max_len_seq() +_mls_taps = {2: [1], 3: [2], 4: [3], 5: [3], 6: [5], 7: [6], 8: [7, 6, 1], + 9: [5], 10: [7], 11: [9], 12: [11, 10, 4], 13: [12, 11, 8], + 14: [13, 12, 2], 15: [14], 16: [15, 13, 4], 17: [14], + 18: [11], 19: [18, 17, 14], 20: [17], 21: [19], 22: [21], + 23: [18], 24: [23, 22, 17], 25: [22], 26: [25, 24, 20], + 27: [26, 25, 22], 28: [25], 29: [27], 30: [29, 28, 7], + 31: [28], 32: [31, 30, 10]} + +def max_len_seq(nbits, state=None, length=None, taps=None): + """ + Maximum length sequence (MLS) generator. + + Parameters + ---------- + nbits : int + Number of bits to use. Length of the resulting sequence will + be ``(2**nbits) - 1``. Note that generating long sequences + (e.g., greater than ``nbits == 16``) can take a long time. + state : array_like, optional + If array, must be of length ``nbits``, and will be cast to binary + (bool) representation. If None, a seed of ones will be used, + producing a repeatable representation. If ``state`` is all + zeros, an error is raised as this is invalid. Default: None. + length : int, optional + Number of samples to compute. If None, the entire length + ``(2**nbits) - 1`` is computed. + taps : array_like, optional + Polynomial taps to use (e.g., ``[7, 6, 1]`` for an 8-bit sequence). + If None, taps will be automatically selected (for up to + ``nbits == 32``). + + Returns + ------- + seq : array + Resulting MLS sequence of 0's and 1's. + state : array + The final state of the shift register. + + Notes + ----- + The algorithm for MLS generation is generically described in: + + https://en.wikipedia.org/wiki/Maximum_length_sequence + + The default values for taps are specifically taken from the first + option listed for each value of ``nbits`` in: + + https://web.archive.org/web/20181001062252/http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_feedback_shift_register_lfsr.htm + + .. versionadded:: 0.15.0 + + Examples + -------- + MLS uses binary convention: + + >>> from scipy.signal import max_len_seq + >>> max_len_seq(4)[0] + array([1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0], dtype=int8) + + MLS has a white spectrum (except for DC): + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from numpy.fft import fft, ifft, fftshift, fftfreq + >>> seq = max_len_seq(6)[0]*2-1 # +1 and -1 + >>> spec = fft(seq) + >>> N = len(seq) + >>> plt.plot(fftshift(fftfreq(N)), fftshift(np.abs(spec)), '.-') + >>> plt.margins(0.1, 0.1) + >>> plt.grid(True) + >>> plt.show() + + Circular autocorrelation of MLS is an impulse: + + >>> acorrcirc = ifft(spec * np.conj(spec)).real + >>> plt.figure() + >>> plt.plot(np.arange(-N/2+1, N/2+1), fftshift(acorrcirc), '.-') + >>> plt.margins(0.1, 0.1) + >>> plt.grid(True) + >>> plt.show() + + Linear autocorrelation of MLS is approximately an impulse: + + >>> acorr = np.correlate(seq, seq, 'full') + >>> plt.figure() + >>> plt.plot(np.arange(-N+1, N), acorr, '.-') + >>> plt.margins(0.1, 0.1) + >>> plt.grid(True) + >>> plt.show() + + """ + taps_dtype = np.int32 if np.intp().itemsize == 4 else np.int64 + if taps is None: + if nbits not in _mls_taps: + known_taps = np.array(list(_mls_taps.keys())) + raise ValueError(f'nbits must be between {known_taps.min()} and ' + f'{known_taps.max()} if taps is None') + taps = np.array(_mls_taps[nbits], taps_dtype) + else: + taps = np.unique(np.array(taps, taps_dtype))[::-1] + if np.any(taps < 0) or np.any(taps > nbits) or taps.size < 1: + raise ValueError('taps must be non-empty with values between ' + 'zero and nbits (inclusive)') + taps = np.array(taps) # needed for Cython and Pythran + n_max = (2**nbits) - 1 + if length is None: + length = n_max + else: + length = int(length) + if length < 0: + raise ValueError('length must be greater than or equal to 0') + # We use int8 instead of bool here because NumPy arrays of bools + # don't seem to work nicely with Cython + if state is None: + state = np.ones(nbits, dtype=np.int8, order='c') + else: + # makes a copy if need be, ensuring it's 0's and 1's + state = np.array(state, dtype=bool, order='c').astype(np.int8) + if state.ndim != 1 or state.size != nbits: + raise ValueError('state must be a 1-D array of size nbits') + if np.all(state == 0): + raise ValueError('state must not be all zeros') + + seq = np.empty(length, dtype=np.int8, order='c') + state = _max_len_seq_inner(taps, state, nbits, length, seq) + return seq, state diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq_inner.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq_inner.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..865e1c7963bb07aa3ba549f2231d44c7f795ca79 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_max_len_seq_inner.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_short_time_fft.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_short_time_fft.py new file mode 100644 index 0000000000000000000000000000000000000000..a43545957105a7ff7088dca49dbb4ea7b717d9eb --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_short_time_fft.py @@ -0,0 +1,1676 @@ +"""Implementation of an FFT-based Short-time Fourier Transform. """ + +# Implementation Notes for this file (as of 2023-07) +# -------------------------------------------------- +# * MyPy version 1.1.1 does not seem to support decorated property methods +# properly. Hence, applying ``@property`` to methods decorated with `@cache`` +# (as tried with the ``lower_border_end`` method) causes a mypy error when +# accessing it as an index (e.g., ``SFT.lower_border_end[0]``). +# * Since the method `stft` and `istft` have identical names as the legacy +# functions in the signal module, referencing them as HTML link in the +# docstrings has to be done by an explicit `~ShortTimeFFT.stft` instead of an +# ambiguous `stft` (The ``~`` hides the class / module name). +# * The HTML documentation currently renders each method/property on a separate +# page without reference to the parent class. Thus, a link to `ShortTimeFFT` +# was added to the "See Also" section of each method/property. These links +# can be removed, when SciPy updates ``pydata-sphinx-theme`` to >= 0.13.3 +# (currently 0.9). Consult Issue 18512 and PR 16660 for further details. +# + +# Provides typing union operator ``|`` in Python 3.9: +from __future__ import annotations +# Linter does not allow to import ``Generator`` from ``typing`` module: +from collections.abc import Generator +from functools import cache, lru_cache, partial +from typing import Callable, get_args, Literal + +import numpy as np + +import scipy.fft as fft_lib +from scipy.signal import detrend +from scipy.signal.windows import get_window + +__all__ = ['ShortTimeFFT'] + + +#: Allowed values for parameter `padding` of method `ShortTimeFFT.stft()`: +PAD_TYPE = Literal['zeros', 'edge', 'even', 'odd'] + +#: Allowed values for property `ShortTimeFFT.fft_mode`: +FFT_MODE_TYPE = Literal['twosided', 'centered', 'onesided', 'onesided2X'] + + +def _calc_dual_canonical_window(win: np.ndarray, hop: int) -> np.ndarray: + """Calculate canonical dual window for 1d window `win` and a time step + of `hop` samples. + + A ``ValueError`` is raised, if the inversion fails. + + This is a separate function not a method, since it is also used in the + class method ``ShortTimeFFT.from_dual()``. + """ + if hop > len(win): + raise ValueError(f"{hop=} is larger than window length of {len(win)}" + + " => STFT not invertible!") + if issubclass(win.dtype.type, np.integer): + raise ValueError("Parameter 'win' cannot be of integer type, but " + + f"{win.dtype=} => STFT not invertible!") + # The calculation of `relative_resolution` does not work for ints. + # Furthermore, `win / DD` casts the integers away, thus an implicit + # cast is avoided, which can always cause confusion when using 32-Bit + # floats. + + w2 = win.real**2 + win.imag**2 # win*win.conj() does not ensure w2 is real + DD = w2.copy() + for k_ in range(hop, len(win), hop): + DD[k_:] += w2[:-k_] + DD[:-k_] += w2[k_:] + + # check DD > 0: + relative_resolution = np.finfo(win.dtype).resolution * max(DD) + if not np.all(DD >= relative_resolution): + raise ValueError("Short-time Fourier Transform not invertible!") + + return win / DD + + +# noinspection PyShadowingNames +class ShortTimeFFT: + r"""Provide a parametrized discrete Short-time Fourier transform (stft) + and its inverse (istft). + + .. currentmodule:: scipy.signal.ShortTimeFFT + + The `~ShortTimeFFT.stft` calculates sequential FFTs by sliding a + window (`win`) over an input signal by `hop` increments. It can be used to + quantify the change of the spectrum over time. + + The `~ShortTimeFFT.stft` is represented by a complex-valued matrix S[q,p] + where the p-th column represents an FFT with the window centered at the + time t[p] = p * `delta_t` = p * `hop` * `T` where `T` is the sampling + interval of the input signal. The q-th row represents the values at the + frequency f[q] = q * `delta_f` with `delta_f` = 1 / (`mfft` * `T`) being + the bin width of the FFT. + + The inverse STFT `~ShortTimeFFT.istft` is calculated by reversing the steps + of the STFT: Take the IFFT of the p-th slice of S[q,p] and multiply the + result with the so-called dual window (see `dual_win`). Shift the result by + p * `delta_t` and add the result to previous shifted results to reconstruct + the signal. If only the dual window is known and the STFT is invertible, + `from_dual` can be used to instantiate this class. + + Due to the convention of time t = 0 being at the first sample of the input + signal, the STFT values typically have negative time slots. Hence, + negative indexes like `p_min` or `k_min` do not indicate counting + backwards from an array's end like in standard Python indexing but being + left of t = 0. + + More detailed information can be found in the :ref:`tutorial_stft` section + of the :ref:`user_guide`. + + Note that all parameters of the initializer, except `scale_to` (which uses + `scaling`) have identical named attributes. + + Parameters + ---------- + win : np.ndarray + The window must be a real- or complex-valued 1d array. + hop : int + The increment in samples, by which the window is shifted in each step. + fs : float + Sampling frequency of input signal and window. Its relation to the + sampling interval `T` is ``T = 1 / fs``. + fft_mode : 'twosided', 'centered', 'onesided', 'onesided2X' + Mode of FFT to be used (default 'onesided'). + See property `fft_mode` for details. + mfft: int | None + Length of the FFT used, if a zero padded FFT is desired. + If ``None`` (default), the length of the window `win` is used. + dual_win : np.ndarray | None + The dual window of `win`. If set to ``None``, it is calculated if + needed. + scale_to : 'magnitude', 'psd' | None + If not ``None`` (default) the window function is scaled, so each STFT + column represents either a 'magnitude' or a power spectral density + ('psd') spectrum. This parameter sets the property `scaling` to the + same value. See method `scale_to` for details. + phase_shift : int | None + If set, add a linear phase `phase_shift` / `mfft` * `f` to each + frequency `f`. The default value 0 ensures that there is no phase shift + on the zeroth slice (in which t=0 is centered). See property + `phase_shift` for more details. + + Examples + -------- + The following example shows the magnitude of the STFT of a sine with + varying frequency :math:`f_i(t)` (marked by a red dashed line in the plot): + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import ShortTimeFFT + >>> from scipy.signal.windows import gaussian + ... + >>> T_x, N = 1 / 20, 1000 # 20 Hz sampling rate for 50 s signal + >>> t_x = np.arange(N) * T_x # time indexes for signal + >>> f_i = 1 * np.arctan((t_x - t_x[N // 2]) / 2) + 5 # varying frequency + >>> x = np.sin(2*np.pi*np.cumsum(f_i)*T_x) # the signal + + The utilized Gaussian window is 50 samples or 2.5 s long. The parameter + ``mfft=200`` in `ShortTimeFFT` causes the spectrum to be oversampled + by a factor of 4: + + >>> g_std = 8 # standard deviation for Gaussian window in samples + >>> w = gaussian(50, std=g_std, sym=True) # symmetric Gaussian window + >>> SFT = ShortTimeFFT(w, hop=10, fs=1/T_x, mfft=200, scale_to='magnitude') + >>> Sx = SFT.stft(x) # perform the STFT + + In the plot, the time extent of the signal `x` is marked by vertical dashed + lines. Note that the SFT produces values outside the time range of `x`. The + shaded areas on the left and the right indicate border effects caused + by the window slices in that area not fully being inside time range of + `x`: + + >>> fig1, ax1 = plt.subplots(figsize=(6., 4.)) # enlarge plot a bit + >>> t_lo, t_hi = SFT.extent(N)[:2] # time range of plot + >>> ax1.set_title(rf"STFT ({SFT.m_num*SFT.T:g}$\,s$ Gaussian window, " + + ... rf"$\sigma_t={g_std*SFT.T}\,$s)") + >>> ax1.set(xlabel=f"Time $t$ in seconds ({SFT.p_num(N)} slices, " + + ... rf"$\Delta t = {SFT.delta_t:g}\,$s)", + ... ylabel=f"Freq. $f$ in Hz ({SFT.f_pts} bins, " + + ... rf"$\Delta f = {SFT.delta_f:g}\,$Hz)", + ... xlim=(t_lo, t_hi)) + ... + >>> im1 = ax1.imshow(abs(Sx), origin='lower', aspect='auto', + ... extent=SFT.extent(N), cmap='viridis') + >>> ax1.plot(t_x, f_i, 'r--', alpha=.5, label='$f_i(t)$') + >>> fig1.colorbar(im1, label="Magnitude $|S_x(t, f)|$") + ... + >>> # Shade areas where window slices stick out to the side: + >>> for t0_, t1_ in [(t_lo, SFT.lower_border_end[0] * SFT.T), + ... (SFT.upper_border_begin(N)[0] * SFT.T, t_hi)]: + ... ax1.axvspan(t0_, t1_, color='w', linewidth=0, alpha=.2) + >>> for t_ in [0, N * SFT.T]: # mark signal borders with vertical line: + ... ax1.axvline(t_, color='y', linestyle='--', alpha=0.5) + >>> ax1.legend() + >>> fig1.tight_layout() + >>> plt.show() + + Reconstructing the signal with the `~ShortTimeFFT.istft` is + straightforward, but note that the length of `x1` should be specified, + since the SFT length increases in `hop` steps: + + >>> SFT.invertible # check if invertible + True + >>> x1 = SFT.istft(Sx, k1=N) + >>> np.allclose(x, x1) + True + + It is possible to calculate the SFT of signal parts: + + >>> p_q = SFT.nearest_k_p(N // 2) + >>> Sx0 = SFT.stft(x[:p_q]) + >>> Sx1 = SFT.stft(x[p_q:]) + + When assembling sequential STFT parts together, the overlap needs to be + considered: + + >>> p0_ub = SFT.upper_border_begin(p_q)[1] - SFT.p_min + >>> p1_le = SFT.lower_border_end[1] - SFT.p_min + >>> Sx01 = np.hstack((Sx0[:, :p0_ub], + ... Sx0[:, p0_ub:] + Sx1[:, :p1_le], + ... Sx1[:, p1_le:])) + >>> np.allclose(Sx01, Sx) # Compare with SFT of complete signal + True + + It is also possible to calculate the `itsft` for signal parts: + + >>> y_p = SFT.istft(Sx, N//3, N//2) + >>> np.allclose(y_p, x[N//3:N//2]) + True + + """ + # immutable attributes (only have getters but no setters): + _win: np.ndarray # window + _dual_win: np.ndarray | None = None # canonical dual window + _hop: int # Step of STFT in number of samples + + # mutable attributes: + _fs: float # sampling frequency of input signal and window + _fft_mode: FFT_MODE_TYPE = 'onesided' # Mode of FFT to use + _mfft: int # length of FFT used - defaults to len(win) + _scaling: Literal['magnitude', 'psd'] | None = None # Scaling of _win + _phase_shift: int | None # amount to shift phase of FFT in samples + + # attributes for caching calculated values: + _fac_mag: float | None = None + _fac_psd: float | None = None + _lower_border_end: tuple[int, int] | None = None + + def __init__(self, win: np.ndarray, hop: int, fs: float, *, + fft_mode: FFT_MODE_TYPE = 'onesided', + mfft: int | None = None, + dual_win: np.ndarray | None = None, + scale_to: Literal['magnitude', 'psd'] | None = None, + phase_shift: int | None = 0): + if not (win.ndim == 1 and win.size > 0): + raise ValueError(f"Parameter win must be 1d, but {win.shape=}!") + if not all(np.isfinite(win)): + raise ValueError("Parameter win must have finite entries!") + if not (hop >= 1 and isinstance(hop, int)): + raise ValueError(f"Parameter {hop=} is not an integer >= 1!") + self._win, self._hop, self.fs = win, hop, fs + + self.mfft = len(win) if mfft is None else mfft + + if dual_win is not None: + if dual_win.shape != win.shape: + raise ValueError(f"{dual_win.shape=} must equal {win.shape=}!") + if not all(np.isfinite(dual_win)): + raise ValueError("Parameter dual_win must be a finite array!") + self._dual_win = dual_win # needs to be set before scaling + + if scale_to is not None: # needs to be set before fft_mode + self.scale_to(scale_to) + + self.fft_mode, self.phase_shift = fft_mode, phase_shift + + @classmethod + def from_dual(cls, dual_win: np.ndarray, hop: int, fs: float, *, + fft_mode: FFT_MODE_TYPE = 'onesided', + mfft: int | None = None, + scale_to: Literal['magnitude', 'psd'] | None = None, + phase_shift: int | None = 0): + r"""Instantiate a `ShortTimeFFT` by only providing a dual window. + + If an STFT is invertible, it is possible to calculate the window `win` + from a given dual window `dual_win`. All other parameters have the + same meaning as in the initializer of `ShortTimeFFT`. + + As explained in the :ref:`tutorial_stft` section of the + :ref:`user_guide`, an invertible STFT can be interpreted as series + expansion of time-shifted and frequency modulated dual windows. E.g., + the series coefficient S[q,p] belongs to the term, which shifted + `dual_win` by p * `delta_t` and multiplied it by + exp( 2 * j * pi * t * q * `delta_f`). + + + Examples + -------- + The following example discusses decomposing a signal into time- and + frequency-shifted Gaussians. A Gaussian with standard deviation of + one made up of 51 samples will be used: + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import ShortTimeFFT + >>> from scipy.signal.windows import gaussian + ... + >>> T, N = 0.1, 51 + >>> d_win = gaussian(N, std=1/T, sym=True) # symmetric Gaussian window + >>> t = T * (np.arange(N) - N//2) + ... + >>> fg1, ax1 = plt.subplots() + >>> ax1.set_title(r"Dual Window: Gaussian with $\sigma_t=1$") + >>> ax1.set(xlabel=f"Time $t$ in seconds ({N} samples, $T={T}$ s)", + ... xlim=(t[0], t[-1]), ylim=(0, 1.1*max(d_win))) + >>> ax1.plot(t, d_win, 'C0-') + + The following plot with the overlap of 41, 11 and 2 samples show how + the `hop` interval affects the shape of the window `win`: + + >>> fig2, axx = plt.subplots(3, 1, sharex='all') + ... + >>> axx[0].set_title(r"Windows for hop$\in\{10, 40, 49\}$") + >>> for c_, h_ in enumerate([10, 40, 49]): + ... SFT = ShortTimeFFT.from_dual(d_win, h_, 1/T) + ... axx[c_].plot(t + h_ * T, SFT.win, 'k--', alpha=.3, label=None) + ... axx[c_].plot(t - h_ * T, SFT.win, 'k:', alpha=.3, label=None) + ... axx[c_].plot(t, SFT.win, f'C{c_+1}', + ... label=r"$\Delta t=%0.1f\,$s" % SFT.delta_t) + ... axx[c_].set_ylim(0, 1.1*max(SFT.win)) + ... axx[c_].legend(loc='center') + >>> axx[-1].set(xlabel=f"Time $t$ in seconds ({N} samples, $T={T}$ s)", + ... xlim=(t[0], t[-1])) + >>> plt.show() + + Beside the window `win` centered at t = 0 the previous (t = -`delta_t`) + and following window (t = `delta_t`) are depicted. It can be seen that + for small `hop` intervals, the window is compact and smooth, having a + good time-frequency concentration in the STFT. For the large `hop` + interval of 4.9 s, the window has small values around t = 0, which are + not covered by the overlap of the adjacent windows, which could lead to + numeric inaccuracies. Furthermore, the peaky shape at the beginning and + the end of the window points to a higher bandwidth, resulting in a + poorer time-frequency resolution of the STFT. + Hence, the choice of the `hop` interval will be a compromise between + a time-frequency resolution and memory requirements demanded by small + `hop` sizes. + + See Also + -------- + from_window: Create instance by wrapping `get_window`. + ShortTimeFFT: Create instance using standard initializer. + """ + win = _calc_dual_canonical_window(dual_win, hop) + return cls(win=win, hop=hop, fs=fs, fft_mode=fft_mode, mfft=mfft, + dual_win=dual_win, scale_to=scale_to, + phase_shift=phase_shift) + + @classmethod + def from_window(cls, win_param: str | tuple | float, + fs: float, nperseg: int, noverlap: int, *, + symmetric_win: bool = False, + fft_mode: FFT_MODE_TYPE = 'onesided', + mfft: int | None = None, + scale_to: Literal['magnitude', 'psd'] | None = None, + phase_shift: int | None = 0): + """Instantiate `ShortTimeFFT` by using `get_window`. + + The method `get_window` is used to create a window of length + `nperseg`. The parameter names `noverlap`, and `nperseg` are used here, + since they more inline with other classical STFT libraries. + + Parameters + ---------- + win_param: Union[str, tuple, float], + Parameters passed to `get_window`. For windows with no parameters, + it may be a string (e.g., ``'hann'``), for parametrized windows a + tuple, (e.g., ``('gaussian', 2.)``) or a single float specifying + the shape parameter of a kaiser window (i.e. ``4.`` and + ``('kaiser', 4.)`` are equal. See `get_window` for more details. + fs : float + Sampling frequency of input signal. Its relation to the + sampling interval `T` is ``T = 1 / fs``. + nperseg: int + Window length in samples, which corresponds to the `m_num`. + noverlap: int + Window overlap in samples. It relates to the `hop` increment by + ``hop = npsereg - noverlap``. + symmetric_win: bool + If ``True`` then a symmetric window is generated, else a periodic + window is generated (default). Though symmetric windows seem for + most applications to be more sensible, the default of a periodic + windows was chosen to correspond to the default of `get_window`. + fft_mode : 'twosided', 'centered', 'onesided', 'onesided2X' + Mode of FFT to be used (default 'onesided'). + See property `fft_mode` for details. + mfft: int | None + Length of the FFT used, if a zero padded FFT is desired. + If ``None`` (default), the length of the window `win` is used. + scale_to : 'magnitude', 'psd' | None + If not ``None`` (default) the window function is scaled, so each + STFT column represents either a 'magnitude' or a power spectral + density ('psd') spectrum. This parameter sets the property + `scaling` to the same value. See method `scale_to` for details. + phase_shift : int | None + If set, add a linear phase `phase_shift` / `mfft` * `f` to each + frequency `f`. The default value 0 ensures that there is no phase + shift on the zeroth slice (in which t=0 is centered). See property + `phase_shift` for more details. + + Examples + -------- + The following instances ``SFT0`` and ``SFT1`` are equivalent: + + >>> from scipy.signal import ShortTimeFFT, get_window + >>> nperseg = 9 # window length + >>> w = get_window(('gaussian', 2.), nperseg) + >>> fs = 128 # sampling frequency + >>> hop = 3 # increment of STFT time slice + >>> SFT0 = ShortTimeFFT(w, hop, fs=fs) + >>> SFT1 = ShortTimeFFT.from_window(('gaussian', 2.), fs, nperseg, + ... noverlap=nperseg-hop) + + See Also + -------- + scipy.signal.get_window: Return a window of a given length and type. + from_dual: Create instance using dual window. + ShortTimeFFT: Create instance using standard initializer. + """ + win = get_window(win_param, nperseg, fftbins=not symmetric_win) + return cls(win, hop=nperseg-noverlap, fs=fs, fft_mode=fft_mode, + mfft=mfft, scale_to=scale_to, phase_shift=phase_shift) + + @property + def win(self) -> np.ndarray: + """Window function as real- or complex-valued 1d array. + + This attribute is read only, since `dual_win` depends on it. + + See Also + -------- + dual_win: Canonical dual window. + m_num: Number of samples in window `win`. + m_num_mid: Center index of window `win`. + mfft: Length of input for the FFT used - may be larger than `m_num`. + hop: ime increment in signal samples for sliding window. + win: Window function as real- or complex-valued 1d array. + ShortTimeFFT: Class this property belongs to. + """ + return self._win + + @property + def hop(self) -> int: + """Time increment in signal samples for sliding window. + + This attribute is read only, since `dual_win` depends on it. + + See Also + -------- + delta_t: Time increment of STFT (``hop*T``) + m_num: Number of samples in window `win`. + m_num_mid: Center index of window `win`. + mfft: Length of input for the FFT used - may be larger than `m_num`. + T: Sampling interval of input signal and of the window. + win: Window function as real- or complex-valued 1d array. + ShortTimeFFT: Class this property belongs to. + """ + return self._hop + + @property + def T(self) -> float: + """Sampling interval of input signal and of the window. + + A ``ValueError`` is raised if it is set to a non-positive value. + + See Also + -------- + delta_t: Time increment of STFT (``hop*T``) + hop: Time increment in signal samples for sliding window. + fs: Sampling frequency (being ``1/T``) + t: Times of STFT for an input signal with `n` samples. + ShortTimeFFT: Class this property belongs to. + """ + return 1 / self._fs + + @T.setter + def T(self, v: float): + """Sampling interval of input signal and of the window. + + A ``ValueError`` is raised if it is set to a non-positive value. + """ + if not (v > 0): + raise ValueError(f"Sampling interval T={v} must be positive!") + self._fs = 1 / v + + @property + def fs(self) -> float: + """Sampling frequency of input signal and of the window. + + The sampling frequency is the inverse of the sampling interval `T`. + A ``ValueError`` is raised if it is set to a non-positive value. + + See Also + -------- + delta_t: Time increment of STFT (``hop*T``) + hop: Time increment in signal samples for sliding window. + T: Sampling interval of input signal and of the window (``1/fs``). + ShortTimeFFT: Class this property belongs to. + """ + return self._fs + + @fs.setter + def fs(self, v: float): + """Sampling frequency of input signal and of the window. + + The sampling frequency is the inverse of the sampling interval `T`. + A ``ValueError`` is raised if it is set to a non-positive value. + """ + if not (v > 0): + raise ValueError(f"Sampling frequency fs={v} must be positive!") + self._fs = v + + @property + def fft_mode(self) -> FFT_MODE_TYPE: + """Mode of utilized FFT ('twosided', 'centered', 'onesided' or + 'onesided2X'). + + It can have the following values: + + 'twosided': + Two-sided FFT, where values for the negative frequencies are in + upper half of the array. Corresponds to :func:`~scipy.fft.fft()`. + 'centered': + Two-sided FFT with the values being ordered along monotonically + increasing frequencies. Corresponds to applying + :func:`~scipy.fft.fftshift()` to :func:`~scipy.fft.fft()`. + 'onesided': + Calculates only values for non-negative frequency values. + Corresponds to :func:`~scipy.fft.rfft()`. + 'onesided2X': + Like `onesided`, but the non-zero frequencies are doubled if + `scaling` is set to 'magnitude' or multiplied by ``sqrt(2)`` if + set to 'psd'. If `scaling` is ``None``, setting `fft_mode` to + `onesided2X` is not allowed. + If the FFT length `mfft` is even, the last FFT value is not paired, + and thus it is not scaled. + + Note that `onesided` and `onesided2X` do not work for complex-valued signals or + complex-valued windows. Furthermore, the frequency values can be obtained by + reading the `f` property, and the number of samples by accessing the `f_pts` + property. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + f: Frequencies values of the STFT. + f_pts: Width of the frequency bins of the STFT. + onesided_fft: True if a one-sided FFT is used. + scaling: Normalization applied to the window function + ShortTimeFFT: Class this property belongs to. + """ + return self._fft_mode + + @fft_mode.setter + def fft_mode(self, t: FFT_MODE_TYPE): + """Set mode of FFT. + + Allowed values are 'twosided', 'centered', 'onesided', 'onesided2X'. + See the property `fft_mode` for more details. + """ + if t not in (fft_mode_types := get_args(FFT_MODE_TYPE)): + raise ValueError(f"fft_mode='{t}' not in {fft_mode_types}!") + + if t in {'onesided', 'onesided2X'} and np.iscomplexobj(self.win): + raise ValueError(f"One-sided spectra, i.e., fft_mode='{t}', " + + "are not allowed for complex-valued windows!") + + if t == 'onesided2X' and self.scaling is None: + raise ValueError(f"For scaling is None, fft_mode='{t}' is invalid!" + "Do scale_to('psd') or scale_to('magnitude')!") + self._fft_mode = t + + @property + def mfft(self) -> int: + """Length of input for the FFT used - may be larger than window + length `m_num`. + + If not set, `mfft` defaults to the window length `m_num`. + + See Also + -------- + f_pts: Number of points along the frequency axis. + f: Frequencies values of the STFT. + m_num: Number of samples in window `win`. + ShortTimeFFT: Class this property belongs to. + """ + return self._mfft + + @mfft.setter + def mfft(self, n_: int): + """Setter for the length of FFT utilized. + + See the property `mfft` for further details. + """ + if not (n_ >= self.m_num): + raise ValueError(f"Attribute mfft={n_} needs to be at least the " + + f"window length m_num={self.m_num}!") + self._mfft = n_ + + @property + def scaling(self) -> Literal['magnitude', 'psd'] | None: + """Normalization applied to the window function + ('magnitude', 'psd' or ``None``). + + If not ``None``, the FFTs can be either interpreted as a magnitude or + a power spectral density spectrum. + + The window function can be scaled by calling the `scale_to` method, + or it is set by the initializer parameter ``scale_to``. + + See Also + -------- + fac_magnitude: Scaling factor for to a magnitude spectrum. + fac_psd: Scaling factor for to a power spectral density spectrum. + fft_mode: Mode of utilized FFT + scale_to: Scale window to obtain 'magnitude' or 'psd' scaling. + ShortTimeFFT: Class this property belongs to. + """ + return self._scaling + + def scale_to(self, scaling: Literal['magnitude', 'psd']): + """Scale window to obtain 'magnitude' or 'psd' scaling for the STFT. + + The window of a 'magnitude' spectrum has an integral of one, i.e., unit + area for non-negative windows. This ensures that absolute the values of + spectrum does not change if the length of the window changes (given + the input signal is stationary). + + To represent the power spectral density ('psd') for varying length + windows the area of the absolute square of the window needs to be + unity. + + The `scaling` property shows the current scaling. The properties + `fac_magnitude` and `fac_psd` show the scaling factors required to + scale the STFT values to a magnitude or a psd spectrum. + + This method is called, if the initializer parameter `scale_to` is set. + + See Also + -------- + fac_magnitude: Scaling factor for to a magnitude spectrum. + fac_psd: Scaling factor for to a power spectral density spectrum. + fft_mode: Mode of utilized FFT + scaling: Normalization applied to the window function. + ShortTimeFFT: Class this method belongs to. + """ + if scaling not in (scaling_values := {'magnitude', 'psd'}): + raise ValueError(f"{scaling=} not in {scaling_values}!") + if self._scaling == scaling: # do nothing + return + + s_fac = self.fac_psd if scaling == 'psd' else self.fac_magnitude + self._win = self._win * s_fac + if self._dual_win is not None: + self._dual_win = self._dual_win / s_fac + self._fac_mag, self._fac_psd = None, None # reset scaling factors + self._scaling = scaling + + @property + def phase_shift(self) -> int | None: + """If set, add linear phase `phase_shift` / `mfft` * `f` to each FFT + slice of frequency `f`. + + Shifting (more precisely `rolling`) an `mfft`-point FFT input by + `phase_shift` samples results in a multiplication of the output by + ``np.exp(2j*np.pi*q*phase_shift/mfft)`` at the frequency q * `delta_f`. + + The default value 0 ensures that there is no phase shift on the + zeroth slice (in which t=0 is centered). + No phase shift (``phase_shift is None``) is equivalent to + ``phase_shift = -mfft//2``. In this case slices are not shifted + before calculating the FFT. + + The absolute value of `phase_shift` is limited to be less than `mfft`. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + f: Frequencies values of the STFT. + mfft: Length of input for the FFT used + ShortTimeFFT: Class this property belongs to. + """ + return self._phase_shift + + @phase_shift.setter + def phase_shift(self, v: int | None): + """The absolute value of the phase shift needs to be less than mfft + samples. + + See the `phase_shift` getter method for more details. + """ + if v is None: + self._phase_shift = v + return + if not isinstance(v, int): + raise ValueError(f"phase_shift={v} has the unit samples. Hence " + + "it needs to be an int or it may be None!") + if not (-self.mfft < v < self.mfft): + raise ValueError("-mfft < phase_shift < mfft does not hold " + + f"for mfft={self.mfft}, phase_shift={v}!") + self._phase_shift = v + + def _x_slices(self, x: np.ndarray, k_off: int, p0: int, p1: int, + padding: PAD_TYPE) -> Generator[np.ndarray, None, None]: + """Generate signal slices along last axis of `x`. + + This method is only used by `stft_detrend`. The parameters are + described in `~ShortTimeFFT.stft`. + """ + if padding not in (padding_types := get_args(PAD_TYPE)): + raise ValueError(f"Parameter {padding=} not in {padding_types}!") + pad_kws: dict[str, dict] = { # possible keywords to pass to np.pad: + 'zeros': dict(mode='constant', constant_values=(0, 0)), + 'edge': dict(mode='edge'), + 'even': dict(mode='reflect', reflect_type='even'), + 'odd': dict(mode='reflect', reflect_type='odd'), + } # typing of pad_kws is needed to make mypy happy + + n, n1 = x.shape[-1], (p1 - p0) * self.hop + k0 = p0 * self.hop - self.m_num_mid + k_off # start sample + k1 = k0 + n1 + self.m_num # end sample + + i0, i1 = max(k0, 0), min(k1, n) # indexes to shorten x + # dimensions for padding x: + pad_width = [(0, 0)] * (x.ndim-1) + [(-min(k0, 0), max(k1 - n, 0))] + + x1 = np.pad(x[..., i0:i1], pad_width, **pad_kws[padding]) + for k_ in range(0, n1, self.hop): + yield x1[..., k_:k_ + self.m_num] + + def stft(self, x: np.ndarray, p0: int | None = None, + p1: int | None = None, *, k_offset: int = 0, + padding: PAD_TYPE = 'zeros', axis: int = -1) \ + -> np.ndarray: + """Perform the short-time Fourier transform. + + A two-dimensional matrix with ``p1-p0`` columns is calculated. + The `f_pts` rows represent value at the frequencies `f`. The q-th + column of the windowed FFT with the window `win` is centered at t[q]. + The columns represent the values at the frequencies `f`. + + Parameters + ---------- + x + The input signal as real or complex valued array. For complex values, the + property `fft_mode` must be set to 'twosided' or 'centered'. + p0 + The first element of the range of slices to calculate. If ``None`` + then it is set to :attr:`p_min`, which is the smallest possible + slice. + p1 + The end of the array. If ``None`` then `p_max(n)` is used. + k_offset + Index of first sample (t = 0) in `x`. + padding + Kind of values which are added, when the sliding window sticks out + on either the lower or upper end of the input `x`. Zeros are added + if the default 'zeros' is set. For 'edge' either the first or the + last value of `x` is used. 'even' pads by reflecting the + signal on the first or last sample and 'odd' additionally + multiplies it with -1. + axis + The axis of `x` over which to compute the STFT. + If not given, the last axis is used. + + Returns + ------- + S + A complex array is returned with the dimension always being larger + by one than of `x`. The last axis always represent the time slices + of the STFT. `axis` defines the frequency axis (default second to + last). E.g., for a one-dimensional `x`, a complex 2d array is + returned, with axis 0 representing frequency and axis 1 the time + slices. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + delta_t: Time increment of STFT + f: Frequencies values of the STFT. + invertible: Check if STFT is invertible. + :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform. + p_range: Determine and validate slice index range. + stft_detrend: STFT with detrended segments. + t: Times of STFT for an input signal with `n` samples. + :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to. + """ + return self.stft_detrend(x, None, p0, p1, k_offset=k_offset, + padding=padding, axis=axis) + + def stft_detrend(self, x: np.ndarray, + detr: Callable[[np.ndarray], np.ndarray] | Literal['linear', 'constant'] | None, # noqa: E501 + p0: int | None = None, p1: int | None = None, *, + k_offset: int = 0, padding: PAD_TYPE = 'zeros', + axis: int = -1) \ + -> np.ndarray: + """Short-time Fourier transform with a trend being subtracted from each + segment beforehand. + + If `detr` is set to 'constant', the mean is subtracted, if set to + "linear", the linear trend is removed. This is achieved by calling + :func:`scipy.signal.detrend`. If `detr` is a function, `detr` is + applied to each segment. + All other parameters have the same meaning as in `~ShortTimeFFT.stft`. + + Note that due to the detrending, the original signal cannot be + reconstructed by the `~ShortTimeFFT.istft`. + + See Also + -------- + invertible: Check if STFT is invertible. + :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform. + :meth:`~ShortTimeFFT.stft`: Short-time Fourier transform + (without detrending). + :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to. + """ + if self.onesided_fft and np.iscomplexobj(x): + raise ValueError(f"Complex-valued `x` not allowed for {self.fft_mode=}'! " + "Set property `fft_mode` to 'twosided' or 'centered'.") + if isinstance(detr, str): + detr = partial(detrend, type=detr) + elif not (detr is None or callable(detr)): + raise ValueError(f"Parameter {detr=} is not a str, function or " + + "None!") + n = x.shape[axis] + if not (n >= (m2p := self.m_num-self.m_num_mid)): + e_str = f'{len(x)=}' if x.ndim == 1 else f'of {axis=} of {x.shape}' + raise ValueError(f"{e_str} must be >= ceil(m_num/2) = {m2p}!") + + if x.ndim > 1: # motivated by the NumPy broadcasting mechanisms: + x = np.moveaxis(x, axis, -1) + # determine slice index range: + p0, p1 = self.p_range(n, p0, p1) + S_shape_1d = (self.f_pts, p1 - p0) + S_shape = x.shape[:-1] + S_shape_1d if x.ndim > 1 else S_shape_1d + S = np.zeros(S_shape, dtype=complex) + for p_, x_ in enumerate(self._x_slices(x, k_offset, p0, p1, padding)): + if detr is not None: + x_ = detr(x_) + S[..., :, p_] = self._fft_func(x_ * self.win.conj()) + if x.ndim > 1: + return np.moveaxis(S, -2, axis if axis >= 0 else axis-1) + return S + + def spectrogram(self, x: np.ndarray, y: np.ndarray | None = None, + detr: Callable[[np.ndarray], np.ndarray] | Literal['linear', 'constant'] | None = None, # noqa: E501 + *, + p0: int | None = None, p1: int | None = None, + k_offset: int = 0, padding: PAD_TYPE = 'zeros', + axis: int = -1) \ + -> np.ndarray: + r"""Calculate spectrogram or cross-spectrogram. + + The spectrogram is the absolute square of the STFT, i.e, it is + ``abs(S[q,p])**2`` for given ``S[q,p]`` and thus is always + non-negative. + For two STFTs ``Sx[q,p], Sy[q,p]``, the cross-spectrogram is defined + as ``Sx[q,p] * np.conj(Sx[q,p])`` and is complex-valued. + This is a convenience function for calling `~ShortTimeFFT.stft` / + `stft_detrend`, hence all parameters are discussed there. If `y` is not + ``None`` it needs to have the same shape as `x`. + + Examples + -------- + The following example shows the spectrogram of a square wave with + varying frequency :math:`f_i(t)` (marked by a green dashed line in the + plot) sampled with 20 Hz: + + >>> import matplotlib.pyplot as plt + >>> import numpy as np + >>> from scipy.signal import square, ShortTimeFFT + >>> from scipy.signal.windows import gaussian + ... + >>> T_x, N = 1 / 20, 1000 # 20 Hz sampling rate for 50 s signal + >>> t_x = np.arange(N) * T_x # time indexes for signal + >>> f_i = 5e-3*(t_x - t_x[N // 3])**2 + 1 # varying frequency + >>> x = square(2*np.pi*np.cumsum(f_i)*T_x) # the signal + + The utitlized Gaussian window is 50 samples or 2.5 s long. The + parameter ``mfft=800`` (oversampling factor 16) and the `hop` interval + of 2 in `ShortTimeFFT` was chosen to produce a sufficient number of + points: + + >>> g_std = 12 # standard deviation for Gaussian window in samples + >>> win = gaussian(50, std=g_std, sym=True) # symmetric Gaussian wind. + >>> SFT = ShortTimeFFT(win, hop=2, fs=1/T_x, mfft=800, scale_to='psd') + >>> Sx2 = SFT.spectrogram(x) # calculate absolute square of STFT + + The plot's colormap is logarithmically scaled as the power spectral + density is in dB. The time extent of the signal `x` is marked by + vertical dashed lines and the shaded areas mark the presence of border + effects: + + >>> fig1, ax1 = plt.subplots(figsize=(6., 4.)) # enlarge plot a bit + >>> t_lo, t_hi = SFT.extent(N)[:2] # time range of plot + >>> ax1.set_title(rf"Spectrogram ({SFT.m_num*SFT.T:g}$\,s$ Gaussian " + + ... rf"window, $\sigma_t={g_std*SFT.T:g}\,$s)") + >>> ax1.set(xlabel=f"Time $t$ in seconds ({SFT.p_num(N)} slices, " + + ... rf"$\Delta t = {SFT.delta_t:g}\,$s)", + ... ylabel=f"Freq. $f$ in Hz ({SFT.f_pts} bins, " + + ... rf"$\Delta f = {SFT.delta_f:g}\,$Hz)", + ... xlim=(t_lo, t_hi)) + >>> Sx_dB = 10 * np.log10(np.fmax(Sx2, 1e-4)) # limit range to -40 dB + >>> im1 = ax1.imshow(Sx_dB, origin='lower', aspect='auto', + ... extent=SFT.extent(N), cmap='magma') + >>> ax1.plot(t_x, f_i, 'g--', alpha=.5, label='$f_i(t)$') + >>> fig1.colorbar(im1, label='Power Spectral Density ' + + ... r"$20\,\log_{10}|S_x(t, f)|$ in dB") + ... + >>> # Shade areas where window slices stick out to the side: + >>> for t0_, t1_ in [(t_lo, SFT.lower_border_end[0] * SFT.T), + ... (SFT.upper_border_begin(N)[0] * SFT.T, t_hi)]: + ... ax1.axvspan(t0_, t1_, color='w', linewidth=0, alpha=.3) + >>> for t_ in [0, N * SFT.T]: # mark signal borders with vertical line + ... ax1.axvline(t_, color='c', linestyle='--', alpha=0.5) + >>> ax1.legend() + >>> fig1.tight_layout() + >>> plt.show() + + The logarithmic scaling reveals the odd harmonics of the square wave, + which are reflected at the Nyquist frequency of 10 Hz. This aliasing + is also the main source of the noise artifacts in the plot. + + + See Also + -------- + :meth:`~ShortTimeFFT.stft`: Perform the short-time Fourier transform. + stft_detrend: STFT with a trend subtracted from each segment. + :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to. + """ + Sx = self.stft_detrend(x, detr, p0, p1, k_offset=k_offset, + padding=padding, axis=axis) + if y is None or y is x: # do spectrogram: + return Sx.real**2 + Sx.imag**2 + # Cross-spectrogram: + Sy = self.stft_detrend(y, detr, p0, p1, k_offset=k_offset, + padding=padding, axis=axis) + return Sx * Sy.conj() + + @property + def dual_win(self) -> np.ndarray: + """Canonical dual window. + + A STFT can be interpreted as the input signal being expressed as a + weighted sum of modulated and time-shifted dual windows. Note that for + a given window there exist many dual windows. The canonical window is + the one with the minimal energy (i.e., :math:`L_2` norm). + + `dual_win` has same length as `win`, namely `m_num` samples. + + If the dual window cannot be calculated a ``ValueError`` is raised. + This attribute is read only and calculated lazily. + + See Also + -------- + dual_win: Canonical dual window. + m_num: Number of samples in window `win`. + win: Window function as real- or complex-valued 1d array. + ShortTimeFFT: Class this property belongs to. + """ + if self._dual_win is None: + self._dual_win = _calc_dual_canonical_window(self.win, self.hop) + return self._dual_win + + @property + def invertible(self) -> bool: + """Check if STFT is invertible. + + This is achieved by trying to calculate the canonical dual window. + + See Also + -------- + :meth:`~ShortTimeFFT.istft`: Inverse short-time Fourier transform. + m_num: Number of samples in window `win` and `dual_win`. + dual_win: Canonical dual window. + win: Window for STFT. + ShortTimeFFT: Class this property belongs to. + """ + try: + return len(self.dual_win) > 0 # call self.dual_win() + except ValueError: + return False + + def istft(self, S: np.ndarray, k0: int = 0, k1: int | None = None, *, + f_axis: int = -2, t_axis: int = -1) \ + -> np.ndarray: + """Inverse short-time Fourier transform. + + It returns an array of dimension ``S.ndim - 1`` which is real + if `onesided_fft` is set, else complex. If the STFT is not + `invertible`, or the parameters are out of bounds a ``ValueError`` is + raised. + + Parameters + ---------- + S + A complex valued array where `f_axis` denotes the frequency + values and the `t-axis` dimension the temporal values of the + STFT values. + k0, k1 + The start and the end index of the reconstructed signal. The + default (``k0 = 0``, ``k1 = None``) assumes that the maximum length + signal should be reconstructed. + f_axis, t_axis + The axes in `S` denoting the frequency and the time dimension. + + Notes + ----- + It is required that `S` has `f_pts` entries along the `f_axis`. For + the `t_axis` it is assumed that the first entry corresponds to + `p_min` * `delta_t` (being <= 0). The length of `t_axis` needs to be + compatible with `k1`. I.e., ``S.shape[t_axis] >= self.p_max(k1)`` must + hold, if `k1` is not ``None``. Else `k1` is set to `k_max` with:: + + q_max = S.shape[t_range] + self.p_min + k_max = (q_max - 1) * self.hop + self.m_num - self.m_num_mid + + The :ref:`tutorial_stft` section of the :ref:`user_guide` discussed the + slicing behavior by means of an example. + + See Also + -------- + invertible: Check if STFT is invertible. + :meth:`~ShortTimeFFT.stft`: Perform Short-time Fourier transform. + :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to. + """ + if f_axis == t_axis: + raise ValueError(f"{f_axis=} may not be equal to {t_axis=}!") + if S.shape[f_axis] != self.f_pts: + raise ValueError(f"{S.shape[f_axis]=} must be equal to " + + f"{self.f_pts=} ({S.shape=})!") + n_min = self.m_num-self.m_num_mid # minimum signal length + if not (S.shape[t_axis] >= (q_num := self.p_num(n_min))): + raise ValueError(f"{S.shape[t_axis]=} needs to have at least " + + f"{q_num} slices ({S.shape=})!") + if t_axis != S.ndim - 1 or f_axis != S.ndim - 2: + t_axis = S.ndim + t_axis if t_axis < 0 else t_axis + f_axis = S.ndim + f_axis if f_axis < 0 else f_axis + S = np.moveaxis(S, (f_axis, t_axis), (-2, -1)) + + q_max = S.shape[-1] + self.p_min + k_max = (q_max - 1) * self.hop + self.m_num - self.m_num_mid + + k1 = k_max if k1 is None else k1 + if not (self.k_min <= k0 < k1 <= k_max): + raise ValueError(f"({self.k_min=}) <= ({k0=}) < ({k1=}) <= " + + f"({k_max=}) is false!") + if not (num_pts := k1 - k0) >= n_min: + raise ValueError(f"({k1=}) - ({k0=}) = {num_pts} has to be at " + + f"least the half the window length {n_min}!") + + q0 = (k0 // self.hop + self.p_min if k0 >= 0 else # p_min always <= 0 + k0 // self.hop) + q1 = min(self.p_max(k1), q_max) + k_q0, k_q1 = self.nearest_k_p(k0), self.nearest_k_p(k1, left=False) + n_pts = k_q1 - k_q0 + self.m_num - self.m_num_mid + x = np.zeros(S.shape[:-2] + (n_pts,), + dtype=float if self.onesided_fft else complex) + for q_ in range(q0, q1): + xs = self._ifft_func(S[..., :, q_ - self.p_min]) * self.dual_win + i0 = q_ * self.hop - self.m_num_mid + i1 = min(i0 + self.m_num, n_pts+k0) + j0, j1 = 0, i1 - i0 + if i0 < k0: # xs sticks out to the left on x: + j0 += k0 - i0 + i0 = k0 + x[..., i0-k0:i1-k0] += xs[..., j0:j1] + x = x[..., :k1-k0] + if x.ndim > 1: + x = np.moveaxis(x, -1, f_axis if f_axis < x.ndim else t_axis) + return x + + @property + def fac_magnitude(self) -> float: + """Factor to multiply the STFT values by to scale each frequency slice + to a magnitude spectrum. + + It is 1 if attribute ``scaling == 'magnitude'``. + The window can be scaled to a magnitude spectrum by using the method + `scale_to`. + + See Also + -------- + fac_psd: Scaling factor for to a power spectral density spectrum. + scale_to: Scale window to obtain 'magnitude' or 'psd' scaling. + scaling: Normalization applied to the window function. + ShortTimeFFT: Class this property belongs to. + """ + if self.scaling == 'magnitude': + return 1 + if self._fac_mag is None: + self._fac_mag = 1 / abs(sum(self.win)) + return self._fac_mag + + @property + def fac_psd(self) -> float: + """Factor to multiply the STFT values by to scale each frequency slice + to a power spectral density (PSD). + + It is 1 if attribute ``scaling == 'psd'``. + The window can be scaled to a psd spectrum by using the method + `scale_to`. + + See Also + -------- + fac_magnitude: Scaling factor for to a magnitude spectrum. + scale_to: Scale window to obtain 'magnitude' or 'psd' scaling. + scaling: Normalization applied to the window function. + ShortTimeFFT: Class this property belongs to. + """ + if self.scaling == 'psd': + return 1 + if self._fac_psd is None: + self._fac_psd = 1 / np.sqrt( + sum(self.win.real**2+self.win.imag**2) / self.T) + return self._fac_psd + + @property + def m_num(self) -> int: + """Number of samples in window `win`. + + Note that the FFT can be oversampled by zero-padding. This is achieved + by setting the `mfft` property. + + See Also + -------- + m_num_mid: Center index of window `win`. + mfft: Length of input for the FFT used - may be larger than `m_num`. + hop: Time increment in signal samples for sliding window. + win: Window function as real- or complex-valued 1d array. + ShortTimeFFT: Class this property belongs to. + """ + return len(self.win) + + @property + def m_num_mid(self) -> int: + """Center index of window `win`. + + For odd `m_num`, ``(m_num - 1) / 2`` is returned and + for even `m_num` (per definition) ``m_num / 2`` is returned. + + See Also + -------- + m_num: Number of samples in window `win`. + mfft: Length of input for the FFT used - may be larger than `m_num`. + hop: ime increment in signal samples for sliding window. + win: Window function as real- or complex-valued 1d array. + ShortTimeFFT: Class this property belongs to. + """ + return self.m_num // 2 + + @cache + def _pre_padding(self) -> tuple[int, int]: + """Smallest signal index and slice index due to padding. + + Since, per convention, for time t=0, n,q is zero, the returned values + are negative or zero. + """ + w2 = self.win.real**2 + self.win.imag**2 + # move window to the left until the overlap with t >= 0 vanishes: + n0 = -self.m_num_mid + for q_, n_ in enumerate(range(n0, n0-self.m_num-1, -self.hop)): + n_next = n_ - self.hop + if n_next + self.m_num <= 0 or all(w2[n_next:] == 0): + return n_, -q_ + raise RuntimeError("This is code line should not have been reached!") + # If this case is reached, it probably means the first slice should be + # returned, i.e.: return n0, 0 + + @property + def k_min(self) -> int: + """The smallest possible signal index of the STFT. + + `k_min` is the index of the left-most non-zero value of the lowest + slice `p_min`. Since the zeroth slice is centered over the zeroth + sample of the input signal, `k_min` is never positive. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_max: First sample index after signal end not touched by a time slice. + lower_border_end: Where pre-padding effects end. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + upper_border_begin: Where post-padding effects start. + ShortTimeFFT: Class this property belongs to. + """ + return self._pre_padding()[0] + + @property + def p_min(self) -> int: + """The smallest possible slice index. + + `p_min` is the index of the left-most slice, where the window still + sticks into the signal, i.e., has non-zero part for t >= 0. + `k_min` is the smallest index where the window function of the slice + `p_min` is non-zero. + + Since, per convention the zeroth slice is centered at t=0, + `p_min` <= 0 always holds. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + ShortTimeFFT: Class this property belongs to. + """ + return self._pre_padding()[1] + + @lru_cache(maxsize=256) + def _post_padding(self, n: int) -> tuple[int, int]: + """Largest signal index and slice index due to padding.""" + w2 = self.win.real**2 + self.win.imag**2 + # move window to the right until the overlap for t < t[n] vanishes: + q1 = n // self.hop # last slice index with t[p1] <= t[n] + k1 = q1 * self.hop - self.m_num_mid + for q_, k_ in enumerate(range(k1, n+self.m_num, self.hop), start=q1): + n_next = k_ + self.hop + if n_next >= n or all(w2[:n-n_next] == 0): + return k_ + self.m_num, q_ + 1 + raise RuntimeError("This is code line should not have been reached!") + # If this case is reached, it probably means the last slice should be + # returned, i.e.: return k1 + self.m_num - self.m_num_mid, q1 + 1 + + def k_max(self, n: int) -> int: + """First sample index after signal end not touched by a time slice. + + `k_max` - 1 is the largest sample index of the slice `p_max` for a + given input signal of `n` samples. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + ShortTimeFFT: Class this method belongs to. + """ + return self._post_padding(n)[0] + + def p_max(self, n: int) -> int: + """Index of first non-overlapping upper time slice for `n` sample + input. + + Note that center point t[p_max] = (p_max(n)-1) * `delta_t` is typically + larger than last time index t[n-1] == (`n`-1) * `T`. The upper border + of samples indexes covered by the window slices is given by `k_max`. + Furthermore, `p_max` does not denote the number of slices `p_num` since + `p_min` is typically less than zero. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + p_min: The smallest possible slice index. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + ShortTimeFFT: Class this method belongs to. + """ + return self._post_padding(n)[1] + + def p_num(self, n: int) -> int: + """Number of time slices for an input signal with `n` samples. + + It is given by `p_num` = `p_max` - `p_min` with `p_min` typically + being negative. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + lower_border_end: Where pre-padding effects end. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_range: Determine and validate slice index range. + upper_border_begin: Where post-padding effects start. + ShortTimeFFT: Class this method belongs to. + """ + return self.p_max(n) - self.p_min + + @property + def lower_border_end(self) -> tuple[int, int]: + """First signal index and first slice index unaffected by pre-padding. + + Describes the point where the window does not stick out to the left + of the signal domain. + A detailed example is provided in the :ref:`tutorial_stft_sliding_win` + section of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + lower_border_end: Where pre-padding effects end. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + upper_border_begin: Where post-padding effects start. + ShortTimeFFT: Class this property belongs to. + """ + # not using @cache decorator due to MyPy limitations + if self._lower_border_end is not None: + return self._lower_border_end + + # first non-zero element in self.win: + m0 = np.flatnonzero(self.win.real**2 + self.win.imag**2)[0] + + # move window to the right until does not stick out to the left: + k0 = -self.m_num_mid + m0 + for q_, k_ in enumerate(range(k0, self.hop + 1, self.hop)): + if k_ + self.hop >= 0: # next entry does not stick out anymore + self._lower_border_end = (k_ + self.m_num, q_ + 1) + return self._lower_border_end + self._lower_border_end = (0, max(self.p_min, 0)) # ends at first slice + return self._lower_border_end + + @lru_cache(maxsize=256) + def upper_border_begin(self, n: int) -> tuple[int, int]: + """First signal index and first slice index affected by post-padding. + + Describes the point where the window does begin stick out to the right + of the signal domain. + A detailed example is given :ref:`tutorial_stft_sliding_win` section + of the :ref:`user_guide`. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + lower_border_end: Where pre-padding effects end. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + p_range: Determine and validate slice index range. + ShortTimeFFT: Class this method belongs to. + """ + w2 = self.win.real**2 + self.win.imag**2 + q2 = n // self.hop + 1 # first t[q] >= t[n] + q1 = max((n-self.m_num) // self.hop - 1, -1) + # move window left until does not stick out to the right: + for q_ in range(q2, q1, -1): + k_ = q_ * self.hop + (self.m_num - self.m_num_mid) + if k_ < n or all(w2[n-k_:] == 0): + return (q_ + 1) * self.hop - self.m_num_mid, q_ + 1 + return 0, 0 # border starts at first slice + + @property + def delta_t(self) -> float: + """Time increment of STFT. + + The time increment `delta_t` = `T` * `hop` represents the sample + increment `hop` converted to time based on the sampling interval `T`. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + hop: Hop size in signal samples for sliding window. + t: Times of STFT for an input signal with `n` samples. + T: Sampling interval of input signal and window `win`. + ShortTimeFFT: Class this property belongs to + """ + return self.T * self.hop + + def p_range(self, n: int, p0: int | None = None, + p1: int | None = None) -> tuple[int, int]: + """Determine and validate slice index range. + + Parameters + ---------- + n : int + Number of samples of input signal, assuming t[0] = 0. + p0 : int | None + First slice index. If 0 then the first slice is centered at t = 0. + If ``None`` then `p_min` is used. Note that p0 may be < 0 if + slices are left of t = 0. + p1 : int | None + End of interval (last value is p1-1). + If ``None`` then `p_max(n)` is used. + + + Returns + ------- + p0_ : int + The fist slice index + p1_ : int + End of interval (last value is p1-1). + + Notes + ----- + A ``ValueError`` is raised if ``p_min <= p0 < p1 <= p_max(n)`` does not + hold. + + See Also + -------- + k_min: The smallest possible signal index. + k_max: First sample index after signal end not touched by a time slice. + lower_border_end: Where pre-padding effects end. + p_min: The smallest possible slice index. + p_max: Index of first non-overlapping upper time slice. + p_num: Number of time slices, i.e., `p_max` - `p_min`. + upper_border_begin: Where post-padding effects start. + ShortTimeFFT: Class this property belongs to. + """ + p_max = self.p_max(n) # shorthand + p0_ = self.p_min if p0 is None else p0 + p1_ = p_max if p1 is None else p1 + if not (self.p_min <= p0_ < p1_ <= p_max): + raise ValueError(f"Invalid Parameter {p0=}, {p1=}, i.e., " + + f"{self.p_min=} <= p0 < p1 <= {p_max=} " + + f"does not hold for signal length {n=}!") + return p0_, p1_ + + @lru_cache(maxsize=1) + def t(self, n: int, p0: int | None = None, p1: int | None = None, + k_offset: int = 0) -> np.ndarray: + """Times of STFT for an input signal with `n` samples. + + Returns a 1d array with times of the `~ShortTimeFFT.stft` values with + the same parametrization. Note that the slices are + ``delta_t = hop * T`` time units apart. + + Parameters + ---------- + n + Number of sample of the input signal. + p0 + The first element of the range of slices to calculate. If ``None`` + then it is set to :attr:`p_min`, which is the smallest possible + slice. + p1 + The end of the array. If ``None`` then `p_max(n)` is used. + k_offset + Index of first sample (t = 0) in `x`. + + + See Also + -------- + delta_t: Time increment of STFT (``hop*T``) + hop: Time increment in signal samples for sliding window. + nearest_k_p: Nearest sample index k_p for which t[k_p] == t[p] holds. + T: Sampling interval of input signal and of the window (``1/fs``). + fs: Sampling frequency (being ``1/T``) + ShortTimeFFT: Class this method belongs to. + """ + p0, p1 = self.p_range(n, p0, p1) + return np.arange(p0, p1) * self.delta_t + k_offset * self.T + + def nearest_k_p(self, k: int, left: bool = True) -> int: + """Return nearest sample index k_p for which t[k_p] == t[p] holds. + + The nearest next smaller time sample p (where t[p] is the center + position of the window of the p-th slice) is p_k = k // `hop`. + If `hop` is a divisor of `k` than `k` is returned. + If `left` is set than p_k * `hop` is returned else (p_k+1) * `hop`. + + This method can be used to slice an input signal into chunks for + calculating the STFT and iSTFT incrementally. + + See Also + -------- + delta_t: Time increment of STFT (``hop*T``) + hop: Time increment in signal samples for sliding window. + T: Sampling interval of input signal and of the window (``1/fs``). + fs: Sampling frequency (being ``1/T``) + t: Times of STFT for an input signal with `n` samples. + ShortTimeFFT: Class this method belongs to. + """ + p_q, remainder = divmod(k, self.hop) + if remainder == 0: + return k + return p_q * self.hop if left else (p_q + 1) * self.hop + + @property + def delta_f(self) -> float: + """Width of the frequency bins of the STFT. + + Return the frequency interval `delta_f` = 1 / (`mfft` * `T`). + + See Also + -------- + delta_t: Time increment of STFT. + f_pts: Number of points along the frequency axis. + f: Frequencies values of the STFT. + mfft: Length of the input for FFT used. + T: Sampling interval. + t: Times of STFT for an input signal with `n` samples. + ShortTimeFFT: Class this property belongs to. + """ + return 1 / (self.mfft * self.T) + + @property + def f_pts(self) -> int: + """Number of points along the frequency axis. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + f: Frequencies values of the STFT. + mfft: Length of the input for FFT used. + ShortTimeFFT: Class this property belongs to. + """ + return self.mfft // 2 + 1 if self.onesided_fft else self.mfft + + @property + def onesided_fft(self) -> bool: + """Return True if a one-sided FFT is used. + + Returns ``True`` if `fft_mode` is either 'onesided' or 'onesided2X'. + + See Also + -------- + fft_mode: Utilized FFT ('twosided', 'centered', 'onesided' or + 'onesided2X') + ShortTimeFFT: Class this property belongs to. + """ + return self.fft_mode in {'onesided', 'onesided2X'} + + @property + def f(self) -> np.ndarray: + """Frequencies values of the STFT. + + A 1d array of length `f_pts` with `delta_f` spaced entries is returned. + + See Also + -------- + delta_f: Width of the frequency bins of the STFT. + f_pts: Number of points along the frequency axis. + mfft: Length of the input for FFT used. + ShortTimeFFT: Class this property belongs to. + """ + if self.fft_mode in {'onesided', 'onesided2X'}: + return fft_lib.rfftfreq(self.mfft, self.T) + elif self.fft_mode == 'twosided': + return fft_lib.fftfreq(self.mfft, self.T) + elif self.fft_mode == 'centered': + return fft_lib.fftshift(fft_lib.fftfreq(self.mfft, self.T)) + # This should never happen but makes the Linters happy: + fft_modes = get_args(FFT_MODE_TYPE) + raise RuntimeError(f"{self.fft_mode=} not in {fft_modes}!") + + def _fft_func(self, x: np.ndarray) -> np.ndarray: + """FFT based on the `fft_mode`, `mfft`, `scaling` and `phase_shift` + attributes. + + For multidimensional arrays the transformation is carried out on the + last axis. + """ + if self.phase_shift is not None: + if x.shape[-1] < self.mfft: # zero pad if needed + z_shape = list(x.shape) + z_shape[-1] = self.mfft - x.shape[-1] + x = np.hstack((x, np.zeros(z_shape, dtype=x.dtype))) + p_s = (self.phase_shift + self.m_num_mid) % self.m_num + x = np.roll(x, -p_s, axis=-1) + + if self.fft_mode == 'twosided': + return fft_lib.fft(x, n=self.mfft, axis=-1) + if self.fft_mode == 'centered': + return fft_lib.fftshift(fft_lib.fft(x, self.mfft, axis=-1), axes=-1) + if self.fft_mode == 'onesided': + return fft_lib.rfft(x, n=self.mfft, axis=-1) + if self.fft_mode == 'onesided2X': + X = fft_lib.rfft(x, n=self.mfft, axis=-1) + # Either squared magnitude (psd) or magnitude is doubled: + fac = np.sqrt(2) if self.scaling == 'psd' else 2 + # For even input length, the last entry is unpaired: + X[..., 1: -1 if self.mfft % 2 == 0 else None] *= fac + return X + # This should never happen but makes the Linter happy: + fft_modes = get_args(FFT_MODE_TYPE) + raise RuntimeError(f"{self.fft_mode=} not in {fft_modes}!") + + def _ifft_func(self, X: np.ndarray) -> np.ndarray: + """Inverse to `_fft_func`. + + Returned is an array of length `m_num`. If the FFT is `onesided` + then a float array is returned else a complex array is returned. + For multidimensional arrays the transformation is carried out on the + last axis. + """ + if self.fft_mode == 'twosided': + x = fft_lib.ifft(X, n=self.mfft, axis=-1) + elif self.fft_mode == 'centered': + x = fft_lib.ifft(fft_lib.ifftshift(X, axes=-1), n=self.mfft, axis=-1) + elif self.fft_mode == 'onesided': + x = fft_lib.irfft(X, n=self.mfft, axis=-1) + elif self.fft_mode == 'onesided2X': + Xc = X.copy() # we do not want to modify function parameters + fac = np.sqrt(2) if self.scaling == 'psd' else 2 + # For even length X the last value is not paired with a negative + # value on the two-sided FFT: + q1 = -1 if self.mfft % 2 == 0 else None + Xc[..., 1:q1] /= fac + x = fft_lib.irfft(Xc, n=self.mfft, axis=-1) + else: # This should never happen but makes the Linter happy: + error_str = f"{self.fft_mode=} not in {get_args(FFT_MODE_TYPE)}!" + raise RuntimeError(error_str) + + if self.phase_shift is None: + return x[:self.m_num] + p_s = (self.phase_shift + self.m_num_mid) % self.m_num + return np.roll(x, p_s, axis=-1)[:self.m_num] + + def extent(self, n: int, axes_seq: Literal['tf', 'ft'] = 'tf', + center_bins: bool = False) -> tuple[float, float, float, float]: + """Return minimum and maximum values time-frequency values. + + A tuple with four floats ``(t0, t1, f0, f1)`` for 'tf' and + ``(f0, f1, t0, t1)`` for 'ft' is returned describing the corners + of the time-frequency domain of the `~ShortTimeFFT.stft`. + That tuple can be passed to `matplotlib.pyplot.imshow` as a parameter + with the same name. + + Parameters + ---------- + n : int + Number of samples in input signal. + axes_seq : {'tf', 'ft'} + Return time extent first and then frequency extent or vice-versa. + center_bins: bool + If set (default ``False``), the values of the time slots and + frequency bins are moved from the side the middle. This is useful, + when plotting the `~ShortTimeFFT.stft` values as step functions, + i.e., with no interpolation. + + See Also + -------- + :func:`matplotlib.pyplot.imshow`: Display data as an image. + :class:`scipy.signal.ShortTimeFFT`: Class this method belongs to. + """ + if axes_seq not in ('tf', 'ft'): + raise ValueError(f"Parameter {axes_seq=} not in ['tf', 'ft']!") + + if self.onesided_fft: + q0, q1 = 0, self.f_pts + elif self.fft_mode == 'centered': + q0 = -self.mfft // 2 + q1 = self.mfft // 2 - 1 if self.mfft % 2 == 0 else self.mfft // 2 + else: + raise ValueError(f"Attribute fft_mode={self.fft_mode} must be " + + "in ['centered', 'onesided', 'onesided2X']") + + p0, p1 = self.p_min, self.p_max(n) # shorthand + if center_bins: + t0, t1 = self.delta_t * (p0 - 0.5), self.delta_t * (p1 - 0.5) + f0, f1 = self.delta_f * (q0 - 0.5), self.delta_f * (q1 - 0.5) + else: + t0, t1 = self.delta_t * p0, self.delta_t * p1 + f0, f1 = self.delta_f * q0, self.delta_f * q1 + return (t0, t1, f0, f1) if axes_seq == 'tf' else (f0, f1, t0, t1) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_signaltools.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_signaltools.py new file mode 100644 index 0000000000000000000000000000000000000000..214b35c596dd524ee2eab586b65586f8886d7538 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_signaltools.py @@ -0,0 +1,4628 @@ +# Author: Travis Oliphant +# 1999 -- 2002 + +import operator +import math +from math import prod as _prod +import timeit +import warnings + +from scipy.spatial import cKDTree +from . import _sigtools +from ._ltisys import dlti +from ._upfirdn import upfirdn, _output_len, _upfirdn_modes +from scipy import linalg, fft as sp_fft +from scipy import ndimage +from scipy.fft._helper import _init_nd_shape_and_axes +import numpy as np +from scipy.special import lambertw +from .windows import get_window +from ._arraytools import axis_slice, axis_reverse, odd_ext, even_ext, const_ext +from ._filter_design import cheby1, _validate_sos, zpk2sos +from ._fir_filter_design import firwin +from ._sosfilt import _sosfilt + + +__all__ = ['correlate', 'correlation_lags', 'correlate2d', + 'convolve', 'convolve2d', 'fftconvolve', 'oaconvolve', + 'order_filter', 'medfilt', 'medfilt2d', 'wiener', 'lfilter', + 'lfiltic', 'sosfilt', 'deconvolve', 'hilbert', 'hilbert2', + 'cmplx_sort', 'unique_roots', 'invres', 'invresz', 'residue', + 'residuez', 'resample', 'resample_poly', 'detrend', + 'lfilter_zi', 'sosfilt_zi', 'sosfiltfilt', 'choose_conv_method', + 'filtfilt', 'decimate', 'vectorstrength'] + + +_modedict = {'valid': 0, 'same': 1, 'full': 2} + +_boundarydict = {'fill': 0, 'pad': 0, 'wrap': 2, 'circular': 2, 'symm': 1, + 'symmetric': 1, 'reflect': 4} + + +def _valfrommode(mode): + try: + return _modedict[mode] + except KeyError as e: + raise ValueError("Acceptable mode flags are 'valid'," + " 'same', or 'full'.") from e + + +def _bvalfromboundary(boundary): + try: + return _boundarydict[boundary] << 2 + except KeyError as e: + raise ValueError("Acceptable boundary flags are 'fill', 'circular' " + "(or 'wrap'), and 'symmetric' (or 'symm').") from e + + +def _inputs_swap_needed(mode, shape1, shape2, axes=None): + """Determine if inputs arrays need to be swapped in `"valid"` mode. + + If in `"valid"` mode, returns whether or not the input arrays need to be + swapped depending on whether `shape1` is at least as large as `shape2` in + every calculated dimension. + + This is important for some of the correlation and convolution + implementations in this module, where the larger array input needs to come + before the smaller array input when operating in this mode. + + Note that if the mode provided is not 'valid', False is immediately + returned. + + """ + if mode != 'valid': + return False + + if not shape1: + return False + + if axes is None: + axes = range(len(shape1)) + + ok1 = all(shape1[i] >= shape2[i] for i in axes) + ok2 = all(shape2[i] >= shape1[i] for i in axes) + + if not (ok1 or ok2): + raise ValueError("For 'valid' mode, one must be at least " + "as large as the other in every dimension") + + return not ok1 + + +def correlate(in1, in2, mode='full', method='auto'): + r""" + Cross-correlate two N-dimensional arrays. + + Cross-correlate `in1` and `in2`, with the output size determined by the + `mode` argument. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear cross-correlation + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + method : str {'auto', 'direct', 'fft'}, optional + A string indicating which method to use to calculate the correlation. + + ``direct`` + The correlation is determined directly from sums, the definition of + correlation. + ``fft`` + The Fast Fourier Transform is used to perform the correlation more + quickly (only available for numerical arrays.) + ``auto`` + Automatically chooses direct or Fourier method based on an estimate + of which is faster (default). See `convolve` Notes for more detail. + + .. versionadded:: 0.19.0 + + Returns + ------- + correlate : array + An N-dimensional array containing a subset of the discrete linear + cross-correlation of `in1` with `in2`. + + See Also + -------- + choose_conv_method : contains more documentation on `method`. + correlation_lags : calculates the lag / displacement indices array for 1D + cross-correlation. + + Notes + ----- + The correlation z of two d-dimensional arrays x and y is defined as:: + + z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...]) + + This way, if x and y are 1-D arrays and ``z = correlate(x, y, 'full')`` + then + + .. math:: + + z[k] = (x * y)(k - N + 1) + = \sum_{l=0}^{||x||-1}x_l y_{l-k+N-1}^{*} + + for :math:`k = 0, 1, ..., ||x|| + ||y|| - 2` + + where :math:`||x||` is the length of ``x``, :math:`N = \max(||x||,||y||)`, + and :math:`y_m` is 0 when m is outside the range of y. + + ``method='fft'`` only works for numerical arrays as it relies on + `fftconvolve`. In certain cases (i.e., arrays of objects or when + rounding integers can lose precision), ``method='direct'`` is always used. + + When using "same" mode with even-length inputs, the outputs of `correlate` + and `correlate2d` differ: There is a 1-index offset between them. + + Examples + -------- + Implement a matched filter using cross-correlation, to recover a signal + that has passed through a noisy channel. + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + >>> sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128) + >>> sig_noise = sig + rng.standard_normal(len(sig)) + >>> corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128 + + >>> clock = np.arange(64, len(sig), 128) + >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True) + >>> ax_orig.plot(sig) + >>> ax_orig.plot(clock, sig[clock], 'ro') + >>> ax_orig.set_title('Original signal') + >>> ax_noise.plot(sig_noise) + >>> ax_noise.set_title('Signal with noise') + >>> ax_corr.plot(corr) + >>> ax_corr.plot(clock, corr[clock], 'ro') + >>> ax_corr.axhline(0.5, ls=':') + >>> ax_corr.set_title('Cross-correlated with rectangular pulse') + >>> ax_orig.margins(0, 0.1) + >>> fig.tight_layout() + >>> plt.show() + + Compute the cross-correlation of a noisy signal with the original signal. + + >>> x = np.arange(128) / 128 + >>> sig = np.sin(2 * np.pi * x) + >>> sig_noise = sig + rng.standard_normal(len(sig)) + >>> corr = signal.correlate(sig_noise, sig) + >>> lags = signal.correlation_lags(len(sig), len(sig_noise)) + >>> corr /= np.max(corr) + + >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, figsize=(4.8, 4.8)) + >>> ax_orig.plot(sig) + >>> ax_orig.set_title('Original signal') + >>> ax_orig.set_xlabel('Sample Number') + >>> ax_noise.plot(sig_noise) + >>> ax_noise.set_title('Signal with noise') + >>> ax_noise.set_xlabel('Sample Number') + >>> ax_corr.plot(lags, corr) + >>> ax_corr.set_title('Cross-correlated signal') + >>> ax_corr.set_xlabel('Lag') + >>> ax_orig.margins(0, 0.1) + >>> ax_noise.margins(0, 0.1) + >>> ax_corr.margins(0, 0.1) + >>> fig.tight_layout() + >>> plt.show() + + """ + in1 = np.asarray(in1) + in2 = np.asarray(in2) + + if in1.ndim == in2.ndim == 0: + return in1 * in2.conj() + elif in1.ndim != in2.ndim: + raise ValueError("in1 and in2 should have the same dimensionality") + + # Don't use _valfrommode, since correlate should not accept numeric modes + try: + val = _modedict[mode] + except KeyError as e: + raise ValueError("Acceptable mode flags are 'valid'," + " 'same', or 'full'.") from e + + # this either calls fftconvolve or this function with method=='direct' + if method in ('fft', 'auto'): + return convolve(in1, _reverse_and_conj(in2), mode, method) + + elif method == 'direct': + # fastpath to faster numpy.correlate for 1d inputs when possible + if _np_conv_ok(in1, in2, mode): + return np.correlate(in1, in2, mode) + + # _correlateND is far slower when in2.size > in1.size, so swap them + # and then undo the effect afterward if mode == 'full'. Also, it fails + # with 'valid' mode if in2 is larger than in1, so swap those, too. + # Don't swap inputs for 'same' mode, since shape of in1 matters. + swapped_inputs = ((mode == 'full') and (in2.size > in1.size) or + _inputs_swap_needed(mode, in1.shape, in2.shape)) + + if swapped_inputs: + in1, in2 = in2, in1 + + if mode == 'valid': + ps = [i - j + 1 for i, j in zip(in1.shape, in2.shape)] + out = np.empty(ps, in1.dtype) + + z = _sigtools._correlateND(in1, in2, out, val) + + else: + ps = [i + j - 1 for i, j in zip(in1.shape, in2.shape)] + + # zero pad input + in1zpadded = np.zeros(ps, in1.dtype) + sc = tuple(slice(0, i) for i in in1.shape) + in1zpadded[sc] = in1.copy() + + if mode == 'full': + out = np.empty(ps, in1.dtype) + elif mode == 'same': + out = np.empty(in1.shape, in1.dtype) + + z = _sigtools._correlateND(in1zpadded, in2, out, val) + + if swapped_inputs: + # Reverse and conjugate to undo the effect of swapping inputs + z = _reverse_and_conj(z) + + return z + + else: + raise ValueError("Acceptable method flags are 'auto'," + " 'direct', or 'fft'.") + + +def correlation_lags(in1_len, in2_len, mode='full'): + r""" + Calculates the lag / displacement indices array for 1D cross-correlation. + + Parameters + ---------- + in1_len : int + First input size. + in2_len : int + Second input size. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output. + See the documentation `correlate` for more information. + + Returns + ------- + lags : array + Returns an array containing cross-correlation lag/displacement indices. + Indices can be indexed with the np.argmax of the correlation to return + the lag/displacement. + + See Also + -------- + correlate : Compute the N-dimensional cross-correlation. + + Notes + ----- + Cross-correlation for continuous functions :math:`f` and :math:`g` is + defined as: + + .. math:: + + \left ( f\star g \right )\left ( \tau \right ) + \triangleq \int_{t_0}^{t_0 +T} + \overline{f\left ( t \right )}g\left ( t+\tau \right )dt + + Where :math:`\tau` is defined as the displacement, also known as the lag. + + Cross correlation for discrete functions :math:`f` and :math:`g` is + defined as: + + .. math:: + \left ( f\star g \right )\left [ n \right ] + \triangleq \sum_{-\infty}^{\infty} + \overline{f\left [ m \right ]}g\left [ m+n \right ] + + Where :math:`n` is the lag. + + Examples + -------- + Cross-correlation of a signal with its time-delayed self. + + >>> import numpy as np + >>> from scipy import signal + >>> rng = np.random.default_rng() + >>> x = rng.standard_normal(1000) + >>> y = np.concatenate([rng.standard_normal(100), x]) + >>> correlation = signal.correlate(x, y, mode="full") + >>> lags = signal.correlation_lags(x.size, y.size, mode="full") + >>> lag = lags[np.argmax(correlation)] + """ + + # calculate lag ranges in different modes of operation + if mode == "full": + # the output is the full discrete linear convolution + # of the inputs. (Default) + lags = np.arange(-in2_len + 1, in1_len) + elif mode == "same": + # the output is the same size as `in1`, centered + # with respect to the 'full' output. + # calculate the full output + lags = np.arange(-in2_len + 1, in1_len) + # determine the midpoint in the full output + mid = lags.size // 2 + # determine lag_bound to be used with respect + # to the midpoint + lag_bound = in1_len // 2 + # calculate lag ranges for even and odd scenarios + if in1_len % 2 == 0: + lags = lags[(mid-lag_bound):(mid+lag_bound)] + else: + lags = lags[(mid-lag_bound):(mid+lag_bound)+1] + elif mode == "valid": + # the output consists only of those elements that do not + # rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + # must be at least as large as the other in every dimension. + + # the lag_bound will be either negative or positive + # this let's us infer how to present the lag range + lag_bound = in1_len - in2_len + if lag_bound >= 0: + lags = np.arange(lag_bound + 1) + else: + lags = np.arange(lag_bound, 1) + return lags + + +def _centered(arr, newshape): + # Return the center newshape portion of the array. + newshape = np.asarray(newshape) + currshape = np.array(arr.shape) + startind = (currshape - newshape) // 2 + endind = startind + newshape + myslice = [slice(startind[k], endind[k]) for k in range(len(endind))] + return arr[tuple(myslice)] + + +def _init_freq_conv_axes(in1, in2, mode, axes, sorted_axes=False): + """Handle the axes argument for frequency-domain convolution. + + Returns the inputs and axes in a standard form, eliminating redundant axes, + swapping the inputs if necessary, and checking for various potential + errors. + + Parameters + ---------- + in1 : array + First input. + in2 : array + Second input. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output. + See the documentation `fftconvolve` for more information. + axes : list of ints + Axes over which to compute the FFTs. + sorted_axes : bool, optional + If `True`, sort the axes. + Default is `False`, do not sort. + + Returns + ------- + in1 : array + The first input, possible swapped with the second input. + in2 : array + The second input, possible swapped with the first input. + axes : list of ints + Axes over which to compute the FFTs. + + """ + s1 = in1.shape + s2 = in2.shape + noaxes = axes is None + + _, axes = _init_nd_shape_and_axes(in1, shape=None, axes=axes) + + if not noaxes and not len(axes): + raise ValueError("when provided, axes cannot be empty") + + # Axes of length 1 can rely on broadcasting rules for multiply, + # no fft needed. + axes = [a for a in axes if s1[a] != 1 and s2[a] != 1] + + if sorted_axes: + axes.sort() + + if not all(s1[a] == s2[a] or s1[a] == 1 or s2[a] == 1 + for a in range(in1.ndim) if a not in axes): + raise ValueError("incompatible shapes for in1 and in2:" + f" {s1} and {s2}") + + # Check that input sizes are compatible with 'valid' mode. + if _inputs_swap_needed(mode, s1, s2, axes=axes): + # Convolution is commutative; order doesn't have any effect on output. + in1, in2 = in2, in1 + + return in1, in2, axes + + +def _freq_domain_conv(in1, in2, axes, shape, calc_fast_len=False): + """Convolve two arrays in the frequency domain. + + This function implements only base the FFT-related operations. + Specifically, it converts the signals to the frequency domain, multiplies + them, then converts them back to the time domain. Calculations of axes, + shapes, convolution mode, etc. are implemented in higher level-functions, + such as `fftconvolve` and `oaconvolve`. Those functions should be used + instead of this one. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + axes : array_like of ints + Axes over which to compute the FFTs. + shape : array_like of ints + The sizes of the FFTs. + calc_fast_len : bool, optional + If `True`, set each value of `shape` to the next fast FFT length. + Default is `False`, use `axes` as-is. + + Returns + ------- + out : array + An N-dimensional array containing the discrete linear convolution of + `in1` with `in2`. + + """ + if not len(axes): + return in1 * in2 + + complex_result = (in1.dtype.kind == 'c' or in2.dtype.kind == 'c') + + if calc_fast_len: + # Speed up FFT by padding to optimal size. + fshape = [ + sp_fft.next_fast_len(shape[a], not complex_result) for a in axes] + else: + fshape = shape + + if not complex_result: + fft, ifft = sp_fft.rfftn, sp_fft.irfftn + else: + fft, ifft = sp_fft.fftn, sp_fft.ifftn + + sp1 = fft(in1, fshape, axes=axes) + sp2 = fft(in2, fshape, axes=axes) + + ret = ifft(sp1 * sp2, fshape, axes=axes) + + if calc_fast_len: + fslice = tuple([slice(sz) for sz in shape]) + ret = ret[fslice] + + return ret + + +def _apply_conv_mode(ret, s1, s2, mode, axes): + """Calculate the convolution result shape based on the `mode` argument. + + Returns the result sliced to the correct size for the given mode. + + Parameters + ---------- + ret : array + The result array, with the appropriate shape for the 'full' mode. + s1 : list of int + The shape of the first input. + s2 : list of int + The shape of the second input. + mode : str {'full', 'valid', 'same'} + A string indicating the size of the output. + See the documentation `fftconvolve` for more information. + axes : list of ints + Axes over which to compute the convolution. + + Returns + ------- + ret : array + A copy of `res`, sliced to the correct size for the given `mode`. + + """ + if mode == "full": + return ret.copy() + elif mode == "same": + return _centered(ret, s1).copy() + elif mode == "valid": + shape_valid = [ret.shape[a] if a not in axes else s1[a] - s2[a] + 1 + for a in range(ret.ndim)] + return _centered(ret, shape_valid).copy() + else: + raise ValueError("acceptable mode flags are 'valid'," + " 'same', or 'full'") + + +def fftconvolve(in1, in2, mode="full", axes=None): + """Convolve two N-dimensional arrays using FFT. + + Convolve `in1` and `in2` using the fast Fourier transform method, with + the output size determined by the `mode` argument. + + This is generally much faster than `convolve` for large arrays (n > ~500), + but can be slower when only a few output values are needed, and can only + output float arrays (int or object array inputs will be cast to float). + + As of v0.19, `convolve` automatically chooses this method or the direct + method based on an estimation of which is faster. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear convolution + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + axes : int or array_like of ints or None, optional + Axes over which to compute the convolution. + The default is over all axes. + + Returns + ------- + out : array + An N-dimensional array containing a subset of the discrete linear + convolution of `in1` with `in2`. + + See Also + -------- + convolve : Uses the direct convolution or FFT convolution algorithm + depending on which is faster. + oaconvolve : Uses the overlap-add method to do convolution, which is + generally faster when the input arrays are large and + significantly different in size. + + Examples + -------- + Autocorrelation of white noise is an impulse. + + >>> import numpy as np + >>> from scipy import signal + >>> rng = np.random.default_rng() + >>> sig = rng.standard_normal(1000) + >>> autocorr = signal.fftconvolve(sig, sig[::-1], mode='full') + + >>> import matplotlib.pyplot as plt + >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1) + >>> ax_orig.plot(sig) + >>> ax_orig.set_title('White noise') + >>> ax_mag.plot(np.arange(-len(sig)+1,len(sig)), autocorr) + >>> ax_mag.set_title('Autocorrelation') + >>> fig.tight_layout() + >>> fig.show() + + Gaussian blur implemented using FFT convolution. Notice the dark borders + around the image, due to the zero-padding beyond its boundaries. + The `convolve2d` function allows for other types of image boundaries, + but is far slower. + + >>> from scipy import datasets + >>> face = datasets.face(gray=True) + >>> kernel = np.outer(signal.windows.gaussian(70, 8), + ... signal.windows.gaussian(70, 8)) + >>> blurred = signal.fftconvolve(face, kernel, mode='same') + + >>> fig, (ax_orig, ax_kernel, ax_blurred) = plt.subplots(3, 1, + ... figsize=(6, 15)) + >>> ax_orig.imshow(face, cmap='gray') + >>> ax_orig.set_title('Original') + >>> ax_orig.set_axis_off() + >>> ax_kernel.imshow(kernel, cmap='gray') + >>> ax_kernel.set_title('Gaussian kernel') + >>> ax_kernel.set_axis_off() + >>> ax_blurred.imshow(blurred, cmap='gray') + >>> ax_blurred.set_title('Blurred') + >>> ax_blurred.set_axis_off() + >>> fig.show() + + """ + in1 = np.asarray(in1) + in2 = np.asarray(in2) + + if in1.ndim == in2.ndim == 0: # scalar inputs + return in1 * in2 + elif in1.ndim != in2.ndim: + raise ValueError("in1 and in2 should have the same dimensionality") + elif in1.size == 0 or in2.size == 0: # empty arrays + return np.array([]) + + in1, in2, axes = _init_freq_conv_axes(in1, in2, mode, axes, + sorted_axes=False) + + s1 = in1.shape + s2 = in2.shape + + shape = [max((s1[i], s2[i])) if i not in axes else s1[i] + s2[i] - 1 + for i in range(in1.ndim)] + + ret = _freq_domain_conv(in1, in2, axes, shape, calc_fast_len=True) + + return _apply_conv_mode(ret, s1, s2, mode, axes) + + +def _calc_oa_lens(s1, s2): + """Calculate the optimal FFT lengths for overlapp-add convolution. + + The calculation is done for a single dimension. + + Parameters + ---------- + s1 : int + Size of the dimension for the first array. + s2 : int + Size of the dimension for the second array. + + Returns + ------- + block_size : int + The size of the FFT blocks. + overlap : int + The amount of overlap between two blocks. + in1_step : int + The size of each step for the first array. + in2_step : int + The size of each step for the first array. + + """ + # Set up the arguments for the conventional FFT approach. + fallback = (s1+s2-1, None, s1, s2) + + # Use conventional FFT convolve if sizes are same. + if s1 == s2 or s1 == 1 or s2 == 1: + return fallback + + if s2 > s1: + s1, s2 = s2, s1 + swapped = True + else: + swapped = False + + # There cannot be a useful block size if s2 is more than half of s1. + if s2 >= s1/2: + return fallback + + # Derivation of optimal block length + # For original formula see: + # https://en.wikipedia.org/wiki/Overlap-add_method + # + # Formula: + # K = overlap = s2-1 + # N = block_size + # C = complexity + # e = exponential, exp(1) + # + # C = (N*(log2(N)+1))/(N-K) + # C = (N*log2(2N))/(N-K) + # C = N/(N-K) * log2(2N) + # C1 = N/(N-K) + # C2 = log2(2N) = ln(2N)/ln(2) + # + # dC1/dN = (1*(N-K)-N)/(N-K)^2 = -K/(N-K)^2 + # dC2/dN = 2/(2*N*ln(2)) = 1/(N*ln(2)) + # + # dC/dN = dC1/dN*C2 + dC2/dN*C1 + # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + N/(N*ln(2)*(N-K)) + # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + 1/(ln(2)*(N-K)) + # dC/dN = -K*ln(2N)/(ln(2)*(N-K)^2) + (N-K)/(ln(2)*(N-K)^2) + # dC/dN = (-K*ln(2N) + (N-K)/(ln(2)*(N-K)^2) + # dC/dN = (N - K*ln(2N) - K)/(ln(2)*(N-K)^2) + # + # Solve for minimum, where dC/dN = 0 + # 0 = (N - K*ln(2N) - K)/(ln(2)*(N-K)^2) + # 0 * ln(2)*(N-K)^2 = N - K*ln(2N) - K + # 0 = N - K*ln(2N) - K + # 0 = N - K*(ln(2N) + 1) + # 0 = N - K*ln(2Ne) + # N = K*ln(2Ne) + # N/K = ln(2Ne) + # + # e^(N/K) = e^ln(2Ne) + # e^(N/K) = 2Ne + # 1/e^(N/K) = 1/(2*N*e) + # e^(N/-K) = 1/(2*N*e) + # e^(N/-K) = K/N*1/(2*K*e) + # N/K*e^(N/-K) = 1/(2*e*K) + # N/-K*e^(N/-K) = -1/(2*e*K) + # + # Using Lambert W function + # https://en.wikipedia.org/wiki/Lambert_W_function + # x = W(y) It is the solution to y = x*e^x + # x = N/-K + # y = -1/(2*e*K) + # + # N/-K = W(-1/(2*e*K)) + # + # N = -K*W(-1/(2*e*K)) + overlap = s2-1 + opt_size = -overlap*lambertw(-1/(2*math.e*overlap), k=-1).real + block_size = sp_fft.next_fast_len(math.ceil(opt_size)) + + # Use conventional FFT convolve if there is only going to be one block. + if block_size >= s1: + return fallback + + if not swapped: + in1_step = block_size-s2+1 + in2_step = s2 + else: + in1_step = s2 + in2_step = block_size-s2+1 + + return block_size, overlap, in1_step, in2_step + + +def oaconvolve(in1, in2, mode="full", axes=None): + """Convolve two N-dimensional arrays using the overlap-add method. + + Convolve `in1` and `in2` using the overlap-add method, with + the output size determined by the `mode` argument. + + This is generally much faster than `convolve` for large arrays (n > ~500), + and generally much faster than `fftconvolve` when one array is much + larger than the other, but can be slower when only a few output values are + needed or when the arrays are very similar in shape, and can only + output float arrays (int or object array inputs will be cast to float). + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear convolution + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + axes : int or array_like of ints or None, optional + Axes over which to compute the convolution. + The default is over all axes. + + Returns + ------- + out : array + An N-dimensional array containing a subset of the discrete linear + convolution of `in1` with `in2`. + + See Also + -------- + convolve : Uses the direct convolution or FFT convolution algorithm + depending on which is faster. + fftconvolve : An implementation of convolution using FFT. + + Notes + ----- + .. versionadded:: 1.4.0 + + References + ---------- + .. [1] Wikipedia, "Overlap-add_method". + https://en.wikipedia.org/wiki/Overlap-add_method + .. [2] Richard G. Lyons. Understanding Digital Signal Processing, + Third Edition, 2011. Chapter 13.10. + ISBN 13: 978-0137-02741-5 + + Examples + -------- + Convolve a 100,000 sample signal with a 512-sample filter. + + >>> import numpy as np + >>> from scipy import signal + >>> rng = np.random.default_rng() + >>> sig = rng.standard_normal(100000) + >>> filt = signal.firwin(512, 0.01) + >>> fsig = signal.oaconvolve(sig, filt) + + >>> import matplotlib.pyplot as plt + >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1) + >>> ax_orig.plot(sig) + >>> ax_orig.set_title('White noise') + >>> ax_mag.plot(fsig) + >>> ax_mag.set_title('Filtered noise') + >>> fig.tight_layout() + >>> fig.show() + + """ + in1 = np.asarray(in1) + in2 = np.asarray(in2) + + if in1.ndim == in2.ndim == 0: # scalar inputs + return in1 * in2 + elif in1.ndim != in2.ndim: + raise ValueError("in1 and in2 should have the same dimensionality") + elif in1.size == 0 or in2.size == 0: # empty arrays + return np.array([]) + elif in1.shape == in2.shape: # Equivalent to fftconvolve + return fftconvolve(in1, in2, mode=mode, axes=axes) + + in1, in2, axes = _init_freq_conv_axes(in1, in2, mode, axes, + sorted_axes=True) + + s1 = in1.shape + s2 = in2.shape + + if not axes: + ret = in1 * in2 + return _apply_conv_mode(ret, s1, s2, mode, axes) + + # Calculate this now since in1 is changed later + shape_final = [None if i not in axes else + s1[i] + s2[i] - 1 for i in range(in1.ndim)] + + # Calculate the block sizes for the output, steps, first and second inputs. + # It is simpler to calculate them all together than doing them in separate + # loops due to all the special cases that need to be handled. + optimal_sizes = ((-1, -1, s1[i], s2[i]) if i not in axes else + _calc_oa_lens(s1[i], s2[i]) for i in range(in1.ndim)) + block_size, overlaps, \ + in1_step, in2_step = zip(*optimal_sizes) + + # Fall back to fftconvolve if there is only one block in every dimension. + if in1_step == s1 and in2_step == s2: + return fftconvolve(in1, in2, mode=mode, axes=axes) + + # Figure out the number of steps and padding. + # This would get too complicated in a list comprehension. + nsteps1 = [] + nsteps2 = [] + pad_size1 = [] + pad_size2 = [] + for i in range(in1.ndim): + if i not in axes: + pad_size1 += [(0, 0)] + pad_size2 += [(0, 0)] + continue + + if s1[i] > in1_step[i]: + curnstep1 = math.ceil((s1[i]+1)/in1_step[i]) + if (block_size[i] - overlaps[i])*curnstep1 < shape_final[i]: + curnstep1 += 1 + + curpad1 = curnstep1*in1_step[i] - s1[i] + else: + curnstep1 = 1 + curpad1 = 0 + + if s2[i] > in2_step[i]: + curnstep2 = math.ceil((s2[i]+1)/in2_step[i]) + if (block_size[i] - overlaps[i])*curnstep2 < shape_final[i]: + curnstep2 += 1 + + curpad2 = curnstep2*in2_step[i] - s2[i] + else: + curnstep2 = 1 + curpad2 = 0 + + nsteps1 += [curnstep1] + nsteps2 += [curnstep2] + pad_size1 += [(0, curpad1)] + pad_size2 += [(0, curpad2)] + + # Pad the array to a size that can be reshaped to the desired shape + # if necessary. + if not all(curpad == (0, 0) for curpad in pad_size1): + in1 = np.pad(in1, pad_size1, mode='constant', constant_values=0) + + if not all(curpad == (0, 0) for curpad in pad_size2): + in2 = np.pad(in2, pad_size2, mode='constant', constant_values=0) + + # Reshape the overlap-add parts to input block sizes. + split_axes = [iax+i for i, iax in enumerate(axes)] + fft_axes = [iax+1 for iax in split_axes] + + # We need to put each new dimension before the corresponding dimension + # being reshaped in order to get the data in the right layout at the end. + reshape_size1 = list(in1_step) + reshape_size2 = list(in2_step) + for i, iax in enumerate(split_axes): + reshape_size1.insert(iax, nsteps1[i]) + reshape_size2.insert(iax, nsteps2[i]) + + in1 = in1.reshape(*reshape_size1) + in2 = in2.reshape(*reshape_size2) + + # Do the convolution. + fft_shape = [block_size[i] for i in axes] + ret = _freq_domain_conv(in1, in2, fft_axes, fft_shape, calc_fast_len=False) + + # Do the overlap-add. + for ax, ax_fft, ax_split in zip(axes, fft_axes, split_axes): + overlap = overlaps[ax] + if overlap is None: + continue + + ret, overpart = np.split(ret, [-overlap], ax_fft) + overpart = np.split(overpart, [-1], ax_split)[0] + + ret_overpart = np.split(ret, [overlap], ax_fft)[0] + ret_overpart = np.split(ret_overpart, [1], ax_split)[1] + ret_overpart += overpart + + # Reshape back to the correct dimensionality. + shape_ret = [ret.shape[i] if i not in fft_axes else + ret.shape[i]*ret.shape[i-1] + for i in range(ret.ndim) if i not in split_axes] + ret = ret.reshape(*shape_ret) + + # Slice to the correct size. + slice_final = tuple([slice(islice) for islice in shape_final]) + ret = ret[slice_final] + + return _apply_conv_mode(ret, s1, s2, mode, axes) + + +def _numeric_arrays(arrays, kinds='buifc'): + """ + See if a list of arrays are all numeric. + + Parameters + ---------- + arrays : array or list of arrays + arrays to check if numeric. + kinds : string-like + The dtypes of the arrays to be checked. If the dtype.kind of + the ndarrays are not in this string the function returns False and + otherwise returns True. + """ + if type(arrays) == np.ndarray: + return arrays.dtype.kind in kinds + for array_ in arrays: + if array_.dtype.kind not in kinds: + return False + return True + + +def _conv_ops(x_shape, h_shape, mode): + """ + Find the number of operations required for direct/fft methods of + convolution. The direct operations were recorded by making a dummy class to + record the number of operations by overriding ``__mul__`` and ``__add__``. + The FFT operations rely on the (well-known) computational complexity of the + FFT (and the implementation of ``_freq_domain_conv``). + + """ + if mode == "full": + out_shape = [n + k - 1 for n, k in zip(x_shape, h_shape)] + elif mode == "valid": + out_shape = [abs(n - k) + 1 for n, k in zip(x_shape, h_shape)] + elif mode == "same": + out_shape = x_shape + else: + raise ValueError("Acceptable mode flags are 'valid'," + f" 'same', or 'full', not mode={mode}") + + s1, s2 = x_shape, h_shape + if len(x_shape) == 1: + s1, s2 = s1[0], s2[0] + if mode == "full": + direct_ops = s1 * s2 + elif mode == "valid": + direct_ops = (s2 - s1 + 1) * s1 if s2 >= s1 else (s1 - s2 + 1) * s2 + elif mode == "same": + direct_ops = (s1 * s2 if s1 < s2 else + s1 * s2 - (s2 // 2) * ((s2 + 1) // 2)) + else: + if mode == "full": + direct_ops = min(_prod(s1), _prod(s2)) * _prod(out_shape) + elif mode == "valid": + direct_ops = min(_prod(s1), _prod(s2)) * _prod(out_shape) + elif mode == "same": + direct_ops = _prod(s1) * _prod(s2) + + full_out_shape = [n + k - 1 for n, k in zip(x_shape, h_shape)] + N = _prod(full_out_shape) + fft_ops = 3 * N * np.log(N) # 3 separate FFTs of size full_out_shape + return fft_ops, direct_ops + + +def _fftconv_faster(x, h, mode): + """ + See if using fftconvolve or convolve is faster. + + Parameters + ---------- + x : np.ndarray + Signal + h : np.ndarray + Kernel + mode : str + Mode passed to convolve + + Returns + ------- + fft_faster : bool + + Notes + ----- + See docstring of `choose_conv_method` for details on tuning hardware. + + See pull request 11031 for more detail: + https://github.com/scipy/scipy/pull/11031. + + """ + fft_ops, direct_ops = _conv_ops(x.shape, h.shape, mode) + offset = -1e-3 if x.ndim == 1 else -1e-4 + constants = { + "valid": (1.89095737e-9, 2.1364985e-10, offset), + "full": (1.7649070e-9, 2.1414831e-10, offset), + "same": (3.2646654e-9, 2.8478277e-10, offset) + if h.size <= x.size + else (3.21635404e-9, 1.1773253e-8, -1e-5), + } if x.ndim == 1 else { + "valid": (1.85927e-9, 2.11242e-8, offset), + "full": (1.99817e-9, 1.66174e-8, offset), + "same": (2.04735e-9, 1.55367e-8, offset), + } + O_fft, O_direct, O_offset = constants[mode] + return O_fft * fft_ops < O_direct * direct_ops + O_offset + + +def _reverse_and_conj(x): + """ + Reverse array `x` in all dimensions and perform the complex conjugate + """ + reverse = (slice(None, None, -1),) * x.ndim + return x[reverse].conj() + + +def _np_conv_ok(volume, kernel, mode): + """ + See if numpy supports convolution of `volume` and `kernel` (i.e. both are + 1D ndarrays and of the appropriate shape). NumPy's 'same' mode uses the + size of the larger input, while SciPy's uses the size of the first input. + + Invalid mode strings will return False and be caught by the calling func. + """ + if volume.ndim == kernel.ndim == 1: + if mode in ('full', 'valid'): + return True + elif mode == 'same': + return volume.size >= kernel.size + else: + return False + + +def _timeit_fast(stmt="pass", setup="pass", repeat=3): + """ + Returns the time the statement/function took, in seconds. + + Faster, less precise version of IPython's timeit. `stmt` can be a statement + written as a string or a callable. + + Will do only 1 loop (like IPython's timeit) with no repetitions + (unlike IPython) for very slow functions. For fast functions, only does + enough loops to take 5 ms, which seems to produce similar results (on + Windows at least), and avoids doing an extraneous cycle that isn't + measured. + + """ + timer = timeit.Timer(stmt, setup) + + # determine number of calls per rep so total time for 1 rep >= 5 ms + x = 0 + for p in range(0, 10): + number = 10**p + x = timer.timeit(number) # seconds + if x >= 5e-3 / 10: # 5 ms for final test, 1/10th that for this one + break + if x > 1: # second + # If it's macroscopic, don't bother with repetitions + best = x + else: + number *= 10 + r = timer.repeat(repeat, number) + best = min(r) + + sec = best / number + return sec + + +def choose_conv_method(in1, in2, mode='full', measure=False): + """ + Find the fastest convolution/correlation method. + + This primarily exists to be called during the ``method='auto'`` option in + `convolve` and `correlate`. It can also be used to determine the value of + ``method`` for many different convolutions of the same dtype/shape. + In addition, it supports timing the convolution to adapt the value of + ``method`` to a particular set of inputs and/or hardware. + + Parameters + ---------- + in1 : array_like + The first argument passed into the convolution function. + in2 : array_like + The second argument passed into the convolution function. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear convolution + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + measure : bool, optional + If True, run and time the convolution of `in1` and `in2` with both + methods and return the fastest. If False (default), predict the fastest + method using precomputed values. + + Returns + ------- + method : str + A string indicating which convolution method is fastest, either + 'direct' or 'fft' + times : dict, optional + A dictionary containing the times (in seconds) needed for each method. + This value is only returned if ``measure=True``. + + See Also + -------- + convolve + correlate + + Notes + ----- + Generally, this method is 99% accurate for 2D signals and 85% accurate + for 1D signals for randomly chosen input sizes. For precision, use + ``measure=True`` to find the fastest method by timing the convolution. + This can be used to avoid the minimal overhead of finding the fastest + ``method`` later, or to adapt the value of ``method`` to a particular set + of inputs. + + Experiments were run on an Amazon EC2 r5a.2xlarge machine to test this + function. These experiments measured the ratio between the time required + when using ``method='auto'`` and the time required for the fastest method + (i.e., ``ratio = time_auto / min(time_fft, time_direct)``). In these + experiments, we found: + + * There is a 95% chance of this ratio being less than 1.5 for 1D signals + and a 99% chance of being less than 2.5 for 2D signals. + * The ratio was always less than 2.5/5 for 1D/2D signals respectively. + * This function is most inaccurate for 1D convolutions that take between 1 + and 10 milliseconds with ``method='direct'``. A good proxy for this + (at least in our experiments) is ``1e6 <= in1.size * in2.size <= 1e7``. + + The 2D results almost certainly generalize to 3D/4D/etc because the + implementation is the same (the 1D implementation is different). + + All the numbers above are specific to the EC2 machine. However, we did find + that this function generalizes fairly decently across hardware. The speed + tests were of similar quality (and even slightly better) than the same + tests performed on the machine to tune this function's numbers (a mid-2014 + 15-inch MacBook Pro with 16GB RAM and a 2.5GHz Intel i7 processor). + + There are cases when `fftconvolve` supports the inputs but this function + returns `direct` (e.g., to protect against floating point integer + precision). + + .. versionadded:: 0.19 + + Examples + -------- + Estimate the fastest method for a given input: + + >>> import numpy as np + >>> from scipy import signal + >>> rng = np.random.default_rng() + >>> img = rng.random((32, 32)) + >>> filter = rng.random((8, 8)) + >>> method = signal.choose_conv_method(img, filter, mode='same') + >>> method + 'fft' + + This can then be applied to other arrays of the same dtype and shape: + + >>> img2 = rng.random((32, 32)) + >>> filter2 = rng.random((8, 8)) + >>> corr2 = signal.correlate(img2, filter2, mode='same', method=method) + >>> conv2 = signal.convolve(img2, filter2, mode='same', method=method) + + The output of this function (``method``) works with `correlate` and + `convolve`. + + """ + volume = np.asarray(in1) + kernel = np.asarray(in2) + + if measure: + times = {} + for method in ['fft', 'direct']: + times[method] = _timeit_fast(lambda: convolve(volume, kernel, + mode=mode, method=method)) + + chosen_method = 'fft' if times['fft'] < times['direct'] else 'direct' + return chosen_method, times + + # for integer input, + # catch when more precision required than float provides (representing an + # integer as float can lose precision in fftconvolve if larger than 2**52) + if any([_numeric_arrays([x], kinds='ui') for x in [volume, kernel]]): + max_value = int(np.abs(volume).max()) * int(np.abs(kernel).max()) + max_value *= int(min(volume.size, kernel.size)) + if max_value > 2**np.finfo('float').nmant - 1: + return 'direct' + + if _numeric_arrays([volume, kernel], kinds='b'): + return 'direct' + + if _numeric_arrays([volume, kernel]): + if _fftconv_faster(volume, kernel, mode): + return 'fft' + + return 'direct' + + +def convolve(in1, in2, mode='full', method='auto'): + """ + Convolve two N-dimensional arrays. + + Convolve `in1` and `in2`, with the output size determined by the + `mode` argument. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear convolution + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + method : str {'auto', 'direct', 'fft'}, optional + A string indicating which method to use to calculate the convolution. + + ``direct`` + The convolution is determined directly from sums, the definition of + convolution. + ``fft`` + The Fourier Transform is used to perform the convolution by calling + `fftconvolve`. + ``auto`` + Automatically chooses direct or Fourier method based on an estimate + of which is faster (default). See Notes for more detail. + + .. versionadded:: 0.19.0 + + Returns + ------- + convolve : array + An N-dimensional array containing a subset of the discrete linear + convolution of `in1` with `in2`. + + Warns + ----- + RuntimeWarning + Use of the FFT convolution on input containing NAN or INF will lead + to the entire output being NAN or INF. Use method='direct' when your + input contains NAN or INF values. + + See Also + -------- + numpy.polymul : performs polynomial multiplication (same operation, but + also accepts poly1d objects) + choose_conv_method : chooses the fastest appropriate convolution method + fftconvolve : Always uses the FFT method. + oaconvolve : Uses the overlap-add method to do convolution, which is + generally faster when the input arrays are large and + significantly different in size. + + Notes + ----- + By default, `convolve` and `correlate` use ``method='auto'``, which calls + `choose_conv_method` to choose the fastest method using pre-computed + values (`choose_conv_method` can also measure real-world timing with a + keyword argument). Because `fftconvolve` relies on floating point numbers, + there are certain constraints that may force `method=direct` (more detail + in `choose_conv_method` docstring). + + Examples + -------- + Smooth a square pulse using a Hann window: + + >>> import numpy as np + >>> from scipy import signal + >>> sig = np.repeat([0., 1., 0.], 100) + >>> win = signal.windows.hann(50) + >>> filtered = signal.convolve(sig, win, mode='same') / sum(win) + + >>> import matplotlib.pyplot as plt + >>> fig, (ax_orig, ax_win, ax_filt) = plt.subplots(3, 1, sharex=True) + >>> ax_orig.plot(sig) + >>> ax_orig.set_title('Original pulse') + >>> ax_orig.margins(0, 0.1) + >>> ax_win.plot(win) + >>> ax_win.set_title('Filter impulse response') + >>> ax_win.margins(0, 0.1) + >>> ax_filt.plot(filtered) + >>> ax_filt.set_title('Filtered signal') + >>> ax_filt.margins(0, 0.1) + >>> fig.tight_layout() + >>> fig.show() + + """ + volume = np.asarray(in1) + kernel = np.asarray(in2) + + if volume.ndim == kernel.ndim == 0: + return volume * kernel + elif volume.ndim != kernel.ndim: + raise ValueError("volume and kernel should have the same " + "dimensionality") + + if _inputs_swap_needed(mode, volume.shape, kernel.shape): + # Convolution is commutative; order doesn't have any effect on output + volume, kernel = kernel, volume + + if method == 'auto': + method = choose_conv_method(volume, kernel, mode=mode) + + if method == 'fft': + out = fftconvolve(volume, kernel, mode=mode) + result_type = np.result_type(volume, kernel) + if result_type.kind in {'u', 'i'}: + out = np.around(out) + + if np.isnan(out.flat[0]) or np.isinf(out.flat[0]): + warnings.warn("Use of fft convolution on input with NAN or inf" + " results in NAN or inf output. Consider using" + " method='direct' instead.", + category=RuntimeWarning, stacklevel=2) + + return out.astype(result_type) + elif method == 'direct': + # fastpath to faster numpy.convolve for 1d inputs when possible + if _np_conv_ok(volume, kernel, mode): + return np.convolve(volume, kernel, mode) + + return correlate(volume, _reverse_and_conj(kernel), mode, 'direct') + else: + raise ValueError("Acceptable method flags are 'auto'," + " 'direct', or 'fft'.") + + +def order_filter(a, domain, rank): + """ + Perform an order filter on an N-D array. + + Perform an order filter on the array in. The domain argument acts as a + mask centered over each pixel. The non-zero elements of domain are + used to select elements surrounding each input pixel which are placed + in a list. The list is sorted, and the output for that pixel is the + element corresponding to rank in the sorted list. + + Parameters + ---------- + a : ndarray + The N-dimensional input array. + domain : array_like + A mask array with the same number of dimensions as `a`. + Each dimension should have an odd number of elements. + rank : int + A non-negative integer which selects the element from the + sorted list (0 corresponds to the smallest element, 1 is the + next smallest element, etc.). + + Returns + ------- + out : ndarray + The results of the order filter in an array with the same + shape as `a`. + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> x = np.arange(25).reshape(5, 5) + >>> domain = np.identity(3) + >>> x + array([[ 0, 1, 2, 3, 4], + [ 5, 6, 7, 8, 9], + [10, 11, 12, 13, 14], + [15, 16, 17, 18, 19], + [20, 21, 22, 23, 24]]) + >>> signal.order_filter(x, domain, 0) + array([[ 0., 0., 0., 0., 0.], + [ 0., 0., 1., 2., 0.], + [ 0., 5., 6., 7., 0.], + [ 0., 10., 11., 12., 0.], + [ 0., 0., 0., 0., 0.]]) + >>> signal.order_filter(x, domain, 2) + array([[ 6., 7., 8., 9., 4.], + [ 11., 12., 13., 14., 9.], + [ 16., 17., 18., 19., 14.], + [ 21., 22., 23., 24., 19.], + [ 20., 21., 22., 23., 24.]]) + + """ + domain = np.asarray(domain) + for dimsize in domain.shape: + if (dimsize % 2) != 1: + raise ValueError("Each dimension of domain argument " + "should have an odd number of elements.") + + a = np.asarray(a) + if a.dtype in [object, 'float128']: + mesg = (f"Using order_filter with arrays of dtype {a.dtype} is " + f"deprecated in SciPy 1.11 and will be removed in SciPy 1.14") + warnings.warn(mesg, DeprecationWarning, stacklevel=2) + + result = _sigtools._order_filterND(a, domain, rank) + else: + result = ndimage.rank_filter(a, rank, footprint=domain, mode='constant') + + return result + + +def medfilt(volume, kernel_size=None): + """ + Perform a median filter on an N-dimensional array. + + Apply a median filter to the input array using a local window-size + given by `kernel_size`. The array will automatically be zero-padded. + + Parameters + ---------- + volume : array_like + An N-dimensional input array. + kernel_size : array_like, optional + A scalar or an N-length list giving the size of the median filter + window in each dimension. Elements of `kernel_size` should be odd. + If `kernel_size` is a scalar, then this scalar is used as the size in + each dimension. Default size is 3 for each dimension. + + Returns + ------- + out : ndarray + An array the same size as input containing the median filtered + result. + + Warns + ----- + UserWarning + If array size is smaller than kernel size along any dimension + + See Also + -------- + scipy.ndimage.median_filter + scipy.signal.medfilt2d + + Notes + ----- + The more general function `scipy.ndimage.median_filter` has a more + efficient implementation of a median filter and therefore runs much faster. + + For 2-dimensional images with ``uint8``, ``float32`` or ``float64`` dtypes, + the specialised function `scipy.signal.medfilt2d` may be faster. + + """ + volume = np.atleast_1d(volume) + if kernel_size is None: + kernel_size = [3] * volume.ndim + kernel_size = np.asarray(kernel_size) + if kernel_size.shape == (): + kernel_size = np.repeat(kernel_size.item(), volume.ndim) + + for k in range(volume.ndim): + if (kernel_size[k] % 2) != 1: + raise ValueError("Each element of kernel_size should be odd.") + if any(k > s for k, s in zip(kernel_size, volume.shape)): + warnings.warn('kernel_size exceeds volume extent: the volume will be ' + 'zero-padded.', + stacklevel=2) + + domain = np.ones(kernel_size, dtype=volume.dtype) + + numels = np.prod(kernel_size, axis=0) + order = numels // 2 + + if volume.dtype in [np.bool_, np.complex64, np.complex128, np.clongdouble, + np.float16]: + raise ValueError(f"dtype={volume.dtype} is not supported by medfilt") + + if volume.dtype.char in ['O', 'g']: + mesg = (f"Using medfilt with arrays of dtype {volume.dtype} is " + f"deprecated in SciPy 1.11 and will be removed in SciPy 1.14") + warnings.warn(mesg, DeprecationWarning, stacklevel=2) + + result = _sigtools._order_filterND(volume, domain, order) + else: + size = math.prod(kernel_size) + result = ndimage.rank_filter(volume, size // 2, size=kernel_size, + mode='constant') + + return result + + +def wiener(im, mysize=None, noise=None): + """ + Perform a Wiener filter on an N-dimensional array. + + Apply a Wiener filter to the N-dimensional array `im`. + + Parameters + ---------- + im : ndarray + An N-dimensional array. + mysize : int or array_like, optional + A scalar or an N-length list giving the size of the Wiener filter + window in each dimension. Elements of mysize should be odd. + If mysize is a scalar, then this scalar is used as the size + in each dimension. + noise : float, optional + The noise-power to use. If None, then noise is estimated as the + average of the local variance of the input. + + Returns + ------- + out : ndarray + Wiener filtered result with the same shape as `im`. + + Notes + ----- + This implementation is similar to wiener2 in Matlab/Octave. + For more details see [1]_ + + References + ---------- + .. [1] Lim, Jae S., Two-Dimensional Signal and Image Processing, + Englewood Cliffs, NJ, Prentice Hall, 1990, p. 548. + + Examples + -------- + >>> from scipy.datasets import face + >>> from scipy.signal import wiener + >>> import matplotlib.pyplot as plt + >>> import numpy as np + >>> rng = np.random.default_rng() + >>> img = rng.random((40, 40)) #Create a random image + >>> filtered_img = wiener(img, (5, 5)) #Filter the image + >>> f, (plot1, plot2) = plt.subplots(1, 2) + >>> plot1.imshow(img) + >>> plot2.imshow(filtered_img) + >>> plt.show() + + """ + im = np.asarray(im) + if mysize is None: + mysize = [3] * im.ndim + mysize = np.asarray(mysize) + if mysize.shape == (): + mysize = np.repeat(mysize.item(), im.ndim) + + # Estimate the local mean + lMean = correlate(im, np.ones(mysize), 'same') / np.prod(mysize, axis=0) + + # Estimate the local variance + lVar = (correlate(im ** 2, np.ones(mysize), 'same') / + np.prod(mysize, axis=0) - lMean ** 2) + + # Estimate the noise power if needed. + if noise is None: + noise = np.mean(np.ravel(lVar), axis=0) + + res = (im - lMean) + res *= (1 - noise / lVar) + res += lMean + out = np.where(lVar < noise, lMean, res) + + return out + + +def convolve2d(in1, in2, mode='full', boundary='fill', fillvalue=0): + """ + Convolve two 2-dimensional arrays. + + Convolve `in1` and `in2` with output size determined by `mode`, and + boundary conditions determined by `boundary` and `fillvalue`. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear convolution + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + boundary : str {'fill', 'wrap', 'symm'}, optional + A flag indicating how to handle boundaries: + + ``fill`` + pad input arrays with fillvalue. (default) + ``wrap`` + circular boundary conditions. + ``symm`` + symmetrical boundary conditions. + + fillvalue : scalar, optional + Value to fill pad input arrays with. Default is 0. + + Returns + ------- + out : ndarray + A 2-dimensional array containing a subset of the discrete linear + convolution of `in1` with `in2`. + + Examples + -------- + Compute the gradient of an image by 2D convolution with a complex Scharr + operator. (Horizontal operator is real, vertical is imaginary.) Use + symmetric boundary condition to avoid creating edges at the image + boundaries. + + >>> import numpy as np + >>> from scipy import signal + >>> from scipy import datasets + >>> ascent = datasets.ascent() + >>> scharr = np.array([[ -3-3j, 0-10j, +3 -3j], + ... [-10+0j, 0+ 0j, +10 +0j], + ... [ -3+3j, 0+10j, +3 +3j]]) # Gx + j*Gy + >>> grad = signal.convolve2d(ascent, scharr, boundary='symm', mode='same') + + >>> import matplotlib.pyplot as plt + >>> fig, (ax_orig, ax_mag, ax_ang) = plt.subplots(3, 1, figsize=(6, 15)) + >>> ax_orig.imshow(ascent, cmap='gray') + >>> ax_orig.set_title('Original') + >>> ax_orig.set_axis_off() + >>> ax_mag.imshow(np.absolute(grad), cmap='gray') + >>> ax_mag.set_title('Gradient magnitude') + >>> ax_mag.set_axis_off() + >>> ax_ang.imshow(np.angle(grad), cmap='hsv') # hsv is cyclic, like angles + >>> ax_ang.set_title('Gradient orientation') + >>> ax_ang.set_axis_off() + >>> fig.show() + + """ + in1 = np.asarray(in1) + in2 = np.asarray(in2) + + if not in1.ndim == in2.ndim == 2: + raise ValueError('convolve2d inputs must both be 2-D arrays') + + if _inputs_swap_needed(mode, in1.shape, in2.shape): + in1, in2 = in2, in1 + + val = _valfrommode(mode) + bval = _bvalfromboundary(boundary) + out = _sigtools._convolve2d(in1, in2, 1, val, bval, fillvalue) + return out + + +def correlate2d(in1, in2, mode='full', boundary='fill', fillvalue=0): + """ + Cross-correlate two 2-dimensional arrays. + + Cross correlate `in1` and `in2` with output size determined by `mode`, and + boundary conditions determined by `boundary` and `fillvalue`. + + Parameters + ---------- + in1 : array_like + First input. + in2 : array_like + Second input. Should have the same number of dimensions as `in1`. + mode : str {'full', 'valid', 'same'}, optional + A string indicating the size of the output: + + ``full`` + The output is the full discrete linear cross-correlation + of the inputs. (Default) + ``valid`` + The output consists only of those elements that do not + rely on the zero-padding. In 'valid' mode, either `in1` or `in2` + must be at least as large as the other in every dimension. + ``same`` + The output is the same size as `in1`, centered + with respect to the 'full' output. + boundary : str {'fill', 'wrap', 'symm'}, optional + A flag indicating how to handle boundaries: + + ``fill`` + pad input arrays with fillvalue. (default) + ``wrap`` + circular boundary conditions. + ``symm`` + symmetrical boundary conditions. + + fillvalue : scalar, optional + Value to fill pad input arrays with. Default is 0. + + Returns + ------- + correlate2d : ndarray + A 2-dimensional array containing a subset of the discrete linear + cross-correlation of `in1` with `in2`. + + Notes + ----- + When using "same" mode with even-length inputs, the outputs of `correlate` + and `correlate2d` differ: There is a 1-index offset between them. + + Examples + -------- + Use 2D cross-correlation to find the location of a template in a noisy + image: + + >>> import numpy as np + >>> from scipy import signal + >>> from scipy import datasets + >>> rng = np.random.default_rng() + >>> face = datasets.face(gray=True) - datasets.face(gray=True).mean() + >>> template = np.copy(face[300:365, 670:750]) # right eye + >>> template -= template.mean() + >>> face = face + rng.standard_normal(face.shape) * 50 # add noise + >>> corr = signal.correlate2d(face, template, boundary='symm', mode='same') + >>> y, x = np.unravel_index(np.argmax(corr), corr.shape) # find the match + + >>> import matplotlib.pyplot as plt + >>> fig, (ax_orig, ax_template, ax_corr) = plt.subplots(3, 1, + ... figsize=(6, 15)) + >>> ax_orig.imshow(face, cmap='gray') + >>> ax_orig.set_title('Original') + >>> ax_orig.set_axis_off() + >>> ax_template.imshow(template, cmap='gray') + >>> ax_template.set_title('Template') + >>> ax_template.set_axis_off() + >>> ax_corr.imshow(corr, cmap='gray') + >>> ax_corr.set_title('Cross-correlation') + >>> ax_corr.set_axis_off() + >>> ax_orig.plot(x, y, 'ro') + >>> fig.show() + + """ + in1 = np.asarray(in1) + in2 = np.asarray(in2) + + if not in1.ndim == in2.ndim == 2: + raise ValueError('correlate2d inputs must both be 2-D arrays') + + swapped_inputs = _inputs_swap_needed(mode, in1.shape, in2.shape) + if swapped_inputs: + in1, in2 = in2, in1 + + val = _valfrommode(mode) + bval = _bvalfromboundary(boundary) + out = _sigtools._convolve2d(in1, in2.conj(), 0, val, bval, fillvalue) + + if swapped_inputs: + out = out[::-1, ::-1] + + return out + + +def medfilt2d(input, kernel_size=3): + """ + Median filter a 2-dimensional array. + + Apply a median filter to the `input` array using a local window-size + given by `kernel_size` (must be odd). The array is zero-padded + automatically. + + Parameters + ---------- + input : array_like + A 2-dimensional input array. + kernel_size : array_like, optional + A scalar or a list of length 2, giving the size of the + median filter window in each dimension. Elements of + `kernel_size` should be odd. If `kernel_size` is a scalar, + then this scalar is used as the size in each dimension. + Default is a kernel of size (3, 3). + + Returns + ------- + out : ndarray + An array the same size as input containing the median filtered + result. + + See Also + -------- + scipy.ndimage.median_filter + + Notes + ----- + This is faster than `medfilt` when the input dtype is ``uint8``, + ``float32``, or ``float64``; for other types, this falls back to + `medfilt`. In some situations, `scipy.ndimage.median_filter` may be + faster than this function. + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> x = np.arange(25).reshape(5, 5) + >>> x + array([[ 0, 1, 2, 3, 4], + [ 5, 6, 7, 8, 9], + [10, 11, 12, 13, 14], + [15, 16, 17, 18, 19], + [20, 21, 22, 23, 24]]) + + # Replaces i,j with the median out of 5*5 window + + >>> signal.medfilt2d(x, kernel_size=5) + array([[ 0, 0, 2, 0, 0], + [ 0, 3, 7, 4, 0], + [ 2, 8, 12, 9, 4], + [ 0, 8, 12, 9, 0], + [ 0, 0, 12, 0, 0]]) + + # Replaces i,j with the median out of default 3*3 window + + >>> signal.medfilt2d(x) + array([[ 0, 1, 2, 3, 0], + [ 1, 6, 7, 8, 4], + [ 6, 11, 12, 13, 9], + [11, 16, 17, 18, 14], + [ 0, 16, 17, 18, 0]]) + + # Replaces i,j with the median out of default 5*3 window + + >>> signal.medfilt2d(x, kernel_size=[5,3]) + array([[ 0, 1, 2, 3, 0], + [ 0, 6, 7, 8, 3], + [ 5, 11, 12, 13, 8], + [ 5, 11, 12, 13, 8], + [ 0, 11, 12, 13, 0]]) + + # Replaces i,j with the median out of default 3*5 window + + >>> signal.medfilt2d(x, kernel_size=[3,5]) + array([[ 0, 0, 2, 1, 0], + [ 1, 5, 7, 6, 3], + [ 6, 10, 12, 11, 8], + [11, 15, 17, 16, 13], + [ 0, 15, 17, 16, 0]]) + + # As seen in the examples, + # kernel numbers must be odd and not exceed original array dim + + """ + image = np.asarray(input) + + # checking dtype.type, rather than just dtype, is necessary for + # excluding np.longdouble with MS Visual C. + if image.dtype.type not in (np.ubyte, np.float32, np.float64): + return medfilt(image, kernel_size) + + if kernel_size is None: + kernel_size = [3] * 2 + kernel_size = np.asarray(kernel_size) + if kernel_size.shape == (): + kernel_size = np.repeat(kernel_size.item(), 2) + + for size in kernel_size: + if (size % 2) != 1: + raise ValueError("Each element of kernel_size should be odd.") + + return _sigtools._medfilt2d(image, kernel_size) + + +def lfilter(b, a, x, axis=-1, zi=None): + """ + Filter data along one-dimension with an IIR or FIR filter. + + Filter a data sequence, `x`, using a digital filter. This works for many + fundamental data types (including Object type). The filter is a direct + form II transposed implementation of the standard difference equation + (see Notes). + + The function `sosfilt` (and filter design using ``output='sos'``) should be + preferred over `lfilter` for most filtering tasks, as second-order sections + have fewer numerical problems. + + Parameters + ---------- + b : array_like + The numerator coefficient vector in a 1-D sequence. + a : array_like + The denominator coefficient vector in a 1-D sequence. If ``a[0]`` + is not 1, then both `a` and `b` are normalized by ``a[0]``. + x : array_like + An N-dimensional input array. + axis : int, optional + The axis of the input data array along which to apply the + linear filter. The filter is applied to each subarray along + this axis. Default is -1. + zi : array_like, optional + Initial conditions for the filter delays. It is a vector + (or array of vectors for an N-dimensional input) of length + ``max(len(a), len(b)) - 1``. If `zi` is None or is not given then + initial rest is assumed. See `lfiltic` for more information. + + Returns + ------- + y : array + The output of the digital filter. + zf : array, optional + If `zi` is None, this is not returned, otherwise, `zf` holds the + final filter delay values. + + See Also + -------- + lfiltic : Construct initial conditions for `lfilter`. + lfilter_zi : Compute initial state (steady state of step response) for + `lfilter`. + filtfilt : A forward-backward filter, to obtain a filter with zero phase. + savgol_filter : A Savitzky-Golay filter. + sosfilt: Filter data using cascaded second-order sections. + sosfiltfilt: A forward-backward filter using second-order sections. + + Notes + ----- + The filter function is implemented as a direct II transposed structure. + This means that the filter implements:: + + a[0]*y[n] = b[0]*x[n] + b[1]*x[n-1] + ... + b[M]*x[n-M] + - a[1]*y[n-1] - ... - a[N]*y[n-N] + + where `M` is the degree of the numerator, `N` is the degree of the + denominator, and `n` is the sample number. It is implemented using + the following difference equations (assuming M = N):: + + a[0]*y[n] = b[0] * x[n] + d[0][n-1] + d[0][n] = b[1] * x[n] - a[1] * y[n] + d[1][n-1] + d[1][n] = b[2] * x[n] - a[2] * y[n] + d[2][n-1] + ... + d[N-2][n] = b[N-1]*x[n] - a[N-1]*y[n] + d[N-1][n-1] + d[N-1][n] = b[N] * x[n] - a[N] * y[n] + + where `d` are the state variables. + + The rational transfer function describing this filter in the + z-transform domain is:: + + -1 -M + b[0] + b[1]z + ... + b[M] z + Y(z) = -------------------------------- X(z) + -1 -N + a[0] + a[1]z + ... + a[N] z + + Examples + -------- + Generate a noisy signal to be filtered: + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + >>> t = np.linspace(-1, 1, 201) + >>> x = (np.sin(2*np.pi*0.75*t*(1-t) + 2.1) + + ... 0.1*np.sin(2*np.pi*1.25*t + 1) + + ... 0.18*np.cos(2*np.pi*3.85*t)) + >>> xn = x + rng.standard_normal(len(t)) * 0.08 + + Create an order 3 lowpass butterworth filter: + + >>> b, a = signal.butter(3, 0.05) + + Apply the filter to xn. Use lfilter_zi to choose the initial condition of + the filter: + + >>> zi = signal.lfilter_zi(b, a) + >>> z, _ = signal.lfilter(b, a, xn, zi=zi*xn[0]) + + Apply the filter again, to have a result filtered at an order the same as + filtfilt: + + >>> z2, _ = signal.lfilter(b, a, z, zi=zi*z[0]) + + Use filtfilt to apply the filter: + + >>> y = signal.filtfilt(b, a, xn) + + Plot the original signal and the various filtered versions: + + >>> plt.figure + >>> plt.plot(t, xn, 'b', alpha=0.75) + >>> plt.plot(t, z, 'r--', t, z2, 'r', t, y, 'k') + >>> plt.legend(('noisy signal', 'lfilter, once', 'lfilter, twice', + ... 'filtfilt'), loc='best') + >>> plt.grid(True) + >>> plt.show() + + """ + b = np.atleast_1d(b) + a = np.atleast_1d(a) + if len(a) == 1: + # This path only supports types fdgFDGO to mirror _linear_filter below. + # Any of b, a, x, or zi can set the dtype, but there is no default + # casting of other types; instead a NotImplementedError is raised. + b = np.asarray(b) + a = np.asarray(a) + if b.ndim != 1 and a.ndim != 1: + raise ValueError('object of too small depth for desired array') + x = _validate_x(x) + inputs = [b, a, x] + if zi is not None: + # _linear_filter does not broadcast zi, but does do expansion of + # singleton dims. + zi = np.asarray(zi) + if zi.ndim != x.ndim: + raise ValueError('object of too small depth for desired array') + expected_shape = list(x.shape) + expected_shape[axis] = b.shape[0] - 1 + expected_shape = tuple(expected_shape) + # check the trivial case where zi is the right shape first + if zi.shape != expected_shape: + strides = zi.ndim * [None] + if axis < 0: + axis += zi.ndim + for k in range(zi.ndim): + if k == axis and zi.shape[k] == expected_shape[k]: + strides[k] = zi.strides[k] + elif k != axis and zi.shape[k] == expected_shape[k]: + strides[k] = zi.strides[k] + elif k != axis and zi.shape[k] == 1: + strides[k] = 0 + else: + raise ValueError('Unexpected shape for zi: expected ' + f'{expected_shape}, found {zi.shape}.') + zi = np.lib.stride_tricks.as_strided(zi, expected_shape, + strides) + inputs.append(zi) + dtype = np.result_type(*inputs) + + if dtype.char not in 'fdgFDGO': + raise NotImplementedError("input type '%s' not supported" % dtype) + + b = np.array(b, dtype=dtype) + a = np.asarray(a, dtype=dtype) + b /= a[0] + x = np.asarray(x, dtype=dtype) + + out_full = np.apply_along_axis(lambda y: np.convolve(b, y), axis, x) + ind = out_full.ndim * [slice(None)] + if zi is not None: + ind[axis] = slice(zi.shape[axis]) + out_full[tuple(ind)] += zi + + ind[axis] = slice(out_full.shape[axis] - len(b) + 1) + out = out_full[tuple(ind)] + + if zi is None: + return out + else: + ind[axis] = slice(out_full.shape[axis] - len(b) + 1, None) + zf = out_full[tuple(ind)] + return out, zf + else: + if zi is None: + return _sigtools._linear_filter(b, a, x, axis) + else: + return _sigtools._linear_filter(b, a, x, axis, zi) + + +def lfiltic(b, a, y, x=None): + """ + Construct initial conditions for lfilter given input and output vectors. + + Given a linear filter (b, a) and initial conditions on the output `y` + and the input `x`, return the initial conditions on the state vector zi + which is used by `lfilter` to generate the output given the input. + + Parameters + ---------- + b : array_like + Linear filter term. + a : array_like + Linear filter term. + y : array_like + Initial conditions. + + If ``N = len(a) - 1``, then ``y = {y[-1], y[-2], ..., y[-N]}``. + + If `y` is too short, it is padded with zeros. + x : array_like, optional + Initial conditions. + + If ``M = len(b) - 1``, then ``x = {x[-1], x[-2], ..., x[-M]}``. + + If `x` is not given, its initial conditions are assumed zero. + + If `x` is too short, it is padded with zeros. + + Returns + ------- + zi : ndarray + The state vector ``zi = {z_0[-1], z_1[-1], ..., z_K-1[-1]}``, + where ``K = max(M, N)``. + + See Also + -------- + lfilter, lfilter_zi + + """ + N = np.size(a) - 1 + M = np.size(b) - 1 + K = max(M, N) + y = np.asarray(y) + + if x is None: + result_type = np.result_type(np.asarray(b), np.asarray(a), y) + if result_type.kind in 'bui': + result_type = np.float64 + x = np.zeros(M, dtype=result_type) + else: + x = np.asarray(x) + + result_type = np.result_type(np.asarray(b), np.asarray(a), y, x) + if result_type.kind in 'bui': + result_type = np.float64 + x = x.astype(result_type) + + L = np.size(x) + if L < M: + x = np.r_[x, np.zeros(M - L)] + + y = y.astype(result_type) + zi = np.zeros(K, result_type) + + L = np.size(y) + if L < N: + y = np.r_[y, np.zeros(N - L)] + + for m in range(M): + zi[m] = np.sum(b[m + 1:] * x[:M - m], axis=0) + + for m in range(N): + zi[m] -= np.sum(a[m + 1:] * y[:N - m], axis=0) + + return zi + + +def deconvolve(signal, divisor): + """Deconvolves ``divisor`` out of ``signal`` using inverse filtering. + + Returns the quotient and remainder such that + ``signal = convolve(divisor, quotient) + remainder`` + + Parameters + ---------- + signal : (N,) array_like + Signal data, typically a recorded signal + divisor : (N,) array_like + Divisor data, typically an impulse response or filter that was + applied to the original signal + + Returns + ------- + quotient : ndarray + Quotient, typically the recovered original signal + remainder : ndarray + Remainder + + See Also + -------- + numpy.polydiv : performs polynomial division (same operation, but + also accepts poly1d objects) + + Examples + -------- + Deconvolve a signal that's been filtered: + + >>> from scipy import signal + >>> original = [0, 1, 0, 0, 1, 1, 0, 0] + >>> impulse_response = [2, 1] + >>> recorded = signal.convolve(impulse_response, original) + >>> recorded + array([0, 2, 1, 0, 2, 3, 1, 0, 0]) + >>> recovered, remainder = signal.deconvolve(recorded, impulse_response) + >>> recovered + array([ 0., 1., 0., 0., 1., 1., 0., 0.]) + + """ + num = np.atleast_1d(signal) + den = np.atleast_1d(divisor) + if num.ndim > 1: + raise ValueError("signal must be 1-D.") + if den.ndim > 1: + raise ValueError("divisor must be 1-D.") + N = len(num) + D = len(den) + if D > N: + quot = [] + rem = num + else: + input = np.zeros(N - D + 1, float) + input[0] = 1 + quot = lfilter(num, den, input) + rem = num - convolve(den, quot, mode='full') + return quot, rem + + +def hilbert(x, N=None, axis=-1): + """ + Compute the analytic signal, using the Hilbert transform. + + The transformation is done along the last axis by default. + + Parameters + ---------- + x : array_like + Signal data. Must be real. + N : int, optional + Number of Fourier components. Default: ``x.shape[axis]`` + axis : int, optional + Axis along which to do the transformation. Default: -1. + + Returns + ------- + xa : ndarray + Analytic signal of `x`, of each 1-D array along `axis` + + Notes + ----- + The analytic signal ``x_a(t)`` of signal ``x(t)`` is: + + .. math:: x_a = F^{-1}(F(x) 2U) = x + i y + + where `F` is the Fourier transform, `U` the unit step function, + and `y` the Hilbert transform of `x`. [1]_ + + In other words, the negative half of the frequency spectrum is zeroed + out, turning the real-valued signal into a complex signal. The Hilbert + transformed signal can be obtained from ``np.imag(hilbert(x))``, and the + original signal from ``np.real(hilbert(x))``. + + References + ---------- + .. [1] Wikipedia, "Analytic signal". + https://en.wikipedia.org/wiki/Analytic_signal + .. [2] Leon Cohen, "Time-Frequency Analysis", 1995. Chapter 2. + .. [3] Alan V. Oppenheim, Ronald W. Schafer. Discrete-Time Signal + Processing, Third Edition, 2009. Chapter 12. + ISBN 13: 978-1292-02572-8 + + Examples + -------- + In this example we use the Hilbert transform to determine the amplitude + envelope and instantaneous frequency of an amplitude-modulated signal. + + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> from scipy.signal import hilbert, chirp + + >>> duration = 1.0 + >>> fs = 400.0 + >>> samples = int(fs*duration) + >>> t = np.arange(samples) / fs + + We create a chirp of which the frequency increases from 20 Hz to 100 Hz and + apply an amplitude modulation. + + >>> signal = chirp(t, 20.0, t[-1], 100.0) + >>> signal *= (1.0 + 0.5 * np.sin(2.0*np.pi*3.0*t) ) + + The amplitude envelope is given by magnitude of the analytic signal. The + instantaneous frequency can be obtained by differentiating the + instantaneous phase in respect to time. The instantaneous phase corresponds + to the phase angle of the analytic signal. + + >>> analytic_signal = hilbert(signal) + >>> amplitude_envelope = np.abs(analytic_signal) + >>> instantaneous_phase = np.unwrap(np.angle(analytic_signal)) + >>> instantaneous_frequency = (np.diff(instantaneous_phase) / + ... (2.0*np.pi) * fs) + + >>> fig, (ax0, ax1) = plt.subplots(nrows=2) + >>> ax0.plot(t, signal, label='signal') + >>> ax0.plot(t, amplitude_envelope, label='envelope') + >>> ax0.set_xlabel("time in seconds") + >>> ax0.legend() + >>> ax1.plot(t[1:], instantaneous_frequency) + >>> ax1.set_xlabel("time in seconds") + >>> ax1.set_ylim(0.0, 120.0) + >>> fig.tight_layout() + + """ + x = np.asarray(x) + if np.iscomplexobj(x): + raise ValueError("x must be real.") + if N is None: + N = x.shape[axis] + if N <= 0: + raise ValueError("N must be positive.") + + Xf = sp_fft.fft(x, N, axis=axis) + h = np.zeros(N, dtype=Xf.dtype) + if N % 2 == 0: + h[0] = h[N // 2] = 1 + h[1:N // 2] = 2 + else: + h[0] = 1 + h[1:(N + 1) // 2] = 2 + + if x.ndim > 1: + ind = [np.newaxis] * x.ndim + ind[axis] = slice(None) + h = h[tuple(ind)] + x = sp_fft.ifft(Xf * h, axis=axis) + return x + + +def hilbert2(x, N=None): + """ + Compute the '2-D' analytic signal of `x` + + Parameters + ---------- + x : array_like + 2-D signal data. + N : int or tuple of two ints, optional + Number of Fourier components. Default is ``x.shape`` + + Returns + ------- + xa : ndarray + Analytic signal of `x` taken along axes (0,1). + + References + ---------- + .. [1] Wikipedia, "Analytic signal", + https://en.wikipedia.org/wiki/Analytic_signal + + """ + x = np.atleast_2d(x) + if x.ndim > 2: + raise ValueError("x must be 2-D.") + if np.iscomplexobj(x): + raise ValueError("x must be real.") + if N is None: + N = x.shape + elif isinstance(N, int): + if N <= 0: + raise ValueError("N must be positive.") + N = (N, N) + elif len(N) != 2 or np.any(np.asarray(N) <= 0): + raise ValueError("When given as a tuple, N must hold exactly " + "two positive integers") + + Xf = sp_fft.fft2(x, N, axes=(0, 1)) + h1 = np.zeros(N[0], dtype=Xf.dtype) + h2 = np.zeros(N[1], dtype=Xf.dtype) + for h in (h1, h2): + N1 = h.shape[0] + if N1 % 2 == 0: + h[0] = h[N1 // 2] = 1 + h[1:N1 // 2] = 2 + else: + h[0] = 1 + h[1:(N1 + 1) // 2] = 2 + + h = h1[:, np.newaxis] * h2[np.newaxis, :] + k = x.ndim + while k > 2: + h = h[:, np.newaxis] + k -= 1 + x = sp_fft.ifft2(Xf * h, axes=(0, 1)) + return x + + +_msg_cplx_sort="""cmplx_sort was deprecated in SciPy 1.12 and will be removed +in SciPy 1.15. The exact equivalent for a numpy array argument is +>>> def cmplx_sort(p): +... idx = np.argsort(abs(p)) +... return np.take(p, idx, 0), idx +""" + +def cmplx_sort(p): + warnings.warn(_msg_cplx_sort, DeprecationWarning, stacklevel=2) + return _cmplx_sort(p) + + +def _cmplx_sort(p): + """Sort roots based on magnitude. + + Parameters + ---------- + p : array_like + The roots to sort, as a 1-D array. + + Returns + ------- + p_sorted : ndarray + Sorted roots. + indx : ndarray + Array of indices needed to sort the input `p`. + + Examples + -------- + >>> from scipy import signal + >>> vals = [1, 4, 1+1.j, 3] + >>> p_sorted, indx = signal.cmplx_sort(vals) + >>> p_sorted + array([1.+0.j, 1.+1.j, 3.+0.j, 4.+0.j]) + >>> indx + array([0, 2, 3, 1]) + """ + p = np.asarray(p) + indx = np.argsort(abs(p)) + return np.take(p, indx, 0), indx + + +def unique_roots(p, tol=1e-3, rtype='min'): + """Determine unique roots and their multiplicities from a list of roots. + + Parameters + ---------- + p : array_like + The list of roots. + tol : float, optional + The tolerance for two roots to be considered equal in terms of + the distance between them. Default is 1e-3. Refer to Notes about + the details on roots grouping. + rtype : {'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}, optional + How to determine the returned root if multiple roots are within + `tol` of each other. + + - 'max', 'maximum': pick the maximum of those roots + - 'min', 'minimum': pick the minimum of those roots + - 'avg', 'mean': take the average of those roots + + When finding minimum or maximum among complex roots they are compared + first by the real part and then by the imaginary part. + + Returns + ------- + unique : ndarray + The list of unique roots. + multiplicity : ndarray + The multiplicity of each root. + + Notes + ----- + If we have 3 roots ``a``, ``b`` and ``c``, such that ``a`` is close to + ``b`` and ``b`` is close to ``c`` (distance is less than `tol`), then it + doesn't necessarily mean that ``a`` is close to ``c``. It means that roots + grouping is not unique. In this function we use "greedy" grouping going + through the roots in the order they are given in the input `p`. + + This utility function is not specific to roots but can be used for any + sequence of values for which uniqueness and multiplicity has to be + determined. For a more general routine, see `numpy.unique`. + + Examples + -------- + >>> from scipy import signal + >>> vals = [0, 1.3, 1.31, 2.8, 1.25, 2.2, 10.3] + >>> uniq, mult = signal.unique_roots(vals, tol=2e-2, rtype='avg') + + Check which roots have multiplicity larger than 1: + + >>> uniq[mult > 1] + array([ 1.305]) + """ + if rtype in ['max', 'maximum']: + reduce = np.max + elif rtype in ['min', 'minimum']: + reduce = np.min + elif rtype in ['avg', 'mean']: + reduce = np.mean + else: + raise ValueError("`rtype` must be one of " + "{'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}") + + p = np.asarray(p) + + points = np.empty((len(p), 2)) + points[:, 0] = np.real(p) + points[:, 1] = np.imag(p) + tree = cKDTree(points) + + p_unique = [] + p_multiplicity = [] + used = np.zeros(len(p), dtype=bool) + for i in range(len(p)): + if used[i]: + continue + + group = tree.query_ball_point(points[i], tol) + group = [x for x in group if not used[x]] + + p_unique.append(reduce(p[group])) + p_multiplicity.append(len(group)) + + used[group] = True + + return np.asarray(p_unique), np.asarray(p_multiplicity) + + +def invres(r, p, k, tol=1e-3, rtype='avg'): + """Compute b(s) and a(s) from partial fraction expansion. + + If `M` is the degree of numerator `b` and `N` the degree of denominator + `a`:: + + b(s) b[0] s**(M) + b[1] s**(M-1) + ... + b[M] + H(s) = ------ = ------------------------------------------ + a(s) a[0] s**(N) + a[1] s**(N-1) + ... + a[N] + + then the partial-fraction expansion H(s) is defined as:: + + r[0] r[1] r[-1] + = -------- + -------- + ... + --------- + k(s) + (s-p[0]) (s-p[1]) (s-p[-1]) + + If there are any repeated roots (closer together than `tol`), then H(s) + has terms like:: + + r[i] r[i+1] r[i+n-1] + -------- + ----------- + ... + ----------- + (s-p[i]) (s-p[i])**2 (s-p[i])**n + + This function is used for polynomials in positive powers of s or z, + such as analog filters or digital filters in controls engineering. For + negative powers of z (typical for digital filters in DSP), use `invresz`. + + Parameters + ---------- + r : array_like + Residues corresponding to the poles. For repeated poles, the residues + must be ordered to correspond to ascending by power fractions. + p : array_like + Poles. Equal poles must be adjacent. + k : array_like + Coefficients of the direct polynomial term. + tol : float, optional + The tolerance for two roots to be considered equal in terms of + the distance between them. Default is 1e-3. See `unique_roots` + for further details. + rtype : {'avg', 'min', 'max'}, optional + Method for computing a root to represent a group of identical roots. + Default is 'avg'. See `unique_roots` for further details. + + Returns + ------- + b : ndarray + Numerator polynomial coefficients. + a : ndarray + Denominator polynomial coefficients. + + See Also + -------- + residue, invresz, unique_roots + + """ + r = np.atleast_1d(r) + p = np.atleast_1d(p) + k = np.trim_zeros(np.atleast_1d(k), 'f') + + unique_poles, multiplicity = _group_poles(p, tol, rtype) + factors, denominator = _compute_factors(unique_poles, multiplicity, + include_powers=True) + + if len(k) == 0: + numerator = 0 + else: + numerator = np.polymul(k, denominator) + + for residue, factor in zip(r, factors): + numerator = np.polyadd(numerator, residue * factor) + + return numerator, denominator + + +def _compute_factors(roots, multiplicity, include_powers=False): + """Compute the total polynomial divided by factors for each root.""" + current = np.array([1]) + suffixes = [current] + for pole, mult in zip(roots[-1:0:-1], multiplicity[-1:0:-1]): + monomial = np.array([1, -pole]) + for _ in range(mult): + current = np.polymul(current, monomial) + suffixes.append(current) + suffixes = suffixes[::-1] + + factors = [] + current = np.array([1]) + for pole, mult, suffix in zip(roots, multiplicity, suffixes): + monomial = np.array([1, -pole]) + block = [] + for i in range(mult): + if i == 0 or include_powers: + block.append(np.polymul(current, suffix)) + current = np.polymul(current, monomial) + factors.extend(reversed(block)) + + return factors, current + + +def _compute_residues(poles, multiplicity, numerator): + denominator_factors, _ = _compute_factors(poles, multiplicity) + numerator = numerator.astype(poles.dtype) + + residues = [] + for pole, mult, factor in zip(poles, multiplicity, + denominator_factors): + if mult == 1: + residues.append(np.polyval(numerator, pole) / + np.polyval(factor, pole)) + else: + numer = numerator.copy() + monomial = np.array([1, -pole]) + factor, d = np.polydiv(factor, monomial) + + block = [] + for _ in range(mult): + numer, n = np.polydiv(numer, monomial) + r = n[0] / d[0] + numer = np.polysub(numer, r * factor) + block.append(r) + + residues.extend(reversed(block)) + + return np.asarray(residues) + + +def residue(b, a, tol=1e-3, rtype='avg'): + """Compute partial-fraction expansion of b(s) / a(s). + + If `M` is the degree of numerator `b` and `N` the degree of denominator + `a`:: + + b(s) b[0] s**(M) + b[1] s**(M-1) + ... + b[M] + H(s) = ------ = ------------------------------------------ + a(s) a[0] s**(N) + a[1] s**(N-1) + ... + a[N] + + then the partial-fraction expansion H(s) is defined as:: + + r[0] r[1] r[-1] + = -------- + -------- + ... + --------- + k(s) + (s-p[0]) (s-p[1]) (s-p[-1]) + + If there are any repeated roots (closer together than `tol`), then H(s) + has terms like:: + + r[i] r[i+1] r[i+n-1] + -------- + ----------- + ... + ----------- + (s-p[i]) (s-p[i])**2 (s-p[i])**n + + This function is used for polynomials in positive powers of s or z, + such as analog filters or digital filters in controls engineering. For + negative powers of z (typical for digital filters in DSP), use `residuez`. + + See Notes for details about the algorithm. + + Parameters + ---------- + b : array_like + Numerator polynomial coefficients. + a : array_like + Denominator polynomial coefficients. + tol : float, optional + The tolerance for two roots to be considered equal in terms of + the distance between them. Default is 1e-3. See `unique_roots` + for further details. + rtype : {'avg', 'min', 'max'}, optional + Method for computing a root to represent a group of identical roots. + Default is 'avg'. See `unique_roots` for further details. + + Returns + ------- + r : ndarray + Residues corresponding to the poles. For repeated poles, the residues + are ordered to correspond to ascending by power fractions. + p : ndarray + Poles ordered by magnitude in ascending order. + k : ndarray + Coefficients of the direct polynomial term. + + See Also + -------- + invres, residuez, numpy.poly, unique_roots + + Notes + ----- + The "deflation through subtraction" algorithm is used for + computations --- method 6 in [1]_. + + The form of partial fraction expansion depends on poles multiplicity in + the exact mathematical sense. However there is no way to exactly + determine multiplicity of roots of a polynomial in numerical computing. + Thus you should think of the result of `residue` with given `tol` as + partial fraction expansion computed for the denominator composed of the + computed poles with empirically determined multiplicity. The choice of + `tol` can drastically change the result if there are close poles. + + References + ---------- + .. [1] J. F. Mahoney, B. D. Sivazlian, "Partial fractions expansion: a + review of computational methodology and efficiency", Journal of + Computational and Applied Mathematics, Vol. 9, 1983. + """ + b = np.asarray(b) + a = np.asarray(a) + if (np.issubdtype(b.dtype, np.complexfloating) + or np.issubdtype(a.dtype, np.complexfloating)): + b = b.astype(complex) + a = a.astype(complex) + else: + b = b.astype(float) + a = a.astype(float) + + b = np.trim_zeros(np.atleast_1d(b), 'f') + a = np.trim_zeros(np.atleast_1d(a), 'f') + + if a.size == 0: + raise ValueError("Denominator `a` is zero.") + + poles = np.roots(a) + if b.size == 0: + return np.zeros(poles.shape), _cmplx_sort(poles)[0], np.array([]) + + if len(b) < len(a): + k = np.empty(0) + else: + k, b = np.polydiv(b, a) + + unique_poles, multiplicity = unique_roots(poles, tol=tol, rtype=rtype) + unique_poles, order = _cmplx_sort(unique_poles) + multiplicity = multiplicity[order] + + residues = _compute_residues(unique_poles, multiplicity, b) + + index = 0 + for pole, mult in zip(unique_poles, multiplicity): + poles[index:index + mult] = pole + index += mult + + return residues / a[0], poles, k + + +def residuez(b, a, tol=1e-3, rtype='avg'): + """Compute partial-fraction expansion of b(z) / a(z). + + If `M` is the degree of numerator `b` and `N` the degree of denominator + `a`:: + + b(z) b[0] + b[1] z**(-1) + ... + b[M] z**(-M) + H(z) = ------ = ------------------------------------------ + a(z) a[0] + a[1] z**(-1) + ... + a[N] z**(-N) + + then the partial-fraction expansion H(z) is defined as:: + + r[0] r[-1] + = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ... + (1-p[0]z**(-1)) (1-p[-1]z**(-1)) + + If there are any repeated roots (closer than `tol`), then the partial + fraction expansion has terms like:: + + r[i] r[i+1] r[i+n-1] + -------------- + ------------------ + ... + ------------------ + (1-p[i]z**(-1)) (1-p[i]z**(-1))**2 (1-p[i]z**(-1))**n + + This function is used for polynomials in negative powers of z, + such as digital filters in DSP. For positive powers, use `residue`. + + See Notes of `residue` for details about the algorithm. + + Parameters + ---------- + b : array_like + Numerator polynomial coefficients. + a : array_like + Denominator polynomial coefficients. + tol : float, optional + The tolerance for two roots to be considered equal in terms of + the distance between them. Default is 1e-3. See `unique_roots` + for further details. + rtype : {'avg', 'min', 'max'}, optional + Method for computing a root to represent a group of identical roots. + Default is 'avg'. See `unique_roots` for further details. + + Returns + ------- + r : ndarray + Residues corresponding to the poles. For repeated poles, the residues + are ordered to correspond to ascending by power fractions. + p : ndarray + Poles ordered by magnitude in ascending order. + k : ndarray + Coefficients of the direct polynomial term. + + See Also + -------- + invresz, residue, unique_roots + """ + b = np.asarray(b) + a = np.asarray(a) + if (np.issubdtype(b.dtype, np.complexfloating) + or np.issubdtype(a.dtype, np.complexfloating)): + b = b.astype(complex) + a = a.astype(complex) + else: + b = b.astype(float) + a = a.astype(float) + + b = np.trim_zeros(np.atleast_1d(b), 'b') + a = np.trim_zeros(np.atleast_1d(a), 'b') + + if a.size == 0: + raise ValueError("Denominator `a` is zero.") + elif a[0] == 0: + raise ValueError("First coefficient of determinant `a` must be " + "non-zero.") + + poles = np.roots(a) + if b.size == 0: + return np.zeros(poles.shape), _cmplx_sort(poles)[0], np.array([]) + + b_rev = b[::-1] + a_rev = a[::-1] + + if len(b_rev) < len(a_rev): + k_rev = np.empty(0) + else: + k_rev, b_rev = np.polydiv(b_rev, a_rev) + + unique_poles, multiplicity = unique_roots(poles, tol=tol, rtype=rtype) + unique_poles, order = _cmplx_sort(unique_poles) + multiplicity = multiplicity[order] + + residues = _compute_residues(1 / unique_poles, multiplicity, b_rev) + + index = 0 + powers = np.empty(len(residues), dtype=int) + for pole, mult in zip(unique_poles, multiplicity): + poles[index:index + mult] = pole + powers[index:index + mult] = 1 + np.arange(mult) + index += mult + + residues *= (-poles) ** powers / a_rev[0] + + return residues, poles, k_rev[::-1] + + +def _group_poles(poles, tol, rtype): + if rtype in ['max', 'maximum']: + reduce = np.max + elif rtype in ['min', 'minimum']: + reduce = np.min + elif rtype in ['avg', 'mean']: + reduce = np.mean + else: + raise ValueError("`rtype` must be one of " + "{'max', 'maximum', 'min', 'minimum', 'avg', 'mean'}") + + unique = [] + multiplicity = [] + + pole = poles[0] + block = [pole] + for i in range(1, len(poles)): + if abs(poles[i] - pole) <= tol: + block.append(pole) + else: + unique.append(reduce(block)) + multiplicity.append(len(block)) + pole = poles[i] + block = [pole] + + unique.append(reduce(block)) + multiplicity.append(len(block)) + + return np.asarray(unique), np.asarray(multiplicity) + + +def invresz(r, p, k, tol=1e-3, rtype='avg'): + """Compute b(z) and a(z) from partial fraction expansion. + + If `M` is the degree of numerator `b` and `N` the degree of denominator + `a`:: + + b(z) b[0] + b[1] z**(-1) + ... + b[M] z**(-M) + H(z) = ------ = ------------------------------------------ + a(z) a[0] + a[1] z**(-1) + ... + a[N] z**(-N) + + then the partial-fraction expansion H(z) is defined as:: + + r[0] r[-1] + = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ... + (1-p[0]z**(-1)) (1-p[-1]z**(-1)) + + If there are any repeated roots (closer than `tol`), then the partial + fraction expansion has terms like:: + + r[i] r[i+1] r[i+n-1] + -------------- + ------------------ + ... + ------------------ + (1-p[i]z**(-1)) (1-p[i]z**(-1))**2 (1-p[i]z**(-1))**n + + This function is used for polynomials in negative powers of z, + such as digital filters in DSP. For positive powers, use `invres`. + + Parameters + ---------- + r : array_like + Residues corresponding to the poles. For repeated poles, the residues + must be ordered to correspond to ascending by power fractions. + p : array_like + Poles. Equal poles must be adjacent. + k : array_like + Coefficients of the direct polynomial term. + tol : float, optional + The tolerance for two roots to be considered equal in terms of + the distance between them. Default is 1e-3. See `unique_roots` + for further details. + rtype : {'avg', 'min', 'max'}, optional + Method for computing a root to represent a group of identical roots. + Default is 'avg'. See `unique_roots` for further details. + + Returns + ------- + b : ndarray + Numerator polynomial coefficients. + a : ndarray + Denominator polynomial coefficients. + + See Also + -------- + residuez, unique_roots, invres + + """ + r = np.atleast_1d(r) + p = np.atleast_1d(p) + k = np.trim_zeros(np.atleast_1d(k), 'b') + + unique_poles, multiplicity = _group_poles(p, tol, rtype) + factors, denominator = _compute_factors(unique_poles, multiplicity, + include_powers=True) + + if len(k) == 0: + numerator = 0 + else: + numerator = np.polymul(k[::-1], denominator[::-1]) + + for residue, factor in zip(r, factors): + numerator = np.polyadd(numerator, residue * factor[::-1]) + + return numerator[::-1], denominator + + +def resample(x, num, t=None, axis=0, window=None, domain='time'): + """ + Resample `x` to `num` samples using Fourier method along the given axis. + + The resampled signal starts at the same value as `x` but is sampled + with a spacing of ``len(x) / num * (spacing of x)``. Because a + Fourier method is used, the signal is assumed to be periodic. + + Parameters + ---------- + x : array_like + The data to be resampled. + num : int + The number of samples in the resampled signal. + t : array_like, optional + If `t` is given, it is assumed to be the equally spaced sample + positions associated with the signal data in `x`. + axis : int, optional + The axis of `x` that is resampled. Default is 0. + window : array_like, callable, string, float, or tuple, optional + Specifies the window applied to the signal in the Fourier + domain. See below for details. + domain : string, optional + A string indicating the domain of the input `x`: + ``time`` Consider the input `x` as time-domain (Default), + ``freq`` Consider the input `x` as frequency-domain. + + Returns + ------- + resampled_x or (resampled_x, resampled_t) + Either the resampled array, or, if `t` was given, a tuple + containing the resampled array and the corresponding resampled + positions. + + See Also + -------- + decimate : Downsample the signal after applying an FIR or IIR filter. + resample_poly : Resample using polyphase filtering and an FIR filter. + + Notes + ----- + The argument `window` controls a Fourier-domain window that tapers + the Fourier spectrum before zero-padding to alleviate ringing in + the resampled values for sampled signals you didn't intend to be + interpreted as band-limited. + + If `window` is a function, then it is called with a vector of inputs + indicating the frequency bins (i.e. fftfreq(x.shape[axis]) ). + + If `window` is an array of the same length as `x.shape[axis]` it is + assumed to be the window to be applied directly in the Fourier + domain (with dc and low-frequency first). + + For any other type of `window`, the function `scipy.signal.get_window` + is called to generate the window. + + The first sample of the returned vector is the same as the first + sample of the input vector. The spacing between samples is changed + from ``dx`` to ``dx * len(x) / num``. + + If `t` is not None, then it is used solely to calculate the resampled + positions `resampled_t` + + As noted, `resample` uses FFT transformations, which can be very + slow if the number of input or output samples is large and prime; + see `scipy.fft.fft`. + + Examples + -------- + Note that the end of the resampled data rises to meet the first + sample of the next cycle: + + >>> import numpy as np + >>> from scipy import signal + + >>> x = np.linspace(0, 10, 20, endpoint=False) + >>> y = np.cos(-x**2/6.0) + >>> f = signal.resample(y, 100) + >>> xnew = np.linspace(0, 10, 100, endpoint=False) + + >>> import matplotlib.pyplot as plt + >>> plt.plot(x, y, 'go-', xnew, f, '.-', 10, y[0], 'ro') + >>> plt.legend(['data', 'resampled'], loc='best') + >>> plt.show() + """ + + if domain not in ('time', 'freq'): + raise ValueError("Acceptable domain flags are 'time' or" + f" 'freq', not domain={domain}") + + x = np.asarray(x) + Nx = x.shape[axis] + + # Check if we can use faster real FFT + real_input = np.isrealobj(x) + + if domain == 'time': + # Forward transform + if real_input: + X = sp_fft.rfft(x, axis=axis) + else: # Full complex FFT + X = sp_fft.fft(x, axis=axis) + else: # domain == 'freq' + X = x + + # Apply window to spectrum + if window is not None: + if callable(window): + W = window(sp_fft.fftfreq(Nx)) + elif isinstance(window, np.ndarray): + if window.shape != (Nx,): + raise ValueError('window must have the same length as data') + W = window + else: + W = sp_fft.ifftshift(get_window(window, Nx)) + + newshape_W = [1] * x.ndim + newshape_W[axis] = X.shape[axis] + if real_input: + # Fold the window back on itself to mimic complex behavior + W_real = W.copy() + W_real[1:] += W_real[-1:0:-1] + W_real[1:] *= 0.5 + X *= W_real[:newshape_W[axis]].reshape(newshape_W) + else: + X *= W.reshape(newshape_W) + + # Copy each half of the original spectrum to the output spectrum, either + # truncating high frequencies (downsampling) or zero-padding them + # (upsampling) + + # Placeholder array for output spectrum + newshape = list(x.shape) + if real_input: + newshape[axis] = num // 2 + 1 + else: + newshape[axis] = num + Y = np.zeros(newshape, X.dtype) + + # Copy positive frequency components (and Nyquist, if present) + N = min(num, Nx) + nyq = N // 2 + 1 # Slice index that includes Nyquist if present + sl = [slice(None)] * x.ndim + sl[axis] = slice(0, nyq) + Y[tuple(sl)] = X[tuple(sl)] + if not real_input: + # Copy negative frequency components + if N > 2: # (slice expression doesn't collapse to empty array) + sl[axis] = slice(nyq - N, None) + Y[tuple(sl)] = X[tuple(sl)] + + # Split/join Nyquist component(s) if present + # So far we have set Y[+N/2]=X[+N/2] + if N % 2 == 0: + if num < Nx: # downsampling + if real_input: + sl[axis] = slice(N//2, N//2 + 1) + Y[tuple(sl)] *= 2. + else: + # select the component of Y at frequency +N/2, + # add the component of X at -N/2 + sl[axis] = slice(-N//2, -N//2 + 1) + Y[tuple(sl)] += X[tuple(sl)] + elif Nx < num: # upsampling + # select the component at frequency +N/2 and halve it + sl[axis] = slice(N//2, N//2 + 1) + Y[tuple(sl)] *= 0.5 + if not real_input: + temp = Y[tuple(sl)] + # set the component at -N/2 equal to the component at +N/2 + sl[axis] = slice(num-N//2, num-N//2 + 1) + Y[tuple(sl)] = temp + + # Inverse transform + if real_input: + y = sp_fft.irfft(Y, num, axis=axis) + else: + y = sp_fft.ifft(Y, axis=axis, overwrite_x=True) + + y *= (float(num) / float(Nx)) + + if t is None: + return y + else: + new_t = np.arange(0, num) * (t[1] - t[0]) * Nx / float(num) + t[0] + return y, new_t + + +def resample_poly(x, up, down, axis=0, window=('kaiser', 5.0), + padtype='constant', cval=None): + """ + Resample `x` along the given axis using polyphase filtering. + + The signal `x` is upsampled by the factor `up`, a zero-phase low-pass + FIR filter is applied, and then it is downsampled by the factor `down`. + The resulting sample rate is ``up / down`` times the original sample + rate. By default, values beyond the boundary of the signal are assumed + to be zero during the filtering step. + + Parameters + ---------- + x : array_like + The data to be resampled. + up : int + The upsampling factor. + down : int + The downsampling factor. + axis : int, optional + The axis of `x` that is resampled. Default is 0. + window : string, tuple, or array_like, optional + Desired window to use to design the low-pass filter, or the FIR filter + coefficients to employ. See below for details. + padtype : string, optional + `constant`, `line`, `mean`, `median`, `maximum`, `minimum` or any of + the other signal extension modes supported by `scipy.signal.upfirdn`. + Changes assumptions on values beyond the boundary. If `constant`, + assumed to be `cval` (default zero). If `line` assumed to continue a + linear trend defined by the first and last points. `mean`, `median`, + `maximum` and `minimum` work as in `np.pad` and assume that the values + beyond the boundary are the mean, median, maximum or minimum + respectively of the array along the axis. + + .. versionadded:: 1.4.0 + cval : float, optional + Value to use if `padtype='constant'`. Default is zero. + + .. versionadded:: 1.4.0 + + Returns + ------- + resampled_x : array + The resampled array. + + See Also + -------- + decimate : Downsample the signal after applying an FIR or IIR filter. + resample : Resample up or down using the FFT method. + + Notes + ----- + This polyphase method will likely be faster than the Fourier method + in `scipy.signal.resample` when the number of samples is large and + prime, or when the number of samples is large and `up` and `down` + share a large greatest common denominator. The length of the FIR + filter used will depend on ``max(up, down) // gcd(up, down)``, and + the number of operations during polyphase filtering will depend on + the filter length and `down` (see `scipy.signal.upfirdn` for details). + + The argument `window` specifies the FIR low-pass filter design. + + If `window` is an array_like it is assumed to be the FIR filter + coefficients. Note that the FIR filter is applied after the upsampling + step, so it should be designed to operate on a signal at a sampling + frequency higher than the original by a factor of `up//gcd(up, down)`. + This function's output will be centered with respect to this array, so it + is best to pass a symmetric filter with an odd number of samples if, as + is usually the case, a zero-phase filter is desired. + + For any other type of `window`, the functions `scipy.signal.get_window` + and `scipy.signal.firwin` are called to generate the appropriate filter + coefficients. + + The first sample of the returned vector is the same as the first + sample of the input vector. The spacing between samples is changed + from ``dx`` to ``dx * down / float(up)``. + + Examples + -------- + By default, the end of the resampled data rises to meet the first + sample of the next cycle for the FFT method, and gets closer to zero + for the polyphase method: + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + + >>> x = np.linspace(0, 10, 20, endpoint=False) + >>> y = np.cos(-x**2/6.0) + >>> f_fft = signal.resample(y, 100) + >>> f_poly = signal.resample_poly(y, 100, 20) + >>> xnew = np.linspace(0, 10, 100, endpoint=False) + + >>> plt.plot(xnew, f_fft, 'b.-', xnew, f_poly, 'r.-') + >>> plt.plot(x, y, 'ko-') + >>> plt.plot(10, y[0], 'bo', 10, 0., 'ro') # boundaries + >>> plt.legend(['resample', 'resamp_poly', 'data'], loc='best') + >>> plt.show() + + This default behaviour can be changed by using the padtype option: + + >>> N = 5 + >>> x = np.linspace(0, 1, N, endpoint=False) + >>> y = 2 + x**2 - 1.7*np.sin(x) + .2*np.cos(11*x) + >>> y2 = 1 + x**3 + 0.1*np.sin(x) + .1*np.cos(11*x) + >>> Y = np.stack([y, y2], axis=-1) + >>> up = 4 + >>> xr = np.linspace(0, 1, N*up, endpoint=False) + + >>> y2 = signal.resample_poly(Y, up, 1, padtype='constant') + >>> y3 = signal.resample_poly(Y, up, 1, padtype='mean') + >>> y4 = signal.resample_poly(Y, up, 1, padtype='line') + + >>> for i in [0,1]: + ... plt.figure() + ... plt.plot(xr, y4[:,i], 'g.', label='line') + ... plt.plot(xr, y3[:,i], 'y.', label='mean') + ... plt.plot(xr, y2[:,i], 'r.', label='constant') + ... plt.plot(x, Y[:,i], 'k-') + ... plt.legend() + >>> plt.show() + + """ + x = np.asarray(x) + if up != int(up): + raise ValueError("up must be an integer") + if down != int(down): + raise ValueError("down must be an integer") + up = int(up) + down = int(down) + if up < 1 or down < 1: + raise ValueError('up and down must be >= 1') + if cval is not None and padtype != 'constant': + raise ValueError('cval has no effect when padtype is ', padtype) + + # Determine our up and down factors + # Use a rational approximation to save computation time on really long + # signals + g_ = math.gcd(up, down) + up //= g_ + down //= g_ + if up == down == 1: + return x.copy() + n_in = x.shape[axis] + n_out = n_in * up + n_out = n_out // down + bool(n_out % down) + + if isinstance(window, (list, np.ndarray)): + window = np.array(window) # use array to force a copy (we modify it) + if window.ndim > 1: + raise ValueError('window must be 1-D') + half_len = (window.size - 1) // 2 + h = window + else: + # Design a linear-phase low-pass FIR filter + max_rate = max(up, down) + f_c = 1. / max_rate # cutoff of FIR filter (rel. to Nyquist) + half_len = 10 * max_rate # reasonable cutoff for sinc-like function + h = firwin(2 * half_len + 1, f_c, + window=window).astype(x.dtype) # match dtype of x + h *= up + + # Zero-pad our filter to put the output samples at the center + n_pre_pad = (down - half_len % down) + n_post_pad = 0 + n_pre_remove = (half_len + n_pre_pad) // down + # We should rarely need to do this given our filter lengths... + while _output_len(len(h) + n_pre_pad + n_post_pad, n_in, + up, down) < n_out + n_pre_remove: + n_post_pad += 1 + h = np.concatenate((np.zeros(n_pre_pad, dtype=h.dtype), h, + np.zeros(n_post_pad, dtype=h.dtype))) + n_pre_remove_end = n_pre_remove + n_out + + # Remove background depending on the padtype option + funcs = {'mean': np.mean, 'median': np.median, + 'minimum': np.amin, 'maximum': np.amax} + upfirdn_kwargs = {'mode': 'constant', 'cval': 0} + if padtype in funcs: + background_values = funcs[padtype](x, axis=axis, keepdims=True) + elif padtype in _upfirdn_modes: + upfirdn_kwargs = {'mode': padtype} + if padtype == 'constant': + if cval is None: + cval = 0 + upfirdn_kwargs['cval'] = cval + else: + raise ValueError( + 'padtype must be one of: maximum, mean, median, minimum, ' + + ', '.join(_upfirdn_modes)) + + if padtype in funcs: + x = x - background_values + + # filter then remove excess + y = upfirdn(h, x, up, down, axis=axis, **upfirdn_kwargs) + keep = [slice(None), ]*x.ndim + keep[axis] = slice(n_pre_remove, n_pre_remove_end) + y_keep = y[tuple(keep)] + + # Add background back + if padtype in funcs: + y_keep += background_values + + return y_keep + + +def vectorstrength(events, period): + ''' + Determine the vector strength of the events corresponding to the given + period. + + The vector strength is a measure of phase synchrony, how well the + timing of the events is synchronized to a single period of a periodic + signal. + + If multiple periods are used, calculate the vector strength of each. + This is called the "resonating vector strength". + + Parameters + ---------- + events : 1D array_like + An array of time points containing the timing of the events. + period : float or array_like + The period of the signal that the events should synchronize to. + The period is in the same units as `events`. It can also be an array + of periods, in which case the outputs are arrays of the same length. + + Returns + ------- + strength : float or 1D array + The strength of the synchronization. 1.0 is perfect synchronization + and 0.0 is no synchronization. If `period` is an array, this is also + an array with each element containing the vector strength at the + corresponding period. + phase : float or array + The phase that the events are most strongly synchronized to in radians. + If `period` is an array, this is also an array with each element + containing the phase for the corresponding period. + + References + ---------- + van Hemmen, JL, Longtin, A, and Vollmayr, AN. Testing resonating vector + strength: Auditory system, electric fish, and noise. + Chaos 21, 047508 (2011); + :doi:`10.1063/1.3670512`. + van Hemmen, JL. Vector strength after Goldberg, Brown, and von Mises: + biological and mathematical perspectives. Biol Cybern. + 2013 Aug;107(4):385-96. :doi:`10.1007/s00422-013-0561-7`. + van Hemmen, JL and Vollmayr, AN. Resonating vector strength: what happens + when we vary the "probing" frequency while keeping the spike times + fixed. Biol Cybern. 2013 Aug;107(4):491-94. + :doi:`10.1007/s00422-013-0560-8`. + ''' + events = np.asarray(events) + period = np.asarray(period) + if events.ndim > 1: + raise ValueError('events cannot have dimensions more than 1') + if period.ndim > 1: + raise ValueError('period cannot have dimensions more than 1') + + # we need to know later if period was originally a scalar + scalarperiod = not period.ndim + + events = np.atleast_2d(events) + period = np.atleast_2d(period) + if (period <= 0).any(): + raise ValueError('periods must be positive') + + # this converts the times to vectors + vectors = np.exp(np.dot(2j*np.pi/period.T, events)) + + # the vector strength is just the magnitude of the mean of the vectors + # the vector phase is the angle of the mean of the vectors + vectormean = np.mean(vectors, axis=1) + strength = abs(vectormean) + phase = np.angle(vectormean) + + # if the original period was a scalar, return scalars + if scalarperiod: + strength = strength[0] + phase = phase[0] + return strength, phase + + +def detrend(data, axis=-1, type='linear', bp=0, overwrite_data=False): + """ + Remove linear trend along axis from data. + + Parameters + ---------- + data : array_like + The input data. + axis : int, optional + The axis along which to detrend the data. By default this is the + last axis (-1). + type : {'linear', 'constant'}, optional + The type of detrending. If ``type == 'linear'`` (default), + the result of a linear least-squares fit to `data` is subtracted + from `data`. + If ``type == 'constant'``, only the mean of `data` is subtracted. + bp : array_like of ints, optional + A sequence of break points. If given, an individual linear fit is + performed for each part of `data` between two break points. + Break points are specified as indices into `data`. This parameter + only has an effect when ``type == 'linear'``. + overwrite_data : bool, optional + If True, perform in place detrending and avoid a copy. Default is False + + Returns + ------- + ret : ndarray + The detrended input data. + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> rng = np.random.default_rng() + >>> npoints = 1000 + >>> noise = rng.standard_normal(npoints) + >>> x = 3 + 2*np.linspace(0, 1, npoints) + noise + >>> (signal.detrend(x) - noise).max() + 0.06 # random + + """ + if type not in ['linear', 'l', 'constant', 'c']: + raise ValueError("Trend type must be 'linear' or 'constant'.") + data = np.asarray(data) + dtype = data.dtype.char + if dtype not in 'dfDF': + dtype = 'd' + if type in ['constant', 'c']: + ret = data - np.mean(data, axis, keepdims=True) + return ret + else: + dshape = data.shape + N = dshape[axis] + bp = np.sort(np.unique(np.concatenate(np.atleast_1d(0, bp, N)))) + if np.any(bp > N): + raise ValueError("Breakpoints must be less than length " + "of data along given axis.") + + # Restructure data so that axis is along first dimension and + # all other dimensions are collapsed into second dimension + rnk = len(dshape) + if axis < 0: + axis = axis + rnk + newdata = np.moveaxis(data, axis, 0) + newdata_shape = newdata.shape + newdata = newdata.reshape(N, -1) + + if not overwrite_data: + newdata = newdata.copy() # make sure we have a copy + if newdata.dtype.char not in 'dfDF': + newdata = newdata.astype(dtype) + +# Nreg = len(bp) - 1 + # Find leastsq fit and remove it for each piece + for m in range(len(bp) - 1): + Npts = bp[m + 1] - bp[m] + A = np.ones((Npts, 2), dtype) + A[:, 0] = np.arange(1, Npts + 1, dtype=dtype) / Npts + sl = slice(bp[m], bp[m + 1]) + coef, resids, rank, s = linalg.lstsq(A, newdata[sl]) + newdata[sl] = newdata[sl] - A @ coef + + # Put data back in original shape. + newdata = newdata.reshape(newdata_shape) + ret = np.moveaxis(newdata, 0, axis) + return ret + + +def lfilter_zi(b, a): + """ + Construct initial conditions for lfilter for step response steady-state. + + Compute an initial state `zi` for the `lfilter` function that corresponds + to the steady state of the step response. + + A typical use of this function is to set the initial state so that the + output of the filter starts at the same value as the first element of + the signal to be filtered. + + Parameters + ---------- + b, a : array_like (1-D) + The IIR filter coefficients. See `lfilter` for more + information. + + Returns + ------- + zi : 1-D ndarray + The initial state for the filter. + + See Also + -------- + lfilter, lfiltic, filtfilt + + Notes + ----- + A linear filter with order m has a state space representation (A, B, C, D), + for which the output y of the filter can be expressed as:: + + z(n+1) = A*z(n) + B*x(n) + y(n) = C*z(n) + D*x(n) + + where z(n) is a vector of length m, A has shape (m, m), B has shape + (m, 1), C has shape (1, m) and D has shape (1, 1) (assuming x(n) is + a scalar). lfilter_zi solves:: + + zi = A*zi + B + + In other words, it finds the initial condition for which the response + to an input of all ones is a constant. + + Given the filter coefficients `a` and `b`, the state space matrices + for the transposed direct form II implementation of the linear filter, + which is the implementation used by scipy.signal.lfilter, are:: + + A = scipy.linalg.companion(a).T + B = b[1:] - a[1:]*b[0] + + assuming `a[0]` is 1.0; if `a[0]` is not 1, `a` and `b` are first + divided by a[0]. + + Examples + -------- + The following code creates a lowpass Butterworth filter. Then it + applies that filter to an array whose values are all 1.0; the + output is also all 1.0, as expected for a lowpass filter. If the + `zi` argument of `lfilter` had not been given, the output would have + shown the transient signal. + + >>> from numpy import array, ones + >>> from scipy.signal import lfilter, lfilter_zi, butter + >>> b, a = butter(5, 0.25) + >>> zi = lfilter_zi(b, a) + >>> y, zo = lfilter(b, a, ones(10), zi=zi) + >>> y + array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]) + + Another example: + + >>> x = array([0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0]) + >>> y, zf = lfilter(b, a, x, zi=zi*x[0]) + >>> y + array([ 0.5 , 0.5 , 0.5 , 0.49836039, 0.48610528, + 0.44399389, 0.35505241]) + + Note that the `zi` argument to `lfilter` was computed using + `lfilter_zi` and scaled by `x[0]`. Then the output `y` has no + transient until the input drops from 0.5 to 0.0. + + """ + + # FIXME: Can this function be replaced with an appropriate + # use of lfiltic? For example, when b,a = butter(N,Wn), + # lfiltic(b, a, y=numpy.ones_like(a), x=numpy.ones_like(b)). + # + + # We could use scipy.signal.normalize, but it uses warnings in + # cases where a ValueError is more appropriate, and it allows + # b to be 2D. + b = np.atleast_1d(b) + if b.ndim != 1: + raise ValueError("Numerator b must be 1-D.") + a = np.atleast_1d(a) + if a.ndim != 1: + raise ValueError("Denominator a must be 1-D.") + + while len(a) > 1 and a[0] == 0.0: + a = a[1:] + if a.size < 1: + raise ValueError("There must be at least one nonzero `a` coefficient.") + + if a[0] != 1.0: + # Normalize the coefficients so a[0] == 1. + b = b / a[0] + a = a / a[0] + + n = max(len(a), len(b)) + + # Pad a or b with zeros so they are the same length. + if len(a) < n: + a = np.r_[a, np.zeros(n - len(a), dtype=a.dtype)] + elif len(b) < n: + b = np.r_[b, np.zeros(n - len(b), dtype=b.dtype)] + + IminusA = np.eye(n - 1, dtype=np.result_type(a, b)) - linalg.companion(a).T + B = b[1:] - a[1:] * b[0] + # Solve zi = A*zi + B + zi = np.linalg.solve(IminusA, B) + + # For future reference: we could also use the following + # explicit formulas to solve the linear system: + # + # zi = np.zeros(n - 1) + # zi[0] = B.sum() / IminusA[:,0].sum() + # asum = 1.0 + # csum = 0.0 + # for k in range(1,n-1): + # asum += a[k] + # csum += b[k] - a[k]*b[0] + # zi[k] = asum*zi[0] - csum + + return zi + + +def sosfilt_zi(sos): + """ + Construct initial conditions for sosfilt for step response steady-state. + + Compute an initial state `zi` for the `sosfilt` function that corresponds + to the steady state of the step response. + + A typical use of this function is to set the initial state so that the + output of the filter starts at the same value as the first element of + the signal to be filtered. + + Parameters + ---------- + sos : array_like + Array of second-order filter coefficients, must have shape + ``(n_sections, 6)``. See `sosfilt` for the SOS filter format + specification. + + Returns + ------- + zi : ndarray + Initial conditions suitable for use with ``sosfilt``, shape + ``(n_sections, 2)``. + + See Also + -------- + sosfilt, zpk2sos + + Notes + ----- + .. versionadded:: 0.16.0 + + Examples + -------- + Filter a rectangular pulse that begins at time 0, with and without + the use of the `zi` argument of `scipy.signal.sosfilt`. + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + + >>> sos = signal.butter(9, 0.125, output='sos') + >>> zi = signal.sosfilt_zi(sos) + >>> x = (np.arange(250) < 100).astype(int) + >>> f1 = signal.sosfilt(sos, x) + >>> f2, zo = signal.sosfilt(sos, x, zi=zi) + + >>> plt.plot(x, 'k--', label='x') + >>> plt.plot(f1, 'b', alpha=0.5, linewidth=2, label='filtered') + >>> plt.plot(f2, 'g', alpha=0.25, linewidth=4, label='filtered with zi') + >>> plt.legend(loc='best') + >>> plt.show() + + """ + sos = np.asarray(sos) + if sos.ndim != 2 or sos.shape[1] != 6: + raise ValueError('sos must be shape (n_sections, 6)') + + if sos.dtype.kind in 'bui': + sos = sos.astype(np.float64) + + n_sections = sos.shape[0] + zi = np.empty((n_sections, 2), dtype=sos.dtype) + scale = 1.0 + for section in range(n_sections): + b = sos[section, :3] + a = sos[section, 3:] + zi[section] = scale * lfilter_zi(b, a) + # If H(z) = B(z)/A(z) is this section's transfer function, then + # b.sum()/a.sum() is H(1), the gain at omega=0. That's the steady + # state value of this section's step response. + scale *= b.sum() / a.sum() + + return zi + + +def _filtfilt_gust(b, a, x, axis=-1, irlen=None): + """Forward-backward IIR filter that uses Gustafsson's method. + + Apply the IIR filter defined by `(b,a)` to `x` twice, first forward + then backward, using Gustafsson's initial conditions [1]_. + + Let ``y_fb`` be the result of filtering first forward and then backward, + and let ``y_bf`` be the result of filtering first backward then forward. + Gustafsson's method is to compute initial conditions for the forward + pass and the backward pass such that ``y_fb == y_bf``. + + Parameters + ---------- + b : scalar or 1-D ndarray + Numerator coefficients of the filter. + a : scalar or 1-D ndarray + Denominator coefficients of the filter. + x : ndarray + Data to be filtered. + axis : int, optional + Axis of `x` to be filtered. Default is -1. + irlen : int or None, optional + The length of the nonnegligible part of the impulse response. + If `irlen` is None, or if the length of the signal is less than + ``2 * irlen``, then no part of the impulse response is ignored. + + Returns + ------- + y : ndarray + The filtered data. + x0 : ndarray + Initial condition for the forward filter. + x1 : ndarray + Initial condition for the backward filter. + + Notes + ----- + Typically the return values `x0` and `x1` are not needed by the + caller. The intended use of these return values is in unit tests. + + References + ---------- + .. [1] F. Gustaffson. Determining the initial states in forward-backward + filtering. Transactions on Signal Processing, 46(4):988-992, 1996. + + """ + # In the comments, "Gustafsson's paper" and [1] refer to the + # paper referenced in the docstring. + + b = np.atleast_1d(b) + a = np.atleast_1d(a) + + order = max(len(b), len(a)) - 1 + if order == 0: + # The filter is just scalar multiplication, with no state. + scale = (b[0] / a[0])**2 + y = scale * x + return y, np.array([]), np.array([]) + + if axis != -1 or axis != x.ndim - 1: + # Move the axis containing the data to the end. + x = np.swapaxes(x, axis, x.ndim - 1) + + # n is the number of samples in the data to be filtered. + n = x.shape[-1] + + if irlen is None or n <= 2*irlen: + m = n + else: + m = irlen + + # Create Obs, the observability matrix (called O in the paper). + # This matrix can be interpreted as the operator that propagates + # an arbitrary initial state to the output, assuming the input is + # zero. + # In Gustafsson's paper, the forward and backward filters are not + # necessarily the same, so he has both O_f and O_b. We use the same + # filter in both directions, so we only need O. The same comment + # applies to S below. + Obs = np.zeros((m, order)) + zi = np.zeros(order) + zi[0] = 1 + Obs[:, 0] = lfilter(b, a, np.zeros(m), zi=zi)[0] + for k in range(1, order): + Obs[k:, k] = Obs[:-k, 0] + + # Obsr is O^R (Gustafsson's notation for row-reversed O) + Obsr = Obs[::-1] + + # Create S. S is the matrix that applies the filter to the reversed + # propagated initial conditions. That is, + # out = S.dot(zi) + # is the same as + # tmp, _ = lfilter(b, a, zeros(), zi=zi) # Propagate ICs. + # out = lfilter(b, a, tmp[::-1]) # Reverse and filter. + + # Equations (5) & (6) of [1] + S = lfilter(b, a, Obs[::-1], axis=0) + + # Sr is S^R (row-reversed S) + Sr = S[::-1] + + # M is [(S^R - O), (O^R - S)] + if m == n: + M = np.hstack((Sr - Obs, Obsr - S)) + else: + # Matrix described in section IV of [1]. + M = np.zeros((2*m, 2*order)) + M[:m, :order] = Sr - Obs + M[m:, order:] = Obsr - S + + # Naive forward-backward and backward-forward filters. + # These have large transients because the filters use zero initial + # conditions. + y_f = lfilter(b, a, x) + y_fb = lfilter(b, a, y_f[..., ::-1])[..., ::-1] + + y_b = lfilter(b, a, x[..., ::-1])[..., ::-1] + y_bf = lfilter(b, a, y_b) + + delta_y_bf_fb = y_bf - y_fb + if m == n: + delta = delta_y_bf_fb + else: + start_m = delta_y_bf_fb[..., :m] + end_m = delta_y_bf_fb[..., -m:] + delta = np.concatenate((start_m, end_m), axis=-1) + + # ic_opt holds the "optimal" initial conditions. + # The following code computes the result shown in the formula + # of the paper between equations (6) and (7). + if delta.ndim == 1: + ic_opt = linalg.lstsq(M, delta)[0] + else: + # Reshape delta so it can be used as an array of multiple + # right-hand-sides in linalg.lstsq. + delta2d = delta.reshape(-1, delta.shape[-1]).T + ic_opt0 = linalg.lstsq(M, delta2d)[0].T + ic_opt = ic_opt0.reshape(delta.shape[:-1] + (M.shape[-1],)) + + # Now compute the filtered signal using equation (7) of [1]. + # First, form [S^R, O^R] and call it W. + if m == n: + W = np.hstack((Sr, Obsr)) + else: + W = np.zeros((2*m, 2*order)) + W[:m, :order] = Sr + W[m:, order:] = Obsr + + # Equation (7) of [1] says + # Y_fb^opt = Y_fb^0 + W * [x_0^opt; x_{N-1}^opt] + # `wic` is (almost) the product on the right. + # W has shape (m, 2*order), and ic_opt has shape (..., 2*order), + # so we can't use W.dot(ic_opt). Instead, we dot ic_opt with W.T, + # so wic has shape (..., m). + wic = ic_opt.dot(W.T) + + # `wic` is "almost" the product of W and the optimal ICs in equation + # (7)--if we're using a truncated impulse response (m < n), `wic` + # contains only the adjustments required for the ends of the signal. + # Here we form y_opt, taking this into account if necessary. + y_opt = y_fb + if m == n: + y_opt += wic + else: + y_opt[..., :m] += wic[..., :m] + y_opt[..., -m:] += wic[..., -m:] + + x0 = ic_opt[..., :order] + x1 = ic_opt[..., -order:] + if axis != -1 or axis != x.ndim - 1: + # Restore the data axis to its original position. + x0 = np.swapaxes(x0, axis, x.ndim - 1) + x1 = np.swapaxes(x1, axis, x.ndim - 1) + y_opt = np.swapaxes(y_opt, axis, x.ndim - 1) + + return y_opt, x0, x1 + + +def filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None, method='pad', + irlen=None): + """ + Apply a digital filter forward and backward to a signal. + + This function applies a linear digital filter twice, once forward and + once backwards. The combined filter has zero phase and a filter order + twice that of the original. + + The function provides options for handling the edges of the signal. + + The function `sosfiltfilt` (and filter design using ``output='sos'``) + should be preferred over `filtfilt` for most filtering tasks, as + second-order sections have fewer numerical problems. + + Parameters + ---------- + b : (N,) array_like + The numerator coefficient vector of the filter. + a : (N,) array_like + The denominator coefficient vector of the filter. If ``a[0]`` + is not 1, then both `a` and `b` are normalized by ``a[0]``. + x : array_like + The array of data to be filtered. + axis : int, optional + The axis of `x` to which the filter is applied. + Default is -1. + padtype : str or None, optional + Must be 'odd', 'even', 'constant', or None. This determines the + type of extension to use for the padded signal to which the filter + is applied. If `padtype` is None, no padding is used. The default + is 'odd'. + padlen : int or None, optional + The number of elements by which to extend `x` at both ends of + `axis` before applying the filter. This value must be less than + ``x.shape[axis] - 1``. ``padlen=0`` implies no padding. + The default value is ``3 * max(len(a), len(b))``. + method : str, optional + Determines the method for handling the edges of the signal, either + "pad" or "gust". When `method` is "pad", the signal is padded; the + type of padding is determined by `padtype` and `padlen`, and `irlen` + is ignored. When `method` is "gust", Gustafsson's method is used, + and `padtype` and `padlen` are ignored. + irlen : int or None, optional + When `method` is "gust", `irlen` specifies the length of the + impulse response of the filter. If `irlen` is None, no part + of the impulse response is ignored. For a long signal, specifying + `irlen` can significantly improve the performance of the filter. + + Returns + ------- + y : ndarray + The filtered output with the same shape as `x`. + + See Also + -------- + sosfiltfilt, lfilter_zi, lfilter, lfiltic, savgol_filter, sosfilt + + Notes + ----- + When `method` is "pad", the function pads the data along the given axis + in one of three ways: odd, even or constant. The odd and even extensions + have the corresponding symmetry about the end point of the data. The + constant extension extends the data with the values at the end points. On + both the forward and backward passes, the initial condition of the + filter is found by using `lfilter_zi` and scaling it by the end point of + the extended data. + + When `method` is "gust", Gustafsson's method [1]_ is used. Initial + conditions are chosen for the forward and backward passes so that the + forward-backward filter gives the same result as the backward-forward + filter. + + The option to use Gustaffson's method was added in scipy version 0.16.0. + + References + ---------- + .. [1] F. Gustaffson, "Determining the initial states in forward-backward + filtering", Transactions on Signal Processing, Vol. 46, pp. 988-992, + 1996. + + Examples + -------- + The examples will use several functions from `scipy.signal`. + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + + First we create a one second signal that is the sum of two pure sine + waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz. + + >>> t = np.linspace(0, 1.0, 2001) + >>> xlow = np.sin(2 * np.pi * 5 * t) + >>> xhigh = np.sin(2 * np.pi * 250 * t) + >>> x = xlow + xhigh + + Now create a lowpass Butterworth filter with a cutoff of 0.125 times + the Nyquist frequency, or 125 Hz, and apply it to ``x`` with `filtfilt`. + The result should be approximately ``xlow``, with no phase shift. + + >>> b, a = signal.butter(8, 0.125) + >>> y = signal.filtfilt(b, a, x, padlen=150) + >>> np.abs(y - xlow).max() + 9.1086182074789912e-06 + + We get a fairly clean result for this artificial example because + the odd extension is exact, and with the moderately long padding, + the filter's transients have dissipated by the time the actual data + is reached. In general, transient effects at the edges are + unavoidable. + + The following example demonstrates the option ``method="gust"``. + + First, create a filter. + + >>> b, a = signal.ellip(4, 0.01, 120, 0.125) # Filter to be applied. + + `sig` is a random input signal to be filtered. + + >>> rng = np.random.default_rng() + >>> n = 60 + >>> sig = rng.standard_normal(n)**3 + 3*rng.standard_normal(n).cumsum() + + Apply `filtfilt` to `sig`, once using the Gustafsson method, and + once using padding, and plot the results for comparison. + + >>> fgust = signal.filtfilt(b, a, sig, method="gust") + >>> fpad = signal.filtfilt(b, a, sig, padlen=50) + >>> plt.plot(sig, 'k-', label='input') + >>> plt.plot(fgust, 'b-', linewidth=4, label='gust') + >>> plt.plot(fpad, 'c-', linewidth=1.5, label='pad') + >>> plt.legend(loc='best') + >>> plt.show() + + The `irlen` argument can be used to improve the performance + of Gustafsson's method. + + Estimate the impulse response length of the filter. + + >>> z, p, k = signal.tf2zpk(b, a) + >>> eps = 1e-9 + >>> r = np.max(np.abs(p)) + >>> approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r))) + >>> approx_impulse_len + 137 + + Apply the filter to a longer signal, with and without the `irlen` + argument. The difference between `y1` and `y2` is small. For long + signals, using `irlen` gives a significant performance improvement. + + >>> x = rng.standard_normal(4000) + >>> y1 = signal.filtfilt(b, a, x, method='gust') + >>> y2 = signal.filtfilt(b, a, x, method='gust', irlen=approx_impulse_len) + >>> print(np.max(np.abs(y1 - y2))) + 2.875334415008979e-10 + + """ + b = np.atleast_1d(b) + a = np.atleast_1d(a) + x = np.asarray(x) + + if method not in ["pad", "gust"]: + raise ValueError("method must be 'pad' or 'gust'.") + + if method == "gust": + y, z1, z2 = _filtfilt_gust(b, a, x, axis=axis, irlen=irlen) + return y + + # method == "pad" + edge, ext = _validate_pad(padtype, padlen, x, axis, + ntaps=max(len(a), len(b))) + + # Get the steady state of the filter's step response. + zi = lfilter_zi(b, a) + + # Reshape zi and create x0 so that zi*x0 broadcasts + # to the correct value for the 'zi' keyword argument + # to lfilter. + zi_shape = [1] * x.ndim + zi_shape[axis] = zi.size + zi = np.reshape(zi, zi_shape) + x0 = axis_slice(ext, stop=1, axis=axis) + + # Forward filter. + (y, zf) = lfilter(b, a, ext, axis=axis, zi=zi * x0) + + # Backward filter. + # Create y0 so zi*y0 broadcasts appropriately. + y0 = axis_slice(y, start=-1, axis=axis) + (y, zf) = lfilter(b, a, axis_reverse(y, axis=axis), axis=axis, zi=zi * y0) + + # Reverse y. + y = axis_reverse(y, axis=axis) + + if edge > 0: + # Slice the actual signal from the extended signal. + y = axis_slice(y, start=edge, stop=-edge, axis=axis) + + return y + + +def _validate_pad(padtype, padlen, x, axis, ntaps): + """Helper to validate padding for filtfilt""" + if padtype not in ['even', 'odd', 'constant', None]: + raise ValueError(("Unknown value '%s' given to padtype. padtype " + "must be 'even', 'odd', 'constant', or None.") % + padtype) + + if padtype is None: + padlen = 0 + + if padlen is None: + # Original padding; preserved for backwards compatibility. + edge = ntaps * 3 + else: + edge = padlen + + # x's 'axis' dimension must be bigger than edge. + if x.shape[axis] <= edge: + raise ValueError("The length of the input vector x must be greater " + "than padlen, which is %d." % edge) + + if padtype is not None and edge > 0: + # Make an extension of length `edge` at each + # end of the input array. + if padtype == 'even': + ext = even_ext(x, edge, axis=axis) + elif padtype == 'odd': + ext = odd_ext(x, edge, axis=axis) + else: + ext = const_ext(x, edge, axis=axis) + else: + ext = x + return edge, ext + + +def _validate_x(x): + x = np.asarray(x) + if x.ndim == 0: + raise ValueError('x must be at least 1-D') + return x + + +def sosfilt(sos, x, axis=-1, zi=None): + """ + Filter data along one dimension using cascaded second-order sections. + + Filter a data sequence, `x`, using a digital IIR filter defined by + `sos`. + + Parameters + ---------- + sos : array_like + Array of second-order filter coefficients, must have shape + ``(n_sections, 6)``. Each row corresponds to a second-order + section, with the first three columns providing the numerator + coefficients and the last three providing the denominator + coefficients. + x : array_like + An N-dimensional input array. + axis : int, optional + The axis of the input data array along which to apply the + linear filter. The filter is applied to each subarray along + this axis. Default is -1. + zi : array_like, optional + Initial conditions for the cascaded filter delays. It is a (at + least 2D) vector of shape ``(n_sections, ..., 2, ...)``, where + ``..., 2, ...`` denotes the shape of `x`, but with ``x.shape[axis]`` + replaced by 2. If `zi` is None or is not given then initial rest + (i.e. all zeros) is assumed. + Note that these initial conditions are *not* the same as the initial + conditions given by `lfiltic` or `lfilter_zi`. + + Returns + ------- + y : ndarray + The output of the digital filter. + zf : ndarray, optional + If `zi` is None, this is not returned, otherwise, `zf` holds the + final filter delay values. + + See Also + -------- + zpk2sos, sos2zpk, sosfilt_zi, sosfiltfilt, sosfreqz + + Notes + ----- + The filter function is implemented as a series of second-order filters + with direct-form II transposed structure. It is designed to minimize + numerical precision errors for high-order filters. + + .. versionadded:: 0.16.0 + + Examples + -------- + Plot a 13th-order filter's impulse response using both `lfilter` and + `sosfilt`, showing the instability that results from trying to do a + 13th-order filter in a single stage (the numerical error pushes some poles + outside of the unit circle): + + >>> import matplotlib.pyplot as plt + >>> from scipy import signal + >>> b, a = signal.ellip(13, 0.009, 80, 0.05, output='ba') + >>> sos = signal.ellip(13, 0.009, 80, 0.05, output='sos') + >>> x = signal.unit_impulse(700) + >>> y_tf = signal.lfilter(b, a, x) + >>> y_sos = signal.sosfilt(sos, x) + >>> plt.plot(y_tf, 'r', label='TF') + >>> plt.plot(y_sos, 'k', label='SOS') + >>> plt.legend(loc='best') + >>> plt.show() + + """ + x = _validate_x(x) + sos, n_sections = _validate_sos(sos) + x_zi_shape = list(x.shape) + x_zi_shape[axis] = 2 + x_zi_shape = tuple([n_sections] + x_zi_shape) + inputs = [sos, x] + if zi is not None: + inputs.append(np.asarray(zi)) + dtype = np.result_type(*inputs) + if dtype.char not in 'fdgFDGO': + raise NotImplementedError("input type '%s' not supported" % dtype) + if zi is not None: + zi = np.array(zi, dtype) # make a copy so that we can operate in place + if zi.shape != x_zi_shape: + raise ValueError('Invalid zi shape. With axis=%r, an input with ' + 'shape %r, and an sos array with %d sections, zi ' + 'must have shape %r, got %r.' % + (axis, x.shape, n_sections, x_zi_shape, zi.shape)) + return_zi = True + else: + zi = np.zeros(x_zi_shape, dtype=dtype) + return_zi = False + axis = axis % x.ndim # make positive + x = np.moveaxis(x, axis, -1) + zi = np.moveaxis(zi, [0, axis + 1], [-2, -1]) + x_shape, zi_shape = x.shape, zi.shape + x = np.reshape(x, (-1, x.shape[-1])) + x = np.array(x, dtype, order='C') # make a copy, can modify in place + zi = np.ascontiguousarray(np.reshape(zi, (-1, n_sections, 2))) + sos = sos.astype(dtype, copy=False) + _sosfilt(sos, x, zi) + x.shape = x_shape + x = np.moveaxis(x, -1, axis) + if return_zi: + zi.shape = zi_shape + zi = np.moveaxis(zi, [-2, -1], [0, axis + 1]) + out = (x, zi) + else: + out = x + return out + + +def sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None): + """ + A forward-backward digital filter using cascaded second-order sections. + + See `filtfilt` for more complete information about this method. + + Parameters + ---------- + sos : array_like + Array of second-order filter coefficients, must have shape + ``(n_sections, 6)``. Each row corresponds to a second-order + section, with the first three columns providing the numerator + coefficients and the last three providing the denominator + coefficients. + x : array_like + The array of data to be filtered. + axis : int, optional + The axis of `x` to which the filter is applied. + Default is -1. + padtype : str or None, optional + Must be 'odd', 'even', 'constant', or None. This determines the + type of extension to use for the padded signal to which the filter + is applied. If `padtype` is None, no padding is used. The default + is 'odd'. + padlen : int or None, optional + The number of elements by which to extend `x` at both ends of + `axis` before applying the filter. This value must be less than + ``x.shape[axis] - 1``. ``padlen=0`` implies no padding. + The default value is:: + + 3 * (2 * len(sos) + 1 - min((sos[:, 2] == 0).sum(), + (sos[:, 5] == 0).sum())) + + The extra subtraction at the end attempts to compensate for poles + and zeros at the origin (e.g. for odd-order filters) to yield + equivalent estimates of `padlen` to those of `filtfilt` for + second-order section filters built with `scipy.signal` functions. + + Returns + ------- + y : ndarray + The filtered output with the same shape as `x`. + + See Also + -------- + filtfilt, sosfilt, sosfilt_zi, sosfreqz + + Notes + ----- + .. versionadded:: 0.18.0 + + Examples + -------- + >>> import numpy as np + >>> from scipy.signal import sosfiltfilt, butter + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Create an interesting signal to filter. + + >>> n = 201 + >>> t = np.linspace(0, 1, n) + >>> x = 1 + (t < 0.5) - 0.25*t**2 + 0.05*rng.standard_normal(n) + + Create a lowpass Butterworth filter, and use it to filter `x`. + + >>> sos = butter(4, 0.125, output='sos') + >>> y = sosfiltfilt(sos, x) + + For comparison, apply an 8th order filter using `sosfilt`. The filter + is initialized using the mean of the first four values of `x`. + + >>> from scipy.signal import sosfilt, sosfilt_zi + >>> sos8 = butter(8, 0.125, output='sos') + >>> zi = x[:4].mean() * sosfilt_zi(sos8) + >>> y2, zo = sosfilt(sos8, x, zi=zi) + + Plot the results. Note that the phase of `y` matches the input, while + `y2` has a significant phase delay. + + >>> plt.plot(t, x, alpha=0.5, label='x(t)') + >>> plt.plot(t, y, label='y(t)') + >>> plt.plot(t, y2, label='y2(t)') + >>> plt.legend(framealpha=1, shadow=True) + >>> plt.grid(alpha=0.25) + >>> plt.xlabel('t') + >>> plt.show() + + """ + sos, n_sections = _validate_sos(sos) + x = _validate_x(x) + + # `method` is "pad"... + ntaps = 2 * n_sections + 1 + ntaps -= min((sos[:, 2] == 0).sum(), (sos[:, 5] == 0).sum()) + edge, ext = _validate_pad(padtype, padlen, x, axis, + ntaps=ntaps) + + # These steps follow the same form as filtfilt with modifications + zi = sosfilt_zi(sos) # shape (n_sections, 2) --> (n_sections, ..., 2, ...) + zi_shape = [1] * x.ndim + zi_shape[axis] = 2 + zi.shape = [n_sections] + zi_shape + x_0 = axis_slice(ext, stop=1, axis=axis) + (y, zf) = sosfilt(sos, ext, axis=axis, zi=zi * x_0) + y_0 = axis_slice(y, start=-1, axis=axis) + (y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=zi * y_0) + y = axis_reverse(y, axis=axis) + if edge > 0: + y = axis_slice(y, start=edge, stop=-edge, axis=axis) + return y + + +def decimate(x, q, n=None, ftype='iir', axis=-1, zero_phase=True): + """ + Downsample the signal after applying an anti-aliasing filter. + + By default, an order 8 Chebyshev type I filter is used. A 30 point FIR + filter with Hamming window is used if `ftype` is 'fir'. + + Parameters + ---------- + x : array_like + The signal to be downsampled, as an N-dimensional array. + q : int + The downsampling factor. When using IIR downsampling, it is recommended + to call `decimate` multiple times for downsampling factors higher than + 13. + n : int, optional + The order of the filter (1 less than the length for 'fir'). Defaults to + 8 for 'iir' and 20 times the downsampling factor for 'fir'. + ftype : str {'iir', 'fir'} or ``dlti`` instance, optional + If 'iir' or 'fir', specifies the type of lowpass filter. If an instance + of an `dlti` object, uses that object to filter before downsampling. + axis : int, optional + The axis along which to decimate. + zero_phase : bool, optional + Prevent phase shift by filtering with `filtfilt` instead of `lfilter` + when using an IIR filter, and shifting the outputs back by the filter's + group delay when using an FIR filter. The default value of ``True`` is + recommended, since a phase shift is generally not desired. + + .. versionadded:: 0.18.0 + + Returns + ------- + y : ndarray + The down-sampled signal. + + See Also + -------- + resample : Resample up or down using the FFT method. + resample_poly : Resample using polyphase filtering and an FIR filter. + + Notes + ----- + The ``zero_phase`` keyword was added in 0.18.0. + The possibility to use instances of ``dlti`` as ``ftype`` was added in + 0.18.0. + + Examples + -------- + + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + + Define wave parameters. + + >>> wave_duration = 3 + >>> sample_rate = 100 + >>> freq = 2 + >>> q = 5 + + Calculate number of samples. + + >>> samples = wave_duration*sample_rate + >>> samples_decimated = int(samples/q) + + Create cosine wave. + + >>> x = np.linspace(0, wave_duration, samples, endpoint=False) + >>> y = np.cos(x*np.pi*freq*2) + + Decimate cosine wave. + + >>> ydem = signal.decimate(y, q) + >>> xnew = np.linspace(0, wave_duration, samples_decimated, endpoint=False) + + Plot original and decimated waves. + + >>> plt.plot(x, y, '.-', xnew, ydem, 'o-') + >>> plt.xlabel('Time, Seconds') + >>> plt.legend(['data', 'decimated'], loc='best') + >>> plt.show() + + """ + + x = np.asarray(x) + q = operator.index(q) + + if n is not None: + n = operator.index(n) + + result_type = x.dtype + if not np.issubdtype(result_type, np.inexact) \ + or result_type.type == np.float16: + # upcast integers and float16 to float64 + result_type = np.float64 + + if ftype == 'fir': + if n is None: + half_len = 10 * q # reasonable cutoff for our sinc-like function + n = 2 * half_len + b, a = firwin(n+1, 1. / q, window='hamming'), 1. + b = np.asarray(b, dtype=result_type) + a = np.asarray(a, dtype=result_type) + elif ftype == 'iir': + iir_use_sos = True + if n is None: + n = 8 + sos = cheby1(n, 0.05, 0.8 / q, output='sos') + sos = np.asarray(sos, dtype=result_type) + elif isinstance(ftype, dlti): + system = ftype._as_zpk() + if system.poles.shape[0] == 0: + # FIR + system = ftype._as_tf() + b, a = system.num, system.den + ftype = 'fir' + elif (any(np.iscomplex(system.poles)) + or any(np.iscomplex(system.poles)) + or np.iscomplex(system.gain)): + # sosfilt & sosfiltfilt don't handle complex coeffs + iir_use_sos = False + system = ftype._as_tf() + b, a = system.num, system.den + else: + iir_use_sos = True + sos = zpk2sos(system.zeros, system.poles, system.gain) + sos = np.asarray(sos, dtype=result_type) + else: + raise ValueError('invalid ftype') + + sl = [slice(None)] * x.ndim + + if ftype == 'fir': + b = b / a + if zero_phase: + y = resample_poly(x, 1, q, axis=axis, window=b) + else: + # upfirdn is generally faster than lfilter by a factor equal to the + # downsampling factor, since it only calculates the needed outputs + n_out = x.shape[axis] // q + bool(x.shape[axis] % q) + y = upfirdn(b, x, up=1, down=q, axis=axis) + sl[axis] = slice(None, n_out, None) + + else: # IIR case + if zero_phase: + if iir_use_sos: + y = sosfiltfilt(sos, x, axis=axis) + else: + y = filtfilt(b, a, x, axis=axis) + else: + if iir_use_sos: + y = sosfilt(sos, x, axis=axis) + else: + y = lfilter(b, a, x, axis=axis) + + sl[axis] = slice(None, None, q) + + return y[tuple(sl)] diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_sosfilt.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_sosfilt.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..9f5be4ce524fbf292b1eaff74dc12e8dfb3e21b5 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_sosfilt.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_spectral_py.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_spectral_py.py new file mode 100644 index 0000000000000000000000000000000000000000..ef7fd2e6e8b79f264f733e54420066de867310a5 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_spectral_py.py @@ -0,0 +1,2101 @@ +"""Tools for spectral analysis. +""" +import numpy as np +from scipy import fft as sp_fft +from . import _signaltools +from .windows import get_window +from ._spectral import _lombscargle +from ._arraytools import const_ext, even_ext, odd_ext, zero_ext +import warnings + + +__all__ = ['periodogram', 'welch', 'lombscargle', 'csd', 'coherence', + 'spectrogram', 'stft', 'istft', 'check_COLA', 'check_NOLA'] + + +def lombscargle(x, + y, + freqs, + precenter=False, + normalize=False): + """ + lombscargle(x, y, freqs) + + Computes the Lomb-Scargle periodogram. + + The Lomb-Scargle periodogram was developed by Lomb [1]_ and further + extended by Scargle [2]_ to find, and test the significance of weak + periodic signals with uneven temporal sampling. + + When *normalize* is False (default) the computed periodogram + is unnormalized, it takes the value ``(A**2) * N/4`` for a harmonic + signal with amplitude A for sufficiently large N. + + When *normalize* is True the computed periodogram is normalized by + the residuals of the data around a constant reference model (at zero). + + Input arrays should be 1-D and will be cast to float64. + + Parameters + ---------- + x : array_like + Sample times. + y : array_like + Measurement values. + freqs : array_like + Angular frequencies for output periodogram. + precenter : bool, optional + Pre-center measurement values by subtracting the mean. + normalize : bool, optional + Compute normalized periodogram. + + Returns + ------- + pgram : array_like + Lomb-Scargle periodogram. + + Raises + ------ + ValueError + If the input arrays `x` and `y` do not have the same shape. + + See Also + -------- + istft: Inverse Short Time Fourier Transform + check_COLA: Check whether the Constant OverLap Add (COLA) constraint is met + welch: Power spectral density by Welch's method + spectrogram: Spectrogram by Welch's method + csd: Cross spectral density by Welch's method + + Notes + ----- + This subroutine calculates the periodogram using a slightly + modified algorithm due to Townsend [3]_ which allows the + periodogram to be calculated using only a single pass through + the input arrays for each frequency. + + The algorithm running time scales roughly as O(x * freqs) or O(N^2) + for a large number of samples and frequencies. + + References + ---------- + .. [1] N.R. Lomb "Least-squares frequency analysis of unequally spaced + data", Astrophysics and Space Science, vol 39, pp. 447-462, 1976 + + .. [2] J.D. Scargle "Studies in astronomical time series analysis. II - + Statistical aspects of spectral analysis of unevenly spaced data", + The Astrophysical Journal, vol 263, pp. 835-853, 1982 + + .. [3] R.H.D. Townsend, "Fast calculation of the Lomb-Scargle + periodogram using graphics processing units.", The Astrophysical + Journal Supplement Series, vol 191, pp. 247-253, 2010 + + Examples + -------- + >>> import numpy as np + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + First define some input parameters for the signal: + + >>> A = 2. + >>> w0 = 1. # rad/sec + >>> nin = 150 + >>> nout = 100000 + + Randomly generate sample times: + + >>> x = rng.uniform(0, 10*np.pi, nin) + + Plot a sine wave for the selected times: + + >>> y = A * np.cos(w0*x) + + Define the array of frequencies for which to compute the periodogram: + + >>> w = np.linspace(0.01, 10, nout) + + Calculate Lomb-Scargle periodogram: + + >>> import scipy.signal as signal + >>> pgram = signal.lombscargle(x, y, w, normalize=True) + + Now make a plot of the input data: + + >>> fig, (ax_t, ax_w) = plt.subplots(2, 1, constrained_layout=True) + >>> ax_t.plot(x, y, 'b+') + >>> ax_t.set_xlabel('Time [s]') + + Then plot the normalized periodogram: + + >>> ax_w.plot(w, pgram) + >>> ax_w.set_xlabel('Angular frequency [rad/s]') + >>> ax_w.set_ylabel('Normalized amplitude') + >>> plt.show() + + """ + x = np.ascontiguousarray(x, dtype=np.float64) + y = np.ascontiguousarray(y, dtype=np.float64) + freqs = np.ascontiguousarray(freqs, dtype=np.float64) + + assert x.ndim == 1 + assert y.ndim == 1 + assert freqs.ndim == 1 + + if precenter: + pgram = _lombscargle(x, y - y.mean(), freqs) + else: + pgram = _lombscargle(x, y, freqs) + + if normalize: + pgram *= 2 / np.dot(y, y) + + return pgram + + +def periodogram(x, fs=1.0, window='boxcar', nfft=None, detrend='constant', + return_onesided=True, scaling='density', axis=-1): + """ + Estimate power spectral density using a periodogram. + + Parameters + ---------- + x : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be equal to the length + of the axis over which the periodogram is computed. Defaults + to 'boxcar'. + nfft : int, optional + Length of the FFT used. If `None` the length of `x` will be + used. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + scaling : { 'density', 'spectrum' }, optional + Selects between computing the power spectral density ('density') + where `Pxx` has units of V**2/Hz and computing the squared magnitude + spectrum ('spectrum') where `Pxx` has units of V**2, if `x` + is measured in V and `fs` is measured in Hz. Defaults to + 'density' + axis : int, optional + Axis along which the periodogram is computed; the default is + over the last axis (i.e. ``axis=-1``). + + Returns + ------- + f : ndarray + Array of sample frequencies. + Pxx : ndarray + Power spectral density or power spectrum of `x`. + + See Also + -------- + welch: Estimate power spectral density using Welch's method + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + + Notes + ----- + Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide` + for a discussion of the scalings of the power spectral density and + the magnitude (squared) spectrum. + + .. versionadded:: 0.12.0 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by + 0.001 V**2/Hz of white noise sampled at 10 kHz. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 2*np.sqrt(2) + >>> freq = 1234.0 + >>> noise_power = 0.001 * fs / 2 + >>> time = np.arange(N) / fs + >>> x = amp*np.sin(2*np.pi*freq*time) + >>> x += rng.normal(scale=np.sqrt(noise_power), size=time.shape) + + Compute and plot the power spectral density. + + >>> f, Pxx_den = signal.periodogram(x, fs) + >>> plt.semilogy(f, Pxx_den) + >>> plt.ylim([1e-7, 1e2]) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('PSD [V**2/Hz]') + >>> plt.show() + + If we average the last half of the spectral density, to exclude the + peak, we can recover the noise power on the signal. + + >>> np.mean(Pxx_den[25000:]) + 0.000985320699252543 + + Now compute and plot the power spectrum. + + >>> f, Pxx_spec = signal.periodogram(x, fs, 'flattop', scaling='spectrum') + >>> plt.figure() + >>> plt.semilogy(f, np.sqrt(Pxx_spec)) + >>> plt.ylim([1e-4, 1e1]) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('Linear spectrum [V RMS]') + >>> plt.show() + + The peak height in the power spectrum is an estimate of the RMS + amplitude. + + >>> np.sqrt(Pxx_spec.max()) + 2.0077340678640727 + + """ + x = np.asarray(x) + + if x.size == 0: + return np.empty(x.shape), np.empty(x.shape) + + if window is None: + window = 'boxcar' + + if nfft is None: + nperseg = x.shape[axis] + elif nfft == x.shape[axis]: + nperseg = nfft + elif nfft > x.shape[axis]: + nperseg = x.shape[axis] + elif nfft < x.shape[axis]: + s = [np.s_[:]]*len(x.shape) + s[axis] = np.s_[:nfft] + x = x[tuple(s)] + nperseg = nfft + nfft = None + + if hasattr(window, 'size'): + if window.size != nperseg: + raise ValueError('the size of the window must be the same size ' + 'of the input on the specified axis') + + return welch(x, fs=fs, window=window, nperseg=nperseg, noverlap=0, + nfft=nfft, detrend=detrend, return_onesided=return_onesided, + scaling=scaling, axis=axis) + + +def welch(x, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, + detrend='constant', return_onesided=True, scaling='density', + axis=-1, average='mean'): + r""" + Estimate power spectral density using Welch's method. + + Welch's method [1]_ computes an estimate of the power spectral + density by dividing the data into overlapping segments, computing a + modified periodogram for each segment and averaging the + periodograms. + + Parameters + ---------- + x : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. + nperseg : int, optional + Length of each segment. Defaults to None, but if window is str or + tuple, is set to 256, and if window is array_like, is set to the + length of the window. + noverlap : int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 2``. Defaults to `None`. + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + scaling : { 'density', 'spectrum' }, optional + Selects between computing the power spectral density ('density') + where `Pxx` has units of V**2/Hz and computing the squared magnitude + spectrum ('spectrum') where `Pxx` has units of V**2, if `x` + is measured in V and `fs` is measured in Hz. Defaults to + 'density' + axis : int, optional + Axis along which the periodogram is computed; the default is + over the last axis (i.e. ``axis=-1``). + average : { 'mean', 'median' }, optional + Method to use when averaging periodograms. Defaults to 'mean'. + + .. versionadded:: 1.2.0 + + Returns + ------- + f : ndarray + Array of sample frequencies. + Pxx : ndarray + Power spectral density or power spectrum of x. + + See Also + -------- + periodogram: Simple, optionally modified periodogram + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + + Notes + ----- + An appropriate amount of overlap will depend on the choice of window + and on your requirements. For the default Hann window an overlap of + 50% is a reasonable trade off between accurately estimating the + signal power, while not over counting any of the data. Narrower + windows may require a larger overlap. + + If `noverlap` is 0, this method is equivalent to Bartlett's method + [2]_. + + Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide` + for a discussion of the scalings of the power spectral density and + the (squared) magnitude spectrum. + + .. versionadded:: 0.12.0 + + References + ---------- + .. [1] P. Welch, "The use of the fast Fourier transform for the + estimation of power spectra: A method based on time averaging + over short, modified periodograms", IEEE Trans. Audio + Electroacoust. vol. 15, pp. 70-73, 1967. + .. [2] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", + Biometrika, vol. 37, pp. 1-16, 1950. + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate a test signal, a 2 Vrms sine wave at 1234 Hz, corrupted by + 0.001 V**2/Hz of white noise sampled at 10 kHz. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 2*np.sqrt(2) + >>> freq = 1234.0 + >>> noise_power = 0.001 * fs / 2 + >>> time = np.arange(N) / fs + >>> x = amp*np.sin(2*np.pi*freq*time) + >>> x += rng.normal(scale=np.sqrt(noise_power), size=time.shape) + + Compute and plot the power spectral density. + + >>> f, Pxx_den = signal.welch(x, fs, nperseg=1024) + >>> plt.semilogy(f, Pxx_den) + >>> plt.ylim([0.5e-3, 1]) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('PSD [V**2/Hz]') + >>> plt.show() + + If we average the last half of the spectral density, to exclude the + peak, we can recover the noise power on the signal. + + >>> np.mean(Pxx_den[256:]) + 0.0009924865443739191 + + Now compute and plot the power spectrum. + + >>> f, Pxx_spec = signal.welch(x, fs, 'flattop', 1024, scaling='spectrum') + >>> plt.figure() + >>> plt.semilogy(f, np.sqrt(Pxx_spec)) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('Linear spectrum [V RMS]') + >>> plt.show() + + The peak height in the power spectrum is an estimate of the RMS + amplitude. + + >>> np.sqrt(Pxx_spec.max()) + 2.0077340678640727 + + If we now introduce a discontinuity in the signal, by increasing the + amplitude of a small portion of the signal by 50, we can see the + corruption of the mean average power spectral density, but using a + median average better estimates the normal behaviour. + + >>> x[int(N//2):int(N//2)+10] *= 50. + >>> f, Pxx_den = signal.welch(x, fs, nperseg=1024) + >>> f_med, Pxx_den_med = signal.welch(x, fs, nperseg=1024, average='median') + >>> plt.semilogy(f, Pxx_den, label='mean') + >>> plt.semilogy(f_med, Pxx_den_med, label='median') + >>> plt.ylim([0.5e-3, 1]) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('PSD [V**2/Hz]') + >>> plt.legend() + >>> plt.show() + + """ + freqs, Pxx = csd(x, x, fs=fs, window=window, nperseg=nperseg, + noverlap=noverlap, nfft=nfft, detrend=detrend, + return_onesided=return_onesided, scaling=scaling, + axis=axis, average=average) + + return freqs, Pxx.real + + +def csd(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, + detrend='constant', return_onesided=True, scaling='density', + axis=-1, average='mean'): + r""" + Estimate the cross power spectral density, Pxy, using Welch's method. + + Parameters + ---------- + x : array_like + Time series of measurement values + y : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` and `y` time series. Defaults + to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. + nperseg : int, optional + Length of each segment. Defaults to None, but if window is str or + tuple, is set to 256, and if window is array_like, is set to the + length of the window. + noverlap: int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 2``. Defaults to `None`. + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + scaling : { 'density', 'spectrum' }, optional + Selects between computing the cross spectral density ('density') + where `Pxy` has units of V**2/Hz and computing the cross spectrum + ('spectrum') where `Pxy` has units of V**2, if `x` and `y` are + measured in V and `fs` is measured in Hz. Defaults to 'density' + axis : int, optional + Axis along which the CSD is computed for both inputs; the + default is over the last axis (i.e. ``axis=-1``). + average : { 'mean', 'median' }, optional + Method to use when averaging periodograms. If the spectrum is + complex, the average is computed separately for the real and + imaginary parts. Defaults to 'mean'. + + .. versionadded:: 1.2.0 + + Returns + ------- + f : ndarray + Array of sample frequencies. + Pxy : ndarray + Cross spectral density or cross power spectrum of x,y. + + See Also + -------- + periodogram: Simple, optionally modified periodogram + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + welch: Power spectral density by Welch's method. [Equivalent to + csd(x,x)] + coherence: Magnitude squared coherence by Welch's method. + + Notes + ----- + By convention, Pxy is computed with the conjugate FFT of X + multiplied by the FFT of Y. + + If the input series differ in length, the shorter series will be + zero-padded to match. + + An appropriate amount of overlap will depend on the choice of window + and on your requirements. For the default Hann window an overlap of + 50% is a reasonable trade off between accurately estimating the + signal power, while not over counting any of the data. Narrower + windows may require a larger overlap. + + Consult the :ref:`tutorial_SpectralAnalysis` section of the :ref:`user_guide` + for a discussion of the scalings of a spectral density and an (amplitude) spectrum. + + .. versionadded:: 0.16.0 + + References + ---------- + .. [1] P. Welch, "The use of the fast Fourier transform for the + estimation of power spectra: A method based on time averaging + over short, modified periodograms", IEEE Trans. Audio + Electroacoust. vol. 15, pp. 70-73, 1967. + .. [2] Rabiner, Lawrence R., and B. Gold. "Theory and Application of + Digital Signal Processing" Prentice-Hall, pp. 414-419, 1975 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate two test signals with some common features. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 20 + >>> freq = 1234.0 + >>> noise_power = 0.001 * fs / 2 + >>> time = np.arange(N) / fs + >>> b, a = signal.butter(2, 0.25, 'low') + >>> x = rng.normal(scale=np.sqrt(noise_power), size=time.shape) + >>> y = signal.lfilter(b, a, x) + >>> x += amp*np.sin(2*np.pi*freq*time) + >>> y += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape) + + Compute and plot the magnitude of the cross spectral density. + + >>> f, Pxy = signal.csd(x, y, fs, nperseg=1024) + >>> plt.semilogy(f, np.abs(Pxy)) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('CSD [V**2/Hz]') + >>> plt.show() + + """ + freqs, _, Pxy = _spectral_helper(x, y, fs, window, nperseg, noverlap, + nfft, detrend, return_onesided, scaling, + axis, mode='psd') + + # Average over windows. + if len(Pxy.shape) >= 2 and Pxy.size > 0: + if Pxy.shape[-1] > 1: + if average == 'median': + # np.median must be passed real arrays for the desired result + bias = _median_bias(Pxy.shape[-1]) + if np.iscomplexobj(Pxy): + Pxy = (np.median(np.real(Pxy), axis=-1) + + 1j * np.median(np.imag(Pxy), axis=-1)) + else: + Pxy = np.median(Pxy, axis=-1) + Pxy /= bias + elif average == 'mean': + Pxy = Pxy.mean(axis=-1) + else: + raise ValueError(f'average must be "median" or "mean", got {average}') + else: + Pxy = np.reshape(Pxy, Pxy.shape[:-1]) + + return freqs, Pxy + + +def spectrogram(x, fs=1.0, window=('tukey', .25), nperseg=None, noverlap=None, + nfft=None, detrend='constant', return_onesided=True, + scaling='density', axis=-1, mode='psd'): + """Compute a spectrogram with consecutive Fourier transforms (legacy function). + + Spectrograms can be used as a way of visualizing the change of a + nonstationary signal's frequency content over time. + + .. legacy:: function + + :class:`ShortTimeFFT` is a newer STFT / ISTFT implementation with more + features also including a :meth:`~ShortTimeFFT.spectrogram` method. + A :ref:`comparison ` between the + implementations can be found in the :ref:`tutorial_stft` section of + the :ref:`user_guide`. + + Parameters + ---------- + x : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. + Defaults to a Tukey window with shape parameter of 0.25. + nperseg : int, optional + Length of each segment. Defaults to None, but if window is str or + tuple, is set to 256, and if window is array_like, is set to the + length of the window. + noverlap : int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 8``. Defaults to `None`. + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + scaling : { 'density', 'spectrum' }, optional + Selects between computing the power spectral density ('density') + where `Sxx` has units of V**2/Hz and computing the power + spectrum ('spectrum') where `Sxx` has units of V**2, if `x` + is measured in V and `fs` is measured in Hz. Defaults to + 'density'. + axis : int, optional + Axis along which the spectrogram is computed; the default is over + the last axis (i.e. ``axis=-1``). + mode : str, optional + Defines what kind of return values are expected. Options are + ['psd', 'complex', 'magnitude', 'angle', 'phase']. 'complex' is + equivalent to the output of `stft` with no padding or boundary + extension. 'magnitude' returns the absolute magnitude of the + STFT. 'angle' and 'phase' return the complex angle of the STFT, + with and without unwrapping, respectively. + + Returns + ------- + f : ndarray + Array of sample frequencies. + t : ndarray + Array of segment times. + Sxx : ndarray + Spectrogram of x. By default, the last axis of Sxx corresponds + to the segment times. + + See Also + -------- + periodogram: Simple, optionally modified periodogram + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + welch: Power spectral density by Welch's method. + csd: Cross spectral density by Welch's method. + ShortTimeFFT: Newer STFT/ISTFT implementation providing more features, + which also includes a :meth:`~ShortTimeFFT.spectrogram` + method. + + Notes + ----- + An appropriate amount of overlap will depend on the choice of window + and on your requirements. In contrast to welch's method, where the + entire data stream is averaged over, one may wish to use a smaller + overlap (or perhaps none at all) when computing a spectrogram, to + maintain some statistical independence between individual segments. + It is for this reason that the default window is a Tukey window with + 1/8th of a window's length overlap at each end. + + + .. versionadded:: 0.16.0 + + References + ---------- + .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck + "Discrete-Time Signal Processing", Prentice Hall, 1999. + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> from scipy.fft import fftshift + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate a test signal, a 2 Vrms sine wave whose frequency is slowly + modulated around 3kHz, corrupted by white noise of exponentially + decreasing magnitude sampled at 10 kHz. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 2 * np.sqrt(2) + >>> noise_power = 0.01 * fs / 2 + >>> time = np.arange(N) / float(fs) + >>> mod = 500*np.cos(2*np.pi*0.25*time) + >>> carrier = amp * np.sin(2*np.pi*3e3*time + mod) + >>> noise = rng.normal(scale=np.sqrt(noise_power), size=time.shape) + >>> noise *= np.exp(-time/5) + >>> x = carrier + noise + + Compute and plot the spectrogram. + + >>> f, t, Sxx = signal.spectrogram(x, fs) + >>> plt.pcolormesh(t, f, Sxx, shading='gouraud') + >>> plt.ylabel('Frequency [Hz]') + >>> plt.xlabel('Time [sec]') + >>> plt.show() + + Note, if using output that is not one sided, then use the following: + + >>> f, t, Sxx = signal.spectrogram(x, fs, return_onesided=False) + >>> plt.pcolormesh(t, fftshift(f), fftshift(Sxx, axes=0), shading='gouraud') + >>> plt.ylabel('Frequency [Hz]') + >>> plt.xlabel('Time [sec]') + >>> plt.show() + + """ + modelist = ['psd', 'complex', 'magnitude', 'angle', 'phase'] + if mode not in modelist: + raise ValueError(f'unknown value for mode {mode}, must be one of {modelist}') + + # need to set default for nperseg before setting default for noverlap below + window, nperseg = _triage_segments(window, nperseg, + input_length=x.shape[axis]) + + # Less overlap than welch, so samples are more statisically independent + if noverlap is None: + noverlap = nperseg // 8 + + if mode == 'psd': + freqs, time, Sxx = _spectral_helper(x, x, fs, window, nperseg, + noverlap, nfft, detrend, + return_onesided, scaling, axis, + mode='psd') + + else: + freqs, time, Sxx = _spectral_helper(x, x, fs, window, nperseg, + noverlap, nfft, detrend, + return_onesided, scaling, axis, + mode='stft') + + if mode == 'magnitude': + Sxx = np.abs(Sxx) + elif mode in ['angle', 'phase']: + Sxx = np.angle(Sxx) + if mode == 'phase': + # Sxx has one additional dimension for time strides + if axis < 0: + axis -= 1 + Sxx = np.unwrap(Sxx, axis=axis) + + # mode =='complex' is same as `stft`, doesn't need modification + + return freqs, time, Sxx + + +def check_COLA(window, nperseg, noverlap, tol=1e-10): + r"""Check whether the Constant OverLap Add (COLA) constraint is met. + + Parameters + ---------- + window : str or tuple or array_like + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. + nperseg : int + Length of each segment. + noverlap : int + Number of points to overlap between segments. + tol : float, optional + The allowed variance of a bin's weighted sum from the median bin + sum. + + Returns + ------- + verdict : bool + `True` if chosen combination satisfies COLA within `tol`, + `False` otherwise + + See Also + -------- + check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met + stft: Short Time Fourier Transform + istft: Inverse Short Time Fourier Transform + + Notes + ----- + In order to enable inversion of an STFT via the inverse STFT in + `istft`, it is sufficient that the signal windowing obeys the constraint of + "Constant OverLap Add" (COLA). This ensures that every point in the input + data is equally weighted, thereby avoiding aliasing and allowing full + reconstruction. + + Some examples of windows that satisfy COLA: + - Rectangular window at overlap of 0, 1/2, 2/3, 3/4, ... + - Bartlett window at overlap of 1/2, 3/4, 5/6, ... + - Hann window at 1/2, 2/3, 3/4, ... + - Any Blackman family window at 2/3 overlap + - Any window with ``noverlap = nperseg-1`` + + A very comprehensive list of other windows may be found in [2]_, + wherein the COLA condition is satisfied when the "Amplitude + Flatness" is unity. + + .. versionadded:: 0.19.0 + + References + ---------- + .. [1] Julius O. Smith III, "Spectral Audio Signal Processing", W3K + Publishing, 2011,ISBN 978-0-9745607-3-1. + .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and + spectral density estimation by the Discrete Fourier transform + (DFT), including a comprehensive list of window functions and + some new at-top windows", 2002, + http://hdl.handle.net/11858/00-001M-0000-0013-557A-5 + + Examples + -------- + >>> from scipy import signal + + Confirm COLA condition for rectangular window of 75% (3/4) overlap: + + >>> signal.check_COLA(signal.windows.boxcar(100), 100, 75) + True + + COLA is not true for 25% (1/4) overlap, though: + + >>> signal.check_COLA(signal.windows.boxcar(100), 100, 25) + False + + "Symmetrical" Hann window (for filter design) is not COLA: + + >>> signal.check_COLA(signal.windows.hann(120, sym=True), 120, 60) + False + + "Periodic" or "DFT-even" Hann window (for FFT analysis) is COLA for + overlap of 1/2, 2/3, 3/4, etc.: + + >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 60) + True + + >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 80) + True + + >>> signal.check_COLA(signal.windows.hann(120, sym=False), 120, 90) + True + + """ + nperseg = int(nperseg) + + if nperseg < 1: + raise ValueError('nperseg must be a positive integer') + + if noverlap >= nperseg: + raise ValueError('noverlap must be less than nperseg.') + noverlap = int(noverlap) + + if isinstance(window, str) or type(window) is tuple: + win = get_window(window, nperseg) + else: + win = np.asarray(window) + if len(win.shape) != 1: + raise ValueError('window must be 1-D') + if win.shape[0] != nperseg: + raise ValueError('window must have length of nperseg') + + step = nperseg - noverlap + binsums = sum(win[ii*step:(ii+1)*step] for ii in range(nperseg//step)) + + if nperseg % step != 0: + binsums[:nperseg % step] += win[-(nperseg % step):] + + deviation = binsums - np.median(binsums) + return np.max(np.abs(deviation)) < tol + + +def check_NOLA(window, nperseg, noverlap, tol=1e-10): + r"""Check whether the Nonzero Overlap Add (NOLA) constraint is met. + + Parameters + ---------- + window : str or tuple or array_like + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. + nperseg : int + Length of each segment. + noverlap : int + Number of points to overlap between segments. + tol : float, optional + The allowed variance of a bin's weighted sum from the median bin + sum. + + Returns + ------- + verdict : bool + `True` if chosen combination satisfies the NOLA constraint within + `tol`, `False` otherwise + + See Also + -------- + check_COLA: Check whether the Constant OverLap Add (COLA) constraint is met + stft: Short Time Fourier Transform + istft: Inverse Short Time Fourier Transform + + Notes + ----- + In order to enable inversion of an STFT via the inverse STFT in + `istft`, the signal windowing must obey the constraint of "nonzero + overlap add" (NOLA): + + .. math:: \sum_{t}w^{2}[n-tH] \ne 0 + + for all :math:`n`, where :math:`w` is the window function, :math:`t` is the + frame index, and :math:`H` is the hop size (:math:`H` = `nperseg` - + `noverlap`). + + This ensures that the normalization factors in the denominator of the + overlap-add inversion equation are not zero. Only very pathological windows + will fail the NOLA constraint. + + .. versionadded:: 1.2.0 + + References + ---------- + .. [1] Julius O. Smith III, "Spectral Audio Signal Processing", W3K + Publishing, 2011,ISBN 978-0-9745607-3-1. + .. [2] G. Heinzel, A. Ruediger and R. Schilling, "Spectrum and + spectral density estimation by the Discrete Fourier transform + (DFT), including a comprehensive list of window functions and + some new at-top windows", 2002, + http://hdl.handle.net/11858/00-001M-0000-0013-557A-5 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + + Confirm NOLA condition for rectangular window of 75% (3/4) overlap: + + >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 75) + True + + NOLA is also true for 25% (1/4) overlap: + + >>> signal.check_NOLA(signal.windows.boxcar(100), 100, 25) + True + + "Symmetrical" Hann window (for filter design) is also NOLA: + + >>> signal.check_NOLA(signal.windows.hann(120, sym=True), 120, 60) + True + + As long as there is overlap, it takes quite a pathological window to fail + NOLA: + + >>> w = np.ones(64, dtype="float") + >>> w[::2] = 0 + >>> signal.check_NOLA(w, 64, 32) + False + + If there is not enough overlap, a window with zeros at the ends will not + work: + + >>> signal.check_NOLA(signal.windows.hann(64), 64, 0) + False + >>> signal.check_NOLA(signal.windows.hann(64), 64, 1) + False + >>> signal.check_NOLA(signal.windows.hann(64), 64, 2) + True + + """ + nperseg = int(nperseg) + + if nperseg < 1: + raise ValueError('nperseg must be a positive integer') + + if noverlap >= nperseg: + raise ValueError('noverlap must be less than nperseg') + if noverlap < 0: + raise ValueError('noverlap must be a nonnegative integer') + noverlap = int(noverlap) + + if isinstance(window, str) or type(window) is tuple: + win = get_window(window, nperseg) + else: + win = np.asarray(window) + if len(win.shape) != 1: + raise ValueError('window must be 1-D') + if win.shape[0] != nperseg: + raise ValueError('window must have length of nperseg') + + step = nperseg - noverlap + binsums = sum(win[ii*step:(ii+1)*step]**2 for ii in range(nperseg//step)) + + if nperseg % step != 0: + binsums[:nperseg % step] += win[-(nperseg % step):]**2 + + return np.min(binsums) > tol + + +def stft(x, fs=1.0, window='hann', nperseg=256, noverlap=None, nfft=None, + detrend=False, return_onesided=True, boundary='zeros', padded=True, + axis=-1, scaling='spectrum'): + r"""Compute the Short Time Fourier Transform (legacy function). + + STFTs can be used as a way of quantifying the change of a + nonstationary signal's frequency and phase content over time. + + .. legacy:: function + + `ShortTimeFFT` is a newer STFT / ISTFT implementation with more + features. A :ref:`comparison ` between the + implementations can be found in the :ref:`tutorial_stft` section of the + :ref:`user_guide`. + + Parameters + ---------- + x : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. + nperseg : int, optional + Length of each segment. Defaults to 256. + noverlap : int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 2``. Defaults to `None`. When + specified, the COLA constraint must be met (see Notes below). + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to `False`. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + boundary : str or None, optional + Specifies whether the input signal is extended at both ends, and + how to generate the new values, in order to center the first + windowed segment on the first input point. This has the benefit + of enabling reconstruction of the first input point when the + employed window function starts at zero. Valid options are + ``['even', 'odd', 'constant', 'zeros', None]``. Defaults to + 'zeros', for zero padding extension. I.e. ``[1, 2, 3, 4]`` is + extended to ``[0, 1, 2, 3, 4, 0]`` for ``nperseg=3``. + padded : bool, optional + Specifies whether the input signal is zero-padded at the end to + make the signal fit exactly into an integer number of window + segments, so that all of the signal is included in the output. + Defaults to `True`. Padding occurs after boundary extension, if + `boundary` is not `None`, and `padded` is `True`, as is the + default. + axis : int, optional + Axis along which the STFT is computed; the default is over the + last axis (i.e. ``axis=-1``). + scaling: {'spectrum', 'psd'} + The default 'spectrum' scaling allows each frequency line of `Zxx` to + be interpreted as a magnitude spectrum. The 'psd' option scales each + line to a power spectral density - it allows to calculate the signal's + energy by numerically integrating over ``abs(Zxx)**2``. + + .. versionadded:: 1.9.0 + + Returns + ------- + f : ndarray + Array of sample frequencies. + t : ndarray + Array of segment times. + Zxx : ndarray + STFT of `x`. By default, the last axis of `Zxx` corresponds + to the segment times. + + See Also + -------- + istft: Inverse Short Time Fourier Transform + ShortTimeFFT: Newer STFT/ISTFT implementation providing more features. + check_COLA: Check whether the Constant OverLap Add (COLA) constraint + is met + check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met + welch: Power spectral density by Welch's method. + spectrogram: Spectrogram by Welch's method. + csd: Cross spectral density by Welch's method. + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + + Notes + ----- + In order to enable inversion of an STFT via the inverse STFT in + `istft`, the signal windowing must obey the constraint of "Nonzero + OverLap Add" (NOLA), and the input signal must have complete + windowing coverage (i.e. ``(x.shape[axis] - nperseg) % + (nperseg-noverlap) == 0``). The `padded` argument may be used to + accomplish this. + + Given a time-domain signal :math:`x[n]`, a window :math:`w[n]`, and a hop + size :math:`H` = `nperseg - noverlap`, the windowed frame at time index + :math:`t` is given by + + .. math:: x_{t}[n]=x[n]w[n-tH] + + The overlap-add (OLA) reconstruction equation is given by + + .. math:: x[n]=\frac{\sum_{t}x_{t}[n]w[n-tH]}{\sum_{t}w^{2}[n-tH]} + + The NOLA constraint ensures that every normalization term that appears + in the denomimator of the OLA reconstruction equation is nonzero. Whether a + choice of `window`, `nperseg`, and `noverlap` satisfy this constraint can + be tested with `check_NOLA`. + + + .. versionadded:: 0.19.0 + + References + ---------- + .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck + "Discrete-Time Signal Processing", Prentice Hall, 1999. + .. [2] Daniel W. Griffin, Jae S. Lim "Signal Estimation from + Modified Short-Time Fourier Transform", IEEE 1984, + 10.1109/TASSP.1984.1164317 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate a test signal, a 2 Vrms sine wave whose frequency is slowly + modulated around 3kHz, corrupted by white noise of exponentially + decreasing magnitude sampled at 10 kHz. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 2 * np.sqrt(2) + >>> noise_power = 0.01 * fs / 2 + >>> time = np.arange(N) / float(fs) + >>> mod = 500*np.cos(2*np.pi*0.25*time) + >>> carrier = amp * np.sin(2*np.pi*3e3*time + mod) + >>> noise = rng.normal(scale=np.sqrt(noise_power), + ... size=time.shape) + >>> noise *= np.exp(-time/5) + >>> x = carrier + noise + + Compute and plot the STFT's magnitude. + + >>> f, t, Zxx = signal.stft(x, fs, nperseg=1000) + >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud') + >>> plt.title('STFT Magnitude') + >>> plt.ylabel('Frequency [Hz]') + >>> plt.xlabel('Time [sec]') + >>> plt.show() + + Compare the energy of the signal `x` with the energy of its STFT: + + >>> E_x = sum(x**2) / fs # Energy of x + >>> # Calculate a two-sided STFT with PSD scaling: + >>> f, t, Zxx = signal.stft(x, fs, nperseg=1000, return_onesided=False, + ... scaling='psd') + >>> # Integrate numerically over abs(Zxx)**2: + >>> df, dt = f[1] - f[0], t[1] - t[0] + >>> E_Zxx = sum(np.sum(Zxx.real**2 + Zxx.imag**2, axis=0) * df) * dt + >>> # The energy is the same, but the numerical errors are quite large: + >>> np.isclose(E_x, E_Zxx, rtol=1e-2) + True + + """ + if scaling == 'psd': + scaling = 'density' + elif scaling != 'spectrum': + raise ValueError(f"Parameter {scaling=} not in ['spectrum', 'psd']!") + + freqs, time, Zxx = _spectral_helper(x, x, fs, window, nperseg, noverlap, + nfft, detrend, return_onesided, + scaling=scaling, axis=axis, + mode='stft', boundary=boundary, + padded=padded) + + return freqs, time, Zxx + + +def istft(Zxx, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, + input_onesided=True, boundary=True, time_axis=-1, freq_axis=-2, + scaling='spectrum'): + r"""Perform the inverse Short Time Fourier transform (legacy function). + + .. legacy:: function + + `ShortTimeFFT` is a newer STFT / ISTFT implementation with more + features. A :ref:`comparison ` between the + implementations can be found in the :ref:`tutorial_stft` section of the + :ref:`user_guide`. + + Parameters + ---------- + Zxx : array_like + STFT of the signal to be reconstructed. If a purely real array + is passed, it will be cast to a complex data type. + fs : float, optional + Sampling frequency of the time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. Must match the window used to generate the + STFT for faithful inversion. + nperseg : int, optional + Number of data points corresponding to each STFT segment. This + parameter must be specified if the number of data points per + segment is odd, or if the STFT was padded via ``nfft > + nperseg``. If `None`, the value depends on the shape of + `Zxx` and `input_onesided`. If `input_onesided` is `True`, + ``nperseg=2*(Zxx.shape[freq_axis] - 1)``. Otherwise, + ``nperseg=Zxx.shape[freq_axis]``. Defaults to `None`. + noverlap : int, optional + Number of points to overlap between segments. If `None`, half + of the segment length. Defaults to `None`. When specified, the + COLA constraint must be met (see Notes below), and should match + the parameter used to generate the STFT. Defaults to `None`. + nfft : int, optional + Number of FFT points corresponding to each STFT segment. This + parameter must be specified if the STFT was padded via ``nfft > + nperseg``. If `None`, the default values are the same as for + `nperseg`, detailed above, with one exception: if + `input_onesided` is True and + ``nperseg==2*Zxx.shape[freq_axis] - 1``, `nfft` also takes on + that value. This case allows the proper inversion of an + odd-length unpadded STFT using ``nfft=None``. Defaults to + `None`. + input_onesided : bool, optional + If `True`, interpret the input array as one-sided FFTs, such + as is returned by `stft` with ``return_onesided=True`` and + `numpy.fft.rfft`. If `False`, interpret the input as a a + two-sided FFT. Defaults to `True`. + boundary : bool, optional + Specifies whether the input signal was extended at its + boundaries by supplying a non-`None` ``boundary`` argument to + `stft`. Defaults to `True`. + time_axis : int, optional + Where the time segments of the STFT is located; the default is + the last axis (i.e. ``axis=-1``). + freq_axis : int, optional + Where the frequency axis of the STFT is located; the default is + the penultimate axis (i.e. ``axis=-2``). + scaling: {'spectrum', 'psd'} + The default 'spectrum' scaling allows each frequency line of `Zxx` to + be interpreted as a magnitude spectrum. The 'psd' option scales each + line to a power spectral density - it allows to calculate the signal's + energy by numerically integrating over ``abs(Zxx)**2``. + + Returns + ------- + t : ndarray + Array of output data times. + x : ndarray + iSTFT of `Zxx`. + + See Also + -------- + stft: Short Time Fourier Transform + ShortTimeFFT: Newer STFT/ISTFT implementation providing more features. + check_COLA: Check whether the Constant OverLap Add (COLA) constraint + is met + check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met + + Notes + ----- + In order to enable inversion of an STFT via the inverse STFT with + `istft`, the signal windowing must obey the constraint of "nonzero + overlap add" (NOLA): + + .. math:: \sum_{t}w^{2}[n-tH] \ne 0 + + This ensures that the normalization factors that appear in the denominator + of the overlap-add reconstruction equation + + .. math:: x[n]=\frac{\sum_{t}x_{t}[n]w[n-tH]}{\sum_{t}w^{2}[n-tH]} + + are not zero. The NOLA constraint can be checked with the `check_NOLA` + function. + + An STFT which has been modified (via masking or otherwise) is not + guaranteed to correspond to a exactly realizible signal. This + function implements the iSTFT via the least-squares estimation + algorithm detailed in [2]_, which produces a signal that minimizes + the mean squared error between the STFT of the returned signal and + the modified STFT. + + + .. versionadded:: 0.19.0 + + References + ---------- + .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck + "Discrete-Time Signal Processing", Prentice Hall, 1999. + .. [2] Daniel W. Griffin, Jae S. Lim "Signal Estimation from + Modified Short-Time Fourier Transform", IEEE 1984, + 10.1109/TASSP.1984.1164317 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate a test signal, a 2 Vrms sine wave at 50Hz corrupted by + 0.001 V**2/Hz of white noise sampled at 1024 Hz. + + >>> fs = 1024 + >>> N = 10*fs + >>> nperseg = 512 + >>> amp = 2 * np.sqrt(2) + >>> noise_power = 0.001 * fs / 2 + >>> time = np.arange(N) / float(fs) + >>> carrier = amp * np.sin(2*np.pi*50*time) + >>> noise = rng.normal(scale=np.sqrt(noise_power), + ... size=time.shape) + >>> x = carrier + noise + + Compute the STFT, and plot its magnitude + + >>> f, t, Zxx = signal.stft(x, fs=fs, nperseg=nperseg) + >>> plt.figure() + >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud') + >>> plt.ylim([f[1], f[-1]]) + >>> plt.title('STFT Magnitude') + >>> plt.ylabel('Frequency [Hz]') + >>> plt.xlabel('Time [sec]') + >>> plt.yscale('log') + >>> plt.show() + + Zero the components that are 10% or less of the carrier magnitude, + then convert back to a time series via inverse STFT + + >>> Zxx = np.where(np.abs(Zxx) >= amp/10, Zxx, 0) + >>> _, xrec = signal.istft(Zxx, fs) + + Compare the cleaned signal with the original and true carrier signals. + + >>> plt.figure() + >>> plt.plot(time, x, time, xrec, time, carrier) + >>> plt.xlim([2, 2.1]) + >>> plt.xlabel('Time [sec]') + >>> plt.ylabel('Signal') + >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier']) + >>> plt.show() + + Note that the cleaned signal does not start as abruptly as the original, + since some of the coefficients of the transient were also removed: + + >>> plt.figure() + >>> plt.plot(time, x, time, xrec, time, carrier) + >>> plt.xlim([0, 0.1]) + >>> plt.xlabel('Time [sec]') + >>> plt.ylabel('Signal') + >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier']) + >>> plt.show() + + """ + # Make sure input is an ndarray of appropriate complex dtype + Zxx = np.asarray(Zxx) + 0j + freq_axis = int(freq_axis) + time_axis = int(time_axis) + + if Zxx.ndim < 2: + raise ValueError('Input stft must be at least 2d!') + + if freq_axis == time_axis: + raise ValueError('Must specify differing time and frequency axes!') + + nseg = Zxx.shape[time_axis] + + if input_onesided: + # Assume even segment length + n_default = 2*(Zxx.shape[freq_axis] - 1) + else: + n_default = Zxx.shape[freq_axis] + + # Check windowing parameters + if nperseg is None: + nperseg = n_default + else: + nperseg = int(nperseg) + if nperseg < 1: + raise ValueError('nperseg must be a positive integer') + + if nfft is None: + if (input_onesided) and (nperseg == n_default + 1): + # Odd nperseg, no FFT padding + nfft = nperseg + else: + nfft = n_default + elif nfft < nperseg: + raise ValueError('nfft must be greater than or equal to nperseg.') + else: + nfft = int(nfft) + + if noverlap is None: + noverlap = nperseg//2 + else: + noverlap = int(noverlap) + if noverlap >= nperseg: + raise ValueError('noverlap must be less than nperseg.') + nstep = nperseg - noverlap + + # Rearrange axes if necessary + if time_axis != Zxx.ndim-1 or freq_axis != Zxx.ndim-2: + # Turn negative indices to positive for the call to transpose + if freq_axis < 0: + freq_axis = Zxx.ndim + freq_axis + if time_axis < 0: + time_axis = Zxx.ndim + time_axis + zouter = list(range(Zxx.ndim)) + for ax in sorted([time_axis, freq_axis], reverse=True): + zouter.pop(ax) + Zxx = np.transpose(Zxx, zouter+[freq_axis, time_axis]) + + # Get window as array + if isinstance(window, str) or type(window) is tuple: + win = get_window(window, nperseg) + else: + win = np.asarray(window) + if len(win.shape) != 1: + raise ValueError('window must be 1-D') + if win.shape[0] != nperseg: + raise ValueError(f'window must have length of {nperseg}') + + ifunc = sp_fft.irfft if input_onesided else sp_fft.ifft + xsubs = ifunc(Zxx, axis=-2, n=nfft)[..., :nperseg, :] + + # Initialize output and normalization arrays + outputlength = nperseg + (nseg-1)*nstep + x = np.zeros(list(Zxx.shape[:-2])+[outputlength], dtype=xsubs.dtype) + norm = np.zeros(outputlength, dtype=xsubs.dtype) + + if np.result_type(win, xsubs) != xsubs.dtype: + win = win.astype(xsubs.dtype) + + if scaling == 'spectrum': + xsubs *= win.sum() + elif scaling == 'psd': + xsubs *= np.sqrt(fs * sum(win**2)) + else: + raise ValueError(f"Parameter {scaling=} not in ['spectrum', 'psd']!") + + # Construct the output from the ifft segments + # This loop could perhaps be vectorized/strided somehow... + for ii in range(nseg): + # Window the ifft + x[..., ii*nstep:ii*nstep+nperseg] += xsubs[..., ii] * win + norm[..., ii*nstep:ii*nstep+nperseg] += win**2 + + # Remove extension points + if boundary: + x = x[..., nperseg//2:-(nperseg//2)] + norm = norm[..., nperseg//2:-(nperseg//2)] + + # Divide out normalization where non-tiny + if np.sum(norm > 1e-10) != len(norm): + warnings.warn( + "NOLA condition failed, STFT may not be invertible." + + (" Possibly due to missing boundary" if not boundary else ""), + stacklevel=2 + ) + x /= np.where(norm > 1e-10, norm, 1.0) + + if input_onesided: + x = x.real + + # Put axes back + if x.ndim > 1: + if time_axis != Zxx.ndim-1: + if freq_axis < time_axis: + time_axis -= 1 + x = np.moveaxis(x, -1, time_axis) + + time = np.arange(x.shape[0])/float(fs) + return time, x + + +def coherence(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, + nfft=None, detrend='constant', axis=-1): + r""" + Estimate the magnitude squared coherence estimate, Cxy, of + discrete-time signals X and Y using Welch's method. + + ``Cxy = abs(Pxy)**2/(Pxx*Pyy)``, where `Pxx` and `Pyy` are power + spectral density estimates of X and Y, and `Pxy` is the cross + spectral density estimate of X and Y. + + Parameters + ---------- + x : array_like + Time series of measurement values + y : array_like + Time series of measurement values + fs : float, optional + Sampling frequency of the `x` and `y` time series. Defaults + to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. + nperseg : int, optional + Length of each segment. Defaults to None, but if window is str or + tuple, is set to 256, and if window is array_like, is set to the + length of the window. + noverlap: int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 2``. Defaults to `None`. + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + axis : int, optional + Axis along which the coherence is computed for both inputs; the + default is over the last axis (i.e. ``axis=-1``). + + Returns + ------- + f : ndarray + Array of sample frequencies. + Cxy : ndarray + Magnitude squared coherence of x and y. + + See Also + -------- + periodogram: Simple, optionally modified periodogram + lombscargle: Lomb-Scargle periodogram for unevenly sampled data + welch: Power spectral density by Welch's method. + csd: Cross spectral density by Welch's method. + + Notes + ----- + An appropriate amount of overlap will depend on the choice of window + and on your requirements. For the default Hann window an overlap of + 50% is a reasonable trade off between accurately estimating the + signal power, while not over counting any of the data. Narrower + windows may require a larger overlap. + + .. versionadded:: 0.16.0 + + References + ---------- + .. [1] P. Welch, "The use of the fast Fourier transform for the + estimation of power spectra: A method based on time averaging + over short, modified periodograms", IEEE Trans. Audio + Electroacoust. vol. 15, pp. 70-73, 1967. + .. [2] Stoica, Petre, and Randolph Moses, "Spectral Analysis of + Signals" Prentice Hall, 2005 + + Examples + -------- + >>> import numpy as np + >>> from scipy import signal + >>> import matplotlib.pyplot as plt + >>> rng = np.random.default_rng() + + Generate two test signals with some common features. + + >>> fs = 10e3 + >>> N = 1e5 + >>> amp = 20 + >>> freq = 1234.0 + >>> noise_power = 0.001 * fs / 2 + >>> time = np.arange(N) / fs + >>> b, a = signal.butter(2, 0.25, 'low') + >>> x = rng.normal(scale=np.sqrt(noise_power), size=time.shape) + >>> y = signal.lfilter(b, a, x) + >>> x += amp*np.sin(2*np.pi*freq*time) + >>> y += rng.normal(scale=0.1*np.sqrt(noise_power), size=time.shape) + + Compute and plot the coherence. + + >>> f, Cxy = signal.coherence(x, y, fs, nperseg=1024) + >>> plt.semilogy(f, Cxy) + >>> plt.xlabel('frequency [Hz]') + >>> plt.ylabel('Coherence') + >>> plt.show() + + """ + freqs, Pxx = welch(x, fs=fs, window=window, nperseg=nperseg, + noverlap=noverlap, nfft=nfft, detrend=detrend, + axis=axis) + _, Pyy = welch(y, fs=fs, window=window, nperseg=nperseg, noverlap=noverlap, + nfft=nfft, detrend=detrend, axis=axis) + _, Pxy = csd(x, y, fs=fs, window=window, nperseg=nperseg, + noverlap=noverlap, nfft=nfft, detrend=detrend, axis=axis) + + Cxy = np.abs(Pxy)**2 / Pxx / Pyy + + return freqs, Cxy + + +def _spectral_helper(x, y, fs=1.0, window='hann', nperseg=None, noverlap=None, + nfft=None, detrend='constant', return_onesided=True, + scaling='density', axis=-1, mode='psd', boundary=None, + padded=False): + """Calculate various forms of windowed FFTs for PSD, CSD, etc. + + This is a helper function that implements the commonality between + the stft, psd, csd, and spectrogram functions. It is not designed to + be called externally. The windows are not averaged over; the result + from each window is returned. + + Parameters + ---------- + x : array_like + Array or sequence containing the data to be analyzed. + y : array_like + Array or sequence containing the data to be analyzed. If this is + the same object in memory as `x` (i.e. ``_spectral_helper(x, + x, ...)``), the extra computations are spared. + fs : float, optional + Sampling frequency of the time series. Defaults to 1.0. + window : str or tuple or array_like, optional + Desired window to use. If `window` is a string or tuple, it is + passed to `get_window` to generate the window values, which are + DFT-even by default. See `get_window` for a list of windows and + required parameters. If `window` is array_like it will be used + directly as the window and its length must be nperseg. Defaults + to a Hann window. + nperseg : int, optional + Length of each segment. Defaults to None, but if window is str or + tuple, is set to 256, and if window is array_like, is set to the + length of the window. + noverlap : int, optional + Number of points to overlap between segments. If `None`, + ``noverlap = nperseg // 2``. Defaults to `None`. + nfft : int, optional + Length of the FFT used, if a zero padded FFT is desired. If + `None`, the FFT length is `nperseg`. Defaults to `None`. + detrend : str or function or `False`, optional + Specifies how to detrend each segment. If `detrend` is a + string, it is passed as the `type` argument to the `detrend` + function. If it is a function, it takes a segment and returns a + detrended segment. If `detrend` is `False`, no detrending is + done. Defaults to 'constant'. + return_onesided : bool, optional + If `True`, return a one-sided spectrum for real data. If + `False` return a two-sided spectrum. Defaults to `True`, but for + complex data, a two-sided spectrum is always returned. + scaling : { 'density', 'spectrum' }, optional + Selects between computing the cross spectral density ('density') + where `Pxy` has units of V**2/Hz and computing the cross + spectrum ('spectrum') where `Pxy` has units of V**2, if `x` + and `y` are measured in V and `fs` is measured in Hz. + Defaults to 'density' + axis : int, optional + Axis along which the FFTs are computed; the default is over the + last axis (i.e. ``axis=-1``). + mode: str {'psd', 'stft'}, optional + Defines what kind of return values are expected. Defaults to + 'psd'. + boundary : str or None, optional + Specifies whether the input signal is extended at both ends, and + how to generate the new values, in order to center the first + windowed segment on the first input point. This has the benefit + of enabling reconstruction of the first input point when the + employed window function starts at zero. Valid options are + ``['even', 'odd', 'constant', 'zeros', None]``. Defaults to + `None`. + padded : bool, optional + Specifies whether the input signal is zero-padded at the end to + make the signal fit exactly into an integer number of window + segments, so that all of the signal is included in the output. + Defaults to `False`. Padding occurs after boundary extension, if + `boundary` is not `None`, and `padded` is `True`. + + Returns + ------- + freqs : ndarray + Array of sample frequencies. + t : ndarray + Array of times corresponding to each data segment + result : ndarray + Array of output data, contents dependent on *mode* kwarg. + + Notes + ----- + Adapted from matplotlib.mlab + + .. versionadded:: 0.16.0 + """ + if mode not in ['psd', 'stft']: + raise ValueError("Unknown value for mode %s, must be one of: " + "{'psd', 'stft'}" % mode) + + boundary_funcs = {'even': even_ext, + 'odd': odd_ext, + 'constant': const_ext, + 'zeros': zero_ext, + None: None} + + if boundary not in boundary_funcs: + raise ValueError("Unknown boundary option '{}', must be one of: {}" + .format(boundary, list(boundary_funcs.keys()))) + + # If x and y are the same object we can save ourselves some computation. + same_data = y is x + + if not same_data and mode != 'psd': + raise ValueError("x and y must be equal if mode is 'stft'") + + axis = int(axis) + + # Ensure we have np.arrays, get outdtype + x = np.asarray(x) + if not same_data: + y = np.asarray(y) + outdtype = np.result_type(x, y, np.complex64) + else: + outdtype = np.result_type(x, np.complex64) + + if not same_data: + # Check if we can broadcast the outer axes together + xouter = list(x.shape) + youter = list(y.shape) + xouter.pop(axis) + youter.pop(axis) + try: + outershape = np.broadcast(np.empty(xouter), np.empty(youter)).shape + except ValueError as e: + raise ValueError('x and y cannot be broadcast together.') from e + + if same_data: + if x.size == 0: + return np.empty(x.shape), np.empty(x.shape), np.empty(x.shape) + else: + if x.size == 0 or y.size == 0: + outshape = outershape + (min([x.shape[axis], y.shape[axis]]),) + emptyout = np.moveaxis(np.empty(outshape), -1, axis) + return emptyout, emptyout, emptyout + + if x.ndim > 1: + if axis != -1: + x = np.moveaxis(x, axis, -1) + if not same_data and y.ndim > 1: + y = np.moveaxis(y, axis, -1) + + # Check if x and y are the same length, zero-pad if necessary + if not same_data: + if x.shape[-1] != y.shape[-1]: + if x.shape[-1] < y.shape[-1]: + pad_shape = list(x.shape) + pad_shape[-1] = y.shape[-1] - x.shape[-1] + x = np.concatenate((x, np.zeros(pad_shape)), -1) + else: + pad_shape = list(y.shape) + pad_shape[-1] = x.shape[-1] - y.shape[-1] + y = np.concatenate((y, np.zeros(pad_shape)), -1) + + if nperseg is not None: # if specified by user + nperseg = int(nperseg) + if nperseg < 1: + raise ValueError('nperseg must be a positive integer') + + # parse window; if array like, then set nperseg = win.shape + win, nperseg = _triage_segments(window, nperseg, input_length=x.shape[-1]) + + if nfft is None: + nfft = nperseg + elif nfft < nperseg: + raise ValueError('nfft must be greater than or equal to nperseg.') + else: + nfft = int(nfft) + + if noverlap is None: + noverlap = nperseg//2 + else: + noverlap = int(noverlap) + if noverlap >= nperseg: + raise ValueError('noverlap must be less than nperseg.') + nstep = nperseg - noverlap + + # Padding occurs after boundary extension, so that the extended signal ends + # in zeros, instead of introducing an impulse at the end. + # I.e. if x = [..., 3, 2] + # extend then pad -> [..., 3, 2, 2, 3, 0, 0, 0] + # pad then extend -> [..., 3, 2, 0, 0, 0, 2, 3] + + if boundary is not None: + ext_func = boundary_funcs[boundary] + x = ext_func(x, nperseg//2, axis=-1) + if not same_data: + y = ext_func(y, nperseg//2, axis=-1) + + if padded: + # Pad to integer number of windowed segments + # I.e make x.shape[-1] = nperseg + (nseg-1)*nstep, with integer nseg + nadd = (-(x.shape[-1]-nperseg) % nstep) % nperseg + zeros_shape = list(x.shape[:-1]) + [nadd] + x = np.concatenate((x, np.zeros(zeros_shape)), axis=-1) + if not same_data: + zeros_shape = list(y.shape[:-1]) + [nadd] + y = np.concatenate((y, np.zeros(zeros_shape)), axis=-1) + + # Handle detrending and window functions + if not detrend: + def detrend_func(d): + return d + elif not hasattr(detrend, '__call__'): + def detrend_func(d): + return _signaltools.detrend(d, type=detrend, axis=-1) + elif axis != -1: + # Wrap this function so that it receives a shape that it could + # reasonably expect to receive. + def detrend_func(d): + d = np.moveaxis(d, -1, axis) + d = detrend(d) + return np.moveaxis(d, axis, -1) + else: + detrend_func = detrend + + if np.result_type(win, np.complex64) != outdtype: + win = win.astype(outdtype) + + if scaling == 'density': + scale = 1.0 / (fs * (win*win).sum()) + elif scaling == 'spectrum': + scale = 1.0 / win.sum()**2 + else: + raise ValueError('Unknown scaling: %r' % scaling) + + if mode == 'stft': + scale = np.sqrt(scale) + + if return_onesided: + if np.iscomplexobj(x): + sides = 'twosided' + warnings.warn('Input data is complex, switching to return_onesided=False', + stacklevel=3) + else: + sides = 'onesided' + if not same_data: + if np.iscomplexobj(y): + sides = 'twosided' + warnings.warn('Input data is complex, switching to ' + 'return_onesided=False', + stacklevel=3) + else: + sides = 'twosided' + + if sides == 'twosided': + freqs = sp_fft.fftfreq(nfft, 1/fs) + elif sides == 'onesided': + freqs = sp_fft.rfftfreq(nfft, 1/fs) + + # Perform the windowed FFTs + result = _fft_helper(x, win, detrend_func, nperseg, noverlap, nfft, sides) + + if not same_data: + # All the same operations on the y data + result_y = _fft_helper(y, win, detrend_func, nperseg, noverlap, nfft, + sides) + result = np.conjugate(result) * result_y + elif mode == 'psd': + result = np.conjugate(result) * result + + result *= scale + if sides == 'onesided' and mode == 'psd': + if nfft % 2: + result[..., 1:] *= 2 + else: + # Last point is unpaired Nyquist freq point, don't double + result[..., 1:-1] *= 2 + + time = np.arange(nperseg/2, x.shape[-1] - nperseg/2 + 1, + nperseg - noverlap)/float(fs) + if boundary is not None: + time -= (nperseg/2) / fs + + result = result.astype(outdtype) + + # All imaginary parts are zero anyways + if same_data and mode != 'stft': + result = result.real + + # Output is going to have new last axis for time/window index, so a + # negative axis index shifts down one + if axis < 0: + axis -= 1 + + # Roll frequency axis back to axis where the data came from + result = np.moveaxis(result, -1, axis) + + return freqs, time, result + + +def _fft_helper(x, win, detrend_func, nperseg, noverlap, nfft, sides): + """ + Calculate windowed FFT, for internal use by + `scipy.signal._spectral_helper`. + + This is a helper function that does the main FFT calculation for + `_spectral helper`. All input validation is performed there, and the + data axis is assumed to be the last axis of x. It is not designed to + be called externally. The windows are not averaged over; the result + from each window is returned. + + Returns + ------- + result : ndarray + Array of FFT data + + Notes + ----- + Adapted from matplotlib.mlab + + .. versionadded:: 0.16.0 + """ + # Created sliding window view of array + if nperseg == 1 and noverlap == 0: + result = x[..., np.newaxis] + else: + step = nperseg - noverlap + result = np.lib.stride_tricks.sliding_window_view( + x, window_shape=nperseg, axis=-1, writeable=True + ) + result = result[..., 0::step, :] + + # Detrend each data segment individually + result = detrend_func(result) + + # Apply window by multiplication + result = win * result + + # Perform the fft. Acts on last axis by default. Zero-pads automatically + if sides == 'twosided': + func = sp_fft.fft + else: + result = result.real + func = sp_fft.rfft + result = func(result, n=nfft) + + return result + + +def _triage_segments(window, nperseg, input_length): + """ + Parses window and nperseg arguments for spectrogram and _spectral_helper. + This is a helper function, not meant to be called externally. + + Parameters + ---------- + window : string, tuple, or ndarray + If window is specified by a string or tuple and nperseg is not + specified, nperseg is set to the default of 256 and returns a window of + that length. + If instead the window is array_like and nperseg is not specified, then + nperseg is set to the length of the window. A ValueError is raised if + the user supplies both an array_like window and a value for nperseg but + nperseg does not equal the length of the window. + + nperseg : int + Length of each segment + + input_length: int + Length of input signal, i.e. x.shape[-1]. Used to test for errors. + + Returns + ------- + win : ndarray + window. If function was called with string or tuple than this will hold + the actual array used as a window. + + nperseg : int + Length of each segment. If window is str or tuple, nperseg is set to + 256. If window is array_like, nperseg is set to the length of the + window. + """ + # parse window; if array like, then set nperseg = win.shape + if isinstance(window, str) or isinstance(window, tuple): + # if nperseg not specified + if nperseg is None: + nperseg = 256 # then change to default + if nperseg > input_length: + warnings.warn(f'nperseg = {nperseg:d} is greater than input length ' + f' = {input_length:d}, using nperseg = {input_length:d}', + stacklevel=3) + nperseg = input_length + win = get_window(window, nperseg) + else: + win = np.asarray(window) + if len(win.shape) != 1: + raise ValueError('window must be 1-D') + if input_length < win.shape[-1]: + raise ValueError('window is longer than input signal') + if nperseg is None: + nperseg = win.shape[0] + elif nperseg is not None: + if nperseg != win.shape[0]: + raise ValueError("value specified for nperseg is different" + " from length of window") + return win, nperseg + + +def _median_bias(n): + """ + Returns the bias of the median of a set of periodograms relative to + the mean. + + See Appendix B from [1]_ for details. + + Parameters + ---------- + n : int + Numbers of periodograms being averaged. + + Returns + ------- + bias : float + Calculated bias. + + References + ---------- + .. [1] B. Allen, W.G. Anderson, P.R. Brady, D.A. Brown, J.D.E. Creighton. + "FINDCHIRP: an algorithm for detection of gravitational waves from + inspiraling compact binaries", Physical Review D 85, 2012, + :arxiv:`gr-qc/0509116` + """ + ii_2 = 2 * np.arange(1., (n-1) // 2 + 1) + return 1 + np.sum(1. / (ii_2 + 1) - 1. / ii_2) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/_upfirdn_apply.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_upfirdn_apply.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..de925c6b66f78d8d1be4507d8489f6250c4f87f3 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/signal/_upfirdn_apply.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/signal/ltisys.py b/env-llmeval/lib/python3.10/site-packages/scipy/signal/ltisys.py new file mode 100644 index 0000000000000000000000000000000000000000..4c261d468e680f5c5a0272a65d76cbd2fa39ae54 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/signal/ltisys.py @@ -0,0 +1,30 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.signal` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + +__all__ = [ # noqa: F822 + 'lti', 'dlti', 'TransferFunction', 'ZerosPolesGain', 'StateSpace', + 'lsim', 'impulse', 'step', 'bode', + 'freqresp', 'place_poles', 'dlsim', 'dstep', 'dimpulse', + 'dfreqresp', 'dbode', 's_qr', 'linalg', + 'tf2zpk', 'zpk2tf', 'normalize', 'freqs', + 'freqz', 'freqs_zpk', 'freqz_zpk', 'tf2ss', 'abcd_normalize', + 'ss2tf', 'zpk2ss', 'ss2zpk', 'cont2discrete', 'atleast_1d', + 'squeeze', 'transpose', 'linspace', + 'LinearTimeInvariant', 'TransferFunctionContinuous', + 'TransferFunctionDiscrete', 'ZerosPolesGainContinuous', + 'ZerosPolesGainDiscrete', 'StateSpaceContinuous', + 'StateSpaceDiscrete', 'Bunch' +] + + +def __dir__(): + return __all__ + + +def 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8.7416055e-04 1.1307517e-03 diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt new file mode 100644 index 0000000000000000000000000000000000000000..7c6b67fa43c5fef11101d28dd46f4c1b325b65ee --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/pdist-cosine-ml.txt @@ -0,0 +1 @@ + 2.5695885e-01 2.6882042e-01 2.3470353e-01 2.9299329e-01 2.2742702e-01 3.1253572e-01 2.4986352e-01 3.0770122e-01 2.5191977e-01 2.7931567e-01 2.8133743e-01 2.6316239e-01 2.6067201e-01 3.2982339e-01 2.8993002e-01 2.5506356e-01 2.8728051e-01 2.4952121e-01 2.8613379e-01 2.6894157e-01 2.3606353e-01 2.1670935e-01 2.3470242e-01 2.4294172e-01 2.4376454e-01 2.3228195e-01 2.3554918e-01 2.4851241e-01 2.0917546e-01 2.4971488e-01 2.4264224e-01 2.7405461e-01 1.9086415e-01 2.6346574e-01 2.5908801e-01 2.2138495e-01 2.2910721e-01 2.2169919e-01 2.0660065e-01 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37 76 52 77 79 58 21 58 10 0 13 32 72 80 3 75 75 25 21 9 79 18 +26 13 36 63 43 2 50 41 65 18 88 44 82 75 73 24 1 30 54 68 15 18 22 50 41 99 27 96 51 53 +22 4 76 11 85 88 28 75 1 2 92 66 63 3 58 43 53 5 1 24 99 90 87 87 41 1 85 37 98 92 +16 39 13 88 60 55 35 11 34 23 23 85 79 41 79 87 65 78 47 83 88 78 35 84 30 61 37 58 25 55 +27 33 15 76 82 79 73 92 93 78 18 38 22 96 63 92 41 9 50 96 14 55 8 60 15 61 97 56 43 22 +42 34 94 11 35 70 50 49 36 34 59 14 87 84 88 83 4 69 29 99 35 24 2 18 97 97 74 88 91 49 +33 25 71 12 60 2 48 22 81 33 27 95 54 25 53 14 20 43 26 96 98 37 64 27 72 33 78 45 22 61 +61 21 91 38 92 47 26 90 78 96 58 41 21 72 81 61 55 9 55 60 28 25 25 74 73 81 64 16 49 39 +90 89 12 93 91 23 82 36 63 58 73 81 49 32 60 39 4 84 73 16 18 26 58 85 46 28 82 91 72 7 +79 41 28 76 33 70 47 6 18 64 40 54 45 61 28 63 87 83 38 9 65 68 62 45 80 63 89 29 20 40 +20 59 58 23 61 79 35 19 78 2 26 48 90 34 69 31 31 42 92 33 18 74 28 47 45 52 36 89 19 40 +58 13 72 24 31 26 73 72 84 29 85 99 20 32 54 92 8 80 86 58 23 80 59 21 76 75 90 76 92 57 +74 53 80 51 8 88 84 63 82 99 97 77 38 9 51 61 37 20 68 47 65 21 53 82 85 96 62 65 35 4 +71 82 14 18 88 79 38 76 66 27 10 10 62 54 80 21 6 57 83 33 52 10 97 37 6 38 12 51 0 84 +95 30 75 92 84 30 55 57 32 44 53 24 77 81 34 84 69 85 91 33 50 72 62 79 62 12 59 75 99 81 +38 42 47 1 11 34 27 77 70 85 89 84 79 15 14 54 78 93 72 68 63 39 98 72 55 32 93 0 13 21 +3 15 10 15 3 31 84 89 53 5 60 41 66 77 45 12 68 68 50 68 99 64 46 54 30 56 2 90 99 78 +66 10 27 89 42 16 9 98 16 2 68 51 0 22 73 60 69 96 37 69 30 36 20 21 51 26 65 13 74 86 +94 58 34 97 77 88 90 75 47 30 6 36 89 66 48 9 20 6 52 45 0 37 99 46 11 53 53 72 94 40 +5 71 50 96 89 71 80 43 27 95 49 9 74 28 62 65 64 97 2 55 58 11 69 0 31 22 73 20 66 11 +63 39 84 62 64 5 56 92 26 86 19 20 56 85 42 48 56 51 54 29 26 95 72 38 70 61 16 54 57 19 +76 97 40 99 73 68 98 92 97 62 73 1 29 72 18 70 90 4 98 95 70 36 65 45 86 36 88 38 64 54 diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt new file mode 100644 index 0000000000000000000000000000000000000000..47ce4a7ae522fc2a2bbaa9d8ca285913b8ef0712 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/data/selfdual-4d-polytope.txt @@ -0,0 +1,27 @@ +# The facets of a self-dual 4-dim regular polytope +# with 24 octahedron facets. Taken from cddlib. +# Format b + Ax >= 0 + 1 1 1 1 1 + 1 1 1 1 -1 + 1 1 1 -1 1 + 1 1 1 -1 -1 + 1 1 -1 1 1 + 1 1 -1 1 -1 + 1 1 -1 -1 1 + 1 1 -1 -1 -1 + 1 -1 1 1 1 + 1 -1 1 1 -1 + 1 -1 1 -1 1 + 1 -1 1 -1 -1 + 1 -1 -1 1 1 + 1 -1 -1 1 -1 + 1 -1 -1 -1 1 + 1 -1 -1 -1 -1 + 1 2 0 0 0 + 1 0 2 0 0 + 1 0 0 2 0 + 1 0 0 0 2 + 1 -2 0 0 0 + 1 0 -2 0 0 + 1 0 0 -2 0 + 1 0 0 0 -2 diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__plotutils.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__plotutils.py new file mode 100644 index 0000000000000000000000000000000000000000..0e2553bf7ad56e97b567e5b334ccf17921f7f7f3 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__plotutils.py @@ -0,0 +1,91 @@ +import pytest +import numpy as np +from numpy.testing import assert_, assert_array_equal, assert_allclose + +try: + import matplotlib + matplotlib.rcParams['backend'] = 'Agg' + import matplotlib.pyplot as plt + has_matplotlib = True +except Exception: + has_matplotlib = False + +from scipy.spatial import \ + delaunay_plot_2d, voronoi_plot_2d, convex_hull_plot_2d, \ + Delaunay, Voronoi, ConvexHull + + +@pytest.mark.skipif(not has_matplotlib, reason="Matplotlib not available") +class TestPlotting: + points = [(0,0), (0,1), (1,0), (1,1)] + + def test_delaunay(self): + # Smoke test + fig = plt.figure() + obj = Delaunay(self.points) + s_before = obj.simplices.copy() + r = delaunay_plot_2d(obj, ax=fig.gca()) + assert_array_equal(obj.simplices, s_before) # shouldn't modify + assert_(r is fig) + delaunay_plot_2d(obj, ax=fig.gca()) + + def test_voronoi(self): + # Smoke test + fig = plt.figure() + obj = Voronoi(self.points) + r = voronoi_plot_2d(obj, ax=fig.gca()) + assert_(r is fig) + voronoi_plot_2d(obj) + voronoi_plot_2d(obj, show_vertices=False) + + def test_convex_hull(self): + # Smoke test + fig = plt.figure() + tri = ConvexHull(self.points) + r = convex_hull_plot_2d(tri, ax=fig.gca()) + assert_(r is fig) + convex_hull_plot_2d(tri) + + def test_gh_19653(self): + # aspect ratio sensitivity of voronoi_plot_2d + # infinite Voronoi edges + points = np.array([[245.059986986012, 10.971011721360075], + [320.49044143557785, 10.970258360366753], + [239.79023081978914, 13.108487516946218], + [263.38325791238833, 12.93241352743668], + [219.53334398353175, 13.346107628161008]]) + vor = Voronoi(points) + fig = voronoi_plot_2d(vor) + ax = fig.gca() + infinite_segments = ax.collections[1].get_segments() + expected_segments = np.array([[[282.77256, -254.76904], + [282.729714, -4544.744698]], + [[282.77256014, -254.76904029], + [430.08561382, 4032.67658742]], + [[229.26733285, -20.39957514], + [-168.17167404, -4291.92545966]], + [[289.93433364, 5151.40412217], + [330.40553385, 9441.18887532]]]) + assert_allclose(infinite_segments, expected_segments) + + def test_gh_19653_smaller_aspect(self): + # reasonable behavior for less extreme aspect + # ratio + points = np.array([[24.059986986012, 10.971011721360075], + [32.49044143557785, 10.970258360366753], + [23.79023081978914, 13.108487516946218], + [26.38325791238833, 12.93241352743668], + [21.53334398353175, 13.346107628161008]]) + vor = Voronoi(points) + fig = voronoi_plot_2d(vor) + ax = fig.gca() + infinite_segments = ax.collections[1].get_segments() + expected_segments = np.array([[[28.274979, 8.335027], + [28.270463, -42.19763338]], + [[28.27497869, 8.33502697], + [43.73223829, 56.44555501]], + [[22.51805823, 11.8621754], + [-12.09266506, -24.95694485]], + [[29.53092448, 78.46952378], + [33.82572726, 128.81934455]]]) + assert_allclose(infinite_segments, expected_segments) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__procrustes.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__procrustes.py new file mode 100644 index 0000000000000000000000000000000000000000..42a3c4d35bd55e2ffecefb691c805f517c56d6ca --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test__procrustes.py @@ -0,0 +1,116 @@ +import numpy as np +from numpy.testing import assert_allclose, assert_equal, assert_almost_equal +from pytest import raises as assert_raises + +from scipy.spatial import procrustes + + +class TestProcrustes: + def setup_method(self): + """creates inputs""" + # an L + self.data1 = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], 'd') + + # a larger, shifted, mirrored L + self.data2 = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], 'd') + + # an L shifted up 1, right 1, and with point 4 shifted an extra .5 + # to the right + # pointwise distance disparity with data1: 3*(2) + (1 + 1.5^2) + self.data3 = np.array([[2, 4], [2, 3], [2, 2], [3, 2.5]], 'd') + + # data4, data5 are standardized (trace(A*A') = 1). + # procrustes should return an identical copy if they are used + # as the first matrix argument. + shiftangle = np.pi / 8 + self.data4 = np.array([[1, 0], [0, 1], [-1, 0], + [0, -1]], 'd') / np.sqrt(4) + self.data5 = np.array([[np.cos(shiftangle), np.sin(shiftangle)], + [np.cos(np.pi / 2 - shiftangle), + np.sin(np.pi / 2 - shiftangle)], + [-np.cos(shiftangle), + -np.sin(shiftangle)], + [-np.cos(np.pi / 2 - shiftangle), + -np.sin(np.pi / 2 - shiftangle)]], + 'd') / np.sqrt(4) + + def test_procrustes(self): + # tests procrustes' ability to match two matrices. + # + # the second matrix is a rotated, shifted, scaled, and mirrored version + # of the first, in two dimensions only + # + # can shift, mirror, and scale an 'L'? + a, b, disparity = procrustes(self.data1, self.data2) + assert_allclose(b, a) + assert_almost_equal(disparity, 0.) + + # if first mtx is standardized, leaves first mtx unchanged? + m4, m5, disp45 = procrustes(self.data4, self.data5) + assert_equal(m4, self.data4) + + # at worst, data3 is an 'L' with one point off by .5 + m1, m3, disp13 = procrustes(self.data1, self.data3) + #assert_(disp13 < 0.5 ** 2) + + def test_procrustes2(self): + # procrustes disparity should not depend on order of matrices + m1, m3, disp13 = procrustes(self.data1, self.data3) + m3_2, m1_2, disp31 = procrustes(self.data3, self.data1) + assert_almost_equal(disp13, disp31) + + # try with 3d, 8 pts per + rand1 = np.array([[2.61955202, 0.30522265, 0.55515826], + [0.41124708, -0.03966978, -0.31854548], + [0.91910318, 1.39451809, -0.15295084], + [2.00452023, 0.50150048, 0.29485268], + [0.09453595, 0.67528885, 0.03283872], + [0.07015232, 2.18892599, -1.67266852], + [0.65029688, 1.60551637, 0.80013549], + [-0.6607528, 0.53644208, 0.17033891]]) + + rand3 = np.array([[0.0809969, 0.09731461, -0.173442], + [-1.84888465, -0.92589646, -1.29335743], + [0.67031855, -1.35957463, 0.41938621], + [0.73967209, -0.20230757, 0.52418027], + [0.17752796, 0.09065607, 0.29827466], + [0.47999368, -0.88455717, -0.57547934], + [-0.11486344, -0.12608506, -0.3395779], + [-0.86106154, -0.28687488, 0.9644429]]) + res1, res3, disp13 = procrustes(rand1, rand3) + res3_2, res1_2, disp31 = procrustes(rand3, rand1) + assert_almost_equal(disp13, disp31) + + def test_procrustes_shape_mismatch(self): + assert_raises(ValueError, procrustes, + np.array([[1, 2], [3, 4]]), + np.array([[5, 6, 7], [8, 9, 10]])) + + def test_procrustes_empty_rows_or_cols(self): + empty = np.array([[]]) + assert_raises(ValueError, procrustes, empty, empty) + + def test_procrustes_no_variation(self): + assert_raises(ValueError, procrustes, + np.array([[42, 42], [42, 42]]), + np.array([[45, 45], [45, 45]])) + + def test_procrustes_bad_number_of_dimensions(self): + # fewer dimensions in one dataset + assert_raises(ValueError, procrustes, + np.array([1, 1, 2, 3, 5, 8]), + np.array([[1, 2], [3, 4]])) + + # fewer dimensions in both datasets + assert_raises(ValueError, procrustes, + np.array([1, 1, 2, 3, 5, 8]), + np.array([1, 1, 2, 3, 5, 8])) + + # zero dimensions + assert_raises(ValueError, procrustes, np.array(7), np.array(11)) + + # extra dimensions + assert_raises(ValueError, procrustes, + np.array([[[11], [7]]]), + np.array([[[5, 13]]])) + diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_distance.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_distance.py new file mode 100644 index 0000000000000000000000000000000000000000..14989b9a2bc674af468f7d241278b02b75b10a8c --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_distance.py @@ -0,0 +1,2267 @@ +# +# Author: Damian Eads +# Date: April 17, 2008 +# +# Copyright (C) 2008 Damian Eads +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# +# 2. Redistributions in binary form must reproduce the above +# copyright notice, this list of conditions and the following +# disclaimer in the documentation and/or other materials provided +# with the distribution. +# +# 3. The name of the author may not be used to endorse or promote +# products derived from this software without specific prior +# written permission. +# +# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS +# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY +# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE +# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, +# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +import sys +import os.path + +from functools import wraps, partial +import weakref + +import numpy as np +import warnings +from numpy.linalg import norm +from numpy.testing import (verbose, assert_, + assert_array_equal, assert_equal, + assert_almost_equal, assert_allclose, + break_cycles, IS_PYPY) +import pytest + +import scipy.spatial.distance + +from scipy.spatial.distance import ( + squareform, pdist, cdist, num_obs_y, num_obs_dm, is_valid_dm, is_valid_y, + _validate_vector, _METRICS_NAMES) + +# these were missing: chebyshev cityblock +# jensenshannon and seuclidean are referenced by string name. +from scipy.spatial.distance import (braycurtis, canberra, chebyshev, cityblock, + correlation, cosine, dice, euclidean, + hamming, jaccard, jensenshannon, + kulczynski1, mahalanobis, + minkowski, rogerstanimoto, + russellrao, seuclidean, sokalmichener, # noqa: F401 + sokalsneath, sqeuclidean, yule) +from scipy._lib._util import np_long, np_ulong + + +@pytest.fixture(params=_METRICS_NAMES, scope="session") +def metric(request): + """ + Fixture for all metrics in scipy.spatial.distance + """ + return request.param + + +_filenames = [ + "cdist-X1.txt", + "cdist-X2.txt", + "iris.txt", + "pdist-boolean-inp.txt", + "pdist-chebyshev-ml-iris.txt", + "pdist-chebyshev-ml.txt", + "pdist-cityblock-ml-iris.txt", + "pdist-cityblock-ml.txt", + "pdist-correlation-ml-iris.txt", + "pdist-correlation-ml.txt", + "pdist-cosine-ml-iris.txt", + "pdist-cosine-ml.txt", + "pdist-double-inp.txt", + "pdist-euclidean-ml-iris.txt", + "pdist-euclidean-ml.txt", + "pdist-hamming-ml.txt", + "pdist-jaccard-ml.txt", + "pdist-jensenshannon-ml-iris.txt", + "pdist-jensenshannon-ml.txt", + "pdist-minkowski-3.2-ml-iris.txt", + "pdist-minkowski-3.2-ml.txt", + "pdist-minkowski-5.8-ml-iris.txt", + "pdist-seuclidean-ml-iris.txt", + "pdist-seuclidean-ml.txt", + "pdist-spearman-ml.txt", + "random-bool-data.txt", + "random-double-data.txt", + "random-int-data.txt", + "random-uint-data.txt", + ] + +_tdist = np.array([[0, 662, 877, 255, 412, 996], + [662, 0, 295, 468, 268, 400], + [877, 295, 0, 754, 564, 138], + [255, 468, 754, 0, 219, 869], + [412, 268, 564, 219, 0, 669], + [996, 400, 138, 869, 669, 0]], dtype='double') + +_ytdist = squareform(_tdist) + +# A hashmap of expected output arrays for the tests. These arrays +# come from a list of text files, which are read prior to testing. +# Each test loads inputs and outputs from this dictionary. +eo = {} + + +def load_testing_files(): + for fn in _filenames: + name = fn.replace(".txt", "").replace("-ml", "") + fqfn = os.path.join(os.path.dirname(__file__), 'data', fn) + fp = open(fqfn) + eo[name] = np.loadtxt(fp) + fp.close() + eo['pdist-boolean-inp'] = np.bool_(eo['pdist-boolean-inp']) + eo['random-bool-data'] = np.bool_(eo['random-bool-data']) + eo['random-float32-data'] = np.float32(eo['random-double-data']) + eo['random-int-data'] = np_long(eo['random-int-data']) + eo['random-uint-data'] = np_ulong(eo['random-uint-data']) + + +load_testing_files() + + +def _is_32bit(): + return np.intp(0).itemsize < 8 + + +def _chk_asarrays(arrays, axis=None): + arrays = [np.asanyarray(a) for a in arrays] + if axis is None: + # np < 1.10 ravel removes subclass from arrays + arrays = [np.ravel(a) if a.ndim != 1 else a + for a in arrays] + axis = 0 + arrays = tuple(np.atleast_1d(a) for a in arrays) + if axis < 0: + if not all(a.ndim == arrays[0].ndim for a in arrays): + raise ValueError("array ndim must be the same for neg axis") + axis = range(arrays[0].ndim)[axis] + return arrays + (axis,) + + +def _chk_weights(arrays, weights=None, axis=None, + force_weights=False, simplify_weights=True, + pos_only=False, neg_check=False, + nan_screen=False, mask_screen=False, + ddof=None): + chked = _chk_asarrays(arrays, axis=axis) + arrays, axis = chked[:-1], chked[-1] + + simplify_weights = simplify_weights and not force_weights + if not force_weights and mask_screen: + force_weights = any(np.ma.getmask(a) is not np.ma.nomask for a in arrays) + + if nan_screen: + has_nans = [np.isnan(np.sum(a)) for a in arrays] + if any(has_nans): + mask_screen = True + force_weights = True + arrays = tuple(np.ma.masked_invalid(a) if has_nan else a + for a, has_nan in zip(arrays, has_nans)) + + if weights is not None: + weights = np.asanyarray(weights) + elif force_weights: + weights = np.ones(arrays[0].shape[axis]) + else: + return arrays + (weights, axis) + + if ddof: + weights = _freq_weights(weights) + + if mask_screen: + weights = _weight_masked(arrays, weights, axis) + + if not all(weights.shape == (a.shape[axis],) for a in arrays): + raise ValueError("weights shape must match arrays along axis") + if neg_check and (weights < 0).any(): + raise ValueError("weights cannot be negative") + + if pos_only: + pos_weights = np.nonzero(weights > 0)[0] + if pos_weights.size < weights.size: + arrays = tuple(np.take(a, pos_weights, axis=axis) for a in arrays) + weights = weights[pos_weights] + if simplify_weights and (weights == 1).all(): + weights = None + return arrays + (weights, axis) + + +def _freq_weights(weights): + if weights is None: + return weights + int_weights = weights.astype(int) + if (weights != int_weights).any(): + raise ValueError("frequency (integer count-type) weights required %s" % weights) + return int_weights + + +def _weight_masked(arrays, weights, axis): + if axis is None: + axis = 0 + weights = np.asanyarray(weights) + for a in arrays: + axis_mask = np.ma.getmask(a) + if axis_mask is np.ma.nomask: + continue + if a.ndim > 1: + not_axes = tuple(i for i in range(a.ndim) if i != axis) + axis_mask = axis_mask.any(axis=not_axes) + weights *= 1 - axis_mask.astype(int) + return weights + + +def _rand_split(arrays, weights, axis, split_per, seed=None): + # Coerce `arrays` to float64 if integer, to avoid nan-to-integer issues + arrays = [arr.astype(np.float64) if np.issubdtype(arr.dtype, np.integer) + else arr for arr in arrays] + + # inverse operation for stats.collapse_weights + weights = np.array(weights, dtype=np.float64) # modified inplace; need a copy + seeded_rand = np.random.RandomState(seed) + + def mytake(a, ix, axis): + record = np.asanyarray(np.take(a, ix, axis=axis)) + return record.reshape([a.shape[i] if i != axis else 1 + for i in range(a.ndim)]) + + n_obs = arrays[0].shape[axis] + assert all(a.shape[axis] == n_obs for a in arrays), \ + "data must be aligned on sample axis" + for i in range(int(split_per) * n_obs): + split_ix = seeded_rand.randint(n_obs + i) + prev_w = weights[split_ix] + q = seeded_rand.rand() + weights[split_ix] = q * prev_w + weights = np.append(weights, (1. - q) * prev_w) + arrays = [np.append(a, mytake(a, split_ix, axis=axis), + axis=axis) for a in arrays] + return arrays, weights + + +def _rough_check(a, b, compare_assert=partial(assert_allclose, atol=1e-5), + key=lambda x: x, w=None): + check_a = key(a) + check_b = key(b) + try: + if np.array(check_a != check_b).any(): # try strict equality for string types + compare_assert(check_a, check_b) + except AttributeError: # masked array + compare_assert(check_a, check_b) + except (TypeError, ValueError): # nested data structure + for a_i, b_i in zip(check_a, check_b): + _rough_check(a_i, b_i, compare_assert=compare_assert) + +# diff from test_stats: +# n_args=2, weight_arg='w', default_axis=None +# ma_safe = False, nan_safe = False +def _weight_checked(fn, n_args=2, default_axis=None, key=lambda x: x, weight_arg='w', + squeeze=True, silent=False, + ones_test=True, const_test=True, dup_test=True, + split_test=True, dud_test=True, ma_safe=False, ma_very_safe=False, + nan_safe=False, split_per=1.0, seed=0, + compare_assert=partial(assert_allclose, atol=1e-5)): + """runs fn on its arguments 2 or 3 ways, checks that the results are the same, + then returns the same thing it would have returned before""" + @wraps(fn) + def wrapped(*args, **kwargs): + result = fn(*args, **kwargs) + + arrays = args[:n_args] + rest = args[n_args:] + weights = kwargs.get(weight_arg, None) + axis = kwargs.get('axis', default_axis) + + chked = _chk_weights(arrays, weights=weights, axis=axis, + force_weights=True, mask_screen=True) + arrays, weights, axis = chked[:-2], chked[-2], chked[-1] + if squeeze: + arrays = [np.atleast_1d(a.squeeze()) for a in arrays] + + try: + # WEIGHTS CHECK 1: EQUAL WEIGHTED OBSERVATIONS + args = tuple(arrays) + rest + if ones_test: + kwargs[weight_arg] = weights + _rough_check(result, fn(*args, **kwargs), key=key) + if const_test: + kwargs[weight_arg] = weights * 101.0 + _rough_check(result, fn(*args, **kwargs), key=key) + kwargs[weight_arg] = weights * 0.101 + try: + _rough_check(result, fn(*args, **kwargs), key=key) + except Exception as e: + raise type(e)((e, arrays, weights)) from e + + # WEIGHTS CHECK 2: ADDL 0-WEIGHTED OBS + if dud_test: + # add randomly resampled rows, weighted at 0 + dud_arrays, dud_weights = _rand_split(arrays, weights, axis, + split_per=split_per, seed=seed) + dud_weights[:weights.size] = weights # not exactly 1 because of masked arrays # noqa: E501 + dud_weights[weights.size:] = 0 + dud_args = tuple(dud_arrays) + rest + kwargs[weight_arg] = dud_weights + _rough_check(result, fn(*dud_args, **kwargs), key=key) + # increase the value of those 0-weighted rows + for a in dud_arrays: + indexer = [slice(None)] * a.ndim + indexer[axis] = slice(weights.size, None) + indexer = tuple(indexer) + a[indexer] = a[indexer] * 101 + dud_args = tuple(dud_arrays) + rest + _rough_check(result, fn(*dud_args, **kwargs), key=key) + # set those 0-weighted rows to NaNs + for a in dud_arrays: + indexer = [slice(None)] * a.ndim + indexer[axis] = slice(weights.size, None) + indexer = tuple(indexer) + a[indexer] = a[indexer] * np.nan + if kwargs.get("nan_policy", None) == "omit" and nan_safe: + dud_args = tuple(dud_arrays) + rest + _rough_check(result, fn(*dud_args, **kwargs), key=key) + # mask out those nan values + if ma_safe: + dud_arrays = [np.ma.masked_invalid(a) for a in dud_arrays] + dud_args = tuple(dud_arrays) + rest + _rough_check(result, fn(*dud_args, **kwargs), key=key) + if ma_very_safe: + kwargs[weight_arg] = None + _rough_check(result, fn(*dud_args, **kwargs), key=key) + del dud_arrays, dud_args, dud_weights + + # WEIGHTS CHECK 3: DUPLICATE DATA (DUMB SPLITTING) + if dup_test: + dup_arrays = [np.append(a, a, axis=axis) for a in arrays] + dup_weights = np.append(weights, weights) / 2.0 + dup_args = tuple(dup_arrays) + rest + kwargs[weight_arg] = dup_weights + _rough_check(result, fn(*dup_args, **kwargs), key=key) + del dup_args, dup_arrays, dup_weights + + # WEIGHT CHECK 3: RANDOM SPLITTING + if split_test and split_per > 0: + split = _rand_split(arrays, weights, axis, + split_per=split_per, seed=seed) + split_arrays, split_weights = split + split_args = tuple(split_arrays) + rest + kwargs[weight_arg] = split_weights + _rough_check(result, fn(*split_args, **kwargs), key=key) + except NotImplementedError as e: + # when some combination of arguments makes weighting impossible, + # this is the desired response + if not silent: + warnings.warn(f"{fn.__name__} NotImplemented weights: {e}", + stacklevel=3) + return result + return wrapped + + +wcdist = _weight_checked(cdist, default_axis=1, squeeze=False) +wcdist_no_const = _weight_checked(cdist, default_axis=1, + squeeze=False, const_test=False) +wpdist = _weight_checked(pdist, default_axis=1, squeeze=False, n_args=1) +wpdist_no_const = _weight_checked(pdist, default_axis=1, squeeze=False, + const_test=False, n_args=1) +wrogerstanimoto = _weight_checked(rogerstanimoto) +wmatching = whamming = _weight_checked(hamming, dud_test=False) +wyule = _weight_checked(yule) +wdice = _weight_checked(dice) +wcityblock = _weight_checked(cityblock) +wchebyshev = _weight_checked(chebyshev) +wcosine = _weight_checked(cosine) +wcorrelation = _weight_checked(correlation) +wkulczynski1 = _weight_checked(kulczynski1) +wjaccard = _weight_checked(jaccard) +weuclidean = _weight_checked(euclidean, const_test=False) +wsqeuclidean = _weight_checked(sqeuclidean, const_test=False) +wbraycurtis = _weight_checked(braycurtis) +wcanberra = _weight_checked(canberra, const_test=False) +wsokalsneath = _weight_checked(sokalsneath) +wsokalmichener = _weight_checked(sokalmichener) +wrussellrao = _weight_checked(russellrao) + + +class TestCdist: + + def setup_method(self): + self.rnd_eo_names = ['random-float32-data', 'random-int-data', + 'random-uint-data', 'random-double-data', + 'random-bool-data'] + self.valid_upcasts = {'bool': [np_ulong, np_long, np.float32, np.float64], + 'uint': [np_long, np.float32, np.float64], + 'int': [np.float32, np.float64], + 'float32': [np.float64]} + + def test_cdist_extra_args(self, metric): + # Tests that args and kwargs are correctly handled + + X1 = [[1., 2., 3.], [1.2, 2.3, 3.4], [2.2, 2.3, 4.4]] + X2 = [[7., 5., 8.], [7.5, 5.8, 8.4], [5.5, 5.8, 4.4]] + kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(3)} + args = [3.14] * 200 + + with pytest.raises(TypeError): + cdist(X1, X2, metric=metric, **kwargs) + with pytest.raises(TypeError): + cdist(X1, X2, metric=eval(metric), **kwargs) + with pytest.raises(TypeError): + cdist(X1, X2, metric="test_" + metric, **kwargs) + with pytest.raises(TypeError): + cdist(X1, X2, metric=metric, *args) + with pytest.raises(TypeError): + cdist(X1, X2, metric=eval(metric), *args) + with pytest.raises(TypeError): + cdist(X1, X2, metric="test_" + metric, *args) + + def test_cdist_extra_args_custom(self): + # Tests that args and kwargs are correctly handled + # also for custom metric + def _my_metric(x, y, arg, kwarg=1, kwarg2=2): + return arg + kwarg + kwarg2 + + X1 = [[1., 2., 3.], [1.2, 2.3, 3.4], [2.2, 2.3, 4.4]] + X2 = [[7., 5., 8.], [7.5, 5.8, 8.4], [5.5, 5.8, 4.4]] + kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(3)} + args = [3.14] * 200 + + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, *args) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, **kwargs) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, kwarg=2.2, kwarg2=3.3) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1, 2, kwarg=2.2) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1, 2, kwarg=2.2) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1.1, 2.2, 3.3) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1.1, 2.2) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1.1) + with pytest.raises(TypeError): + cdist(X1, X2, _my_metric, 1.1, kwarg=2.2, kwarg2=3.3) + + # this should work + assert_allclose(cdist(X1, X2, metric=_my_metric, + arg=1.1, kwarg2=3.3), 5.4) + + def test_cdist_euclidean_random_unicode(self): + eps = 1e-15 + X1 = eo['cdist-X1'] + X2 = eo['cdist-X2'] + Y1 = wcdist_no_const(X1, X2, 'euclidean') + Y2 = wcdist_no_const(X1, X2, 'test_euclidean') + assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2) + + @pytest.mark.parametrize("p", [0.1, 0.25, 1.0, 1.23, + 2.0, 3.8, 4.6, np.inf]) + def test_cdist_minkowski_random(self, p): + eps = 1e-13 + X1 = eo['cdist-X1'] + X2 = eo['cdist-X2'] + Y1 = wcdist_no_const(X1, X2, 'minkowski', p=p) + Y2 = wcdist_no_const(X1, X2, 'test_minkowski', p=p) + assert_allclose(Y1, Y2, atol=0, rtol=eps, verbose=verbose > 2) + + def test_cdist_cosine_random(self): + eps = 1e-14 + X1 = eo['cdist-X1'] + X2 = eo['cdist-X2'] + Y1 = wcdist(X1, X2, 'cosine') + + # Naive implementation + def norms(X): + return np.linalg.norm(X, axis=1).reshape(-1, 1) + + Y2 = 1 - np.dot((X1 / norms(X1)), (X2 / norms(X2)).T) + + assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2) + + def test_cdist_mahalanobis(self): + # 1-dimensional observations + x1 = np.array([[2], [3]]) + x2 = np.array([[2], [5]]) + dist = cdist(x1, x2, metric='mahalanobis') + assert_allclose(dist, [[0.0, np.sqrt(4.5)], [np.sqrt(0.5), np.sqrt(2)]]) + + # 2-dimensional observations + x1 = np.array([[0, 0], [-1, 0]]) + x2 = np.array([[0, 2], [1, 0], [0, -2]]) + dist = cdist(x1, x2, metric='mahalanobis') + rt2 = np.sqrt(2) + assert_allclose(dist, [[rt2, rt2, rt2], [2, 2 * rt2, 2]]) + + # Too few observations + with pytest.raises(ValueError): + cdist([[0, 1]], [[2, 3]], metric='mahalanobis') + + def test_cdist_custom_notdouble(self): + class myclass: + pass + + def _my_metric(x, y): + if not isinstance(x[0], myclass) or not isinstance(y[0], myclass): + raise ValueError("Type has been changed") + return 1.123 + data = np.array([[myclass()]], dtype=object) + cdist_y = cdist(data, data, metric=_my_metric) + right_y = 1.123 + assert_equal(cdist_y, right_y, verbose=verbose > 2) + + def _check_calling_conventions(self, X1, X2, metric, eps=1e-07, **kwargs): + # helper function for test_cdist_calling_conventions + try: + y1 = cdist(X1, X2, metric=metric, **kwargs) + y2 = cdist(X1, X2, metric=eval(metric), **kwargs) + y3 = cdist(X1, X2, metric="test_" + metric, **kwargs) + except Exception as e: + e_cls = e.__class__ + if verbose > 2: + print(e_cls.__name__) + print(e) + with pytest.raises(e_cls): + cdist(X1, X2, metric=metric, **kwargs) + with pytest.raises(e_cls): + cdist(X1, X2, metric=eval(metric), **kwargs) + with pytest.raises(e_cls): + cdist(X1, X2, metric="test_" + metric, **kwargs) + else: + assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2) + assert_allclose(y1, y3, rtol=eps, verbose=verbose > 2) + + def test_cdist_calling_conventions(self, metric): + # Ensures that specifying the metric with a str or scipy function + # gives the same behaviour (i.e. same result or same exception). + # NOTE: The correctness should be checked within each metric tests. + for eo_name in self.rnd_eo_names: + # subsampling input data to speed-up tests + # NOTE: num samples needs to be > than dimensions for mahalanobis + X1 = eo[eo_name][::5, ::-2] + X2 = eo[eo_name][1::5, ::2] + if verbose > 2: + print("testing: ", metric, " with: ", eo_name) + if metric in {'dice', 'yule', + 'rogerstanimoto', + 'russellrao', 'sokalmichener', + 'sokalsneath', + 'kulczynski1'} and 'bool' not in eo_name: + # python version permits non-bools e.g. for fuzzy logic + continue + self._check_calling_conventions(X1, X2, metric) + + # Testing built-in metrics with extra args + if metric == "seuclidean": + X12 = np.vstack([X1, X2]).astype(np.float64) + V = np.var(X12, axis=0, ddof=1) + self._check_calling_conventions(X1, X2, metric, V=V) + elif metric == "mahalanobis": + X12 = np.vstack([X1, X2]).astype(np.float64) + V = np.atleast_2d(np.cov(X12.T)) + VI = np.array(np.linalg.inv(V).T) + self._check_calling_conventions(X1, X2, metric, VI=VI) + + def test_cdist_dtype_equivalence(self, metric): + # Tests that the result is not affected by type up-casting + eps = 1e-07 + tests = [(eo['random-bool-data'], self.valid_upcasts['bool']), + (eo['random-uint-data'], self.valid_upcasts['uint']), + (eo['random-int-data'], self.valid_upcasts['int']), + (eo['random-float32-data'], self.valid_upcasts['float32'])] + for test in tests: + X1 = test[0][::5, ::-2] + X2 = test[0][1::5, ::2] + try: + y1 = cdist(X1, X2, metric=metric) + except Exception as e: + e_cls = e.__class__ + if verbose > 2: + print(e_cls.__name__) + print(e) + for new_type in test[1]: + X1new = new_type(X1) + X2new = new_type(X2) + with pytest.raises(e_cls): + cdist(X1new, X2new, metric=metric) + else: + for new_type in test[1]: + y2 = cdist(new_type(X1), new_type(X2), metric=metric) + assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2) + + def test_cdist_out(self, metric): + # Test that out parameter works properly + eps = 1e-15 + X1 = eo['cdist-X1'] + X2 = eo['cdist-X2'] + out_r, out_c = X1.shape[0], X2.shape[0] + + kwargs = dict() + if metric == 'minkowski': + kwargs['p'] = 1.23 + out1 = np.empty((out_r, out_c), dtype=np.float64) + Y1 = cdist(X1, X2, metric, **kwargs) + Y2 = cdist(X1, X2, metric, out=out1, **kwargs) + + # test that output is numerically equivalent + assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2) + + # test that Y_test1 and out1 are the same object + assert_(Y2 is out1) + + # test for incorrect shape + out2 = np.empty((out_r-1, out_c+1), dtype=np.float64) + with pytest.raises(ValueError): + cdist(X1, X2, metric, out=out2, **kwargs) + + # test for C-contiguous order + out3 = np.empty( + (2 * out_r, 2 * out_c), dtype=np.float64)[::2, ::2] + out4 = np.empty((out_r, out_c), dtype=np.float64, order='F') + with pytest.raises(ValueError): + cdist(X1, X2, metric, out=out3, **kwargs) + with pytest.raises(ValueError): + cdist(X1, X2, metric, out=out4, **kwargs) + + # test for incorrect dtype + out5 = np.empty((out_r, out_c), dtype=np.int64) + with pytest.raises(ValueError): + cdist(X1, X2, metric, out=out5, **kwargs) + + def test_striding(self, metric): + # test that striding is handled correct with calls to + # _copy_array_if_base_present + eps = 1e-15 + X1 = eo['cdist-X1'][::2, ::2] + X2 = eo['cdist-X2'][::2, ::2] + X1_copy = X1.copy() + X2_copy = X2.copy() + + # confirm equivalence + assert_equal(X1, X1_copy) + assert_equal(X2, X2_copy) + # confirm contiguity + assert_(not X1.flags.c_contiguous) + assert_(not X2.flags.c_contiguous) + assert_(X1_copy.flags.c_contiguous) + assert_(X2_copy.flags.c_contiguous) + + kwargs = dict() + if metric == 'minkowski': + kwargs['p'] = 1.23 + Y1 = cdist(X1, X2, metric, **kwargs) + Y2 = cdist(X1_copy, X2_copy, metric, **kwargs) + # test that output is numerically equivalent + assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2) + + def test_cdist_refcount(self, metric): + x1 = np.random.rand(10, 10) + x2 = np.random.rand(10, 10) + + kwargs = dict() + if metric == 'minkowski': + kwargs['p'] = 1.23 + + out = cdist(x1, x2, metric=metric, **kwargs) + + # Check reference counts aren't messed up. If we only hold weak + # references, the arrays should be deallocated. + weak_refs = [weakref.ref(v) for v in (x1, x2, out)] + del x1, x2, out + + if IS_PYPY: + break_cycles() + assert all(weak_ref() is None for weak_ref in weak_refs) + + +class TestPdist: + + def setup_method(self): + self.rnd_eo_names = ['random-float32-data', 'random-int-data', + 'random-uint-data', 'random-double-data', + 'random-bool-data'] + self.valid_upcasts = {'bool': [np_ulong, np_long, np.float32, np.float64], + 'uint': [np_long, np.float32, np.float64], + 'int': [np.float32, np.float64], + 'float32': [np.float64]} + + def test_pdist_extra_args(self, metric): + # Tests that args and kwargs are correctly handled + X1 = [[1., 2.], [1.2, 2.3], [2.2, 2.3]] + kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(2)} + args = [3.14] * 200 + + with pytest.raises(TypeError): + pdist(X1, metric=metric, **kwargs) + with pytest.raises(TypeError): + pdist(X1, metric=eval(metric), **kwargs) + with pytest.raises(TypeError): + pdist(X1, metric="test_" + metric, **kwargs) + with pytest.raises(TypeError): + pdist(X1, metric=metric, *args) + with pytest.raises(TypeError): + pdist(X1, metric=eval(metric), *args) + with pytest.raises(TypeError): + pdist(X1, metric="test_" + metric, *args) + + def test_pdist_extra_args_custom(self): + # Tests that args and kwargs are correctly handled + # also for custom metric + def _my_metric(x, y, arg, kwarg=1, kwarg2=2): + return arg + kwarg + kwarg2 + + X1 = [[1., 2.], [1.2, 2.3], [2.2, 2.3]] + kwargs = {"N0tV4l1D_p4raM": 3.14, "w": np.arange(2)} + args = [3.14] * 200 + + with pytest.raises(TypeError): + pdist(X1, _my_metric) + with pytest.raises(TypeError): + pdist(X1, _my_metric, *args) + with pytest.raises(TypeError): + pdist(X1, _my_metric, **kwargs) + with pytest.raises(TypeError): + pdist(X1, _my_metric, kwarg=2.2, kwarg2=3.3) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1, 2, kwarg=2.2) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1, 2, kwarg=2.2) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1.1, 2.2, 3.3) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1.1, 2.2) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1.1) + with pytest.raises(TypeError): + pdist(X1, _my_metric, 1.1, kwarg=2.2, kwarg2=3.3) + + # these should work + assert_allclose(pdist(X1, metric=_my_metric, + arg=1.1, kwarg2=3.3), 5.4) + + def test_pdist_euclidean_random(self): + eps = 1e-07 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-euclidean'] + Y_test1 = wpdist_no_const(X, 'euclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_euclidean_random_u(self): + eps = 1e-07 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-euclidean'] + Y_test1 = wpdist_no_const(X, 'euclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_euclidean_random_float32(self): + eps = 1e-07 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-euclidean'] + Y_test1 = wpdist_no_const(X, 'euclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_euclidean_random_nonC(self): + eps = 1e-07 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-euclidean'] + Y_test2 = wpdist_no_const(X, 'test_euclidean') + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_euclidean_iris_double(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-euclidean-iris'] + Y_test1 = wpdist_no_const(X, 'euclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_euclidean_iris_float32(self): + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-euclidean-iris'] + Y_test1 = wpdist_no_const(X, 'euclidean') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + @pytest.mark.slow + def test_pdist_euclidean_iris_nonC(self): + # Test pdist(X, 'test_euclidean') [the non-C implementation] on the + # Iris data set. + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-euclidean-iris'] + Y_test2 = wpdist_no_const(X, 'test_euclidean') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_seuclidean_random(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-seuclidean'] + Y_test1 = pdist(X, 'seuclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_seuclidean_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-seuclidean'] + Y_test1 = pdist(X, 'seuclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + # Check no error is raise when V has float32 dtype (#11171). + V = np.var(X, axis=0, ddof=1) + Y_test2 = pdist(X, 'seuclidean', V=V) + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_seuclidean_random_nonC(self): + # Test pdist(X, 'test_sqeuclidean') [the non-C implementation] + eps = 1e-07 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-seuclidean'] + Y_test2 = pdist(X, 'test_seuclidean') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_seuclidean_iris(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-seuclidean-iris'] + Y_test1 = pdist(X, 'seuclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_seuclidean_iris_float32(self): + # Tests pdist(X, 'seuclidean') on the Iris data set (float32). + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-seuclidean-iris'] + Y_test1 = pdist(X, 'seuclidean') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_seuclidean_iris_nonC(self): + # Test pdist(X, 'test_seuclidean') [the non-C implementation] on the + # Iris data set. + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-seuclidean-iris'] + Y_test2 = pdist(X, 'test_seuclidean') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_cosine_random(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-cosine'] + Y_test1 = wpdist(X, 'cosine') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_cosine_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-cosine'] + Y_test1 = wpdist(X, 'cosine') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_cosine_random_nonC(self): + # Test pdist(X, 'test_cosine') [the non-C implementation] + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-cosine'] + Y_test2 = wpdist(X, 'test_cosine') + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_cosine_iris(self): + eps = 1e-05 + X = eo['iris'] + Y_right = eo['pdist-cosine-iris'] + Y_test1 = wpdist(X, 'cosine') + assert_allclose(Y_test1, Y_right, atol=eps) + + @pytest.mark.slow + def test_pdist_cosine_iris_float32(self): + eps = 1e-05 + X = np.float32(eo['iris']) + Y_right = eo['pdist-cosine-iris'] + Y_test1 = wpdist(X, 'cosine') + assert_allclose(Y_test1, Y_right, atol=eps, verbose=verbose > 2) + + @pytest.mark.slow + def test_pdist_cosine_iris_nonC(self): + eps = 1e-05 + X = eo['iris'] + Y_right = eo['pdist-cosine-iris'] + Y_test2 = wpdist(X, 'test_cosine') + assert_allclose(Y_test2, Y_right, atol=eps) + + def test_pdist_cosine_bounds(self): + # Test adapted from @joernhees's example at gh-5208: case where + # cosine distance used to be negative. XXX: very sensitive to the + # specific norm computation. + x = np.abs(np.random.RandomState(1337).rand(91)) + X = np.vstack([x, x]) + assert_(wpdist(X, 'cosine')[0] >= 0, + msg='cosine distance should be non-negative') + + def test_pdist_cityblock_random(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-cityblock'] + Y_test1 = wpdist_no_const(X, 'cityblock') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_cityblock_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-cityblock'] + Y_test1 = wpdist_no_const(X, 'cityblock') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_cityblock_random_nonC(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-cityblock'] + Y_test2 = wpdist_no_const(X, 'test_cityblock') + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_cityblock_iris(self): + eps = 1e-14 + X = eo['iris'] + Y_right = eo['pdist-cityblock-iris'] + Y_test1 = wpdist_no_const(X, 'cityblock') + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_cityblock_iris_float32(self): + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-cityblock-iris'] + Y_test1 = wpdist_no_const(X, 'cityblock') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + @pytest.mark.slow + def test_pdist_cityblock_iris_nonC(self): + # Test pdist(X, 'test_cityblock') [the non-C implementation] on the + # Iris data set. + eps = 1e-14 + X = eo['iris'] + Y_right = eo['pdist-cityblock-iris'] + Y_test2 = wpdist_no_const(X, 'test_cityblock') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_correlation_random(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-correlation'] + Y_test1 = wpdist(X, 'correlation') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_correlation_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-correlation'] + Y_test1 = wpdist(X, 'correlation') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_correlation_random_nonC(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-correlation'] + Y_test2 = wpdist(X, 'test_correlation') + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_correlation_iris(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-correlation-iris'] + Y_test1 = wpdist(X, 'correlation') + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_correlation_iris_float32(self): + eps = 1e-7 + X = eo['iris'] + Y_right = np.float32(eo['pdist-correlation-iris']) + Y_test1 = wpdist(X, 'correlation') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + @pytest.mark.slow + def test_pdist_correlation_iris_nonC(self): + if sys.maxsize > 2**32: + eps = 1e-7 + else: + pytest.skip("see gh-16456") + X = eo['iris'] + Y_right = eo['pdist-correlation-iris'] + Y_test2 = wpdist(X, 'test_correlation') + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.parametrize("p", [0.1, 0.25, 1.0, 2.0, 3.2, np.inf]) + def test_pdist_minkowski_random_p(self, p): + eps = 1e-13 + X = eo['pdist-double-inp'] + Y1 = wpdist_no_const(X, 'minkowski', p=p) + Y2 = wpdist_no_const(X, 'test_minkowski', p=p) + assert_allclose(Y1, Y2, atol=0, rtol=eps) + + def test_pdist_minkowski_random(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-minkowski-3.2'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2) + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_minkowski_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-minkowski-3.2'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2) + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_minkowski_random_nonC(self): + eps = 1e-7 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-minkowski-3.2'] + Y_test2 = wpdist_no_const(X, 'test_minkowski', p=3.2) + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_minkowski_3_2_iris(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-minkowski-3.2-iris'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2) + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_minkowski_3_2_iris_float32(self): + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-minkowski-3.2-iris'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=3.2) + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_minkowski_3_2_iris_nonC(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-minkowski-3.2-iris'] + Y_test2 = wpdist_no_const(X, 'test_minkowski', p=3.2) + assert_allclose(Y_test2, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_minkowski_5_8_iris(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-minkowski-5.8-iris'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=5.8) + assert_allclose(Y_test1, Y_right, rtol=eps) + + @pytest.mark.slow + def test_pdist_minkowski_5_8_iris_float32(self): + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-minkowski-5.8-iris'] + Y_test1 = wpdist_no_const(X, 'minkowski', p=5.8) + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + @pytest.mark.slow + def test_pdist_minkowski_5_8_iris_nonC(self): + eps = 1e-7 + X = eo['iris'] + Y_right = eo['pdist-minkowski-5.8-iris'] + Y_test2 = wpdist_no_const(X, 'test_minkowski', p=5.8) + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_mahalanobis(self): + # 1-dimensional observations + x = np.array([2.0, 2.0, 3.0, 5.0]).reshape(-1, 1) + dist = pdist(x, metric='mahalanobis') + assert_allclose(dist, [0.0, np.sqrt(0.5), np.sqrt(4.5), + np.sqrt(0.5), np.sqrt(4.5), np.sqrt(2.0)]) + + # 2-dimensional observations + x = np.array([[0, 0], [-1, 0], [0, 2], [1, 0], [0, -2]]) + dist = pdist(x, metric='mahalanobis') + rt2 = np.sqrt(2) + assert_allclose(dist, [rt2, rt2, rt2, rt2, 2, 2 * rt2, 2, 2, 2 * rt2, 2]) + + # Too few observations + with pytest.raises(ValueError): + wpdist([[0, 1], [2, 3]], metric='mahalanobis') + + def test_pdist_hamming_random(self): + eps = 1e-15 + X = eo['pdist-boolean-inp'] + Y_right = eo['pdist-hamming'] + Y_test1 = wpdist(X, 'hamming') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_hamming_random_float32(self): + eps = 1e-15 + X = np.float32(eo['pdist-boolean-inp']) + Y_right = eo['pdist-hamming'] + Y_test1 = wpdist(X, 'hamming') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_hamming_random_nonC(self): + eps = 1e-15 + X = eo['pdist-boolean-inp'] + Y_right = eo['pdist-hamming'] + Y_test2 = wpdist(X, 'test_hamming') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_dhamming_random(self): + eps = 1e-15 + X = np.float64(eo['pdist-boolean-inp']) + Y_right = eo['pdist-hamming'] + Y_test1 = wpdist(X, 'hamming') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_dhamming_random_float32(self): + eps = 1e-15 + X = np.float32(eo['pdist-boolean-inp']) + Y_right = eo['pdist-hamming'] + Y_test1 = wpdist(X, 'hamming') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_dhamming_random_nonC(self): + eps = 1e-15 + X = np.float64(eo['pdist-boolean-inp']) + Y_right = eo['pdist-hamming'] + Y_test2 = wpdist(X, 'test_hamming') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_jaccard_random(self): + eps = 1e-8 + X = eo['pdist-boolean-inp'] + Y_right = eo['pdist-jaccard'] + Y_test1 = wpdist(X, 'jaccard') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_jaccard_random_float32(self): + eps = 1e-8 + X = np.float32(eo['pdist-boolean-inp']) + Y_right = eo['pdist-jaccard'] + Y_test1 = wpdist(X, 'jaccard') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_jaccard_random_nonC(self): + eps = 1e-8 + X = eo['pdist-boolean-inp'] + Y_right = eo['pdist-jaccard'] + Y_test2 = wpdist(X, 'test_jaccard') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_djaccard_random(self): + eps = 1e-8 + X = np.float64(eo['pdist-boolean-inp']) + Y_right = eo['pdist-jaccard'] + Y_test1 = wpdist(X, 'jaccard') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_djaccard_random_float32(self): + eps = 1e-8 + X = np.float32(eo['pdist-boolean-inp']) + Y_right = eo['pdist-jaccard'] + Y_test1 = wpdist(X, 'jaccard') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_djaccard_allzeros(self): + eps = 1e-15 + Y = pdist(np.zeros((5, 3)), 'jaccard') + assert_allclose(np.zeros(10), Y, rtol=eps) + + def test_pdist_djaccard_random_nonC(self): + eps = 1e-8 + X = np.float64(eo['pdist-boolean-inp']) + Y_right = eo['pdist-jaccard'] + Y_test2 = wpdist(X, 'test_jaccard') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_jensenshannon_random(self): + eps = 1e-11 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-jensenshannon'] + Y_test1 = pdist(X, 'jensenshannon') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_jensenshannon_random_float32(self): + eps = 1e-8 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-jensenshannon'] + Y_test1 = pdist(X, 'jensenshannon') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + def test_pdist_jensenshannon_random_nonC(self): + eps = 1e-11 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-jensenshannon'] + Y_test2 = pdist(X, 'test_jensenshannon') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_jensenshannon_iris(self): + if _is_32bit(): + # Test failing on 32-bit Linux on Azure otherwise, see gh-12810 + eps = 2.5e-10 + else: + eps = 1e-12 + + X = eo['iris'] + Y_right = eo['pdist-jensenshannon-iris'] + Y_test1 = pdist(X, 'jensenshannon') + assert_allclose(Y_test1, Y_right, atol=eps) + + def test_pdist_jensenshannon_iris_float32(self): + eps = 1e-06 + X = np.float32(eo['iris']) + Y_right = eo['pdist-jensenshannon-iris'] + Y_test1 = pdist(X, 'jensenshannon') + assert_allclose(Y_test1, Y_right, atol=eps, verbose=verbose > 2) + + def test_pdist_jensenshannon_iris_nonC(self): + eps = 5e-5 + X = eo['iris'] + Y_right = eo['pdist-jensenshannon-iris'] + Y_test2 = pdist(X, 'test_jensenshannon') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_djaccard_allzeros_nonC(self): + eps = 1e-15 + Y = pdist(np.zeros((5, 3)), 'test_jaccard') + assert_allclose(np.zeros(10), Y, rtol=eps) + + def test_pdist_chebyshev_random(self): + eps = 1e-8 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-chebyshev'] + Y_test1 = pdist(X, 'chebyshev') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_chebyshev_random_float32(self): + eps = 1e-7 + X = np.float32(eo['pdist-double-inp']) + Y_right = eo['pdist-chebyshev'] + Y_test1 = pdist(X, 'chebyshev') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + def test_pdist_chebyshev_random_nonC(self): + eps = 1e-8 + X = eo['pdist-double-inp'] + Y_right = eo['pdist-chebyshev'] + Y_test2 = pdist(X, 'test_chebyshev') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_chebyshev_iris(self): + eps = 1e-14 + X = eo['iris'] + Y_right = eo['pdist-chebyshev-iris'] + Y_test1 = pdist(X, 'chebyshev') + assert_allclose(Y_test1, Y_right, rtol=eps) + + def test_pdist_chebyshev_iris_float32(self): + eps = 1e-5 + X = np.float32(eo['iris']) + Y_right = eo['pdist-chebyshev-iris'] + Y_test1 = pdist(X, 'chebyshev') + assert_allclose(Y_test1, Y_right, rtol=eps, verbose=verbose > 2) + + def test_pdist_chebyshev_iris_nonC(self): + eps = 1e-14 + X = eo['iris'] + Y_right = eo['pdist-chebyshev-iris'] + Y_test2 = pdist(X, 'test_chebyshev') + assert_allclose(Y_test2, Y_right, rtol=eps) + + def test_pdist_matching_mtica1(self): + # Test matching(*,*) with mtica example #1 (nums). + m = wmatching(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wmatching(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + assert_allclose(m, 0.6, rtol=0, atol=1e-10) + assert_allclose(m2, 0.6, rtol=0, atol=1e-10) + + def test_pdist_matching_mtica2(self): + # Test matching(*,*) with mtica example #2. + m = wmatching(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wmatching(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + assert_allclose(m, 2 / 3, rtol=0, atol=1e-10) + assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10) + + def test_pdist_jaccard_mtica1(self): + m = wjaccard(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wjaccard(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + assert_allclose(m, 0.6, rtol=0, atol=1e-10) + assert_allclose(m2, 0.6, rtol=0, atol=1e-10) + + def test_pdist_jaccard_mtica2(self): + m = wjaccard(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wjaccard(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + assert_allclose(m, 2 / 3, rtol=0, atol=1e-10) + assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10) + + def test_pdist_yule_mtica1(self): + m = wyule(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wyule(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 2, rtol=0, atol=1e-10) + assert_allclose(m2, 2, rtol=0, atol=1e-10) + + def test_pdist_yule_mtica2(self): + m = wyule(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wyule(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 2, rtol=0, atol=1e-10) + assert_allclose(m2, 2, rtol=0, atol=1e-10) + + def test_pdist_dice_mtica1(self): + m = wdice(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wdice(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 3 / 7, rtol=0, atol=1e-10) + assert_allclose(m2, 3 / 7, rtol=0, atol=1e-10) + + def test_pdist_dice_mtica2(self): + m = wdice(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wdice(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 0.5, rtol=0, atol=1e-10) + assert_allclose(m2, 0.5, rtol=0, atol=1e-10) + + def test_pdist_sokalsneath_mtica1(self): + m = sokalsneath(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = sokalsneath(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 3 / 4, rtol=0, atol=1e-10) + assert_allclose(m2, 3 / 4, rtol=0, atol=1e-10) + + def test_pdist_sokalsneath_mtica2(self): + m = wsokalsneath(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wsokalsneath(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 4 / 5, rtol=0, atol=1e-10) + assert_allclose(m2, 4 / 5, rtol=0, atol=1e-10) + + def test_pdist_rogerstanimoto_mtica1(self): + m = wrogerstanimoto(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wrogerstanimoto(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 3 / 4, rtol=0, atol=1e-10) + assert_allclose(m2, 3 / 4, rtol=0, atol=1e-10) + + def test_pdist_rogerstanimoto_mtica2(self): + m = wrogerstanimoto(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wrogerstanimoto(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 4 / 5, rtol=0, atol=1e-10) + assert_allclose(m2, 4 / 5, rtol=0, atol=1e-10) + + def test_pdist_russellrao_mtica1(self): + m = wrussellrao(np.array([1, 0, 1, 1, 0]), + np.array([1, 1, 0, 1, 1])) + m2 = wrussellrao(np.array([1, 0, 1, 1, 0], dtype=bool), + np.array([1, 1, 0, 1, 1], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 3 / 5, rtol=0, atol=1e-10) + assert_allclose(m2, 3 / 5, rtol=0, atol=1e-10) + + def test_pdist_russellrao_mtica2(self): + m = wrussellrao(np.array([1, 0, 1]), + np.array([1, 1, 0])) + m2 = wrussellrao(np.array([1, 0, 1], dtype=bool), + np.array([1, 1, 0], dtype=bool)) + if verbose > 2: + print(m) + assert_allclose(m, 2 / 3, rtol=0, atol=1e-10) + assert_allclose(m2, 2 / 3, rtol=0, atol=1e-10) + + @pytest.mark.slow + def test_pdist_canberra_match(self): + D = eo['iris'] + if verbose > 2: + print(D.shape, D.dtype) + eps = 1e-15 + y1 = wpdist_no_const(D, "canberra") + y2 = wpdist_no_const(D, "test_canberra") + assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2) + + def test_pdist_canberra_ticket_711(self): + # Test pdist(X, 'canberra') to see if Canberra gives the right result + # as reported on gh-1238. + eps = 1e-8 + pdist_y = wpdist_no_const(([3.3], [3.4]), "canberra") + right_y = 0.01492537 + assert_allclose(pdist_y, right_y, atol=eps, verbose=verbose > 2) + + def test_pdist_custom_notdouble(self): + # tests that when using a custom metric the data type is not altered + class myclass: + pass + + def _my_metric(x, y): + if not isinstance(x[0], myclass) or not isinstance(y[0], myclass): + raise ValueError("Type has been changed") + return 1.123 + data = np.array([[myclass()], [myclass()]], dtype=object) + pdist_y = pdist(data, metric=_my_metric) + right_y = 1.123 + assert_equal(pdist_y, right_y, verbose=verbose > 2) + + def _check_calling_conventions(self, X, metric, eps=1e-07, **kwargs): + # helper function for test_pdist_calling_conventions + try: + y1 = pdist(X, metric=metric, **kwargs) + y2 = pdist(X, metric=eval(metric), **kwargs) + y3 = pdist(X, metric="test_" + metric, **kwargs) + except Exception as e: + e_cls = e.__class__ + if verbose > 2: + print(e_cls.__name__) + print(e) + with pytest.raises(e_cls): + pdist(X, metric=metric, **kwargs) + with pytest.raises(e_cls): + pdist(X, metric=eval(metric), **kwargs) + with pytest.raises(e_cls): + pdist(X, metric="test_" + metric, **kwargs) + else: + assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2) + assert_allclose(y1, y3, rtol=eps, verbose=verbose > 2) + + def test_pdist_calling_conventions(self, metric): + # Ensures that specifying the metric with a str or scipy function + # gives the same behaviour (i.e. same result or same exception). + # NOTE: The correctness should be checked within each metric tests. + # NOTE: Extra args should be checked with a dedicated test + for eo_name in self.rnd_eo_names: + # subsampling input data to speed-up tests + # NOTE: num samples needs to be > than dimensions for mahalanobis + X = eo[eo_name][::5, ::2] + if verbose > 2: + print("testing: ", metric, " with: ", eo_name) + if metric in {'dice', 'yule', 'matching', + 'rogerstanimoto', 'russellrao', 'sokalmichener', + 'sokalsneath', + 'kulczynski1'} and 'bool' not in eo_name: + # python version permits non-bools e.g. for fuzzy logic + continue + self._check_calling_conventions(X, metric) + + # Testing built-in metrics with extra args + if metric == "seuclidean": + V = np.var(X.astype(np.float64), axis=0, ddof=1) + self._check_calling_conventions(X, metric, V=V) + elif metric == "mahalanobis": + V = np.atleast_2d(np.cov(X.astype(np.float64).T)) + VI = np.array(np.linalg.inv(V).T) + self._check_calling_conventions(X, metric, VI=VI) + + def test_pdist_dtype_equivalence(self, metric): + # Tests that the result is not affected by type up-casting + eps = 1e-07 + tests = [(eo['random-bool-data'], self.valid_upcasts['bool']), + (eo['random-uint-data'], self.valid_upcasts['uint']), + (eo['random-int-data'], self.valid_upcasts['int']), + (eo['random-float32-data'], self.valid_upcasts['float32'])] + for test in tests: + X1 = test[0][::5, ::2] + try: + y1 = pdist(X1, metric=metric) + except Exception as e: + e_cls = e.__class__ + if verbose > 2: + print(e_cls.__name__) + print(e) + for new_type in test[1]: + X2 = new_type(X1) + with pytest.raises(e_cls): + pdist(X2, metric=metric) + else: + for new_type in test[1]: + y2 = pdist(new_type(X1), metric=metric) + assert_allclose(y1, y2, rtol=eps, verbose=verbose > 2) + + def test_pdist_out(self, metric): + # Test that out parameter works properly + eps = 1e-15 + X = eo['random-float32-data'][::5, ::2] + out_size = int((X.shape[0] * (X.shape[0] - 1)) / 2) + + kwargs = dict() + if metric == 'minkowski': + kwargs['p'] = 1.23 + out1 = np.empty(out_size, dtype=np.float64) + Y_right = pdist(X, metric, **kwargs) + Y_test1 = pdist(X, metric, out=out1, **kwargs) + + # test that output is numerically equivalent + assert_allclose(Y_test1, Y_right, rtol=eps) + + # test that Y_test1 and out1 are the same object + assert_(Y_test1 is out1) + + # test for incorrect shape + out2 = np.empty(out_size + 3, dtype=np.float64) + with pytest.raises(ValueError): + pdist(X, metric, out=out2, **kwargs) + + # test for (C-)contiguous output + out3 = np.empty(2 * out_size, dtype=np.float64)[::2] + with pytest.raises(ValueError): + pdist(X, metric, out=out3, **kwargs) + + # test for incorrect dtype + out5 = np.empty(out_size, dtype=np.int64) + with pytest.raises(ValueError): + pdist(X, metric, out=out5, **kwargs) + + def test_striding(self, metric): + # test that striding is handled correct with calls to + # _copy_array_if_base_present + eps = 1e-15 + X = eo['random-float32-data'][::5, ::2] + X_copy = X.copy() + + # confirm contiguity + assert_(not X.flags.c_contiguous) + assert_(X_copy.flags.c_contiguous) + + kwargs = dict() + if metric == 'minkowski': + kwargs['p'] = 1.23 + Y1 = pdist(X, metric, **kwargs) + Y2 = pdist(X_copy, metric, **kwargs) + # test that output is numerically equivalent + assert_allclose(Y1, Y2, rtol=eps, verbose=verbose > 2) + +class TestSomeDistanceFunctions: + + def setup_method(self): + # 1D arrays + x = np.array([1.0, 2.0, 3.0]) + y = np.array([1.0, 1.0, 5.0]) + + self.cases = [(x, y)] + + def test_minkowski(self): + for x, y in self.cases: + dist1 = minkowski(x, y, p=1) + assert_almost_equal(dist1, 3.0) + dist1p5 = minkowski(x, y, p=1.5) + assert_almost_equal(dist1p5, (1.0 + 2.0**1.5)**(2. / 3)) + dist2 = minkowski(x, y, p=2) + assert_almost_equal(dist2, 5.0 ** 0.5) + dist0p25 = minkowski(x, y, p=0.25) + assert_almost_equal(dist0p25, (1.0 + 2.0 ** 0.25) ** 4) + + # Check that casting input to minimum scalar type doesn't affect result + # (issue #10262). This could be extended to more test inputs with + # np.min_scalar_type(np.max(input_matrix)). + a = np.array([352, 916]) + b = np.array([350, 660]) + assert_equal(minkowski(a, b), + minkowski(a.astype('uint16'), b.astype('uint16'))) + + def test_euclidean(self): + for x, y in self.cases: + dist = weuclidean(x, y) + assert_almost_equal(dist, np.sqrt(5)) + + def test_sqeuclidean(self): + for x, y in self.cases: + dist = wsqeuclidean(x, y) + assert_almost_equal(dist, 5.0) + + def test_cosine(self): + for x, y in self.cases: + dist = wcosine(x, y) + assert_almost_equal(dist, 1.0 - 18.0 / (np.sqrt(14) * np.sqrt(27))) + + def test_cosine_output_dtype(self): + # Regression test for gh-19541 + assert isinstance(wcorrelation([1, 1], [1, 1], centered=False), float) + assert isinstance(wcosine([1, 1], [1, 1]), float) + + def test_correlation(self): + xm = np.array([-1.0, 0, 1.0]) + ym = np.array([-4.0 / 3, -4.0 / 3, 5.0 - 7.0 / 3]) + for x, y in self.cases: + dist = wcorrelation(x, y) + assert_almost_equal(dist, 1.0 - np.dot(xm, ym) / (norm(xm) * norm(ym))) + + def test_correlation_positive(self): + # Regression test for gh-12320 (negative return value due to rounding + x = np.array([0., 0., 0., 0., 0., 0., -2., 0., 0., 0., -2., -2., -2., + 0., -2., 0., -2., 0., 0., -1., -2., 0., 1., 0., 0., -2., + 0., 0., -2., 0., -2., -2., -2., -2., -2., -2., 0.]) + y = np.array([1., 1., 1., 1., 1., 1., -1., 1., 1., 1., -1., -1., -1., + 1., -1., 1., -1., 1., 1., 0., -1., 1., 2., 1., 1., -1., + 1., 1., -1., 1., -1., -1., -1., -1., -1., -1., 1.]) + dist = correlation(x, y) + assert 0 <= dist <= 10 * np.finfo(np.float64).eps + + def test_mahalanobis(self): + x = np.array([1.0, 2.0, 3.0]) + y = np.array([1.0, 1.0, 5.0]) + vi = np.array([[2.0, 1.0, 0.0], [1.0, 2.0, 1.0], [0.0, 1.0, 2.0]]) + for x, y in self.cases: + dist = mahalanobis(x, y, vi) + assert_almost_equal(dist, np.sqrt(6.0)) + + +class TestSquareForm: + checked_dtypes = [np.float64, np.float32, np.int32, np.int8, bool] + + def test_squareform_matrix(self): + for dtype in self.checked_dtypes: + self.check_squareform_matrix(dtype) + + def test_squareform_vector(self): + for dtype in self.checked_dtypes: + self.check_squareform_vector(dtype) + + def check_squareform_matrix(self, dtype): + A = np.zeros((0, 0), dtype=dtype) + rA = squareform(A) + assert_equal(rA.shape, (0,)) + assert_equal(rA.dtype, dtype) + + A = np.zeros((1, 1), dtype=dtype) + rA = squareform(A) + assert_equal(rA.shape, (0,)) + assert_equal(rA.dtype, dtype) + + A = np.array([[0, 4.2], [4.2, 0]], dtype=dtype) + rA = squareform(A) + assert_equal(rA.shape, (1,)) + assert_equal(rA.dtype, dtype) + assert_array_equal(rA, np.array([4.2], dtype=dtype)) + + def check_squareform_vector(self, dtype): + v = np.zeros((0,), dtype=dtype) + rv = squareform(v) + assert_equal(rv.shape, (1, 1)) + assert_equal(rv.dtype, dtype) + assert_array_equal(rv, [[0]]) + + v = np.array([8.3], dtype=dtype) + rv = squareform(v) + assert_equal(rv.shape, (2, 2)) + assert_equal(rv.dtype, dtype) + assert_array_equal(rv, np.array([[0, 8.3], [8.3, 0]], dtype=dtype)) + + def test_squareform_multi_matrix(self): + for n in range(2, 5): + self.check_squareform_multi_matrix(n) + + def check_squareform_multi_matrix(self, n): + X = np.random.rand(n, 4) + Y = wpdist_no_const(X) + assert_equal(len(Y.shape), 1) + A = squareform(Y) + Yr = squareform(A) + s = A.shape + k = 0 + if verbose >= 3: + print(A.shape, Y.shape, Yr.shape) + assert_equal(len(s), 2) + assert_equal(len(Yr.shape), 1) + assert_equal(s[0], s[1]) + for i in range(0, s[0]): + for j in range(i + 1, s[1]): + if i != j: + assert_equal(A[i, j], Y[k]) + k += 1 + else: + assert_equal(A[i, j], 0) + + +class TestNumObsY: + + def test_num_obs_y_multi_matrix(self): + for n in range(2, 10): + X = np.random.rand(n, 4) + Y = wpdist_no_const(X) + assert_equal(num_obs_y(Y), n) + + def test_num_obs_y_1(self): + # Tests num_obs_y(y) on a condensed distance matrix over 1 + # observations. Expecting exception. + with pytest.raises(ValueError): + self.check_y(1) + + def test_num_obs_y_2(self): + # Tests num_obs_y(y) on a condensed distance matrix over 2 + # observations. + assert_(self.check_y(2)) + + def test_num_obs_y_3(self): + assert_(self.check_y(3)) + + def test_num_obs_y_4(self): + assert_(self.check_y(4)) + + def test_num_obs_y_5_10(self): + for i in range(5, 16): + self.minit(i) + + def test_num_obs_y_2_100(self): + # Tests num_obs_y(y) on 100 improper condensed distance matrices. + # Expecting exception. + a = set() + for n in range(2, 16): + a.add(n * (n - 1) / 2) + for i in range(5, 105): + if i not in a: + with pytest.raises(ValueError): + self.bad_y(i) + + def minit(self, n): + assert_(self.check_y(n)) + + def bad_y(self, n): + y = np.random.rand(n) + return num_obs_y(y) + + def check_y(self, n): + return num_obs_y(self.make_y(n)) == n + + def make_y(self, n): + return np.random.rand((n * (n - 1)) // 2) + + +class TestNumObsDM: + + def test_num_obs_dm_multi_matrix(self): + for n in range(1, 10): + X = np.random.rand(n, 4) + Y = wpdist_no_const(X) + A = squareform(Y) + if verbose >= 3: + print(A.shape, Y.shape) + assert_equal(num_obs_dm(A), n) + + def test_num_obs_dm_0(self): + # Tests num_obs_dm(D) on a 0x0 distance matrix. Expecting exception. + assert_(self.check_D(0)) + + def test_num_obs_dm_1(self): + # Tests num_obs_dm(D) on a 1x1 distance matrix. + assert_(self.check_D(1)) + + def test_num_obs_dm_2(self): + assert_(self.check_D(2)) + + def test_num_obs_dm_3(self): + assert_(self.check_D(2)) + + def test_num_obs_dm_4(self): + assert_(self.check_D(4)) + + def check_D(self, n): + return num_obs_dm(self.make_D(n)) == n + + def make_D(self, n): + return np.random.rand(n, n) + + +def is_valid_dm_throw(D): + return is_valid_dm(D, throw=True) + + +class TestIsValidDM: + + def test_is_valid_dm_improper_shape_1D_E(self): + D = np.zeros((5,), dtype=np.float64) + with pytest.raises(ValueError): + is_valid_dm_throw(D) + + def test_is_valid_dm_improper_shape_1D_F(self): + D = np.zeros((5,), dtype=np.float64) + assert_equal(is_valid_dm(D), False) + + def test_is_valid_dm_improper_shape_3D_E(self): + D = np.zeros((3, 3, 3), dtype=np.float64) + with pytest.raises(ValueError): + is_valid_dm_throw(D) + + def test_is_valid_dm_improper_shape_3D_F(self): + D = np.zeros((3, 3, 3), dtype=np.float64) + assert_equal(is_valid_dm(D), False) + + def test_is_valid_dm_nonzero_diagonal_E(self): + y = np.random.rand(10) + D = squareform(y) + for i in range(0, 5): + D[i, i] = 2.0 + with pytest.raises(ValueError): + is_valid_dm_throw(D) + + def test_is_valid_dm_nonzero_diagonal_F(self): + y = np.random.rand(10) + D = squareform(y) + for i in range(0, 5): + D[i, i] = 2.0 + assert_equal(is_valid_dm(D), False) + + def test_is_valid_dm_asymmetric_E(self): + y = np.random.rand(10) + D = squareform(y) + D[1, 3] = D[3, 1] + 1 + with pytest.raises(ValueError): + is_valid_dm_throw(D) + + def test_is_valid_dm_asymmetric_F(self): + y = np.random.rand(10) + D = squareform(y) + D[1, 3] = D[3, 1] + 1 + assert_equal(is_valid_dm(D), False) + + def test_is_valid_dm_correct_1_by_1(self): + D = np.zeros((1, 1), dtype=np.float64) + assert_equal(is_valid_dm(D), True) + + def test_is_valid_dm_correct_2_by_2(self): + y = np.random.rand(1) + D = squareform(y) + assert_equal(is_valid_dm(D), True) + + def test_is_valid_dm_correct_3_by_3(self): + y = np.random.rand(3) + D = squareform(y) + assert_equal(is_valid_dm(D), True) + + def test_is_valid_dm_correct_4_by_4(self): + y = np.random.rand(6) + D = squareform(y) + assert_equal(is_valid_dm(D), True) + + def test_is_valid_dm_correct_5_by_5(self): + y = np.random.rand(10) + D = squareform(y) + assert_equal(is_valid_dm(D), True) + + +def is_valid_y_throw(y): + return is_valid_y(y, throw=True) + + +class TestIsValidY: + # If test case name ends on "_E" then an exception is expected for the + # given input, if it ends in "_F" then False is expected for the is_valid_y + # check. Otherwise the input is expected to be valid. + + def test_is_valid_y_improper_shape_2D_E(self): + y = np.zeros((3, 3,), dtype=np.float64) + with pytest.raises(ValueError): + is_valid_y_throw(y) + + def test_is_valid_y_improper_shape_2D_F(self): + y = np.zeros((3, 3,), dtype=np.float64) + assert_equal(is_valid_y(y), False) + + def test_is_valid_y_improper_shape_3D_E(self): + y = np.zeros((3, 3, 3), dtype=np.float64) + with pytest.raises(ValueError): + is_valid_y_throw(y) + + def test_is_valid_y_improper_shape_3D_F(self): + y = np.zeros((3, 3, 3), dtype=np.float64) + assert_equal(is_valid_y(y), False) + + def test_is_valid_y_correct_2_by_2(self): + y = self.correct_n_by_n(2) + assert_equal(is_valid_y(y), True) + + def test_is_valid_y_correct_3_by_3(self): + y = self.correct_n_by_n(3) + assert_equal(is_valid_y(y), True) + + def test_is_valid_y_correct_4_by_4(self): + y = self.correct_n_by_n(4) + assert_equal(is_valid_y(y), True) + + def test_is_valid_y_correct_5_by_5(self): + y = self.correct_n_by_n(5) + assert_equal(is_valid_y(y), True) + + def test_is_valid_y_2_100(self): + a = set() + for n in range(2, 16): + a.add(n * (n - 1) / 2) + for i in range(5, 105): + if i not in a: + with pytest.raises(ValueError): + self.bad_y(i) + + def bad_y(self, n): + y = np.random.rand(n) + return is_valid_y(y, throw=True) + + def correct_n_by_n(self, n): + y = np.random.rand((n * (n - 1)) // 2) + return y + + +@pytest.mark.parametrize("p", [-10.0, -0.5, 0.0]) +def test_bad_p(p): + # Raise ValueError if p <=0. + with pytest.raises(ValueError): + minkowski([1, 2], [3, 4], p) + with pytest.raises(ValueError): + minkowski([1, 2], [3, 4], p, [1, 1]) + + +def test_sokalsneath_all_false(): + # Regression test for ticket #876 + with pytest.raises(ValueError): + sokalsneath([False, False, False], [False, False, False]) + + +def test_canberra(): + # Regression test for ticket #1430. + assert_equal(wcanberra([1, 2, 3], [2, 4, 6]), 1) + assert_equal(wcanberra([1, 1, 0, 0], [1, 0, 1, 0]), 2) + + +def test_braycurtis(): + # Regression test for ticket #1430. + assert_almost_equal(wbraycurtis([1, 2, 3], [2, 4, 6]), 1. / 3, decimal=15) + assert_almost_equal(wbraycurtis([1, 1, 0, 0], [1, 0, 1, 0]), 0.5, decimal=15) + + +def test_euclideans(): + # Regression test for ticket #1328. + x1 = np.array([1, 1, 1]) + x2 = np.array([0, 0, 0]) + + # Basic test of the calculation. + assert_almost_equal(wsqeuclidean(x1, x2), 3.0, decimal=14) + assert_almost_equal(weuclidean(x1, x2), np.sqrt(3), decimal=14) + + # Check flattening for (1, N) or (N, 1) inputs + with pytest.raises(ValueError, match="Input vector should be 1-D"): + weuclidean(x1[np.newaxis, :], x2[np.newaxis, :]), np.sqrt(3) + with pytest.raises(ValueError, match="Input vector should be 1-D"): + wsqeuclidean(x1[np.newaxis, :], x2[np.newaxis, :]) + with pytest.raises(ValueError, match="Input vector should be 1-D"): + wsqeuclidean(x1[:, np.newaxis], x2[:, np.newaxis]) + + # Distance metrics only defined for vectors (= 1-D) + x = np.arange(4).reshape(2, 2) + with pytest.raises(ValueError): + weuclidean(x, x) + with pytest.raises(ValueError): + wsqeuclidean(x, x) + + # Another check, with random data. + rs = np.random.RandomState(1234567890) + x = rs.rand(10) + y = rs.rand(10) + d1 = weuclidean(x, y) + d2 = wsqeuclidean(x, y) + assert_almost_equal(d1**2, d2, decimal=14) + + +def test_hamming_unequal_length(): + # Regression test for gh-4290. + x = [0, 0, 1] + y = [1, 0, 1, 0] + # Used to give an AttributeError from ndarray.mean called on bool + with pytest.raises(ValueError): + whamming(x, y) + + +def test_hamming_unequal_length_with_w(): + u = [0, 0, 1] + v = [0, 0, 1] + w = [1, 0, 1, 0] + msg = "'w' should have the same length as 'u' and 'v'." + with pytest.raises(ValueError, match=msg): + whamming(u, v, w) + + +def test_hamming_string_array(): + # https://github.com/scikit-learn/scikit-learn/issues/4014 + a = np.array(['eggs', 'spam', 'spam', 'eggs', 'spam', 'spam', 'spam', + 'spam', 'spam', 'spam', 'spam', 'eggs', 'eggs', 'spam', + 'eggs', 'eggs', 'eggs', 'eggs', 'eggs', 'spam'], + dtype='|S4') + b = np.array(['eggs', 'spam', 'spam', 'eggs', 'eggs', 'spam', 'spam', + 'spam', 'spam', 'eggs', 'spam', 'eggs', 'spam', 'eggs', + 'spam', 'spam', 'eggs', 'spam', 'spam', 'eggs'], + dtype='|S4') + desired = 0.45 + assert_allclose(whamming(a, b), desired) + + +def test_minkowski_w(): + # Regression test for gh-8142. + arr_in = np.array([[83.33333333, 100., 83.33333333, 100., 36., + 60., 90., 150., 24., 48.], + [83.33333333, 100., 83.33333333, 100., 36., + 60., 90., 150., 24., 48.]]) + p0 = pdist(arr_in, metric='minkowski', p=1, w=None) + c0 = cdist(arr_in, arr_in, metric='minkowski', p=1, w=None) + p1 = pdist(arr_in, metric='minkowski', p=1) + c1 = cdist(arr_in, arr_in, metric='minkowski', p=1) + + assert_allclose(p0, p1, rtol=1e-15) + assert_allclose(c0, c1, rtol=1e-15) + + +def test_sqeuclidean_dtypes(): + # Assert that sqeuclidean returns the right types of values. + # Integer types should be converted to floating for stability. + # Floating point types should be the same as the input. + x = [1, 2, 3] + y = [4, 5, 6] + + for dtype in [np.int8, np.int16, np.int32, np.int64]: + d = wsqeuclidean(np.asarray(x, dtype=dtype), np.asarray(y, dtype=dtype)) + assert_(np.issubdtype(d.dtype, np.floating)) + + for dtype in [np.uint8, np.uint16, np.uint32, np.uint64]: + umax = np.iinfo(dtype).max + d1 = wsqeuclidean([0], np.asarray([umax], dtype=dtype)) + d2 = wsqeuclidean(np.asarray([umax], dtype=dtype), [0]) + + assert_equal(d1, d2) + assert_equal(d1, np.float64(umax)**2) + + dtypes = [np.float32, np.float64, np.complex64, np.complex128] + for dtype in ['float16', 'float128']: + # These aren't present in older numpy versions; float128 may also not + # be present on all platforms. + if hasattr(np, dtype): + dtypes.append(getattr(np, dtype)) + + for dtype in dtypes: + d = wsqeuclidean(np.asarray(x, dtype=dtype), np.asarray(y, dtype=dtype)) + assert_equal(d.dtype, dtype) + + +def test_sokalmichener(): + # Test that sokalmichener has the same result for bool and int inputs. + p = [True, True, False] + q = [True, False, True] + x = [int(b) for b in p] + y = [int(b) for b in q] + dist1 = sokalmichener(p, q) + dist2 = sokalmichener(x, y) + # These should be exactly the same. + assert_equal(dist1, dist2) + + +def test_sokalmichener_with_weight(): + # from: | 1 | | 0 | + # to: | 1 | | 1 | + # weight| | 1 | | 0.2 + ntf = 0 * 1 + 0 * 0.2 + nft = 0 * 1 + 1 * 0.2 + ntt = 1 * 1 + 0 * 0.2 + nff = 0 * 1 + 0 * 0.2 + expected = 2 * (nft + ntf) / (ntt + nff + 2 * (nft + ntf)) + assert_almost_equal(expected, 0.2857143) + actual = sokalmichener([1, 0], [1, 1], w=[1, 0.2]) + assert_almost_equal(expected, actual) + + a1 = [False, False, True, True, True, False, False, True, True, True, True, + True, True, False, True, False, False, False, True, True] + a2 = [True, True, True, False, False, True, True, True, False, True, + True, True, True, True, False, False, False, True, True, True] + + for w in [0.05, 0.1, 1.0, 20.0]: + assert_almost_equal(sokalmichener(a2, a1, [w]), 0.6666666666666666) + + +def test_modifies_input(metric): + # test whether cdist or pdist modifies input arrays + X1 = np.asarray([[1., 2., 3.], + [1.2, 2.3, 3.4], + [2.2, 2.3, 4.4], + [22.2, 23.3, 44.4]]) + X1_copy = X1.copy() + cdist(X1, X1, metric) + pdist(X1, metric) + assert_array_equal(X1, X1_copy) + + +def test_Xdist_deprecated_args(metric): + # testing both cdist and pdist deprecated warnings + X1 = np.asarray([[1., 2., 3.], + [1.2, 2.3, 3.4], + [2.2, 2.3, 4.4], + [22.2, 23.3, 44.4]]) + + with pytest.raises(TypeError): + cdist(X1, X1, metric, 2.) + + with pytest.raises(TypeError): + pdist(X1, metric, 2.) + + for arg in ["p", "V", "VI"]: + kwargs = {arg: "foo"} + + if ((arg == "V" and metric == "seuclidean") + or (arg == "VI" and metric == "mahalanobis") + or (arg == "p" and metric == "minkowski")): + continue + + with pytest.raises(TypeError): + cdist(X1, X1, metric, **kwargs) + + with pytest.raises(TypeError): + pdist(X1, metric, **kwargs) + + +def test_Xdist_non_negative_weights(metric): + X = eo['random-float32-data'][::5, ::2] + w = np.ones(X.shape[1]) + w[::5] = -w[::5] + + if metric in ['seuclidean', 'mahalanobis', 'jensenshannon']: + pytest.skip("not applicable") + + for m in [metric, eval(metric), "test_" + metric]: + with pytest.raises(ValueError): + pdist(X, m, w=w) + with pytest.raises(ValueError): + cdist(X, X, m, w=w) + + +def test__validate_vector(): + x = [1, 2, 3] + y = _validate_vector(x) + assert_array_equal(y, x) + + y = _validate_vector(x, dtype=np.float64) + assert_array_equal(y, x) + assert_equal(y.dtype, np.float64) + + x = [1] + y = _validate_vector(x) + assert_equal(y.ndim, 1) + assert_equal(y, x) + + x = 1 + with pytest.raises(ValueError, match="Input vector should be 1-D"): + _validate_vector(x) + + x = np.arange(5).reshape(1, -1, 1) + with pytest.raises(ValueError, match="Input vector should be 1-D"): + _validate_vector(x) + + x = [[1, 2], [3, 4]] + with pytest.raises(ValueError, match="Input vector should be 1-D"): + _validate_vector(x) + +def test_yule_all_same(): + # Test yule avoids a divide by zero when exactly equal + x = np.ones((2, 6), dtype=bool) + d = wyule(x[0], x[0]) + assert d == 0.0 + + d = pdist(x, 'yule') + assert_equal(d, [0.0]) + + d = cdist(x[:1], x[:1], 'yule') + assert_equal(d, [[0.0]]) + + +def test_jensenshannon(): + assert_almost_equal(jensenshannon([1.0, 0.0, 0.0], [0.0, 1.0, 0.0], 2.0), + 1.0) + assert_almost_equal(jensenshannon([1.0, 0.0], [0.5, 0.5]), + 0.46450140402245893) + assert_almost_equal(jensenshannon([1.0, 0.0, 0.0], [1.0, 0.0, 0.0]), 0.0) + + assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=0), + [0.0, 0.0]) + assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=1), + [0.0649045]) + assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=0, + keepdims=True), [[0.0, 0.0]]) + assert_almost_equal(jensenshannon([[1.0, 2.0]], [[0.5, 1.5]], axis=1, + keepdims=True), [[0.0649045]]) + + a = np.array([[1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12]]) + b = np.array([[13, 14, 15, 16], + [17, 18, 19, 20], + [21, 22, 23, 24]]) + + assert_almost_equal(jensenshannon(a, b, axis=0), + [0.1954288, 0.1447697, 0.1138377, 0.0927636]) + assert_almost_equal(jensenshannon(a, b, axis=1), + [0.1402339, 0.0399106, 0.0201815]) + + +def test_gh_17703(): + arr_1 = np.array([1, 0, 0]) + arr_2 = np.array([2, 0, 0]) + expected = dice(arr_1, arr_2) + actual = pdist([arr_1, arr_2], metric='dice') + assert_allclose(actual, expected) + actual = cdist(np.atleast_2d(arr_1), + np.atleast_2d(arr_2), metric='dice') + assert_allclose(actual, expected) + + +def test_immutable_input(metric): + if metric in ("jensenshannon", "mahalanobis", "seuclidean"): + pytest.skip("not applicable") + x = np.arange(10, dtype=np.float64) + x.setflags(write=False) + getattr(scipy.spatial.distance, metric)(x, x, w=x) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_hausdorff.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_hausdorff.py new file mode 100644 index 0000000000000000000000000000000000000000..c5a5255a7c6c1a9c85f4526ec1bcae67f745307b --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_hausdorff.py @@ -0,0 +1,172 @@ +import numpy as np +from numpy.testing import (assert_allclose, + assert_array_equal, + assert_equal) +import pytest +from scipy.spatial.distance import directed_hausdorff +from scipy.spatial import distance +from scipy._lib._util import check_random_state + + +class TestHausdorff: + # Test various properties of the directed Hausdorff code. + + def setup_method(self): + np.random.seed(1234) + random_angles = np.random.random(100) * np.pi * 2 + random_columns = np.column_stack( + (random_angles, random_angles, np.zeros(100))) + random_columns[..., 0] = np.cos(random_columns[..., 0]) + random_columns[..., 1] = np.sin(random_columns[..., 1]) + random_columns_2 = np.column_stack( + (random_angles, random_angles, np.zeros(100))) + random_columns_2[1:, 0] = np.cos(random_columns_2[1:, 0]) * 2.0 + random_columns_2[1:, 1] = np.sin(random_columns_2[1:, 1]) * 2.0 + # move one point farther out so we don't have two perfect circles + random_columns_2[0, 0] = np.cos(random_columns_2[0, 0]) * 3.3 + random_columns_2[0, 1] = np.sin(random_columns_2[0, 1]) * 3.3 + self.path_1 = random_columns + self.path_2 = random_columns_2 + self.path_1_4d = np.insert(self.path_1, 3, 5, axis=1) + self.path_2_4d = np.insert(self.path_2, 3, 27, axis=1) + + def test_symmetry(self): + # Ensure that the directed (asymmetric) Hausdorff distance is + # actually asymmetric + + forward = directed_hausdorff(self.path_1, self.path_2)[0] + reverse = directed_hausdorff(self.path_2, self.path_1)[0] + assert forward != reverse + + def test_brute_force_comparison_forward(self): + # Ensure that the algorithm for directed_hausdorff gives the + # same result as the simple / brute force approach in the + # forward direction. + actual = directed_hausdorff(self.path_1, self.path_2)[0] + # brute force over rows: + expected = max(np.amin(distance.cdist(self.path_1, self.path_2), + axis=1)) + assert_allclose(actual, expected) + + def test_brute_force_comparison_reverse(self): + # Ensure that the algorithm for directed_hausdorff gives the + # same result as the simple / brute force approach in the + # reverse direction. + actual = directed_hausdorff(self.path_2, self.path_1)[0] + # brute force over columns: + expected = max(np.amin(distance.cdist(self.path_1, self.path_2), + axis=0)) + assert_allclose(actual, expected) + + def test_degenerate_case(self): + # The directed Hausdorff distance must be zero if both input + # data arrays match. + actual = directed_hausdorff(self.path_1, self.path_1)[0] + assert_allclose(actual, 0.0) + + def test_2d_data_forward(self): + # Ensure that 2D data is handled properly for a simple case + # relative to brute force approach. + actual = directed_hausdorff(self.path_1[..., :2], + self.path_2[..., :2])[0] + expected = max(np.amin(distance.cdist(self.path_1[..., :2], + self.path_2[..., :2]), + axis=1)) + assert_allclose(actual, expected) + + def test_4d_data_reverse(self): + # Ensure that 4D data is handled properly for a simple case + # relative to brute force approach. + actual = directed_hausdorff(self.path_2_4d, self.path_1_4d)[0] + # brute force over columns: + expected = max(np.amin(distance.cdist(self.path_1_4d, self.path_2_4d), + axis=0)) + assert_allclose(actual, expected) + + def test_indices(self): + # Ensure that correct point indices are returned -- they should + # correspond to the Hausdorff pair + path_simple_1 = np.array([[-1,-12],[0,0], [1,1], [3,7], [1,2]]) + path_simple_2 = np.array([[0,0], [1,1], [4,100], [10,9]]) + actual = directed_hausdorff(path_simple_2, path_simple_1)[1:] + expected = (2, 3) + assert_array_equal(actual, expected) + + def test_random_state(self): + # ensure that the global random state is not modified because + # the directed Hausdorff algorithm uses randomization + rs = check_random_state(None) + old_global_state = rs.get_state() + directed_hausdorff(self.path_1, self.path_2) + rs2 = check_random_state(None) + new_global_state = rs2.get_state() + assert_equal(new_global_state, old_global_state) + + @pytest.mark.parametrize("seed", [None, 27870671]) + def test_random_state_None_int(self, seed): + # check that seed values of None or int do not alter global + # random state + rs = check_random_state(None) + old_global_state = rs.get_state() + directed_hausdorff(self.path_1, self.path_2, seed) + rs2 = check_random_state(None) + new_global_state = rs2.get_state() + assert_equal(new_global_state, old_global_state) + + def test_invalid_dimensions(self): + # Ensure that a ValueError is raised when the number of columns + # is not the same + rng = np.random.default_rng(189048172503940875434364128139223470523) + A = rng.random((3, 2)) + B = rng.random((3, 5)) + msg = r"need to have the same number of columns" + with pytest.raises(ValueError, match=msg): + directed_hausdorff(A, B) + + @pytest.mark.parametrize("A, B, seed, expected", [ + # the two cases from gh-11332 + ([(0,0)], + [(0,1), (0,0)], + 0, + (0.0, 0, 1)), + ([(0,0)], + [(0,1), (0,0)], + 1, + (0.0, 0, 1)), + # slightly more complex case + ([(-5, 3), (0,0)], + [(0,1), (0,0), (-5, 3)], + 77098, + # the maximum minimum distance will + # be the last one found, but a unique + # solution is not guaranteed more broadly + (0.0, 1, 1)), + ]) + def test_subsets(self, A, B, seed, expected): + # verify fix for gh-11332 + actual = directed_hausdorff(u=A, v=B, seed=seed) + # check distance + assert_allclose(actual[0], expected[0]) + # check indices + assert actual[1:] == expected[1:] + + +@pytest.mark.xslow +def test_massive_arr_overflow(): + # on 64-bit systems we should be able to + # handle arrays that exceed the indexing + # size of a 32-bit signed integer + try: + import psutil + except ModuleNotFoundError: + pytest.skip("psutil required to check available memory") + if psutil.virtual_memory().available < 80*2**30: + # Don't run the test if there is less than 80 gig of RAM available. + pytest.skip('insufficient memory available to run this test') + size = int(3e9) + arr1 = np.zeros(shape=(size, 2)) + arr2 = np.zeros(shape=(3, 2)) + arr1[size - 1] = [5, 5] + actual = directed_hausdorff(u=arr1, v=arr2) + assert_allclose(actual[0], 7.0710678118654755) + assert_allclose(actual[1], size - 1) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_kdtree.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_kdtree.py new file mode 100644 index 0000000000000000000000000000000000000000..faf87872ea3b69d86d9d2fc90b546e409914ba53 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_kdtree.py @@ -0,0 +1,1533 @@ +# Copyright Anne M. Archibald 2008 +# Released under the scipy license + +import os +from numpy.testing import (assert_equal, assert_array_equal, assert_, + assert_almost_equal, assert_array_almost_equal, + assert_allclose) +from pytest import raises as assert_raises +import pytest +from platform import python_implementation +import numpy as np +from scipy.spatial import KDTree, Rectangle, distance_matrix, cKDTree +from scipy.spatial._ckdtree import cKDTreeNode +from scipy.spatial import minkowski_distance + +import itertools + +@pytest.fixture(params=[KDTree, cKDTree]) +def kdtree_type(request): + return request.param + + +def KDTreeTest(kls): + """Class decorator to create test cases for KDTree and cKDTree + + Tests use the class variable ``kdtree_type`` as the tree constructor. + """ + if not kls.__name__.startswith('_Test'): + raise RuntimeError("Expected a class name starting with _Test") + + for tree in (KDTree, cKDTree): + test_name = kls.__name__[1:] + '_' + tree.__name__ + + if test_name in globals(): + raise RuntimeError("Duplicated test name: " + test_name) + + # Create a new sub-class with kdtree_type defined + test_case = type(test_name, (kls,), {'kdtree_type': tree}) + globals()[test_name] = test_case + return kls + + +def distance_box(a, b, p, boxsize): + diff = a - b + diff[diff > 0.5 * boxsize] -= boxsize + diff[diff < -0.5 * boxsize] += boxsize + d = minkowski_distance(diff, 0, p) + return d + +class ConsistencyTests: + def distance(self, a, b, p): + return minkowski_distance(a, b, p) + + def test_nearest(self): + x = self.x + d, i = self.kdtree.query(x, 1) + assert_almost_equal(d**2, np.sum((x-self.data[i])**2)) + eps = 1e-8 + assert_(np.all(np.sum((self.data-x[np.newaxis, :])**2, axis=1) > d**2-eps)) + + def test_m_nearest(self): + x = self.x + m = self.m + dd, ii = self.kdtree.query(x, m) + d = np.amax(dd) + i = ii[np.argmax(dd)] + assert_almost_equal(d**2, np.sum((x-self.data[i])**2)) + eps = 1e-8 + assert_equal( + np.sum(np.sum((self.data-x[np.newaxis, :])**2, axis=1) < d**2+eps), + m, + ) + + def test_points_near(self): + x = self.x + d = self.d + dd, ii = self.kdtree.query(x, k=self.kdtree.n, distance_upper_bound=d) + eps = 1e-8 + hits = 0 + for near_d, near_i in zip(dd, ii): + if near_d == np.inf: + continue + hits += 1 + assert_almost_equal(near_d**2, np.sum((x-self.data[near_i])**2)) + assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}") + assert_equal(np.sum(self.distance(self.data, x, 2) < d**2+eps), hits) + + def test_points_near_l1(self): + x = self.x + d = self.d + dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=1, distance_upper_bound=d) + eps = 1e-8 + hits = 0 + for near_d, near_i in zip(dd, ii): + if near_d == np.inf: + continue + hits += 1 + assert_almost_equal(near_d, self.distance(x, self.data[near_i], 1)) + assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}") + assert_equal(np.sum(self.distance(self.data, x, 1) < d+eps), hits) + + def test_points_near_linf(self): + x = self.x + d = self.d + dd, ii = self.kdtree.query(x, k=self.kdtree.n, p=np.inf, distance_upper_bound=d) + eps = 1e-8 + hits = 0 + for near_d, near_i in zip(dd, ii): + if near_d == np.inf: + continue + hits += 1 + assert_almost_equal(near_d, self.distance(x, self.data[near_i], np.inf)) + assert_(near_d < d+eps, f"near_d={near_d:g} should be less than {d:g}") + assert_equal(np.sum(self.distance(self.data, x, np.inf) < d+eps), hits) + + def test_approx(self): + x = self.x + k = self.k + eps = 0.1 + d_real, i_real = self.kdtree.query(x, k) + d, i = self.kdtree.query(x, k, eps=eps) + assert_(np.all(d <= d_real*(1+eps))) + + +@KDTreeTest +class _Test_random(ConsistencyTests): + def setup_method(self): + self.n = 100 + self.m = 4 + np.random.seed(1234) + self.data = np.random.randn(self.n, self.m) + self.kdtree = self.kdtree_type(self.data, leafsize=2) + self.x = np.random.randn(self.m) + self.d = 0.2 + self.k = 10 + + +@KDTreeTest +class _Test_random_far(_Test_random): + def setup_method(self): + super().setup_method() + self.x = np.random.randn(self.m)+10 + + +@KDTreeTest +class _Test_small(ConsistencyTests): + def setup_method(self): + self.data = np.array([[0, 0, 0], + [0, 0, 1], + [0, 1, 0], + [0, 1, 1], + [1, 0, 0], + [1, 0, 1], + [1, 1, 0], + [1, 1, 1]]) + self.kdtree = self.kdtree_type(self.data) + self.n = self.kdtree.n + self.m = self.kdtree.m + np.random.seed(1234) + self.x = np.random.randn(3) + self.d = 0.5 + self.k = 4 + + def test_nearest(self): + assert_array_equal( + self.kdtree.query((0, 0, 0.1), 1), + (0.1, 0)) + + def test_nearest_two(self): + assert_array_equal( + self.kdtree.query((0, 0, 0.1), 2), + ([0.1, 0.9], [0, 1])) + + +@KDTreeTest +class _Test_small_nonleaf(_Test_small): + def setup_method(self): + super().setup_method() + self.kdtree = self.kdtree_type(self.data, leafsize=1) + + +class Test_vectorization_KDTree: + def setup_method(self): + self.data = np.array([[0, 0, 0], + [0, 0, 1], + [0, 1, 0], + [0, 1, 1], + [1, 0, 0], + [1, 0, 1], + [1, 1, 0], + [1, 1, 1]]) + self.kdtree = KDTree(self.data) + + def test_single_query(self): + d, i = self.kdtree.query(np.array([0, 0, 0])) + assert_(isinstance(d, float)) + assert_(np.issubdtype(i, np.signedinteger)) + + def test_vectorized_query(self): + d, i = self.kdtree.query(np.zeros((2, 4, 3))) + assert_equal(np.shape(d), (2, 4)) + assert_equal(np.shape(i), (2, 4)) + + def test_single_query_multiple_neighbors(self): + s = 23 + kk = self.kdtree.n+s + d, i = self.kdtree.query(np.array([0, 0, 0]), k=kk) + assert_equal(np.shape(d), (kk,)) + assert_equal(np.shape(i), (kk,)) + assert_(np.all(~np.isfinite(d[-s:]))) + assert_(np.all(i[-s:] == self.kdtree.n)) + + def test_vectorized_query_multiple_neighbors(self): + s = 23 + kk = self.kdtree.n+s + d, i = self.kdtree.query(np.zeros((2, 4, 3)), k=kk) + assert_equal(np.shape(d), (2, 4, kk)) + assert_equal(np.shape(i), (2, 4, kk)) + assert_(np.all(~np.isfinite(d[:, :, -s:]))) + assert_(np.all(i[:, :, -s:] == self.kdtree.n)) + + def test_query_raises_for_k_none(self): + x = 1.0 + with pytest.raises(ValueError, match="k must be an integer or*"): + self.kdtree.query(x, k=None) + +class Test_vectorization_cKDTree: + def setup_method(self): + self.data = np.array([[0, 0, 0], + [0, 0, 1], + [0, 1, 0], + [0, 1, 1], + [1, 0, 0], + [1, 0, 1], + [1, 1, 0], + [1, 1, 1]]) + self.kdtree = cKDTree(self.data) + + def test_single_query(self): + d, i = self.kdtree.query([0, 0, 0]) + assert_(isinstance(d, float)) + assert_(isinstance(i, int)) + + def test_vectorized_query(self): + d, i = self.kdtree.query(np.zeros((2, 4, 3))) + assert_equal(np.shape(d), (2, 4)) + assert_equal(np.shape(i), (2, 4)) + + def test_vectorized_query_noncontiguous_values(self): + np.random.seed(1234) + qs = np.random.randn(3, 1000).T + ds, i_s = self.kdtree.query(qs) + for q, d, i in zip(qs, ds, i_s): + assert_equal(self.kdtree.query(q), (d, i)) + + def test_single_query_multiple_neighbors(self): + s = 23 + kk = self.kdtree.n+s + d, i = self.kdtree.query([0, 0, 0], k=kk) + assert_equal(np.shape(d), (kk,)) + assert_equal(np.shape(i), (kk,)) + assert_(np.all(~np.isfinite(d[-s:]))) + assert_(np.all(i[-s:] == self.kdtree.n)) + + def test_vectorized_query_multiple_neighbors(self): + s = 23 + kk = self.kdtree.n+s + d, i = self.kdtree.query(np.zeros((2, 4, 3)), k=kk) + assert_equal(np.shape(d), (2, 4, kk)) + assert_equal(np.shape(i), (2, 4, kk)) + assert_(np.all(~np.isfinite(d[:, :, -s:]))) + assert_(np.all(i[:, :, -s:] == self.kdtree.n)) + +class ball_consistency: + tol = 0.0 + + def distance(self, a, b, p): + return minkowski_distance(a * 1.0, b * 1.0, p) + + def test_in_ball(self): + x = np.atleast_2d(self.x) + d = np.broadcast_to(self.d, x.shape[:-1]) + l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps) + for i, ind in enumerate(l): + dist = self.distance(self.data[ind], x[i], self.p) - d[i]*(1.+self.eps) + norm = self.distance(self.data[ind], x[i], self.p) + d[i]*(1.+self.eps) + assert_array_equal(dist < self.tol * norm, True) + + def test_found_all(self): + x = np.atleast_2d(self.x) + d = np.broadcast_to(self.d, x.shape[:-1]) + l = self.T.query_ball_point(x, self.d, p=self.p, eps=self.eps) + for i, ind in enumerate(l): + c = np.ones(self.T.n, dtype=bool) + c[ind] = False + dist = self.distance(self.data[c], x[i], self.p) - d[i]/(1.+self.eps) + norm = self.distance(self.data[c], x[i], self.p) + d[i]/(1.+self.eps) + assert_array_equal(dist > -self.tol * norm, True) + +@KDTreeTest +class _Test_random_ball(ball_consistency): + def setup_method(self): + n = 100 + m = 4 + np.random.seed(1234) + self.data = np.random.randn(n, m) + self.T = self.kdtree_type(self.data, leafsize=2) + self.x = np.random.randn(m) + self.p = 2. + self.eps = 0 + self.d = 0.2 + + +@KDTreeTest +class _Test_random_ball_periodic(ball_consistency): + def distance(self, a, b, p): + return distance_box(a, b, p, 1.0) + + def setup_method(self): + n = 10000 + m = 4 + np.random.seed(1234) + self.data = np.random.uniform(size=(n, m)) + self.T = self.kdtree_type(self.data, leafsize=2, boxsize=1) + self.x = np.full(m, 0.1) + self.p = 2. + self.eps = 0 + self.d = 0.2 + + def test_in_ball_outside(self): + l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps) + for i in l: + assert_(self.distance(self.data[i], self.x, self.p) <= self.d*(1.+self.eps)) + l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps) + for i in l: + assert_(self.distance(self.data[i], self.x, self.p) <= self.d*(1.+self.eps)) + + def test_found_all_outside(self): + c = np.ones(self.T.n, dtype=bool) + l = self.T.query_ball_point(self.x + 1.0, self.d, p=self.p, eps=self.eps) + c[l] = False + assert np.all( + self.distance(self.data[c], self.x, self.p) >= self.d/(1.+self.eps) + ) + + l = self.T.query_ball_point(self.x - 1.0, self.d, p=self.p, eps=self.eps) + c[l] = False + assert np.all( + self.distance(self.data[c], self.x, self.p) >= self.d/(1.+self.eps) + ) + + +@KDTreeTest +class _Test_random_ball_largep_issue9890(ball_consistency): + + # allow some roundoff errors due to numerical issues + tol = 1e-13 + + def setup_method(self): + n = 1000 + m = 2 + np.random.seed(123) + self.data = np.random.randint(100, 1000, size=(n, m)) + self.T = self.kdtree_type(self.data) + self.x = self.data + self.p = 100 + self.eps = 0 + self.d = 10 + + +@KDTreeTest +class _Test_random_ball_approx(_Test_random_ball): + + def setup_method(self): + super().setup_method() + self.eps = 0.1 + + +@KDTreeTest +class _Test_random_ball_approx_periodic(_Test_random_ball): + + def setup_method(self): + super().setup_method() + self.eps = 0.1 + + +@KDTreeTest +class _Test_random_ball_far(_Test_random_ball): + + def setup_method(self): + super().setup_method() + self.d = 2. + +@KDTreeTest +class _Test_random_ball_far_periodic(_Test_random_ball_periodic): + + def setup_method(self): + super().setup_method() + self.d = 2. + + +@KDTreeTest +class _Test_random_ball_l1(_Test_random_ball): + + def setup_method(self): + super().setup_method() + self.p = 1 + + +@KDTreeTest +class _Test_random_ball_linf(_Test_random_ball): + + def setup_method(self): + super().setup_method() + self.p = np.inf + + +def test_random_ball_vectorized(kdtree_type): + n = 20 + m = 5 + np.random.seed(1234) + T = kdtree_type(np.random.randn(n, m)) + + r = T.query_ball_point(np.random.randn(2, 3, m), 1) + assert_equal(r.shape, (2, 3)) + assert_(isinstance(r[0, 0], list)) + + +def test_query_ball_point_multithreading(kdtree_type): + np.random.seed(0) + n = 5000 + k = 2 + points = np.random.randn(n, k) + T = kdtree_type(points) + l1 = T.query_ball_point(points, 0.003, workers=1) + l2 = T.query_ball_point(points, 0.003, workers=64) + l3 = T.query_ball_point(points, 0.003, workers=-1) + + for i in range(n): + if l1[i] or l2[i]: + assert_array_equal(l1[i], l2[i]) + + for i in range(n): + if l1[i] or l3[i]: + assert_array_equal(l1[i], l3[i]) + + +class two_trees_consistency: + + def distance(self, a, b, p): + return minkowski_distance(a, b, p) + + def test_all_in_ball(self): + r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps) + for i, l in enumerate(r): + for j in l: + assert (self.distance(self.data1[i], self.data2[j], self.p) + <= self.d*(1.+self.eps)) + + def test_found_all(self): + r = self.T1.query_ball_tree(self.T2, self.d, p=self.p, eps=self.eps) + for i, l in enumerate(r): + c = np.ones(self.T2.n, dtype=bool) + c[l] = False + assert np.all(self.distance(self.data2[c], self.data1[i], self.p) + >= self.d/(1.+self.eps)) + + +@KDTreeTest +class _Test_two_random_trees(two_trees_consistency): + + def setup_method(self): + n = 50 + m = 4 + np.random.seed(1234) + self.data1 = np.random.randn(n, m) + self.T1 = self.kdtree_type(self.data1, leafsize=2) + self.data2 = np.random.randn(n, m) + self.T2 = self.kdtree_type(self.data2, leafsize=2) + self.p = 2. + self.eps = 0 + self.d = 0.2 + + +@KDTreeTest +class _Test_two_random_trees_periodic(two_trees_consistency): + def distance(self, a, b, p): + return distance_box(a, b, p, 1.0) + + def setup_method(self): + n = 50 + m = 4 + np.random.seed(1234) + self.data1 = np.random.uniform(size=(n, m)) + self.T1 = self.kdtree_type(self.data1, leafsize=2, boxsize=1.0) + self.data2 = np.random.uniform(size=(n, m)) + self.T2 = self.kdtree_type(self.data2, leafsize=2, boxsize=1.0) + self.p = 2. + self.eps = 0 + self.d = 0.2 + + +@KDTreeTest +class _Test_two_random_trees_far(_Test_two_random_trees): + + def setup_method(self): + super().setup_method() + self.d = 2 + + +@KDTreeTest +class _Test_two_random_trees_far_periodic(_Test_two_random_trees_periodic): + + def setup_method(self): + super().setup_method() + self.d = 2 + + +@KDTreeTest +class _Test_two_random_trees_linf(_Test_two_random_trees): + + def setup_method(self): + super().setup_method() + self.p = np.inf + + +@KDTreeTest +class _Test_two_random_trees_linf_periodic(_Test_two_random_trees_periodic): + + def setup_method(self): + super().setup_method() + self.p = np.inf + + +class Test_rectangle: + + def setup_method(self): + self.rect = Rectangle([0, 0], [1, 1]) + + def test_min_inside(self): + assert_almost_equal(self.rect.min_distance_point([0.5, 0.5]), 0) + + def test_min_one_side(self): + assert_almost_equal(self.rect.min_distance_point([0.5, 1.5]), 0.5) + + def test_min_two_sides(self): + assert_almost_equal(self.rect.min_distance_point([2, 2]), np.sqrt(2)) + + def test_max_inside(self): + assert_almost_equal(self.rect.max_distance_point([0.5, 0.5]), 1/np.sqrt(2)) + + def test_max_one_side(self): + assert_almost_equal(self.rect.max_distance_point([0.5, 1.5]), + np.hypot(0.5, 1.5)) + + def test_max_two_sides(self): + assert_almost_equal(self.rect.max_distance_point([2, 2]), 2*np.sqrt(2)) + + def test_split(self): + less, greater = self.rect.split(0, 0.1) + assert_array_equal(less.maxes, [0.1, 1]) + assert_array_equal(less.mins, [0, 0]) + assert_array_equal(greater.maxes, [1, 1]) + assert_array_equal(greater.mins, [0.1, 0]) + + +def test_distance_l2(): + assert_almost_equal(minkowski_distance([0, 0], [1, 1], 2), np.sqrt(2)) + + +def test_distance_l1(): + assert_almost_equal(minkowski_distance([0, 0], [1, 1], 1), 2) + + +def test_distance_linf(): + assert_almost_equal(minkowski_distance([0, 0], [1, 1], np.inf), 1) + + +def test_distance_vectorization(): + np.random.seed(1234) + x = np.random.randn(10, 1, 3) + y = np.random.randn(1, 7, 3) + assert_equal(minkowski_distance(x, y).shape, (10, 7)) + + +class count_neighbors_consistency: + def test_one_radius(self): + r = 0.2 + assert_equal(self.T1.count_neighbors(self.T2, r), + np.sum([len(l) for l in self.T1.query_ball_tree(self.T2, r)])) + + def test_large_radius(self): + r = 1000 + assert_equal(self.T1.count_neighbors(self.T2, r), + np.sum([len(l) for l in self.T1.query_ball_tree(self.T2, r)])) + + def test_multiple_radius(self): + rs = np.exp(np.linspace(np.log(0.01), np.log(10), 3)) + results = self.T1.count_neighbors(self.T2, rs) + assert_(np.all(np.diff(results) >= 0)) + for r, result in zip(rs, results): + assert_equal(self.T1.count_neighbors(self.T2, r), result) + +@KDTreeTest +class _Test_count_neighbors(count_neighbors_consistency): + def setup_method(self): + n = 50 + m = 2 + np.random.seed(1234) + self.T1 = self.kdtree_type(np.random.randn(n, m), leafsize=2) + self.T2 = self.kdtree_type(np.random.randn(n, m), leafsize=2) + + +class sparse_distance_matrix_consistency: + + def distance(self, a, b, p): + return minkowski_distance(a, b, p) + + def test_consistency_with_neighbors(self): + M = self.T1.sparse_distance_matrix(self.T2, self.r) + r = self.T1.query_ball_tree(self.T2, self.r) + for i, l in enumerate(r): + for j in l: + assert_almost_equal( + M[i, j], + self.distance(self.T1.data[i], self.T2.data[j], self.p), + decimal=14 + ) + for ((i, j), d) in M.items(): + assert_(j in r[i]) + + def test_zero_distance(self): + # raises an exception for bug 870 (FIXME: Does it?) + self.T1.sparse_distance_matrix(self.T1, self.r) + + def test_consistency(self): + # Test consistency with a distance_matrix + M1 = self.T1.sparse_distance_matrix(self.T2, self.r) + expected = distance_matrix(self.T1.data, self.T2.data) + expected[expected > self.r] = 0 + assert_array_almost_equal(M1.toarray(), expected, decimal=14) + + def test_against_logic_error_regression(self): + # regression test for gh-5077 logic error + np.random.seed(0) + too_many = np.array(np.random.randn(18, 2), dtype=int) + tree = self.kdtree_type( + too_many, balanced_tree=False, compact_nodes=False) + d = tree.sparse_distance_matrix(tree, 3).toarray() + assert_array_almost_equal(d, d.T, decimal=14) + + def test_ckdtree_return_types(self): + # brute-force reference + ref = np.zeros((self.n, self.n)) + for i in range(self.n): + for j in range(self.n): + v = self.data1[i, :] - self.data2[j, :] + ref[i, j] = np.dot(v, v) + ref = np.sqrt(ref) + ref[ref > self.r] = 0. + # test return type 'dict' + dist = np.zeros((self.n, self.n)) + r = self.T1.sparse_distance_matrix(self.T2, self.r, output_type='dict') + for i, j in r.keys(): + dist[i, j] = r[(i, j)] + assert_array_almost_equal(ref, dist, decimal=14) + # test return type 'ndarray' + dist = np.zeros((self.n, self.n)) + r = self.T1.sparse_distance_matrix(self.T2, self.r, + output_type='ndarray') + for k in range(r.shape[0]): + i = r['i'][k] + j = r['j'][k] + v = r['v'][k] + dist[i, j] = v + assert_array_almost_equal(ref, dist, decimal=14) + # test return type 'dok_matrix' + r = self.T1.sparse_distance_matrix(self.T2, self.r, + output_type='dok_matrix') + assert_array_almost_equal(ref, r.toarray(), decimal=14) + # test return type 'coo_matrix' + r = self.T1.sparse_distance_matrix(self.T2, self.r, + output_type='coo_matrix') + assert_array_almost_equal(ref, r.toarray(), decimal=14) + + +@KDTreeTest +class _Test_sparse_distance_matrix(sparse_distance_matrix_consistency): + def setup_method(self): + n = 50 + m = 4 + np.random.seed(1234) + data1 = np.random.randn(n, m) + data2 = np.random.randn(n, m) + self.T1 = self.kdtree_type(data1, leafsize=2) + self.T2 = self.kdtree_type(data2, leafsize=2) + self.r = 0.5 + self.p = 2 + self.data1 = data1 + self.data2 = data2 + self.n = n + self.m = m + + +def test_distance_matrix(): + m = 10 + n = 11 + k = 4 + np.random.seed(1234) + xs = np.random.randn(m, k) + ys = np.random.randn(n, k) + ds = distance_matrix(xs, ys) + assert_equal(ds.shape, (m, n)) + for i in range(m): + for j in range(n): + assert_almost_equal(minkowski_distance(xs[i], ys[j]), ds[i, j]) + + +def test_distance_matrix_looping(): + m = 10 + n = 11 + k = 4 + np.random.seed(1234) + xs = np.random.randn(m, k) + ys = np.random.randn(n, k) + ds = distance_matrix(xs, ys) + dsl = distance_matrix(xs, ys, threshold=1) + assert_equal(ds, dsl) + + +def check_onetree_query(T, d): + r = T.query_ball_tree(T, d) + s = set() + for i, l in enumerate(r): + for j in l: + if i < j: + s.add((i, j)) + + assert_(s == T.query_pairs(d)) + +def test_onetree_query(kdtree_type): + np.random.seed(0) + n = 50 + k = 4 + points = np.random.randn(n, k) + T = kdtree_type(points) + check_onetree_query(T, 0.1) + + points = np.random.randn(3*n, k) + points[:n] *= 0.001 + points[n:2*n] += 2 + T = kdtree_type(points) + check_onetree_query(T, 0.1) + check_onetree_query(T, 0.001) + check_onetree_query(T, 0.00001) + check_onetree_query(T, 1e-6) + + +def test_query_pairs_single_node(kdtree_type): + tree = kdtree_type([[0, 1]]) + assert_equal(tree.query_pairs(0.5), set()) + + +def test_kdtree_query_pairs(kdtree_type): + np.random.seed(0) + n = 50 + k = 2 + r = 0.1 + r2 = r**2 + points = np.random.randn(n, k) + T = kdtree_type(points) + # brute force reference + brute = set() + for i in range(n): + for j in range(i+1, n): + v = points[i, :] - points[j, :] + if np.dot(v, v) <= r2: + brute.add((i, j)) + l0 = sorted(brute) + # test default return type + s = T.query_pairs(r) + l1 = sorted(s) + assert_array_equal(l0, l1) + # test return type 'set' + s = T.query_pairs(r, output_type='set') + l1 = sorted(s) + assert_array_equal(l0, l1) + # test return type 'ndarray' + s = set() + arr = T.query_pairs(r, output_type='ndarray') + for i in range(arr.shape[0]): + s.add((int(arr[i, 0]), int(arr[i, 1]))) + l2 = sorted(s) + assert_array_equal(l0, l2) + + +def test_query_pairs_eps(kdtree_type): + spacing = np.sqrt(2) + # irrational spacing to have potential rounding errors + x_range = np.linspace(0, 3 * spacing, 4) + y_range = np.linspace(0, 3 * spacing, 4) + xy_array = [(xi, yi) for xi in x_range for yi in y_range] + tree = kdtree_type(xy_array) + pairs_eps = tree.query_pairs(r=spacing, eps=.1) + # result: 24 with eps, 16 without due to rounding + pairs = tree.query_pairs(r=spacing * 1.01) + # result: 24 + assert_equal(pairs, pairs_eps) + + +def test_ball_point_ints(kdtree_type): + # Regression test for #1373. + x, y = np.mgrid[0:4, 0:4] + points = list(zip(x.ravel(), y.ravel())) + tree = kdtree_type(points) + assert_equal(sorted([4, 8, 9, 12]), + sorted(tree.query_ball_point((2, 0), 1))) + points = np.asarray(points, dtype=float) + tree = kdtree_type(points) + assert_equal(sorted([4, 8, 9, 12]), + sorted(tree.query_ball_point((2, 0), 1))) + + +def test_kdtree_comparisons(): + # Regression test: node comparisons were done wrong in 0.12 w/Py3. + nodes = [KDTree.node() for _ in range(3)] + assert_equal(sorted(nodes), sorted(nodes[::-1])) + + +def test_kdtree_build_modes(kdtree_type): + # check if different build modes for KDTree give similar query results + np.random.seed(0) + n = 5000 + k = 4 + points = np.random.randn(n, k) + T1 = kdtree_type(points).query(points, k=5)[-1] + T2 = kdtree_type(points, compact_nodes=False).query(points, k=5)[-1] + T3 = kdtree_type(points, balanced_tree=False).query(points, k=5)[-1] + T4 = kdtree_type(points, compact_nodes=False, + balanced_tree=False).query(points, k=5)[-1] + assert_array_equal(T1, T2) + assert_array_equal(T1, T3) + assert_array_equal(T1, T4) + +def test_kdtree_pickle(kdtree_type): + # test if it is possible to pickle a KDTree + import pickle + np.random.seed(0) + n = 50 + k = 4 + points = np.random.randn(n, k) + T1 = kdtree_type(points) + tmp = pickle.dumps(T1) + T2 = pickle.loads(tmp) + T1 = T1.query(points, k=5)[-1] + T2 = T2.query(points, k=5)[-1] + assert_array_equal(T1, T2) + +def test_kdtree_pickle_boxsize(kdtree_type): + # test if it is possible to pickle a periodic KDTree + import pickle + np.random.seed(0) + n = 50 + k = 4 + points = np.random.uniform(size=(n, k)) + T1 = kdtree_type(points, boxsize=1.0) + tmp = pickle.dumps(T1) + T2 = pickle.loads(tmp) + T1 = T1.query(points, k=5)[-1] + T2 = T2.query(points, k=5)[-1] + assert_array_equal(T1, T2) + +def test_kdtree_copy_data(kdtree_type): + # check if copy_data=True makes the kd-tree + # impervious to data corruption by modification of + # the data arrray + np.random.seed(0) + n = 5000 + k = 4 + points = np.random.randn(n, k) + T = kdtree_type(points, copy_data=True) + q = points.copy() + T1 = T.query(q, k=5)[-1] + points[...] = np.random.randn(n, k) + T2 = T.query(q, k=5)[-1] + assert_array_equal(T1, T2) + +def test_ckdtree_parallel(kdtree_type, monkeypatch): + # check if parallel=True also generates correct query results + np.random.seed(0) + n = 5000 + k = 4 + points = np.random.randn(n, k) + T = kdtree_type(points) + T1 = T.query(points, k=5, workers=64)[-1] + T2 = T.query(points, k=5, workers=-1)[-1] + T3 = T.query(points, k=5)[-1] + assert_array_equal(T1, T2) + assert_array_equal(T1, T3) + + monkeypatch.setattr(os, 'cpu_count', lambda: None) + with pytest.raises(NotImplementedError, match="Cannot determine the"): + T.query(points, 1, workers=-1) + + +def test_ckdtree_view(): + # Check that the nodes can be correctly viewed from Python. + # This test also sanity checks each node in the cKDTree, and + # thus verifies the internal structure of the kd-tree. + np.random.seed(0) + n = 100 + k = 4 + points = np.random.randn(n, k) + kdtree = cKDTree(points) + + # walk the whole kd-tree and sanity check each node + def recurse_tree(n): + assert_(isinstance(n, cKDTreeNode)) + if n.split_dim == -1: + assert_(n.lesser is None) + assert_(n.greater is None) + assert_(n.indices.shape[0] <= kdtree.leafsize) + else: + recurse_tree(n.lesser) + recurse_tree(n.greater) + x = n.lesser.data_points[:, n.split_dim] + y = n.greater.data_points[:, n.split_dim] + assert_(x.max() < y.min()) + + recurse_tree(kdtree.tree) + # check that indices are correctly retrieved + n = kdtree.tree + assert_array_equal(np.sort(n.indices), range(100)) + # check that data_points are correctly retrieved + assert_array_equal(kdtree.data[n.indices, :], n.data_points) + +# KDTree is specialized to type double points, so no need to make +# a unit test corresponding to test_ball_point_ints() + +def test_kdtree_list_k(kdtree_type): + # check kdtree periodic boundary + n = 200 + m = 2 + klist = [1, 2, 3] + kint = 3 + + np.random.seed(1234) + data = np.random.uniform(size=(n, m)) + kdtree = kdtree_type(data, leafsize=1) + + # check agreement between arange(1, k+1) and k + dd, ii = kdtree.query(data, klist) + dd1, ii1 = kdtree.query(data, kint) + assert_equal(dd, dd1) + assert_equal(ii, ii1) + + # now check skipping one element + klist = np.array([1, 3]) + kint = 3 + dd, ii = kdtree.query(data, kint) + dd1, ii1 = kdtree.query(data, klist) + assert_equal(dd1, dd[..., klist - 1]) + assert_equal(ii1, ii[..., klist - 1]) + + # check k == 1 special case + # and k == [1] non-special case + dd, ii = kdtree.query(data, 1) + dd1, ii1 = kdtree.query(data, [1]) + assert_equal(len(dd.shape), 1) + assert_equal(len(dd1.shape), 2) + assert_equal(dd, np.ravel(dd1)) + assert_equal(ii, np.ravel(ii1)) + +def test_kdtree_box(kdtree_type): + # check ckdtree periodic boundary + n = 2000 + m = 3 + k = 3 + np.random.seed(1234) + data = np.random.uniform(size=(n, m)) + kdtree = kdtree_type(data, leafsize=1, boxsize=1.0) + + # use the standard python KDTree for the simulated periodic box + kdtree2 = kdtree_type(data, leafsize=1) + + for p in [1, 2, 3.0, np.inf]: + dd, ii = kdtree.query(data, k, p=p) + + dd1, ii1 = kdtree.query(data + 1.0, k, p=p) + assert_almost_equal(dd, dd1) + assert_equal(ii, ii1) + + dd1, ii1 = kdtree.query(data - 1.0, k, p=p) + assert_almost_equal(dd, dd1) + assert_equal(ii, ii1) + + dd2, ii2 = simulate_periodic_box(kdtree2, data, k, boxsize=1.0, p=p) + assert_almost_equal(dd, dd2) + assert_equal(ii, ii2) + +def test_kdtree_box_0boxsize(kdtree_type): + # check ckdtree periodic boundary that mimics non-periodic + n = 2000 + m = 2 + k = 3 + np.random.seed(1234) + data = np.random.uniform(size=(n, m)) + kdtree = kdtree_type(data, leafsize=1, boxsize=0.0) + + # use the standard python KDTree for the simulated periodic box + kdtree2 = kdtree_type(data, leafsize=1) + + for p in [1, 2, np.inf]: + dd, ii = kdtree.query(data, k, p=p) + + dd1, ii1 = kdtree2.query(data, k, p=p) + assert_almost_equal(dd, dd1) + assert_equal(ii, ii1) + +def test_kdtree_box_upper_bounds(kdtree_type): + data = np.linspace(0, 2, 10).reshape(-1, 2) + data[:, 1] += 10 + with pytest.raises(ValueError): + kdtree_type(data, leafsize=1, boxsize=1.0) + with pytest.raises(ValueError): + kdtree_type(data, leafsize=1, boxsize=(0.0, 2.0)) + # skip a dimension. + kdtree_type(data, leafsize=1, boxsize=(2.0, 0.0)) + +def test_kdtree_box_lower_bounds(kdtree_type): + data = np.linspace(-1, 1, 10) + assert_raises(ValueError, kdtree_type, data, leafsize=1, boxsize=1.0) + +def simulate_periodic_box(kdtree, data, k, boxsize, p): + dd = [] + ii = [] + x = np.arange(3 ** data.shape[1]) + nn = np.array(np.unravel_index(x, [3] * data.shape[1])).T + nn = nn - 1.0 + for n in nn: + image = data + n * 1.0 * boxsize + dd2, ii2 = kdtree.query(image, k, p=p) + dd2 = dd2.reshape(-1, k) + ii2 = ii2.reshape(-1, k) + dd.append(dd2) + ii.append(ii2) + dd = np.concatenate(dd, axis=-1) + ii = np.concatenate(ii, axis=-1) + + result = np.empty([len(data), len(nn) * k], dtype=[ + ('ii', 'i8'), + ('dd', 'f8')]) + result['ii'][:] = ii + result['dd'][:] = dd + result.sort(order='dd') + return result['dd'][:, :k], result['ii'][:, :k] + + +@pytest.mark.skipif(python_implementation() == 'PyPy', + reason="Fails on PyPy CI runs. See #9507") +def test_ckdtree_memuse(): + # unit test adaptation of gh-5630 + + # NOTE: this will fail when run via valgrind, + # because rss is no longer a reliable memory usage indicator. + + try: + import resource + except ImportError: + # resource is not available on Windows + return + # Make some data + dx, dy = 0.05, 0.05 + y, x = np.mgrid[slice(1, 5 + dy, dy), + slice(1, 5 + dx, dx)] + z = np.sin(x)**10 + np.cos(10 + y*x) * np.cos(x) + z_copy = np.empty_like(z) + z_copy[:] = z + # Place FILLVAL in z_copy at random number of random locations + FILLVAL = 99. + mask = np.random.randint(0, z.size, np.random.randint(50) + 5) + z_copy.flat[mask] = FILLVAL + igood = np.vstack(np.nonzero(x != FILLVAL)).T + ibad = np.vstack(np.nonzero(x == FILLVAL)).T + mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss + # burn-in + for i in range(10): + tree = cKDTree(igood) + # count memleaks while constructing and querying cKDTree + num_leaks = 0 + for i in range(100): + mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss + tree = cKDTree(igood) + dist, iquery = tree.query(ibad, k=4, p=2) + new_mem_use = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss + if new_mem_use > mem_use: + num_leaks += 1 + # ideally zero leaks, but errors might accidentally happen + # outside cKDTree + assert_(num_leaks < 10) + +def test_kdtree_weights(kdtree_type): + + data = np.linspace(0, 1, 4).reshape(-1, 1) + tree1 = kdtree_type(data, leafsize=1) + weights = np.ones(len(data), dtype='f4') + + nw = tree1._build_weights(weights) + assert_array_equal(nw, [4, 2, 1, 1, 2, 1, 1]) + + assert_raises(ValueError, tree1._build_weights, weights[:-1]) + + for i in range(10): + # since weights are uniform, these shall agree: + c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, i)) + c2 = tree1.count_neighbors(tree1, np.linspace(0, 10, i), + weights=(weights, weights)) + c3 = tree1.count_neighbors(tree1, np.linspace(0, 10, i), + weights=(weights, None)) + c4 = tree1.count_neighbors(tree1, np.linspace(0, 10, i), + weights=(None, weights)) + tree1.count_neighbors(tree1, np.linspace(0, 10, i), + weights=weights) + + assert_array_equal(c1, c2) + assert_array_equal(c1, c3) + assert_array_equal(c1, c4) + + for i in range(len(data)): + # this tests removal of one data point by setting weight to 0 + w1 = weights.copy() + w1[i] = 0 + data2 = data[w1 != 0] + tree2 = kdtree_type(data2) + + c1 = tree1.count_neighbors(tree1, np.linspace(0, 10, 100), + weights=(w1, w1)) + # "c2 is correct" + c2 = tree2.count_neighbors(tree2, np.linspace(0, 10, 100)) + + assert_array_equal(c1, c2) + + #this asserts for two different trees, singular weights + # crashes + assert_raises(ValueError, tree1.count_neighbors, + tree2, np.linspace(0, 10, 100), weights=w1) + +def test_kdtree_count_neighbous_multiple_r(kdtree_type): + n = 2000 + m = 2 + np.random.seed(1234) + data = np.random.normal(size=(n, m)) + kdtree = kdtree_type(data, leafsize=1) + r0 = [0, 0.01, 0.01, 0.02, 0.05] + i0 = np.arange(len(r0)) + n0 = kdtree.count_neighbors(kdtree, r0) + nnc = kdtree.count_neighbors(kdtree, r0, cumulative=False) + assert_equal(n0, nnc.cumsum()) + + for i, r in zip(itertools.permutations(i0), + itertools.permutations(r0)): + # permute n0 by i and it shall agree + n = kdtree.count_neighbors(kdtree, r) + assert_array_equal(n, n0[list(i)]) + +def test_len0_arrays(kdtree_type): + # make sure len-0 arrays are handled correctly + # in range queries (gh-5639) + np.random.seed(1234) + X = np.random.rand(10, 2) + Y = np.random.rand(10, 2) + tree = kdtree_type(X) + # query_ball_point (single) + d, i = tree.query([.5, .5], k=1) + z = tree.query_ball_point([.5, .5], 0.1*d) + assert_array_equal(z, []) + # query_ball_point (multiple) + d, i = tree.query(Y, k=1) + mind = d.min() + z = tree.query_ball_point(Y, 0.1*mind) + y = np.empty(shape=(10, ), dtype=object) + y.fill([]) + assert_array_equal(y, z) + # query_ball_tree + other = kdtree_type(Y) + y = tree.query_ball_tree(other, 0.1*mind) + assert_array_equal(10*[[]], y) + # count_neighbors + y = tree.count_neighbors(other, 0.1*mind) + assert_(y == 0) + # sparse_distance_matrix + y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dok_matrix') + assert_array_equal(y == np.zeros((10, 10)), True) + y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='coo_matrix') + assert_array_equal(y == np.zeros((10, 10)), True) + y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='dict') + assert_equal(y, {}) + y = tree.sparse_distance_matrix(other, 0.1*mind, output_type='ndarray') + _dtype = [('i', np.intp), ('j', np.intp), ('v', np.float64)] + res_dtype = np.dtype(_dtype, align=True) + z = np.empty(shape=(0, ), dtype=res_dtype) + assert_array_equal(y, z) + # query_pairs + d, i = tree.query(X, k=2) + mind = d[:, -1].min() + y = tree.query_pairs(0.1*mind, output_type='set') + assert_equal(y, set()) + y = tree.query_pairs(0.1*mind, output_type='ndarray') + z = np.empty(shape=(0, 2), dtype=np.intp) + assert_array_equal(y, z) + +def test_kdtree_duplicated_inputs(kdtree_type): + # check kdtree with duplicated inputs + n = 1024 + for m in range(1, 8): + data = np.ones((n, m)) + data[n//2:] = 2 + + for balanced, compact in itertools.product((False, True), repeat=2): + kdtree = kdtree_type(data, balanced_tree=balanced, + compact_nodes=compact, leafsize=1) + assert kdtree.size == 3 + + tree = (kdtree.tree if kdtree_type is cKDTree else + kdtree.tree._node) + + assert_equal( + np.sort(tree.lesser.indices), + np.arange(0, n // 2)) + assert_equal( + np.sort(tree.greater.indices), + np.arange(n // 2, n)) + + +def test_kdtree_noncumulative_nondecreasing(kdtree_type): + # check kdtree with duplicated inputs + + # it shall not divide more than 3 nodes. + # root left (1), and right (2) + kdtree = kdtree_type([[0]], leafsize=1) + + assert_raises(ValueError, kdtree.count_neighbors, + kdtree, [0.1, 0], cumulative=False) + +def test_short_knn(kdtree_type): + + # The test case is based on github: #6425 by @SteveDoyle2 + + xyz = np.array([ + [0., 0., 0.], + [1.01, 0., 0.], + [0., 1., 0.], + [0., 1.01, 0.], + [1., 0., 0.], + [1., 1., 0.]], + dtype='float64') + + ckdt = kdtree_type(xyz) + + deq, ieq = ckdt.query(xyz, k=4, distance_upper_bound=0.2) + + assert_array_almost_equal(deq, + [[0., np.inf, np.inf, np.inf], + [0., 0.01, np.inf, np.inf], + [0., 0.01, np.inf, np.inf], + [0., 0.01, np.inf, np.inf], + [0., 0.01, np.inf, np.inf], + [0., np.inf, np.inf, np.inf]]) + +def test_query_ball_point_vector_r(kdtree_type): + + np.random.seed(1234) + data = np.random.normal(size=(100, 3)) + query = np.random.normal(size=(100, 3)) + tree = kdtree_type(data) + d = np.random.uniform(0, 0.3, size=len(query)) + + rvector = tree.query_ball_point(query, d) + rscalar = [tree.query_ball_point(qi, di) for qi, di in zip(query, d)] + for a, b in zip(rvector, rscalar): + assert_array_equal(sorted(a), sorted(b)) + +def test_query_ball_point_length(kdtree_type): + + np.random.seed(1234) + data = np.random.normal(size=(100, 3)) + query = np.random.normal(size=(100, 3)) + tree = kdtree_type(data) + d = 0.3 + + length = tree.query_ball_point(query, d, return_length=True) + length2 = [len(ind) for ind in tree.query_ball_point(query, d, return_length=False)] + length3 = [len(tree.query_ball_point(qi, d)) for qi in query] + length4 = [tree.query_ball_point(qi, d, return_length=True) for qi in query] + assert_array_equal(length, length2) + assert_array_equal(length, length3) + assert_array_equal(length, length4) + +def test_discontiguous(kdtree_type): + + np.random.seed(1234) + data = np.random.normal(size=(100, 3)) + d_contiguous = np.arange(100) * 0.04 + d_discontiguous = np.ascontiguousarray( + np.arange(100)[::-1] * 0.04)[::-1] + query_contiguous = np.random.normal(size=(100, 3)) + query_discontiguous = np.ascontiguousarray(query_contiguous.T).T + assert query_discontiguous.strides[-1] != query_contiguous.strides[-1] + assert d_discontiguous.strides[-1] != d_contiguous.strides[-1] + + tree = kdtree_type(data) + + length1 = tree.query_ball_point(query_contiguous, + d_contiguous, return_length=True) + length2 = tree.query_ball_point(query_discontiguous, + d_discontiguous, return_length=True) + + assert_array_equal(length1, length2) + + d1, i1 = tree.query(query_contiguous, 1) + d2, i2 = tree.query(query_discontiguous, 1) + + assert_array_equal(d1, d2) + assert_array_equal(i1, i2) + + +@pytest.mark.parametrize("balanced_tree, compact_nodes", + [(True, False), + (True, True), + (False, False), + (False, True)]) +def test_kdtree_empty_input(kdtree_type, balanced_tree, compact_nodes): + # https://github.com/scipy/scipy/issues/5040 + np.random.seed(1234) + empty_v3 = np.empty(shape=(0, 3)) + query_v3 = np.ones(shape=(1, 3)) + query_v2 = np.ones(shape=(2, 3)) + + tree = kdtree_type(empty_v3, balanced_tree=balanced_tree, + compact_nodes=compact_nodes) + length = tree.query_ball_point(query_v3, 0.3, return_length=True) + assert length == 0 + + dd, ii = tree.query(query_v2, 2) + assert ii.shape == (2, 2) + assert dd.shape == (2, 2) + assert np.isinf(dd).all() + + N = tree.count_neighbors(tree, [0, 1]) + assert_array_equal(N, [0, 0]) + + M = tree.sparse_distance_matrix(tree, 0.3) + assert M.shape == (0, 0) + +@KDTreeTest +class _Test_sorted_query_ball_point: + def setup_method(self): + np.random.seed(1234) + self.x = np.random.randn(100, 1) + self.ckdt = self.kdtree_type(self.x) + + def test_return_sorted_True(self): + idxs_list = self.ckdt.query_ball_point(self.x, 1., return_sorted=True) + for idxs in idxs_list: + assert_array_equal(idxs, sorted(idxs)) + + for xi in self.x: + idxs = self.ckdt.query_ball_point(xi, 1., return_sorted=True) + assert_array_equal(idxs, sorted(idxs)) + + def test_return_sorted_None(self): + """Previous behavior was to sort the returned indices if there were + multiple points per query but not sort them if there was a single point + per query.""" + idxs_list = self.ckdt.query_ball_point(self.x, 1.) + for idxs in idxs_list: + assert_array_equal(idxs, sorted(idxs)) + + idxs_list_single = [self.ckdt.query_ball_point(xi, 1.) for xi in self.x] + idxs_list_False = self.ckdt.query_ball_point(self.x, 1., return_sorted=False) + for idxs0, idxs1 in zip(idxs_list_False, idxs_list_single): + assert_array_equal(idxs0, idxs1) + + +def test_kdtree_complex_data(): + # Test that KDTree rejects complex input points (gh-9108) + points = np.random.rand(10, 2).view(complex) + + with pytest.raises(TypeError, match="complex data"): + t = KDTree(points) + + t = KDTree(points.real) + + with pytest.raises(TypeError, match="complex data"): + t.query(points) + + with pytest.raises(TypeError, match="complex data"): + t.query_ball_point(points, r=1) + + +def test_kdtree_tree_access(): + # Test KDTree.tree can be used to traverse the KDTree + np.random.seed(1234) + points = np.random.rand(100, 4) + t = KDTree(points) + root = t.tree + + assert isinstance(root, KDTree.innernode) + assert root.children == points.shape[0] + + # Visit the tree and assert some basic properties for each node + nodes = [root] + while nodes: + n = nodes.pop(-1) + + if isinstance(n, KDTree.leafnode): + assert isinstance(n.children, int) + assert n.children == len(n.idx) + assert_array_equal(points[n.idx], n._node.data_points) + else: + assert isinstance(n, KDTree.innernode) + assert isinstance(n.split_dim, int) + assert 0 <= n.split_dim < t.m + assert isinstance(n.split, float) + assert isinstance(n.children, int) + assert n.children == n.less.children + n.greater.children + nodes.append(n.greater) + nodes.append(n.less) + + +def test_kdtree_attributes(): + # Test KDTree's attributes are available + np.random.seed(1234) + points = np.random.rand(100, 4) + t = KDTree(points) + + assert isinstance(t.m, int) + assert t.n == points.shape[0] + + assert isinstance(t.n, int) + assert t.m == points.shape[1] + + assert isinstance(t.leafsize, int) + assert t.leafsize == 10 + + assert_array_equal(t.maxes, np.amax(points, axis=0)) + assert_array_equal(t.mins, np.amin(points, axis=0)) + assert t.data is points + + +@pytest.mark.parametrize("kdtree_class", [KDTree, cKDTree]) +def test_kdtree_count_neighbors_weighted(kdtree_class): + np.random.seed(1234) + r = np.arange(0.05, 1, 0.05) + + A = np.random.random(21).reshape((7,3)) + B = np.random.random(45).reshape((15,3)) + + wA = np.random.random(7) + wB = np.random.random(15) + + kdA = kdtree_class(A) + kdB = kdtree_class(B) + + nAB = kdA.count_neighbors(kdB, r, cumulative=False, weights=(wA,wB)) + + # Compare against brute-force + weights = wA[None, :] * wB[:, None] + dist = np.linalg.norm(A[None, :, :] - B[:, None, :], axis=-1) + expect = [np.sum(weights[(prev_radius < dist) & (dist <= radius)]) + for prev_radius, radius in zip(itertools.chain([0], r[:-1]), r)] + assert_allclose(nAB, expect) + + +def test_kdtree_nan(): + vals = [1, 5, -10, 7, -4, -16, -6, 6, 3, -11] + n = len(vals) + data = np.concatenate([vals, np.full(n, np.nan)])[:, None] + with pytest.raises(ValueError, match="must be finite"): + KDTree(data) + + +def test_nonfinite_inputs_gh_18223(): + rng = np.random.default_rng(12345) + coords = rng.uniform(size=(100, 3), low=0.0, high=0.1) + t = KDTree(coords, balanced_tree=False, compact_nodes=False) + bad_coord = [np.nan for _ in range(3)] + + with pytest.raises(ValueError, match="must be finite"): + t.query(bad_coord) + with pytest.raises(ValueError, match="must be finite"): + t.query_ball_point(bad_coord, 1) + + coords[0, :] = np.nan + with pytest.raises(ValueError, match="must be finite"): + KDTree(coords, balanced_tree=True, compact_nodes=False) + with pytest.raises(ValueError, match="must be finite"): + KDTree(coords, balanced_tree=False, compact_nodes=True) + with pytest.raises(ValueError, match="must be finite"): + KDTree(coords, balanced_tree=True, compact_nodes=True) + with pytest.raises(ValueError, match="must be finite"): + KDTree(coords, balanced_tree=False, compact_nodes=False) + + +@pytest.mark.parametrize("incantation", [cKDTree, KDTree]) +def test_gh_18800(incantation): + # our prohibition on non-finite values + # in kd-tree workflows means we need + # coercion to NumPy arrays enforced + + class ArrLike(np.ndarray): + def __new__(cls, input_array): + obj = np.asarray(input_array).view(cls) + # we override all() to mimic the problem + # pandas DataFrames encountered in gh-18800 + obj.all = None + return obj + + def __array_finalize__(self, obj): + if obj is None: + return + self.all = getattr(obj, 'all', None) + + points = [ + [66.22, 32.54], + [22.52, 22.39], + [31.01, 81.21], + ] + arr = np.array(points) + arr_like = ArrLike(arr) + tree = incantation(points, 10) + tree.query(arr_like, 1) + tree.query_ball_point(arr_like, 200) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_qhull.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_qhull.py new file mode 100644 index 0000000000000000000000000000000000000000..dcf55e8f05b580aa49821600f75d5ab6f7573870 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_qhull.py @@ -0,0 +1,1178 @@ +import os +import copy + +import numpy as np +from numpy.testing import (assert_equal, assert_almost_equal, + assert_, assert_allclose, assert_array_equal) +import pytest +from pytest import raises as assert_raises + +import scipy.spatial._qhull as qhull +from scipy.spatial import cKDTree as KDTree +from scipy.spatial import Voronoi + +import itertools + +def sorted_tuple(x): + return tuple(sorted(x)) + + +def assert_unordered_tuple_list_equal(a, b, tpl=tuple): + if isinstance(a, np.ndarray): + a = a.tolist() + if isinstance(b, np.ndarray): + b = b.tolist() + a = list(map(tpl, a)) + a.sort() + b = list(map(tpl, b)) + b.sort() + assert_equal(a, b) + + +np.random.seed(1234) + +points = [(0,0), (0,1), (1,0), (1,1), (0.5, 0.5), (0.5, 1.5)] + +pathological_data_1 = np.array([ + [-3.14,-3.14], [-3.14,-2.36], [-3.14,-1.57], [-3.14,-0.79], + [-3.14,0.0], [-3.14,0.79], [-3.14,1.57], [-3.14,2.36], + [-3.14,3.14], [-2.36,-3.14], [-2.36,-2.36], [-2.36,-1.57], + [-2.36,-0.79], [-2.36,0.0], [-2.36,0.79], [-2.36,1.57], + [-2.36,2.36], [-2.36,3.14], [-1.57,-0.79], [-1.57,0.79], + [-1.57,-1.57], [-1.57,0.0], [-1.57,1.57], [-1.57,-3.14], + [-1.57,-2.36], [-1.57,2.36], [-1.57,3.14], [-0.79,-1.57], + [-0.79,1.57], [-0.79,-3.14], [-0.79,-2.36], [-0.79,-0.79], + [-0.79,0.0], [-0.79,0.79], [-0.79,2.36], [-0.79,3.14], + [0.0,-3.14], [0.0,-2.36], [0.0,-1.57], [0.0,-0.79], [0.0,0.0], + [0.0,0.79], [0.0,1.57], [0.0,2.36], [0.0,3.14], [0.79,-3.14], + [0.79,-2.36], [0.79,-0.79], [0.79,0.0], [0.79,0.79], + [0.79,2.36], [0.79,3.14], [0.79,-1.57], [0.79,1.57], + [1.57,-3.14], [1.57,-2.36], [1.57,2.36], [1.57,3.14], + [1.57,-1.57], [1.57,0.0], [1.57,1.57], [1.57,-0.79], + [1.57,0.79], [2.36,-3.14], [2.36,-2.36], [2.36,-1.57], + [2.36,-0.79], [2.36,0.0], [2.36,0.79], [2.36,1.57], + [2.36,2.36], [2.36,3.14], [3.14,-3.14], [3.14,-2.36], + [3.14,-1.57], [3.14,-0.79], [3.14,0.0], [3.14,0.79], + [3.14,1.57], [3.14,2.36], [3.14,3.14], +]) + +pathological_data_2 = np.array([ + [-1, -1], [-1, 0], [-1, 1], + [0, -1], [0, 0], [0, 1], + [1, -1 - np.finfo(np.float64).eps], [1, 0], [1, 1], +]) + +bug_2850_chunks = [np.random.rand(10, 2), + np.array([[0,0], [0,1], [1,0], [1,1]]) # add corners + ] + +# same with some additional chunks +bug_2850_chunks_2 = (bug_2850_chunks + + [np.random.rand(10, 2), + 0.25 + np.array([[0,0], [0,1], [1,0], [1,1]])]) + +DATASETS = { + 'some-points': np.asarray(points), + 'random-2d': np.random.rand(30, 2), + 'random-3d': np.random.rand(30, 3), + 'random-4d': np.random.rand(30, 4), + 'random-5d': np.random.rand(30, 5), + 'random-6d': np.random.rand(10, 6), + 'random-7d': np.random.rand(10, 7), + 'random-8d': np.random.rand(10, 8), + 'pathological-1': pathological_data_1, + 'pathological-2': pathological_data_2 +} + +INCREMENTAL_DATASETS = { + 'bug-2850': (bug_2850_chunks, None), + 'bug-2850-2': (bug_2850_chunks_2, None), +} + + +def _add_inc_data(name, chunksize): + """ + Generate incremental datasets from basic data sets + """ + points = DATASETS[name] + ndim = points.shape[1] + + opts = None + nmin = ndim + 2 + + if name == 'some-points': + # since Qz is not allowed, use QJ + opts = 'QJ Pp' + elif name == 'pathological-1': + # include enough points so that we get different x-coordinates + nmin = 12 + + chunks = [points[:nmin]] + for j in range(nmin, len(points), chunksize): + chunks.append(points[j:j+chunksize]) + + new_name = "%s-chunk-%d" % (name, chunksize) + assert new_name not in INCREMENTAL_DATASETS + INCREMENTAL_DATASETS[new_name] = (chunks, opts) + + +for name in DATASETS: + for chunksize in 1, 4, 16: + _add_inc_data(name, chunksize) + + +class Test_Qhull: + def test_swapping(self): + # Check that Qhull state swapping works + + x = qhull._Qhull(b'v', + np.array([[0,0],[0,1],[1,0],[1,1.],[0.5,0.5]]), + b'Qz') + xd = copy.deepcopy(x.get_voronoi_diagram()) + + y = qhull._Qhull(b'v', + np.array([[0,0],[0,1],[1,0],[1,2.]]), + b'Qz') + yd = copy.deepcopy(y.get_voronoi_diagram()) + + xd2 = copy.deepcopy(x.get_voronoi_diagram()) + x.close() + yd2 = copy.deepcopy(y.get_voronoi_diagram()) + y.close() + + assert_raises(RuntimeError, x.get_voronoi_diagram) + assert_raises(RuntimeError, y.get_voronoi_diagram) + + assert_allclose(xd[0], xd2[0]) + assert_unordered_tuple_list_equal(xd[1], xd2[1], tpl=sorted_tuple) + assert_unordered_tuple_list_equal(xd[2], xd2[2], tpl=sorted_tuple) + assert_unordered_tuple_list_equal(xd[3], xd2[3], tpl=sorted_tuple) + assert_array_equal(xd[4], xd2[4]) + + assert_allclose(yd[0], yd2[0]) + assert_unordered_tuple_list_equal(yd[1], yd2[1], tpl=sorted_tuple) + assert_unordered_tuple_list_equal(yd[2], yd2[2], tpl=sorted_tuple) + assert_unordered_tuple_list_equal(yd[3], yd2[3], tpl=sorted_tuple) + assert_array_equal(yd[4], yd2[4]) + + x.close() + assert_raises(RuntimeError, x.get_voronoi_diagram) + y.close() + assert_raises(RuntimeError, y.get_voronoi_diagram) + + def test_issue_8051(self): + points = np.array( + [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2],[2, 0], [2, 1], [2, 2]] + ) + Voronoi(points) + + +class TestUtilities: + """ + Check that utility functions work. + + """ + + def test_find_simplex(self): + # Simple check that simplex finding works + points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64) + tri = qhull.Delaunay(points) + + # +---+ + # |\ 0| + # | \ | + # |1 \| + # +---+ + + assert_equal(tri.simplices, [[1, 3, 2], [3, 1, 0]]) + + for p in [(0.25, 0.25, 1), + (0.75, 0.75, 0), + (0.3, 0.2, 1)]: + i = tri.find_simplex(p[:2]) + assert_equal(i, p[2], err_msg=f'{p!r}') + j = qhull.tsearch(tri, p[:2]) + assert_equal(i, j) + + def test_plane_distance(self): + # Compare plane distance from hyperplane equations obtained from Qhull + # to manually computed plane equations + x = np.array([(0,0), (1, 1), (1, 0), (0.99189033, 0.37674127), + (0.99440079, 0.45182168)], dtype=np.float64) + p = np.array([0.99966555, 0.15685619], dtype=np.float64) + + tri = qhull.Delaunay(x) + + z = tri.lift_points(x) + pz = tri.lift_points(p) + + dist = tri.plane_distance(p) + + for j, v in enumerate(tri.simplices): + x1 = z[v[0]] + x2 = z[v[1]] + x3 = z[v[2]] + + n = np.cross(x1 - x3, x2 - x3) + n /= np.sqrt(np.dot(n, n)) + n *= -np.sign(n[2]) + + d = np.dot(n, pz - x3) + + assert_almost_equal(dist[j], d) + + def test_convex_hull(self): + # Simple check that the convex hull seems to works + points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64) + tri = qhull.Delaunay(points) + + # +---+ + # |\ 0| + # | \ | + # |1 \| + # +---+ + + assert_equal(tri.convex_hull, [[3, 2], [1, 2], [1, 0], [3, 0]]) + + def test_volume_area(self): + #Basic check that we get back the correct volume and area for a cube + points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), + (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)]) + hull = qhull.ConvexHull(points) + + assert_allclose(hull.volume, 1., rtol=1e-14, + err_msg="Volume of cube is incorrect") + assert_allclose(hull.area, 6., rtol=1e-14, + err_msg="Area of cube is incorrect") + + def test_random_volume_area(self): + #Test that the results for a random 10-point convex are + #coherent with the output of qconvex Qt s FA + points = np.array([(0.362568364506, 0.472712355305, 0.347003084477), + (0.733731893414, 0.634480295684, 0.950513180209), + (0.511239955611, 0.876839441267, 0.418047827863), + (0.0765906233393, 0.527373281342, 0.6509863541), + (0.146694972056, 0.596725793348, 0.894860986685), + (0.513808585741, 0.069576205858, 0.530890338876), + (0.512343805118, 0.663537132612, 0.037689295973), + (0.47282965018, 0.462176697655, 0.14061843691), + (0.240584597123, 0.778660020591, 0.722913476339), + (0.951271745935, 0.967000673944, 0.890661319684)]) + + hull = qhull.ConvexHull(points) + assert_allclose(hull.volume, 0.14562013, rtol=1e-07, + err_msg="Volume of random polyhedron is incorrect") + assert_allclose(hull.area, 1.6670425, rtol=1e-07, + err_msg="Area of random polyhedron is incorrect") + + def test_incremental_volume_area_random_input(self): + """Test that incremental mode gives the same volume/area as + non-incremental mode and incremental mode with restart""" + nr_points = 20 + dim = 3 + points = np.random.random((nr_points, dim)) + inc_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True) + inc_restart_hull = qhull.ConvexHull(points[:dim+1, :], incremental=True) + for i in range(dim+1, nr_points): + hull = qhull.ConvexHull(points[:i+1, :]) + inc_hull.add_points(points[i:i+1, :]) + inc_restart_hull.add_points(points[i:i+1, :], restart=True) + assert_allclose(hull.volume, inc_hull.volume, rtol=1e-7) + assert_allclose(hull.volume, inc_restart_hull.volume, rtol=1e-7) + assert_allclose(hull.area, inc_hull.area, rtol=1e-7) + assert_allclose(hull.area, inc_restart_hull.area, rtol=1e-7) + + def _check_barycentric_transforms(self, tri, err_msg="", + unit_cube=False, + unit_cube_tol=0): + """Check that a triangulation has reasonable barycentric transforms""" + vertices = tri.points[tri.simplices] + sc = 1/(tri.ndim + 1.0) + centroids = vertices.sum(axis=1) * sc + + # Either: (i) the simplex has a `nan` barycentric transform, + # or, (ii) the centroid is in the simplex + + def barycentric_transform(tr, x): + r = tr[:,-1,:] + Tinv = tr[:,:-1,:] + return np.einsum('ijk,ik->ij', Tinv, x - r) + + eps = np.finfo(float).eps + + c = barycentric_transform(tri.transform, centroids) + with np.errstate(invalid="ignore"): + ok = np.isnan(c).all(axis=1) | (abs(c - sc)/sc < 0.1).all(axis=1) + + assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}") + + # Invalid simplices must be (nearly) zero volume + q = vertices[:,:-1,:] - vertices[:,-1,None,:] + volume = np.array([np.linalg.det(q[k,:,:]) + for k in range(tri.nsimplex)]) + ok = np.isfinite(tri.transform[:,0,0]) | (volume < np.sqrt(eps)) + assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}") + + # Also, find_simplex for the centroid should end up in some + # simplex for the non-degenerate cases + j = tri.find_simplex(centroids) + ok = (j != -1) | np.isnan(tri.transform[:,0,0]) + assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}") + + if unit_cube: + # If in unit cube, no interior point should be marked out of hull + at_boundary = (centroids <= unit_cube_tol).any(axis=1) + at_boundary |= (centroids >= 1 - unit_cube_tol).any(axis=1) + + ok = (j != -1) | at_boundary + assert_(ok.all(), f"{err_msg} {np.nonzero(~ok)}") + + def test_degenerate_barycentric_transforms(self): + # The triangulation should not produce invalid barycentric + # transforms that stump the simplex finding + data = np.load(os.path.join(os.path.dirname(__file__), 'data', + 'degenerate_pointset.npz')) + points = data['c'] + data.close() + + tri = qhull.Delaunay(points) + + # Check that there are not too many invalid simplices + bad_count = np.isnan(tri.transform[:,0,0]).sum() + assert_(bad_count < 23, bad_count) + + # Check the transforms + self._check_barycentric_transforms(tri) + + @pytest.mark.slow + def test_more_barycentric_transforms(self): + # Triangulate some "nasty" grids + + eps = np.finfo(float).eps + + npoints = {2: 70, 3: 11, 4: 5, 5: 3} + + for ndim in range(2, 6): + # Generate an uniform grid in n-d unit cube + x = np.linspace(0, 1, npoints[ndim]) + grid = np.c_[ + list(map(np.ravel, np.broadcast_arrays(*np.ix_(*([x]*ndim))))) + ].T + + err_msg = "ndim=%d" % ndim + + # Check using regular grid + tri = qhull.Delaunay(grid) + self._check_barycentric_transforms(tri, err_msg=err_msg, + unit_cube=True) + + # Check with eps-perturbations + np.random.seed(1234) + m = (np.random.rand(grid.shape[0]) < 0.2) + grid[m,:] += 2*eps*(np.random.rand(*grid[m,:].shape) - 0.5) + + tri = qhull.Delaunay(grid) + self._check_barycentric_transforms(tri, err_msg=err_msg, + unit_cube=True, + unit_cube_tol=2*eps) + + # Check with duplicated data + tri = qhull.Delaunay(np.r_[grid, grid]) + self._check_barycentric_transforms(tri, err_msg=err_msg, + unit_cube=True, + unit_cube_tol=2*eps) + + +class TestVertexNeighborVertices: + def _check(self, tri): + expected = [set() for j in range(tri.points.shape[0])] + for s in tri.simplices: + for a in s: + for b in s: + if a != b: + expected[a].add(b) + + indptr, indices = tri.vertex_neighbor_vertices + + got = [set(map(int, indices[indptr[j]:indptr[j+1]])) + for j in range(tri.points.shape[0])] + + assert_equal(got, expected, err_msg=f"{got!r} != {expected!r}") + + def test_triangle(self): + points = np.array([(0,0), (0,1), (1,0)], dtype=np.float64) + tri = qhull.Delaunay(points) + self._check(tri) + + def test_rectangle(self): + points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64) + tri = qhull.Delaunay(points) + self._check(tri) + + def test_complicated(self): + points = np.array([(0,0), (0,1), (1,1), (1,0), + (0.5, 0.5), (0.9, 0.5)], dtype=np.float64) + tri = qhull.Delaunay(points) + self._check(tri) + + +class TestDelaunay: + """ + Check that triangulation works. + + """ + def test_masked_array_fails(self): + masked_array = np.ma.masked_all(1) + assert_raises(ValueError, qhull.Delaunay, masked_array) + + def test_array_with_nans_fails(self): + points_with_nan = np.array([(0,0), (0,1), (1,1), (1,np.nan)], dtype=np.float64) + assert_raises(ValueError, qhull.Delaunay, points_with_nan) + + def test_nd_simplex(self): + # simple smoke test: triangulate a n-dimensional simplex + for nd in range(2, 8): + points = np.zeros((nd+1, nd)) + for j in range(nd): + points[j,j] = 1.0 + points[-1,:] = 1.0 + + tri = qhull.Delaunay(points) + + tri.simplices.sort() + + assert_equal(tri.simplices, np.arange(nd+1, dtype=int)[None, :]) + assert_equal(tri.neighbors, -1 + np.zeros((nd+1), dtype=int)[None,:]) + + def test_2d_square(self): + # simple smoke test: 2d square + points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.float64) + tri = qhull.Delaunay(points) + + assert_equal(tri.simplices, [[1, 3, 2], [3, 1, 0]]) + assert_equal(tri.neighbors, [[-1, -1, 1], [-1, -1, 0]]) + + def test_duplicate_points(self): + x = np.array([0, 1, 0, 1], dtype=np.float64) + y = np.array([0, 0, 1, 1], dtype=np.float64) + + xp = np.r_[x, x] + yp = np.r_[y, y] + + # shouldn't fail on duplicate points + qhull.Delaunay(np.c_[x, y]) + qhull.Delaunay(np.c_[xp, yp]) + + def test_pathological(self): + # both should succeed + points = DATASETS['pathological-1'] + tri = qhull.Delaunay(points) + assert_equal(tri.points[tri.simplices].max(), points.max()) + assert_equal(tri.points[tri.simplices].min(), points.min()) + + points = DATASETS['pathological-2'] + tri = qhull.Delaunay(points) + assert_equal(tri.points[tri.simplices].max(), points.max()) + assert_equal(tri.points[tri.simplices].min(), points.min()) + + def test_joggle(self): + # Check that the option QJ indeed guarantees that all input points + # occur as vertices of the triangulation + + points = np.random.rand(10, 2) + points = np.r_[points, points] # duplicate input data + + tri = qhull.Delaunay(points, qhull_options="QJ Qbb Pp") + assert_array_equal(np.unique(tri.simplices.ravel()), + np.arange(len(points))) + + def test_coplanar(self): + # Check that the coplanar point output option indeed works + points = np.random.rand(10, 2) + points = np.r_[points, points] # duplicate input data + + tri = qhull.Delaunay(points) + + assert_(len(np.unique(tri.simplices.ravel())) == len(points)//2) + assert_(len(tri.coplanar) == len(points)//2) + + assert_(len(np.unique(tri.coplanar[:,2])) == len(points)//2) + + assert_(np.all(tri.vertex_to_simplex >= 0)) + + def test_furthest_site(self): + points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)] + tri = qhull.Delaunay(points, furthest_site=True) + + expected = np.array([(1, 4, 0), (4, 2, 0)]) # from Qhull + assert_array_equal(tri.simplices, expected) + + @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS)) + def test_incremental(self, name): + # Test incremental construction of the triangulation + + chunks, opts = INCREMENTAL_DATASETS[name] + points = np.concatenate(chunks, axis=0) + + obj = qhull.Delaunay(chunks[0], incremental=True, + qhull_options=opts) + for chunk in chunks[1:]: + obj.add_points(chunk) + + obj2 = qhull.Delaunay(points) + + obj3 = qhull.Delaunay(chunks[0], incremental=True, + qhull_options=opts) + if len(chunks) > 1: + obj3.add_points(np.concatenate(chunks[1:], axis=0), + restart=True) + + # Check that the incremental mode agrees with upfront mode + if name.startswith('pathological'): + # XXX: These produce valid but different triangulations. + # They look OK when plotted, but how to check them? + + assert_array_equal(np.unique(obj.simplices.ravel()), + np.arange(points.shape[0])) + assert_array_equal(np.unique(obj2.simplices.ravel()), + np.arange(points.shape[0])) + else: + assert_unordered_tuple_list_equal(obj.simplices, obj2.simplices, + tpl=sorted_tuple) + + assert_unordered_tuple_list_equal(obj2.simplices, obj3.simplices, + tpl=sorted_tuple) + + +def assert_hulls_equal(points, facets_1, facets_2): + # Check that two convex hulls constructed from the same point set + # are equal + + facets_1 = set(map(sorted_tuple, facets_1)) + facets_2 = set(map(sorted_tuple, facets_2)) + + if facets_1 != facets_2 and points.shape[1] == 2: + # The direct check fails for the pathological cases + # --- then the convex hull from Delaunay differs (due + # to rounding error etc.) from the hull computed + # otherwise, by the question whether (tricoplanar) + # points that lie almost exactly on the hull are + # included as vertices of the hull or not. + # + # So we check the result, and accept it if the Delaunay + # hull line segments are a subset of the usual hull. + + eps = 1000 * np.finfo(float).eps + + for a, b in facets_1: + for ap, bp in facets_2: + t = points[bp] - points[ap] + t /= np.linalg.norm(t) # tangent + n = np.array([-t[1], t[0]]) # normal + + # check that the two line segments are parallel + # to the same line + c1 = np.dot(n, points[b] - points[ap]) + c2 = np.dot(n, points[a] - points[ap]) + if not np.allclose(np.dot(c1, n), 0): + continue + if not np.allclose(np.dot(c2, n), 0): + continue + + # Check that the segment (a, b) is contained in (ap, bp) + c1 = np.dot(t, points[a] - points[ap]) + c2 = np.dot(t, points[b] - points[ap]) + c3 = np.dot(t, points[bp] - points[ap]) + if c1 < -eps or c1 > c3 + eps: + continue + if c2 < -eps or c2 > c3 + eps: + continue + + # OK: + break + else: + raise AssertionError("comparison fails") + + # it was OK + return + + assert_equal(facets_1, facets_2) + + +class TestConvexHull: + def test_masked_array_fails(self): + masked_array = np.ma.masked_all(1) + assert_raises(ValueError, qhull.ConvexHull, masked_array) + + def test_array_with_nans_fails(self): + points_with_nan = np.array([(0,0), (1,1), (2,np.nan)], dtype=np.float64) + assert_raises(ValueError, qhull.ConvexHull, points_with_nan) + + @pytest.mark.parametrize("name", sorted(DATASETS)) + def test_hull_consistency_tri(self, name): + # Check that a convex hull returned by qhull in ndim + # and the hull constructed from ndim delaunay agree + points = DATASETS[name] + + tri = qhull.Delaunay(points) + hull = qhull.ConvexHull(points) + + assert_hulls_equal(points, tri.convex_hull, hull.simplices) + + # Check that the hull extremes are as expected + if points.shape[1] == 2: + assert_equal(np.unique(hull.simplices), np.sort(hull.vertices)) + else: + assert_equal(np.unique(hull.simplices), hull.vertices) + + @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS)) + def test_incremental(self, name): + # Test incremental construction of the convex hull + chunks, _ = INCREMENTAL_DATASETS[name] + points = np.concatenate(chunks, axis=0) + + obj = qhull.ConvexHull(chunks[0], incremental=True) + for chunk in chunks[1:]: + obj.add_points(chunk) + + obj2 = qhull.ConvexHull(points) + + obj3 = qhull.ConvexHull(chunks[0], incremental=True) + if len(chunks) > 1: + obj3.add_points(np.concatenate(chunks[1:], axis=0), + restart=True) + + # Check that the incremental mode agrees with upfront mode + assert_hulls_equal(points, obj.simplices, obj2.simplices) + assert_hulls_equal(points, obj.simplices, obj3.simplices) + + def test_vertices_2d(self): + # The vertices should be in counterclockwise order in 2-D + np.random.seed(1234) + points = np.random.rand(30, 2) + + hull = qhull.ConvexHull(points) + assert_equal(np.unique(hull.simplices), np.sort(hull.vertices)) + + # Check counterclockwiseness + x, y = hull.points[hull.vertices].T + angle = np.arctan2(y - y.mean(), x - x.mean()) + assert_(np.all(np.diff(np.unwrap(angle)) > 0)) + + def test_volume_area(self): + # Basic check that we get back the correct volume and area for a cube + points = np.array([(0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), + (0, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, 1)]) + tri = qhull.ConvexHull(points) + + assert_allclose(tri.volume, 1., rtol=1e-14) + assert_allclose(tri.area, 6., rtol=1e-14) + + @pytest.mark.parametrize("incremental", [False, True]) + def test_good2d(self, incremental): + # Make sure the QGn option gives the correct value of "good". + points = np.array([[0.2, 0.2], + [0.2, 0.4], + [0.4, 0.4], + [0.4, 0.2], + [0.3, 0.6]]) + hull = qhull.ConvexHull(points=points, + incremental=incremental, + qhull_options='QG4') + expected = np.array([False, True, False, False], dtype=bool) + actual = hull.good + assert_equal(actual, expected) + + @pytest.mark.parametrize("visibility", [ + "QG4", # visible=True + "QG-4", # visible=False + ]) + @pytest.mark.parametrize("new_gen, expected", [ + # add generator that places QG4 inside hull + # so all facets are invisible + (np.array([[0.3, 0.7]]), + np.array([False, False, False, False, False], dtype=bool)), + # adding a generator on the opposite side of the square + # should preserve the single visible facet & add one invisible + # facet + (np.array([[0.3, -0.7]]), + np.array([False, True, False, False, False], dtype=bool)), + # split the visible facet on top of the square into two + # visible facets, with visibility at the end of the array + # because add_points concatenates + (np.array([[0.3, 0.41]]), + np.array([False, False, False, True, True], dtype=bool)), + # with our current Qhull options, coplanarity will not count + # for visibility; this case shifts one visible & one invisible + # facet & adds a coplanar facet + # simplex at index position 2 is the shifted visible facet + # the final simplex is the coplanar facet + (np.array([[0.5, 0.6], [0.6, 0.6]]), + np.array([False, False, True, False, False], dtype=bool)), + # place the new generator such that it envelops the query + # point within the convex hull, but only just barely within + # the double precision limit + # NOTE: testing exact degeneracy is less predictable than this + # scenario, perhaps because of the default Qt option we have + # enabled for Qhull to handle precision matters + (np.array([[0.3, 0.6 + 1e-16]]), + np.array([False, False, False, False, False], dtype=bool)), + ]) + def test_good2d_incremental_changes(self, new_gen, expected, + visibility): + # use the usual square convex hull + # generators from test_good2d + points = np.array([[0.2, 0.2], + [0.2, 0.4], + [0.4, 0.4], + [0.4, 0.2], + [0.3, 0.6]]) + hull = qhull.ConvexHull(points=points, + incremental=True, + qhull_options=visibility) + hull.add_points(new_gen) + actual = hull.good + if '-' in visibility: + expected = np.invert(expected) + assert_equal(actual, expected) + + @pytest.mark.parametrize("incremental", [False, True]) + def test_good2d_no_option(self, incremental): + # handle case where good attribute doesn't exist + # because Qgn or Qg-n wasn't specified + points = np.array([[0.2, 0.2], + [0.2, 0.4], + [0.4, 0.4], + [0.4, 0.2], + [0.3, 0.6]]) + hull = qhull.ConvexHull(points=points, + incremental=incremental) + actual = hull.good + assert actual is None + # preserve None after incremental addition + if incremental: + hull.add_points(np.zeros((1, 2))) + actual = hull.good + assert actual is None + + @pytest.mark.parametrize("incremental", [False, True]) + def test_good2d_inside(self, incremental): + # Make sure the QGn option gives the correct value of "good". + # When point n is inside the convex hull of the rest, good is + # all False. + points = np.array([[0.2, 0.2], + [0.2, 0.4], + [0.4, 0.4], + [0.4, 0.2], + [0.3, 0.3]]) + hull = qhull.ConvexHull(points=points, + incremental=incremental, + qhull_options='QG4') + expected = np.array([False, False, False, False], dtype=bool) + actual = hull.good + assert_equal(actual, expected) + + @pytest.mark.parametrize("incremental", [False, True]) + def test_good3d(self, incremental): + # Make sure the QGn option gives the correct value of "good" + # for a 3d figure + points = np.array([[0.0, 0.0, 0.0], + [0.90029516, -0.39187448, 0.18948093], + [0.48676420, -0.72627633, 0.48536925], + [0.57651530, -0.81179274, -0.09285832], + [0.67846893, -0.71119562, 0.18406710]]) + hull = qhull.ConvexHull(points=points, + incremental=incremental, + qhull_options='QG0') + expected = np.array([True, False, False, False], dtype=bool) + assert_equal(hull.good, expected) + +class TestVoronoi: + + @pytest.mark.parametrize("qhull_opts, extra_pts", [ + # option Qz (default for SciPy) will add + # an extra point at infinity + ("Qbb Qc Qz", 1), + ("Qbb Qc", 0), + ]) + @pytest.mark.parametrize("n_pts", [50, 100]) + @pytest.mark.parametrize("ndim", [2, 3]) + def test_point_region_structure(self, + qhull_opts, + n_pts, + extra_pts, + ndim): + # see gh-16773 + rng = np.random.default_rng(7790) + points = rng.random((n_pts, ndim)) + vor = Voronoi(points, qhull_options=qhull_opts) + pt_region = vor.point_region + assert pt_region.max() == n_pts - 1 + extra_pts + assert pt_region.size == len(vor.regions) - extra_pts + assert len(vor.regions) == n_pts + extra_pts + assert vor.points.shape[0] == n_pts + # if there is an empty sublist in the Voronoi + # regions data structure, it should never be + # indexed because it corresponds to an internally + # added point at infinity and is not a member of the + # generators (input points) + if extra_pts: + sublens = [len(x) for x in vor.regions] + # only one point at infinity (empty region) + # is allowed + assert sublens.count(0) == 1 + assert sublens.index(0) not in pt_region + + def test_masked_array_fails(self): + masked_array = np.ma.masked_all(1) + assert_raises(ValueError, qhull.Voronoi, masked_array) + + def test_simple(self): + # Simple case with known Voronoi diagram + points = [(0, 0), (0, 1), (0, 2), + (1, 0), (1, 1), (1, 2), + (2, 0), (2, 1), (2, 2)] + + # qhull v o Fv Qbb Qc Qz < dat + output = """ + 2 + 5 10 1 + -10.101 -10.101 + 0.5 0.5 + 0.5 1.5 + 1.5 0.5 + 1.5 1.5 + 2 0 1 + 3 2 0 1 + 2 0 2 + 3 3 0 1 + 4 1 2 4 3 + 3 4 0 2 + 2 0 3 + 3 4 0 3 + 2 0 4 + 0 + 12 + 4 0 3 0 1 + 4 0 1 0 1 + 4 1 4 1 2 + 4 1 2 0 2 + 4 2 5 0 2 + 4 3 4 1 3 + 4 3 6 0 3 + 4 4 5 2 4 + 4 4 7 3 4 + 4 5 8 0 4 + 4 6 7 0 3 + 4 7 8 0 4 + """ + self._compare_qvoronoi(points, output) + + def _compare_qvoronoi(self, points, output, **kw): + """Compare to output from 'qvoronoi o Fv < data' to Voronoi()""" + + # Parse output + output = [list(map(float, x.split())) for x in output.strip().splitlines()] + nvertex = int(output[1][0]) + vertices = list(map(tuple, output[3:2+nvertex])) # exclude inf + nregion = int(output[1][1]) + regions = [[int(y)-1 for y in x[1:]] + for x in output[2+nvertex:2+nvertex+nregion]] + ridge_points = [[int(y) for y in x[1:3]] + for x in output[3+nvertex+nregion:]] + ridge_vertices = [[int(y)-1 for y in x[3:]] + for x in output[3+nvertex+nregion:]] + + # Compare results + vor = qhull.Voronoi(points, **kw) + + def sorttuple(x): + return tuple(sorted(x)) + + assert_allclose(vor.vertices, vertices) + assert_equal(set(map(tuple, vor.regions)), + set(map(tuple, regions))) + + p1 = list(zip(list(map(sorttuple, ridge_points)), + list(map(sorttuple, ridge_vertices)))) + p2 = list(zip(list(map(sorttuple, vor.ridge_points.tolist())), + list(map(sorttuple, vor.ridge_vertices)))) + p1.sort() + p2.sort() + + assert_equal(p1, p2) + + @pytest.mark.parametrize("name", sorted(DATASETS)) + def test_ridges(self, name): + # Check that the ridges computed by Voronoi indeed separate + # the regions of nearest neighborhood, by comparing the result + # to KDTree. + + points = DATASETS[name] + + tree = KDTree(points) + vor = qhull.Voronoi(points) + + for p, v in vor.ridge_dict.items(): + # consider only finite ridges + if not np.all(np.asarray(v) >= 0): + continue + + ridge_midpoint = vor.vertices[v].mean(axis=0) + d = 1e-6 * (points[p[0]] - ridge_midpoint) + + dist, k = tree.query(ridge_midpoint + d, k=1) + assert_equal(k, p[0]) + + dist, k = tree.query(ridge_midpoint - d, k=1) + assert_equal(k, p[1]) + + def test_furthest_site(self): + points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)] + + # qhull v o Fv Qbb Qc Qu < dat + output = """ + 2 + 3 5 1 + -10.101 -10.101 + 0.6000000000000001 0.5 + 0.5 0.6000000000000001 + 3 0 2 1 + 2 0 1 + 2 0 2 + 0 + 3 0 2 1 + 5 + 4 0 2 0 2 + 4 0 4 1 2 + 4 0 1 0 1 + 4 1 4 0 1 + 4 2 4 0 2 + """ + self._compare_qvoronoi(points, output, furthest_site=True) + + def test_furthest_site_flag(self): + points = [(0, 0), (0, 1), (1, 0), (0.5, 0.5), (1.1, 1.1)] + + vor = Voronoi(points) + assert_equal(vor.furthest_site,False) + vor = Voronoi(points,furthest_site=True) + assert_equal(vor.furthest_site,True) + + @pytest.mark.parametrize("name", sorted(INCREMENTAL_DATASETS)) + def test_incremental(self, name): + # Test incremental construction of the triangulation + + if INCREMENTAL_DATASETS[name][0][0].shape[1] > 3: + # too slow (testing of the result --- qhull is still fast) + return + + chunks, opts = INCREMENTAL_DATASETS[name] + points = np.concatenate(chunks, axis=0) + + obj = qhull.Voronoi(chunks[0], incremental=True, + qhull_options=opts) + for chunk in chunks[1:]: + obj.add_points(chunk) + + obj2 = qhull.Voronoi(points) + + obj3 = qhull.Voronoi(chunks[0], incremental=True, + qhull_options=opts) + if len(chunks) > 1: + obj3.add_points(np.concatenate(chunks[1:], axis=0), + restart=True) + + # -- Check that the incremental mode agrees with upfront mode + assert_equal(len(obj.point_region), len(obj2.point_region)) + assert_equal(len(obj.point_region), len(obj3.point_region)) + + # The vertices may be in different order or duplicated in + # the incremental map + for objx in obj, obj3: + vertex_map = {-1: -1} + for i, v in enumerate(objx.vertices): + for j, v2 in enumerate(obj2.vertices): + if np.allclose(v, v2): + vertex_map[i] = j + + def remap(x): + if hasattr(x, '__len__'): + return tuple({remap(y) for y in x}) + try: + return vertex_map[x] + except KeyError as e: + message = (f"incremental result has spurious vertex " + f"at {objx.vertices[x]!r}") + raise AssertionError(message) from e + + def simplified(x): + items = set(map(sorted_tuple, x)) + if () in items: + items.remove(()) + items = [x for x in items if len(x) > 1] + items.sort() + return items + + assert_equal( + simplified(remap(objx.regions)), + simplified(obj2.regions) + ) + assert_equal( + simplified(remap(objx.ridge_vertices)), + simplified(obj2.ridge_vertices) + ) + + # XXX: compare ridge_points --- not clear exactly how to do this + + +class Test_HalfspaceIntersection: + def assert_unordered_allclose(self, arr1, arr2, rtol=1e-7): + """Check that every line in arr1 is only once in arr2""" + assert_equal(arr1.shape, arr2.shape) + + truths = np.zeros((arr1.shape[0],), dtype=bool) + for l1 in arr1: + indexes = np.nonzero((abs(arr2 - l1) < rtol).all(axis=1))[0] + assert_equal(indexes.shape, (1,)) + truths[indexes[0]] = True + assert_(truths.all()) + + @pytest.mark.parametrize("dt", [np.float64, int]) + def test_cube_halfspace_intersection(self, dt): + halfspaces = np.array([[-1, 0, 0], + [0, -1, 0], + [1, 0, -2], + [0, 1, -2]], dtype=dt) + feasible_point = np.array([1, 1], dtype=dt) + + points = np.array([[0.0, 0.0], [2.0, 0.0], [0.0, 2.0], [2.0, 2.0]]) + + hull = qhull.HalfspaceIntersection(halfspaces, feasible_point) + + assert_allclose(hull.intersections, points) + + def test_self_dual_polytope_intersection(self): + fname = os.path.join(os.path.dirname(__file__), 'data', + 'selfdual-4d-polytope.txt') + ineqs = np.genfromtxt(fname) + halfspaces = -np.hstack((ineqs[:, 1:], ineqs[:, :1])) + + feas_point = np.array([0., 0., 0., 0.]) + hs = qhull.HalfspaceIntersection(halfspaces, feas_point) + + assert_equal(hs.intersections.shape, (24, 4)) + + assert_almost_equal(hs.dual_volume, 32.0) + assert_equal(len(hs.dual_facets), 24) + for facet in hs.dual_facets: + assert_equal(len(facet), 6) + + dists = halfspaces[:, -1] + halfspaces[:, :-1].dot(feas_point) + self.assert_unordered_allclose((halfspaces[:, :-1].T/dists).T, hs.dual_points) + + points = itertools.permutations([0., 0., 0.5, -0.5]) + for point in points: + assert_equal(np.sum((hs.intersections == point).all(axis=1)), 1) + + def test_wrong_feasible_point(self): + halfspaces = np.array([[-1.0, 0.0, 0.0], + [0.0, -1.0, 0.0], + [1.0, 0.0, -1.0], + [0.0, 1.0, -1.0]]) + feasible_point = np.array([0.5, 0.5, 0.5]) + #Feasible point is (ndim,) instead of (ndim-1,) + assert_raises(ValueError, + qhull.HalfspaceIntersection, halfspaces, feasible_point) + feasible_point = np.array([[0.5], [0.5]]) + #Feasible point is (ndim-1, 1) instead of (ndim-1,) + assert_raises(ValueError, + qhull.HalfspaceIntersection, halfspaces, feasible_point) + feasible_point = np.array([[0.5, 0.5]]) + #Feasible point is (1, ndim-1) instead of (ndim-1,) + assert_raises(ValueError, + qhull.HalfspaceIntersection, halfspaces, feasible_point) + + feasible_point = np.array([-0.5, -0.5]) + #Feasible point is outside feasible region + assert_raises(qhull.QhullError, + qhull.HalfspaceIntersection, halfspaces, feasible_point) + + def test_incremental(self): + #Cube + halfspaces = np.array([[0., 0., -1., -0.5], + [0., -1., 0., -0.5], + [-1., 0., 0., -0.5], + [1., 0., 0., -0.5], + [0., 1., 0., -0.5], + [0., 0., 1., -0.5]]) + #Cut each summit + extra_normals = np.array([[1., 1., 1.], + [1., 1., -1.], + [1., -1., 1.], + [1, -1., -1.]]) + offsets = np.array([[-1.]]*8) + extra_halfspaces = np.hstack((np.vstack((extra_normals, -extra_normals)), + offsets)) + + feas_point = np.array([0., 0., 0.]) + + inc_hs = qhull.HalfspaceIntersection(halfspaces, feas_point, incremental=True) + + inc_res_hs = qhull.HalfspaceIntersection(halfspaces, feas_point, + incremental=True) + + for i, ehs in enumerate(extra_halfspaces): + inc_hs.add_halfspaces(ehs[np.newaxis, :]) + + inc_res_hs.add_halfspaces(ehs[np.newaxis, :], restart=True) + + total = np.vstack((halfspaces, extra_halfspaces[:i+1, :])) + + hs = qhull.HalfspaceIntersection(total, feas_point) + + assert_allclose(inc_hs.halfspaces, inc_res_hs.halfspaces) + assert_allclose(inc_hs.halfspaces, hs.halfspaces) + + #Direct computation and restart should have points in same order + assert_allclose(hs.intersections, inc_res_hs.intersections) + #Incremental will have points in different order than direct computation + self.assert_unordered_allclose(inc_hs.intersections, hs.intersections) + + inc_hs.close() + + def test_cube(self): + # Halfspaces of the cube: + halfspaces = np.array([[-1., 0., 0., 0.], # x >= 0 + [1., 0., 0., -1.], # x <= 1 + [0., -1., 0., 0.], # y >= 0 + [0., 1., 0., -1.], # y <= 1 + [0., 0., -1., 0.], # z >= 0 + [0., 0., 1., -1.]]) # z <= 1 + point = np.array([0.5, 0.5, 0.5]) + + hs = qhull.HalfspaceIntersection(halfspaces, point) + + # qhalf H0.5,0.5,0.5 o < input.txt + qhalf_points = np.array([ + [-2, 0, 0], + [2, 0, 0], + [0, -2, 0], + [0, 2, 0], + [0, 0, -2], + [0, 0, 2]]) + qhalf_facets = [ + [2, 4, 0], + [4, 2, 1], + [5, 2, 0], + [2, 5, 1], + [3, 4, 1], + [4, 3, 0], + [5, 3, 1], + [3, 5, 0]] + + assert len(qhalf_facets) == len(hs.dual_facets) + for a, b in zip(qhalf_facets, hs.dual_facets): + assert set(a) == set(b) # facet orientation can differ + + assert_allclose(hs.dual_points, qhalf_points) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_slerp.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_slerp.py new file mode 100644 index 0000000000000000000000000000000000000000..4754d5254fa6df6de7ce4cc464bba5be150862b2 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_slerp.py @@ -0,0 +1,416 @@ +import numpy as np +from numpy.testing import assert_allclose + +import pytest +from scipy.spatial import geometric_slerp + + +def _generate_spherical_points(ndim=3, n_pts=2): + # generate uniform points on sphere + # see: https://stackoverflow.com/a/23785326 + # tentatively extended to arbitrary dims + # for 0-sphere it will always produce antipodes + np.random.seed(123) + points = np.random.normal(size=(n_pts, ndim)) + points /= np.linalg.norm(points, axis=1)[:, np.newaxis] + return points[0], points[1] + + +class TestGeometricSlerp: + # Test various properties of the geometric slerp code + + @pytest.mark.parametrize("n_dims", [2, 3, 5, 7, 9]) + @pytest.mark.parametrize("n_pts", [0, 3, 17]) + def test_shape_property(self, n_dims, n_pts): + # geometric_slerp output shape should match + # input dimensionality & requested number + # of interpolation points + start, end = _generate_spherical_points(n_dims, 2) + + actual = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, n_pts)) + + assert actual.shape == (n_pts, n_dims) + + @pytest.mark.parametrize("n_dims", [2, 3, 5, 7, 9]) + @pytest.mark.parametrize("n_pts", [3, 17]) + def test_include_ends(self, n_dims, n_pts): + # geometric_slerp should return a data structure + # that includes the start and end coordinates + # when t includes 0 and 1 ends + # this is convenient for plotting surfaces represented + # by interpolations for example + + # the generator doesn't work so well for the unit + # sphere (it always produces antipodes), so use + # custom values there + start, end = _generate_spherical_points(n_dims, 2) + + actual = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, n_pts)) + + assert_allclose(actual[0], start) + assert_allclose(actual[-1], end) + + @pytest.mark.parametrize("start, end", [ + # both arrays are not flat + (np.zeros((1, 3)), np.ones((1, 3))), + # only start array is not flat + (np.zeros((1, 3)), np.ones(3)), + # only end array is not flat + (np.zeros(1), np.ones((3, 1))), + ]) + def test_input_shape_flat(self, start, end): + # geometric_slerp should handle input arrays that are + # not flat appropriately + with pytest.raises(ValueError, match='one-dimensional'): + geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 10)) + + @pytest.mark.parametrize("start, end", [ + # 7-D and 3-D ends + (np.zeros(7), np.ones(3)), + # 2-D and 1-D ends + (np.zeros(2), np.ones(1)), + # empty, "3D" will also get caught this way + (np.array([]), np.ones(3)), + ]) + def test_input_dim_mismatch(self, start, end): + # geometric_slerp must appropriately handle cases where + # an interpolation is attempted across two different + # dimensionalities + with pytest.raises(ValueError, match='dimensions'): + geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 10)) + + @pytest.mark.parametrize("start, end", [ + # both empty + (np.array([]), np.array([])), + ]) + def test_input_at_least1d(self, start, end): + # empty inputs to geometric_slerp must + # be handled appropriately when not detected + # by mismatch + with pytest.raises(ValueError, match='at least two-dim'): + geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 10)) + + @pytest.mark.parametrize("start, end, expected", [ + # North and South Poles are definitely antipodes + # but should be handled gracefully now + (np.array([0, 0, 1.0]), np.array([0, 0, -1.0]), "warning"), + # this case will issue a warning & be handled + # gracefully as well; + # North Pole was rotated very slightly + # using r = R.from_euler('x', 0.035, degrees=True) + # to achieve Euclidean distance offset from diameter by + # 9.328908379124812e-08, within the default tol + (np.array([0.00000000e+00, + -6.10865200e-04, + 9.99999813e-01]), np.array([0, 0, -1.0]), "warning"), + # this case should succeed without warning because a + # sufficiently large + # rotation was applied to North Pole point to shift it + # to a Euclidean distance of 2.3036691931821451e-07 + # from South Pole, which is larger than tol + (np.array([0.00000000e+00, + -9.59930941e-04, + 9.99999539e-01]), np.array([0, 0, -1.0]), "success"), + ]) + def test_handle_antipodes(self, start, end, expected): + # antipodal points must be handled appropriately; + # there are an infinite number of possible geodesic + # interpolations between them in higher dims + if expected == "warning": + with pytest.warns(UserWarning, match='antipodes'): + res = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 10)) + else: + res = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 10)) + + # antipodes or near-antipodes should still produce + # slerp paths on the surface of the sphere (but they + # may be ambiguous): + assert_allclose(np.linalg.norm(res, axis=1), 1.0) + + @pytest.mark.parametrize("start, end, expected", [ + # 2-D with n_pts=4 (two new interpolation points) + # this is an actual circle + (np.array([1, 0]), + np.array([0, 1]), + np.array([[1, 0], + [np.sqrt(3) / 2, 0.5], # 30 deg on unit circle + [0.5, np.sqrt(3) / 2], # 60 deg on unit circle + [0, 1]])), + # likewise for 3-D (add z = 0 plane) + # this is an ordinary sphere + (np.array([1, 0, 0]), + np.array([0, 1, 0]), + np.array([[1, 0, 0], + [np.sqrt(3) / 2, 0.5, 0], + [0.5, np.sqrt(3) / 2, 0], + [0, 1, 0]])), + # for 5-D, pad more columns with constants + # zeros are easiest--non-zero values on unit + # circle are more difficult to reason about + # at higher dims + (np.array([1, 0, 0, 0, 0]), + np.array([0, 1, 0, 0, 0]), + np.array([[1, 0, 0, 0, 0], + [np.sqrt(3) / 2, 0.5, 0, 0, 0], + [0.5, np.sqrt(3) / 2, 0, 0, 0], + [0, 1, 0, 0, 0]])), + + ]) + def test_straightforward_examples(self, start, end, expected): + # some straightforward interpolation tests, sufficiently + # simple to use the unit circle to deduce expected values; + # for larger dimensions, pad with constants so that the + # data is N-D but simpler to reason about + actual = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 4)) + assert_allclose(actual, expected, atol=1e-16) + + @pytest.mark.parametrize("t", [ + # both interval ends clearly violate limits + np.linspace(-20, 20, 300), + # only one interval end violating limit slightly + np.linspace(-0.0001, 0.0001, 17), + ]) + def test_t_values_limits(self, t): + # geometric_slerp() should appropriately handle + # interpolation parameters < 0 and > 1 + with pytest.raises(ValueError, match='interpolation parameter'): + _ = geometric_slerp(start=np.array([1, 0]), + end=np.array([0, 1]), + t=t) + + @pytest.mark.parametrize("start, end", [ + (np.array([1]), + np.array([0])), + (np.array([0]), + np.array([1])), + (np.array([-17.7]), + np.array([165.9])), + ]) + def test_0_sphere_handling(self, start, end): + # it does not make sense to interpolate the set of + # two points that is the 0-sphere + with pytest.raises(ValueError, match='at least two-dim'): + _ = geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 4)) + + @pytest.mark.parametrize("tol", [ + # an integer currently raises + 5, + # string raises + "7", + # list and arrays also raise + [5, 6, 7], np.array(9.0), + ]) + def test_tol_type(self, tol): + # geometric_slerp() should raise if tol is not + # a suitable float type + with pytest.raises(ValueError, match='must be a float'): + _ = geometric_slerp(start=np.array([1, 0]), + end=np.array([0, 1]), + t=np.linspace(0, 1, 5), + tol=tol) + + @pytest.mark.parametrize("tol", [ + -5e-6, + -7e-10, + ]) + def test_tol_sign(self, tol): + # geometric_slerp() currently handles negative + # tol values, as long as they are floats + _ = geometric_slerp(start=np.array([1, 0]), + end=np.array([0, 1]), + t=np.linspace(0, 1, 5), + tol=tol) + + @pytest.mark.parametrize("start, end", [ + # 1-sphere (circle) with one point at origin + # and the other on the circle + (np.array([1, 0]), np.array([0, 0])), + # 2-sphere (normal sphere) with both points + # just slightly off sphere by the same amount + # in different directions + (np.array([1 + 1e-6, 0, 0]), + np.array([0, 1 - 1e-6, 0])), + # same thing in 4-D + (np.array([1 + 1e-6, 0, 0, 0]), + np.array([0, 1 - 1e-6, 0, 0])), + ]) + def test_unit_sphere_enforcement(self, start, end): + # geometric_slerp() should raise on input that clearly + # cannot be on an n-sphere of radius 1 + with pytest.raises(ValueError, match='unit n-sphere'): + geometric_slerp(start=start, + end=end, + t=np.linspace(0, 1, 5)) + + @pytest.mark.parametrize("start, end", [ + # 1-sphere 45 degree case + (np.array([1, 0]), + np.array([np.sqrt(2) / 2., + np.sqrt(2) / 2.])), + # 2-sphere 135 degree case + (np.array([1, 0]), + np.array([-np.sqrt(2) / 2., + np.sqrt(2) / 2.])), + ]) + @pytest.mark.parametrize("t_func", [ + np.linspace, np.logspace]) + def test_order_handling(self, start, end, t_func): + # geometric_slerp() should handle scenarios with + # ascending and descending t value arrays gracefully; + # results should simply be reversed + + # for scrambled / unsorted parameters, the same values + # should be returned, just in scrambled order + + num_t_vals = 20 + np.random.seed(789) + forward_t_vals = t_func(0, 10, num_t_vals) + # normalize to max of 1 + forward_t_vals /= forward_t_vals.max() + reverse_t_vals = np.flipud(forward_t_vals) + shuffled_indices = np.arange(num_t_vals) + np.random.shuffle(shuffled_indices) + scramble_t_vals = forward_t_vals.copy()[shuffled_indices] + + forward_results = geometric_slerp(start=start, + end=end, + t=forward_t_vals) + reverse_results = geometric_slerp(start=start, + end=end, + t=reverse_t_vals) + scrambled_results = geometric_slerp(start=start, + end=end, + t=scramble_t_vals) + + # check fidelity to input order + assert_allclose(forward_results, np.flipud(reverse_results)) + assert_allclose(forward_results[shuffled_indices], + scrambled_results) + + @pytest.mark.parametrize("t", [ + # string: + "15, 5, 7", + # complex numbers currently produce a warning + # but not sure we need to worry about it too much: + # [3 + 1j, 5 + 2j], + ]) + def test_t_values_conversion(self, t): + with pytest.raises(ValueError): + _ = geometric_slerp(start=np.array([1]), + end=np.array([0]), + t=t) + + def test_accept_arraylike(self): + # array-like support requested by reviewer + # in gh-10380 + actual = geometric_slerp([1, 0], [0, 1], [0, 1/3, 0.5, 2/3, 1]) + + # expected values are based on visual inspection + # of the unit circle for the progressions along + # the circumference provided in t + expected = np.array([[1, 0], + [np.sqrt(3) / 2, 0.5], + [np.sqrt(2) / 2, + np.sqrt(2) / 2], + [0.5, np.sqrt(3) / 2], + [0, 1]], dtype=np.float64) + # Tyler's original Cython implementation of geometric_slerp + # can pass at atol=0 here, but on balance we will accept + # 1e-16 for an implementation that avoids Cython and + # makes up accuracy ground elsewhere + assert_allclose(actual, expected, atol=1e-16) + + def test_scalar_t(self): + # when t is a scalar, return value is a single + # interpolated point of the appropriate dimensionality + # requested by reviewer in gh-10380 + actual = geometric_slerp([1, 0], [0, 1], 0.5) + expected = np.array([np.sqrt(2) / 2, + np.sqrt(2) / 2], dtype=np.float64) + assert actual.shape == (2,) + assert_allclose(actual, expected) + + @pytest.mark.parametrize('start', [ + np.array([1, 0, 0]), + np.array([0, 1]), + ]) + @pytest.mark.parametrize('t', [ + np.array(1), + np.array([1]), + np.array([[1]]), + np.array([[[1]]]), + np.array([]), + np.linspace(0, 1, 5), + ]) + def test_degenerate_input(self, start, t): + if np.asarray(t).ndim > 1: + with pytest.raises(ValueError): + geometric_slerp(start=start, end=start, t=t) + else: + + shape = (t.size,) + start.shape + expected = np.full(shape, start) + + actual = geometric_slerp(start=start, end=start, t=t) + assert_allclose(actual, expected) + + # Check that degenerate and non-degenerate + # inputs yield the same size + non_degenerate = geometric_slerp(start=start, end=start[::-1], t=t) + assert actual.size == non_degenerate.size + + @pytest.mark.parametrize('k', np.logspace(-10, -1, 10)) + def test_numerical_stability_pi(self, k): + # geometric_slerp should have excellent numerical + # stability for angles approaching pi between + # the start and end points + angle = np.pi - k + ts = np.linspace(0, 1, 100) + P = np.array([1, 0, 0, 0]) + Q = np.array([np.cos(angle), np.sin(angle), 0, 0]) + # the test should only be enforced for cases where + # geometric_slerp determines that the input is actually + # on the unit sphere + with np.testing.suppress_warnings() as sup: + sup.filter(UserWarning) + result = geometric_slerp(P, Q, ts, 1e-18) + norms = np.linalg.norm(result, axis=1) + error = np.max(np.abs(norms - 1)) + assert error < 4e-15 + + @pytest.mark.parametrize('t', [ + [[0, 0.5]], + [[[[[[[[[0, 0.5]]]]]]]]], + ]) + def test_interpolation_param_ndim(self, t): + # regression test for gh-14465 + arr1 = np.array([0, 1]) + arr2 = np.array([1, 0]) + + with pytest.raises(ValueError): + geometric_slerp(start=arr1, + end=arr2, + t=t) + + with pytest.raises(ValueError): + geometric_slerp(start=arr1, + end=arr1, + t=t) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_spherical_voronoi.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_spherical_voronoi.py new file mode 100644 index 0000000000000000000000000000000000000000..621a961ebb6e495701763af4ded10b431a63a992 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/tests/test_spherical_voronoi.py @@ -0,0 +1,358 @@ +import numpy as np +import itertools +from numpy.testing import (assert_equal, + assert_almost_equal, + assert_array_equal, + assert_array_almost_equal) +import pytest +from pytest import raises as assert_raises +from scipy.spatial import SphericalVoronoi, distance +from scipy.optimize import linear_sum_assignment +from scipy.constants import golden as phi +from scipy.special import gamma + + +TOL = 1E-10 + + +def _generate_tetrahedron(): + return np.array([[1, 1, 1], [1, -1, -1], [-1, 1, -1], [-1, -1, 1]]) + + +def _generate_cube(): + return np.array(list(itertools.product([-1, 1.], repeat=3))) + + +def _generate_octahedron(): + return np.array([[-1, 0, 0], [+1, 0, 0], [0, -1, 0], + [0, +1, 0], [0, 0, -1], [0, 0, +1]]) + + +def _generate_dodecahedron(): + + x1 = _generate_cube() + x2 = np.array([[0, -phi, -1 / phi], + [0, -phi, +1 / phi], + [0, +phi, -1 / phi], + [0, +phi, +1 / phi]]) + x3 = np.array([[-1 / phi, 0, -phi], + [+1 / phi, 0, -phi], + [-1 / phi, 0, +phi], + [+1 / phi, 0, +phi]]) + x4 = np.array([[-phi, -1 / phi, 0], + [-phi, +1 / phi, 0], + [+phi, -1 / phi, 0], + [+phi, +1 / phi, 0]]) + return np.concatenate((x1, x2, x3, x4)) + + +def _generate_icosahedron(): + x = np.array([[0, -1, -phi], + [0, -1, +phi], + [0, +1, -phi], + [0, +1, +phi]]) + return np.concatenate([np.roll(x, i, axis=1) for i in range(3)]) + + +def _generate_polytope(name): + polygons = ["triangle", "square", "pentagon", "hexagon", "heptagon", + "octagon", "nonagon", "decagon", "undecagon", "dodecagon"] + polyhedra = ["tetrahedron", "cube", "octahedron", "dodecahedron", + "icosahedron"] + if name not in polygons and name not in polyhedra: + raise ValueError("unrecognized polytope") + + if name in polygons: + n = polygons.index(name) + 3 + thetas = np.linspace(0, 2 * np.pi, n, endpoint=False) + p = np.vstack([np.cos(thetas), np.sin(thetas)]).T + elif name == "tetrahedron": + p = _generate_tetrahedron() + elif name == "cube": + p = _generate_cube() + elif name == "octahedron": + p = _generate_octahedron() + elif name == "dodecahedron": + p = _generate_dodecahedron() + elif name == "icosahedron": + p = _generate_icosahedron() + + return p / np.linalg.norm(p, axis=1, keepdims=True) + + +def _hypersphere_area(dim, radius): + # https://en.wikipedia.org/wiki/N-sphere#Closed_forms + return 2 * np.pi**(dim / 2) / gamma(dim / 2) * radius**(dim - 1) + + +def _sample_sphere(n, dim, seed=None): + # Sample points uniformly at random from the hypersphere + rng = np.random.RandomState(seed=seed) + points = rng.randn(n, dim) + points /= np.linalg.norm(points, axis=1, keepdims=True) + return points + + +class TestSphericalVoronoi: + + def setup_method(self): + self.points = np.array([ + [-0.78928481, -0.16341094, 0.59188373], + [-0.66839141, 0.73309634, 0.12578818], + [0.32535778, -0.92476944, -0.19734181], + [-0.90177102, -0.03785291, -0.43055335], + [0.71781344, 0.68428936, 0.12842096], + [-0.96064876, 0.23492353, -0.14820556], + [0.73181537, -0.22025898, -0.6449281], + [0.79979205, 0.54555747, 0.25039913]] + ) + + def test_constructor(self): + center = np.array([1, 2, 3]) + radius = 2 + s1 = SphericalVoronoi(self.points) + # user input checks in SphericalVoronoi now require + # the radius / center to match the generators so adjust + # accordingly here + s2 = SphericalVoronoi(self.points * radius, radius) + s3 = SphericalVoronoi(self.points + center, center=center) + s4 = SphericalVoronoi(self.points * radius + center, radius, center) + assert_array_equal(s1.center, np.array([0, 0, 0])) + assert_equal(s1.radius, 1) + assert_array_equal(s2.center, np.array([0, 0, 0])) + assert_equal(s2.radius, 2) + assert_array_equal(s3.center, center) + assert_equal(s3.radius, 1) + assert_array_equal(s4.center, center) + assert_equal(s4.radius, radius) + + # Test a non-sequence/-ndarray based array-like + s5 = SphericalVoronoi(memoryview(self.points)) # type: ignore[arg-type] + assert_array_equal(s5.center, np.array([0, 0, 0])) + assert_equal(s5.radius, 1) + + def test_vertices_regions_translation_invariance(self): + sv_origin = SphericalVoronoi(self.points) + center = np.array([1, 1, 1]) + sv_translated = SphericalVoronoi(self.points + center, center=center) + assert_equal(sv_origin.regions, sv_translated.regions) + assert_array_almost_equal(sv_origin.vertices + center, + sv_translated.vertices) + + def test_vertices_regions_scaling_invariance(self): + sv_unit = SphericalVoronoi(self.points) + sv_scaled = SphericalVoronoi(self.points * 2, 2) + assert_equal(sv_unit.regions, sv_scaled.regions) + assert_array_almost_equal(sv_unit.vertices * 2, + sv_scaled.vertices) + + def test_old_radius_api_error(self): + with pytest.raises(ValueError, match='`radius` is `None`. *'): + SphericalVoronoi(self.points, radius=None) + + def test_sort_vertices_of_regions(self): + sv = SphericalVoronoi(self.points) + unsorted_regions = sv.regions + sv.sort_vertices_of_regions() + assert_equal(sorted(sv.regions), sorted(unsorted_regions)) + + def test_sort_vertices_of_regions_flattened(self): + expected = sorted([[0, 6, 5, 2, 3], [2, 3, 10, 11, 8, 7], [0, 6, 4, 1], + [4, 8, 7, 5, 6], [9, 11, 10], [2, 7, 5], + [1, 4, 8, 11, 9], [0, 3, 10, 9, 1]]) + expected = list(itertools.chain(*sorted(expected))) # type: ignore + sv = SphericalVoronoi(self.points) + sv.sort_vertices_of_regions() + actual = list(itertools.chain(*sorted(sv.regions))) + assert_array_equal(actual, expected) + + def test_sort_vertices_of_regions_dimensionality(self): + points = np.array([[1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, 1], + [0.5, 0.5, 0.5, 0.5]]) + with pytest.raises(TypeError, match="three-dimensional"): + sv = SphericalVoronoi(points) + sv.sort_vertices_of_regions() + + def test_num_vertices(self): + # for any n >= 3, a spherical Voronoi diagram has 2n - 4 + # vertices; this is a direct consequence of Euler's formula + # as explained by Dinis and Mamede (2010) Proceedings of the + # 2010 International Symposium on Voronoi Diagrams in Science + # and Engineering + sv = SphericalVoronoi(self.points) + expected = self.points.shape[0] * 2 - 4 + actual = sv.vertices.shape[0] + assert_equal(actual, expected) + + def test_voronoi_circles(self): + sv = SphericalVoronoi(self.points) + for vertex in sv.vertices: + distances = distance.cdist(sv.points, np.array([vertex])) + closest = np.array(sorted(distances)[0:3]) + assert_almost_equal(closest[0], closest[1], 7, str(vertex)) + assert_almost_equal(closest[0], closest[2], 7, str(vertex)) + + def test_duplicate_point_handling(self): + # an exception should be raised for degenerate generators + # related to Issue# 7046 + self.degenerate = np.concatenate((self.points, self.points)) + with assert_raises(ValueError): + SphericalVoronoi(self.degenerate) + + def test_incorrect_radius_handling(self): + # an exception should be raised if the radius provided + # cannot possibly match the input generators + with assert_raises(ValueError): + SphericalVoronoi(self.points, radius=0.98) + + def test_incorrect_center_handling(self): + # an exception should be raised if the center provided + # cannot possibly match the input generators + with assert_raises(ValueError): + SphericalVoronoi(self.points, center=[0.1, 0, 0]) + + @pytest.mark.parametrize("dim", range(2, 6)) + @pytest.mark.parametrize("shift", [False, True]) + def test_single_hemisphere_handling(self, dim, shift): + n = 10 + points = _sample_sphere(n, dim, seed=0) + points[:, 0] = np.abs(points[:, 0]) + center = (np.arange(dim) + 1) * shift + sv = SphericalVoronoi(points + center, center=center) + dots = np.einsum('ij,ij->i', sv.vertices - center, + sv.points[sv._simplices[:, 0]] - center) + circumradii = np.arccos(np.clip(dots, -1, 1)) + assert np.max(circumradii) > np.pi / 2 + + @pytest.mark.parametrize("n", [1, 2, 10]) + @pytest.mark.parametrize("dim", range(2, 6)) + @pytest.mark.parametrize("shift", [False, True]) + def test_rank_deficient(self, n, dim, shift): + center = (np.arange(dim) + 1) * shift + points = _sample_sphere(n, dim - 1, seed=0) + points = np.hstack([points, np.zeros((n, 1))]) + with pytest.raises(ValueError, match="Rank of input points"): + SphericalVoronoi(points + center, center=center) + + @pytest.mark.parametrize("dim", range(2, 6)) + def test_higher_dimensions(self, dim): + n = 100 + points = _sample_sphere(n, dim, seed=0) + sv = SphericalVoronoi(points) + assert sv.vertices.shape[1] == dim + assert len(sv.regions) == n + + # verify Euler characteristic + cell_counts = [] + simplices = np.sort(sv._simplices) + for i in range(1, dim + 1): + cells = [] + for indices in itertools.combinations(range(dim), i): + cells.append(simplices[:, list(indices)]) + cells = np.unique(np.concatenate(cells), axis=0) + cell_counts.append(len(cells)) + expected_euler = 1 + (-1)**(dim-1) + actual_euler = sum([(-1)**i * e for i, e in enumerate(cell_counts)]) + assert expected_euler == actual_euler + + @pytest.mark.parametrize("dim", range(2, 6)) + def test_cross_polytope_regions(self, dim): + # The hypercube is the dual of the cross-polytope, so the voronoi + # vertices of the cross-polytope lie on the points of the hypercube. + + # generate points of the cross-polytope + points = np.concatenate((-np.eye(dim), np.eye(dim))) + sv = SphericalVoronoi(points) + assert all([len(e) == 2**(dim - 1) for e in sv.regions]) + + # generate points of the hypercube + expected = np.vstack(list(itertools.product([-1, 1], repeat=dim))) + expected = expected.astype(np.float64) / np.sqrt(dim) + + # test that Voronoi vertices are correctly placed + dist = distance.cdist(sv.vertices, expected) + res = linear_sum_assignment(dist) + assert dist[res].sum() < TOL + + @pytest.mark.parametrize("dim", range(2, 6)) + def test_hypercube_regions(self, dim): + # The cross-polytope is the dual of the hypercube, so the voronoi + # vertices of the hypercube lie on the points of the cross-polytope. + + # generate points of the hypercube + points = np.vstack(list(itertools.product([-1, 1], repeat=dim))) + points = points.astype(np.float64) / np.sqrt(dim) + sv = SphericalVoronoi(points) + + # generate points of the cross-polytope + expected = np.concatenate((-np.eye(dim), np.eye(dim))) + + # test that Voronoi vertices are correctly placed + dist = distance.cdist(sv.vertices, expected) + res = linear_sum_assignment(dist) + assert dist[res].sum() < TOL + + @pytest.mark.parametrize("n", [10, 500]) + @pytest.mark.parametrize("dim", [2, 3]) + @pytest.mark.parametrize("radius", [0.5, 1, 2]) + @pytest.mark.parametrize("shift", [False, True]) + @pytest.mark.parametrize("single_hemisphere", [False, True]) + def test_area_reconstitution(self, n, dim, radius, shift, + single_hemisphere): + points = _sample_sphere(n, dim, seed=0) + + # move all points to one side of the sphere for single-hemisphere test + if single_hemisphere: + points[:, 0] = np.abs(points[:, 0]) + + center = (np.arange(dim) + 1) * shift + points = radius * points + center + + sv = SphericalVoronoi(points, radius=radius, center=center) + areas = sv.calculate_areas() + assert_almost_equal(areas.sum(), _hypersphere_area(dim, radius)) + + @pytest.mark.parametrize("poly", ["triangle", "dodecagon", + "tetrahedron", "cube", "octahedron", + "dodecahedron", "icosahedron"]) + def test_equal_area_reconstitution(self, poly): + points = _generate_polytope(poly) + n, dim = points.shape + sv = SphericalVoronoi(points) + areas = sv.calculate_areas() + assert_almost_equal(areas, _hypersphere_area(dim, 1) / n) + + def test_area_unsupported_dimension(self): + dim = 4 + points = np.concatenate((-np.eye(dim), np.eye(dim))) + sv = SphericalVoronoi(points) + with pytest.raises(TypeError, match="Only supported"): + sv.calculate_areas() + + @pytest.mark.parametrize("radius", [1, 1.]) + @pytest.mark.parametrize("center", [None, (1, 2, 3), (1., 2., 3.)]) + def test_attribute_types(self, radius, center): + points = radius * self.points + if center is not None: + points += center + + sv = SphericalVoronoi(points, radius=radius, center=center) + assert sv.points.dtype is np.dtype(np.float64) + assert sv.center.dtype is np.dtype(np.float64) + assert isinstance(sv.radius, float) + + def test_region_types(self): + # Tests that region integer type does not change + # See Issue #13412 + sv = SphericalVoronoi(self.points) + dtype = type(sv.regions[0][0]) + # also enforce nested list type per gh-19177 + for region in sv.regions: + assert isinstance(region, list) + sv.sort_vertices_of_regions() + assert type(sv.regions[0][0]) == dtype + sv.sort_vertices_of_regions() + assert type(sv.regions[0][0]) == dtype diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.cpython-310-x86_64-linux-gnu.so b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.cpython-310-x86_64-linux-gnu.so new file mode 100644 index 0000000000000000000000000000000000000000..c610538cdfc644601f5113c98df8beb3345c49a6 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.cpython-310-x86_64-linux-gnu.so differ diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.pyi b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.pyi new file mode 100644 index 0000000000000000000000000000000000000000..e7665001535e2fd44c14fc2b0488e0e2eee3b542 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation.pyi @@ -0,0 +1,65 @@ +from __future__ import annotations +from typing import TYPE_CHECKING +from collections.abc import Sequence +import numpy as np + +if TYPE_CHECKING: + import numpy.typing as npt + +_IntegerType = int | np.integer + + +class Rotation: + def __init__(self, quat: npt.ArrayLike, normalize: bool = ..., copy: bool = ...) -> None: ... + @property + def single(self) -> bool: ... + def __len__(self) -> int: ... + @classmethod + def from_quat(cls, quat: npt.ArrayLike) -> Rotation: ... + @classmethod + def from_matrix(cls, matrix: npt.ArrayLike) -> Rotation: ... + @classmethod + def from_rotvec(cls, rotvec: npt.ArrayLike, degrees: bool = ...) -> Rotation: ... + @classmethod + def from_euler(cls, seq: str, angles: float | npt.ArrayLike, degrees: bool = ...) -> Rotation: ... + @classmethod + def from_davenport(cls, axes: npt.ArrayLike, order: str, angles: float | npt.ArrayLike, degrees: bool = ...) -> Rotation: ... + @classmethod + def from_mrp(cls, mrp: npt.ArrayLike) -> Rotation: ... + def as_quat(self, canonical: bool) -> np.ndarray: ... + def as_matrix(self) -> np.ndarray: ... + def as_rotvec(self, degrees: bool = ...) -> np.ndarray: ... + def as_euler(self, seq: str, degrees: bool = ...) -> np.ndarray: ... + def as_davenport(self, axes: npt.ArrayLike, order: str, degrees: bool = ...) -> np.ndarray: ... + def as_mrp(self) -> np.ndarray: ... + @classmethod + def concatenate(cls, rotations: Sequence[Rotation]) -> Rotation: ... + def apply(self, vectors: npt.ArrayLike, inverse: bool = ...) -> np.ndarray: ... + def __mul__(self, other: Rotation) -> Rotation: ... + def __pow__(self, n: float, modulus: int | None) -> Rotation: ... + def inv(self) -> Rotation: ... + def magnitude(self) -> np.ndarray | float: ... + def approx_equal(self, other: Rotation, atol: float | None, degrees: bool = ...) -> np.ndarray | bool: ... + def mean(self, weights: npt.ArrayLike | None = ...) -> Rotation: ... + def reduce(self, left: Rotation | None = ..., right: Rotation | None = ..., + return_indices: bool = ...) -> Rotation | tuple[Rotation, np.ndarray, np.ndarray]: ... + @classmethod + def create_group(cls, group: str, axis: str = ...) -> Rotation: ... + def __getitem__(self, indexer: int | slice | npt.ArrayLike) -> Rotation: ... + @classmethod + def identity(cls, num: int | None = ...) -> Rotation: ... + @classmethod + def random(cls, num: int | None = ..., + random_state: _IntegerType | np.random.Generator | np.random.RandomState | None = ...) -> Rotation: ... + @classmethod + def align_vectors(cls, a: npt.ArrayLike, b: npt.ArrayLike, + weights: npt.ArrayLike | None = ..., + return_sensitivity: bool = ...) -> tuple[Rotation, float] | tuple[Rotation, float, np.ndarray]:... + +class Slerp: + times: np.ndarray + timedelta: np.ndarray + rotations: Rotation + rotvecs: np.ndarray + def __init__(self, times: npt.ArrayLike, rotations: Rotation) -> None: ... + def __call__(self, times: npt.ArrayLike) -> Rotation: ... diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation_spline.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation_spline.py new file mode 100644 index 0000000000000000000000000000000000000000..1c07129721e3652d018ffc3be485e6ed785f5564 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/_rotation_spline.py @@ -0,0 +1,460 @@ +import numpy as np +from scipy.linalg import solve_banded +from ._rotation import Rotation + + +def _create_skew_matrix(x): + """Create skew-symmetric matrices corresponding to vectors. + + Parameters + ---------- + x : ndarray, shape (n, 3) + Set of vectors. + + Returns + ------- + ndarray, shape (n, 3, 3) + """ + result = np.zeros((len(x), 3, 3)) + result[:, 0, 1] = -x[:, 2] + result[:, 0, 2] = x[:, 1] + result[:, 1, 0] = x[:, 2] + result[:, 1, 2] = -x[:, 0] + result[:, 2, 0] = -x[:, 1] + result[:, 2, 1] = x[:, 0] + return result + + +def _matrix_vector_product_of_stacks(A, b): + """Compute the product of stack of matrices and vectors.""" + return np.einsum("ijk,ik->ij", A, b) + + +def _angular_rate_to_rotvec_dot_matrix(rotvecs): + """Compute matrices to transform angular rates to rot. vector derivatives. + + The matrices depend on the current attitude represented as a rotation + vector. + + Parameters + ---------- + rotvecs : ndarray, shape (n, 3) + Set of rotation vectors. + + Returns + ------- + ndarray, shape (n, 3, 3) + """ + norm = np.linalg.norm(rotvecs, axis=1) + k = np.empty_like(norm) + + mask = norm > 1e-4 + nm = norm[mask] + k[mask] = (1 - 0.5 * nm / np.tan(0.5 * nm)) / nm**2 + mask = ~mask + nm = norm[mask] + k[mask] = 1/12 + 1/720 * nm**2 + + skew = _create_skew_matrix(rotvecs) + + result = np.empty((len(rotvecs), 3, 3)) + result[:] = np.identity(3) + result[:] += 0.5 * skew + result[:] += k[:, None, None] * np.matmul(skew, skew) + + return result + + +def _rotvec_dot_to_angular_rate_matrix(rotvecs): + """Compute matrices to transform rot. vector derivatives to angular rates. + + The matrices depend on the current attitude represented as a rotation + vector. + + Parameters + ---------- + rotvecs : ndarray, shape (n, 3) + Set of rotation vectors. + + Returns + ------- + ndarray, shape (n, 3, 3) + """ + norm = np.linalg.norm(rotvecs, axis=1) + k1 = np.empty_like(norm) + k2 = np.empty_like(norm) + + mask = norm > 1e-4 + nm = norm[mask] + k1[mask] = (1 - np.cos(nm)) / nm ** 2 + k2[mask] = (nm - np.sin(nm)) / nm ** 3 + + mask = ~mask + nm = norm[mask] + k1[mask] = 0.5 - nm ** 2 / 24 + k2[mask] = 1 / 6 - nm ** 2 / 120 + + skew = _create_skew_matrix(rotvecs) + + result = np.empty((len(rotvecs), 3, 3)) + result[:] = np.identity(3) + result[:] -= k1[:, None, None] * skew + result[:] += k2[:, None, None] * np.matmul(skew, skew) + + return result + + +def _angular_acceleration_nonlinear_term(rotvecs, rotvecs_dot): + """Compute the non-linear term in angular acceleration. + + The angular acceleration contains a quadratic term with respect to + the derivative of the rotation vector. This function computes that. + + Parameters + ---------- + rotvecs : ndarray, shape (n, 3) + Set of rotation vectors. + rotvecs_dot : ndarray, shape (n, 3) + Set of rotation vector derivatives. + + Returns + ------- + ndarray, shape (n, 3) + """ + norm = np.linalg.norm(rotvecs, axis=1) + dp = np.sum(rotvecs * rotvecs_dot, axis=1) + cp = np.cross(rotvecs, rotvecs_dot) + ccp = np.cross(rotvecs, cp) + dccp = np.cross(rotvecs_dot, cp) + + k1 = np.empty_like(norm) + k2 = np.empty_like(norm) + k3 = np.empty_like(norm) + + mask = norm > 1e-4 + nm = norm[mask] + k1[mask] = (-nm * np.sin(nm) - 2 * (np.cos(nm) - 1)) / nm ** 4 + k2[mask] = (-2 * nm + 3 * np.sin(nm) - nm * np.cos(nm)) / nm ** 5 + k3[mask] = (nm - np.sin(nm)) / nm ** 3 + + mask = ~mask + nm = norm[mask] + k1[mask] = 1/12 - nm ** 2 / 180 + k2[mask] = -1/60 + nm ** 2 / 12604 + k3[mask] = 1/6 - nm ** 2 / 120 + + dp = dp[:, None] + k1 = k1[:, None] + k2 = k2[:, None] + k3 = k3[:, None] + + return dp * (k1 * cp + k2 * ccp) + k3 * dccp + + +def _compute_angular_rate(rotvecs, rotvecs_dot): + """Compute angular rates given rotation vectors and its derivatives. + + Parameters + ---------- + rotvecs : ndarray, shape (n, 3) + Set of rotation vectors. + rotvecs_dot : ndarray, shape (n, 3) + Set of rotation vector derivatives. + + Returns + ------- + ndarray, shape (n, 3) + """ + return _matrix_vector_product_of_stacks( + _rotvec_dot_to_angular_rate_matrix(rotvecs), rotvecs_dot) + + +def _compute_angular_acceleration(rotvecs, rotvecs_dot, rotvecs_dot_dot): + """Compute angular acceleration given rotation vector and its derivatives. + + Parameters + ---------- + rotvecs : ndarray, shape (n, 3) + Set of rotation vectors. + rotvecs_dot : ndarray, shape (n, 3) + Set of rotation vector derivatives. + rotvecs_dot_dot : ndarray, shape (n, 3) + Set of rotation vector second derivatives. + + Returns + ------- + ndarray, shape (n, 3) + """ + return (_compute_angular_rate(rotvecs, rotvecs_dot_dot) + + _angular_acceleration_nonlinear_term(rotvecs, rotvecs_dot)) + + +def _create_block_3_diagonal_matrix(A, B, d): + """Create a 3-diagonal block matrix as banded. + + The matrix has the following structure: + + DB... + ADB.. + .ADB. + ..ADB + ...AD + + The blocks A, B and D are 3-by-3 matrices. The D matrices has the form + d * I. + + Parameters + ---------- + A : ndarray, shape (n, 3, 3) + Stack of A blocks. + B : ndarray, shape (n, 3, 3) + Stack of B blocks. + d : ndarray, shape (n + 1,) + Values for diagonal blocks. + + Returns + ------- + ndarray, shape (11, 3 * (n + 1)) + Matrix in the banded form as used by `scipy.linalg.solve_banded`. + """ + ind = np.arange(3) + ind_blocks = np.arange(len(A)) + + A_i = np.empty_like(A, dtype=int) + A_i[:] = ind[:, None] + A_i += 3 * (1 + ind_blocks[:, None, None]) + + A_j = np.empty_like(A, dtype=int) + A_j[:] = ind + A_j += 3 * ind_blocks[:, None, None] + + B_i = np.empty_like(B, dtype=int) + B_i[:] = ind[:, None] + B_i += 3 * ind_blocks[:, None, None] + + B_j = np.empty_like(B, dtype=int) + B_j[:] = ind + B_j += 3 * (1 + ind_blocks[:, None, None]) + + diag_i = diag_j = np.arange(3 * len(d)) + i = np.hstack((A_i.ravel(), B_i.ravel(), diag_i)) + j = np.hstack((A_j.ravel(), B_j.ravel(), diag_j)) + values = np.hstack((A.ravel(), B.ravel(), np.repeat(d, 3))) + + u = 5 + l = 5 + result = np.zeros((u + l + 1, 3 * len(d))) + result[u + i - j, j] = values + return result + + +class RotationSpline: + """Interpolate rotations with continuous angular rate and acceleration. + + The rotation vectors between each consecutive orientation are cubic + functions of time and it is guaranteed that angular rate and acceleration + are continuous. Such interpolation are analogous to cubic spline + interpolation. + + Refer to [1]_ for math and implementation details. + + Parameters + ---------- + times : array_like, shape (N,) + Times of the known rotations. At least 2 times must be specified. + rotations : `Rotation` instance + Rotations to perform the interpolation between. Must contain N + rotations. + + Methods + ------- + __call__ + + References + ---------- + .. [1] `Smooth Attitude Interpolation + `_ + + Examples + -------- + >>> from scipy.spatial.transform import Rotation, RotationSpline + >>> import numpy as np + + Define the sequence of times and rotations from the Euler angles: + + >>> times = [0, 10, 20, 40] + >>> angles = [[-10, 20, 30], [0, 15, 40], [-30, 45, 30], [20, 45, 90]] + >>> rotations = Rotation.from_euler('XYZ', angles, degrees=True) + + Create the interpolator object: + + >>> spline = RotationSpline(times, rotations) + + Interpolate the Euler angles, angular rate and acceleration: + + >>> angular_rate = np.rad2deg(spline(times, 1)) + >>> angular_acceleration = np.rad2deg(spline(times, 2)) + >>> times_plot = np.linspace(times[0], times[-1], 100) + >>> angles_plot = spline(times_plot).as_euler('XYZ', degrees=True) + >>> angular_rate_plot = np.rad2deg(spline(times_plot, 1)) + >>> angular_acceleration_plot = np.rad2deg(spline(times_plot, 2)) + + On this plot you see that Euler angles are continuous and smooth: + + >>> import matplotlib.pyplot as plt + >>> plt.plot(times_plot, angles_plot) + >>> plt.plot(times, angles, 'x') + >>> plt.title("Euler angles") + >>> plt.show() + + The angular rate is also smooth: + + >>> plt.plot(times_plot, angular_rate_plot) + >>> plt.plot(times, angular_rate, 'x') + >>> plt.title("Angular rate") + >>> plt.show() + + The angular acceleration is continuous, but not smooth. Also note that + the angular acceleration is not a piecewise-linear function, because + it is different from the second derivative of the rotation vector (which + is a piecewise-linear function as in the cubic spline). + + >>> plt.plot(times_plot, angular_acceleration_plot) + >>> plt.plot(times, angular_acceleration, 'x') + >>> plt.title("Angular acceleration") + >>> plt.show() + """ + # Parameters for the solver for angular rate. + MAX_ITER = 10 + TOL = 1e-9 + + def _solve_for_angular_rates(self, dt, angular_rates, rotvecs): + angular_rate_first = angular_rates[0].copy() + + A = _angular_rate_to_rotvec_dot_matrix(rotvecs) + A_inv = _rotvec_dot_to_angular_rate_matrix(rotvecs) + M = _create_block_3_diagonal_matrix( + 2 * A_inv[1:-1] / dt[1:-1, None, None], + 2 * A[1:-1] / dt[1:-1, None, None], + 4 * (1 / dt[:-1] + 1 / dt[1:])) + + b0 = 6 * (rotvecs[:-1] * dt[:-1, None] ** -2 + + rotvecs[1:] * dt[1:, None] ** -2) + b0[0] -= 2 / dt[0] * A_inv[0].dot(angular_rate_first) + b0[-1] -= 2 / dt[-1] * A[-1].dot(angular_rates[-1]) + + for iteration in range(self.MAX_ITER): + rotvecs_dot = _matrix_vector_product_of_stacks(A, angular_rates) + delta_beta = _angular_acceleration_nonlinear_term( + rotvecs[:-1], rotvecs_dot[:-1]) + b = b0 - delta_beta + angular_rates_new = solve_banded((5, 5), M, b.ravel()) + angular_rates_new = angular_rates_new.reshape((-1, 3)) + + delta = np.abs(angular_rates_new - angular_rates[:-1]) + angular_rates[:-1] = angular_rates_new + if np.all(delta < self.TOL * (1 + np.abs(angular_rates_new))): + break + + rotvecs_dot = _matrix_vector_product_of_stacks(A, angular_rates) + angular_rates = np.vstack((angular_rate_first, angular_rates[:-1])) + + return angular_rates, rotvecs_dot + + def __init__(self, times, rotations): + from scipy.interpolate import PPoly + + if rotations.single: + raise ValueError("`rotations` must be a sequence of rotations.") + + if len(rotations) == 1: + raise ValueError("`rotations` must contain at least 2 rotations.") + + times = np.asarray(times, dtype=float) + if times.ndim != 1: + raise ValueError("`times` must be 1-dimensional.") + + if len(times) != len(rotations): + raise ValueError("Expected number of rotations to be equal to " + "number of timestamps given, got {} rotations " + "and {} timestamps." + .format(len(rotations), len(times))) + + dt = np.diff(times) + if np.any(dt <= 0): + raise ValueError("Values in `times` must be in a strictly " + "increasing order.") + + rotvecs = (rotations[:-1].inv() * rotations[1:]).as_rotvec() + angular_rates = rotvecs / dt[:, None] + + if len(rotations) == 2: + rotvecs_dot = angular_rates + else: + angular_rates, rotvecs_dot = self._solve_for_angular_rates( + dt, angular_rates, rotvecs) + + dt = dt[:, None] + coeff = np.empty((4, len(times) - 1, 3)) + coeff[0] = (-2 * rotvecs + dt * angular_rates + + dt * rotvecs_dot) / dt ** 3 + coeff[1] = (3 * rotvecs - 2 * dt * angular_rates + - dt * rotvecs_dot) / dt ** 2 + coeff[2] = angular_rates + coeff[3] = 0 + + self.times = times + self.rotations = rotations + self.interpolator = PPoly(coeff, times) + + def __call__(self, times, order=0): + """Compute interpolated values. + + Parameters + ---------- + times : float or array_like + Times of interest. + order : {0, 1, 2}, optional + Order of differentiation: + + * 0 (default) : return Rotation + * 1 : return the angular rate in rad/sec + * 2 : return the angular acceleration in rad/sec/sec + + Returns + ------- + Interpolated Rotation, angular rate or acceleration. + """ + if order not in [0, 1, 2]: + raise ValueError("`order` must be 0, 1 or 2.") + + times = np.asarray(times, dtype=float) + if times.ndim > 1: + raise ValueError("`times` must be at most 1-dimensional.") + + singe_time = times.ndim == 0 + times = np.atleast_1d(times) + + rotvecs = self.interpolator(times) + if order == 0: + index = np.searchsorted(self.times, times, side='right') + index -= 1 + index[index < 0] = 0 + n_segments = len(self.times) - 1 + index[index > n_segments - 1] = n_segments - 1 + result = self.rotations[index] * Rotation.from_rotvec(rotvecs) + elif order == 1: + rotvecs_dot = self.interpolator(times, 1) + result = _compute_angular_rate(rotvecs, rotvecs_dot) + elif order == 2: + rotvecs_dot = self.interpolator(times, 1) + rotvecs_dot_dot = self.interpolator(times, 2) + result = _compute_angular_acceleration(rotvecs, rotvecs_dot, + rotvecs_dot_dot) + else: + assert False + + if singe_time: + result = result[0] + + return result diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/rotation.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/rotation.py new file mode 100644 index 0000000000000000000000000000000000000000..8aee10d960cffe9ce8aa7581ca633c6aad1d17a8 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/rotation.py @@ -0,0 +1,24 @@ +# This file is not meant for public use and will be removed in SciPy v2.0.0. +# Use the `scipy.spatial` namespace for importing the functions +# included below. + +from scipy._lib.deprecation import _sub_module_deprecation + + +__all__ = [ # noqa: F822 + 'Rotation', + 'Slerp', + 'check_random_state', + 'create_group', + 're', +] + + +def __dir__(): + return __all__ + + +def __getattr__(name): + return _sub_module_deprecation(sub_package="spatial.transform", module="rotation", + private_modules=["_rotation"], all=__all__, + attribute=name) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/__init__.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/__pycache__/__init__.cpython-310.pyc b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 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0000000000000000000000000000000000000000..8a1176d4a2619c14dc8faa24115a2f0952c16180 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation.py @@ -0,0 +1,1880 @@ +import pytest + +import numpy as np +from numpy.testing import assert_equal, assert_array_almost_equal +from numpy.testing import assert_allclose +from scipy.spatial.transform import Rotation, Slerp +from scipy.stats import special_ortho_group +from itertools import permutations + +import pickle +import copy + +def basis_vec(axis): + if axis == 'x': + return [1, 0, 0] + elif axis == 'y': + return [0, 1, 0] + elif axis == 'z': + return [0, 0, 1] + +def test_generic_quat_matrix(): + x = np.array([[3, 4, 0, 0], [5, 12, 0, 0]]) + r = Rotation.from_quat(x) + expected_quat = x / np.array([[5], [13]]) + assert_array_almost_equal(r.as_quat(), expected_quat) + + +def test_from_single_1d_quaternion(): + x = np.array([3, 4, 0, 0]) + r = Rotation.from_quat(x) + expected_quat = x / 5 + assert_array_almost_equal(r.as_quat(), expected_quat) + + +def test_from_single_2d_quaternion(): + x = np.array([[3, 4, 0, 0]]) + r = Rotation.from_quat(x) + expected_quat = x / 5 + assert_array_almost_equal(r.as_quat(), expected_quat) + + +def test_from_square_quat_matrix(): + # Ensure proper norm array broadcasting + x = np.array([ + [3, 0, 0, 4], + [5, 0, 12, 0], + [0, 0, 0, 1], + [-1, -1, -1, 1], + [0, 0, 0, -1], # Check double cover + [-1, -1, -1, -1] # Check double cover + ]) + r = Rotation.from_quat(x) + expected_quat = x / np.array([[5], [13], [1], [2], [1], [2]]) + assert_array_almost_equal(r.as_quat(), expected_quat) + + +def test_quat_double_to_canonical_single_cover(): + x = np.array([ + [-1, 0, 0, 0], + [0, -1, 0, 0], + [0, 0, -1, 0], + [0, 0, 0, -1], + [-1, -1, -1, -1] + ]) + r = Rotation.from_quat(x) + expected_quat = np.abs(x) / np.linalg.norm(x, axis=1)[:, None] + assert_allclose(r.as_quat(canonical=True), expected_quat) + + +def test_quat_double_cover(): + # See the Rotation.from_quat() docstring for scope of the quaternion + # double cover property. + # Check from_quat and as_quat(canonical=False) + q = np.array([0, 0, 0, -1]) + r = Rotation.from_quat(q) + assert_equal(q, r.as_quat(canonical=False)) + + # Check composition and inverse + q = np.array([1, 0, 0, 1])/np.sqrt(2) # 90 deg rotation about x + r = Rotation.from_quat(q) + r3 = r*r*r + assert_allclose(r.as_quat(canonical=False)*np.sqrt(2), + [1, 0, 0, 1]) + assert_allclose(r.inv().as_quat(canonical=False)*np.sqrt(2), + [-1, 0, 0, 1]) + assert_allclose(r3.as_quat(canonical=False)*np.sqrt(2), + [1, 0, 0, -1]) + assert_allclose(r3.inv().as_quat(canonical=False)*np.sqrt(2), + [-1, 0, 0, -1]) + + # More sanity checks + assert_allclose((r*r.inv()).as_quat(canonical=False), + [0, 0, 0, 1], atol=2e-16) + assert_allclose((r3*r3.inv()).as_quat(canonical=False), + [0, 0, 0, 1], atol=2e-16) + assert_allclose((r*r3).as_quat(canonical=False), + [0, 0, 0, -1], atol=2e-16) + assert_allclose((r.inv()*r3.inv()).as_quat(canonical=False), + [0, 0, 0, -1], atol=2e-16) + + +def test_malformed_1d_from_quat(): + with pytest.raises(ValueError): + Rotation.from_quat(np.array([1, 2, 3])) + + +def test_malformed_2d_from_quat(): + with pytest.raises(ValueError): + Rotation.from_quat(np.array([ + [1, 2, 3, 4, 5], + [4, 5, 6, 7, 8] + ])) + + +def test_zero_norms_from_quat(): + x = np.array([ + [3, 4, 0, 0], + [0, 0, 0, 0], + [5, 0, 12, 0] + ]) + with pytest.raises(ValueError): + Rotation.from_quat(x) + + +def test_as_matrix_single_1d_quaternion(): + quat = [0, 0, 0, 1] + mat = Rotation.from_quat(quat).as_matrix() + # mat.shape == (3,3) due to 1d input + assert_array_almost_equal(mat, np.eye(3)) + + +def test_as_matrix_single_2d_quaternion(): + quat = [[0, 0, 1, 1]] + mat = Rotation.from_quat(quat).as_matrix() + assert_equal(mat.shape, (1, 3, 3)) + expected_mat = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + assert_array_almost_equal(mat[0], expected_mat) + + +def test_as_matrix_from_square_input(): + quats = [ + [0, 0, 1, 1], + [0, 1, 0, 1], + [0, 0, 0, 1], + [0, 0, 0, -1] + ] + mat = Rotation.from_quat(quats).as_matrix() + assert_equal(mat.shape, (4, 3, 3)) + + expected0 = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + assert_array_almost_equal(mat[0], expected0) + + expected1 = np.array([ + [0, 0, 1], + [0, 1, 0], + [-1, 0, 0] + ]) + assert_array_almost_equal(mat[1], expected1) + + assert_array_almost_equal(mat[2], np.eye(3)) + assert_array_almost_equal(mat[3], np.eye(3)) + + +def test_as_matrix_from_generic_input(): + quats = [ + [0, 0, 1, 1], + [0, 1, 0, 1], + [1, 2, 3, 4] + ] + mat = Rotation.from_quat(quats).as_matrix() + assert_equal(mat.shape, (3, 3, 3)) + + expected0 = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + assert_array_almost_equal(mat[0], expected0) + + expected1 = np.array([ + [0, 0, 1], + [0, 1, 0], + [-1, 0, 0] + ]) + assert_array_almost_equal(mat[1], expected1) + + expected2 = np.array([ + [0.4, -2, 2.2], + [2.8, 1, 0.4], + [-1, 2, 2] + ]) / 3 + assert_array_almost_equal(mat[2], expected2) + + +def test_from_single_2d_matrix(): + mat = [ + [0, 0, 1], + [1, 0, 0], + [0, 1, 0] + ] + expected_quat = [0.5, 0.5, 0.5, 0.5] + assert_array_almost_equal( + Rotation.from_matrix(mat).as_quat(), + expected_quat) + + +def test_from_single_3d_matrix(): + mat = np.array([ + [0, 0, 1], + [1, 0, 0], + [0, 1, 0] + ]).reshape((1, 3, 3)) + expected_quat = np.array([0.5, 0.5, 0.5, 0.5]).reshape((1, 4)) + assert_array_almost_equal( + Rotation.from_matrix(mat).as_quat(), + expected_quat) + + +def test_from_matrix_calculation(): + expected_quat = np.array([1, 1, 6, 1]) / np.sqrt(39) + mat = np.array([ + [-0.8974359, -0.2564103, 0.3589744], + [0.3589744, -0.8974359, 0.2564103], + [0.2564103, 0.3589744, 0.8974359] + ]) + assert_array_almost_equal( + Rotation.from_matrix(mat).as_quat(), + expected_quat) + assert_array_almost_equal( + Rotation.from_matrix(mat.reshape((1, 3, 3))).as_quat(), + expected_quat.reshape((1, 4))) + + +def test_matrix_calculation_pipeline(): + mat = special_ortho_group.rvs(3, size=10, random_state=0) + assert_array_almost_equal(Rotation.from_matrix(mat).as_matrix(), mat) + + +def test_from_matrix_ortho_output(): + rnd = np.random.RandomState(0) + mat = rnd.random_sample((100, 3, 3)) + ortho_mat = Rotation.from_matrix(mat).as_matrix() + + mult_result = np.einsum('...ij,...jk->...ik', ortho_mat, + ortho_mat.transpose((0, 2, 1))) + + eye3d = np.zeros((100, 3, 3)) + for i in range(3): + eye3d[:, i, i] = 1.0 + + assert_array_almost_equal(mult_result, eye3d) + + +def test_from_1d_single_rotvec(): + rotvec = [1, 0, 0] + expected_quat = np.array([0.4794255, 0, 0, 0.8775826]) + result = Rotation.from_rotvec(rotvec) + assert_array_almost_equal(result.as_quat(), expected_quat) + + +def test_from_2d_single_rotvec(): + rotvec = [[1, 0, 0]] + expected_quat = np.array([[0.4794255, 0, 0, 0.8775826]]) + result = Rotation.from_rotvec(rotvec) + assert_array_almost_equal(result.as_quat(), expected_quat) + + +def test_from_generic_rotvec(): + rotvec = [ + [1, 2, 2], + [1, -1, 0.5], + [0, 0, 0] + ] + expected_quat = np.array([ + [0.3324983, 0.6649967, 0.6649967, 0.0707372], + [0.4544258, -0.4544258, 0.2272129, 0.7316889], + [0, 0, 0, 1] + ]) + assert_array_almost_equal( + Rotation.from_rotvec(rotvec).as_quat(), + expected_quat) + + +def test_from_rotvec_small_angle(): + rotvec = np.array([ + [5e-4 / np.sqrt(3), -5e-4 / np.sqrt(3), 5e-4 / np.sqrt(3)], + [0.2, 0.3, 0.4], + [0, 0, 0] + ]) + + quat = Rotation.from_rotvec(rotvec).as_quat() + # cos(theta/2) ~~ 1 for small theta + assert_allclose(quat[0, 3], 1) + # sin(theta/2) / theta ~~ 0.5 for small theta + assert_allclose(quat[0, :3], rotvec[0] * 0.5) + + assert_allclose(quat[1, 3], 0.9639685) + assert_allclose( + quat[1, :3], + np.array([ + 0.09879603932153465, + 0.14819405898230198, + 0.19759207864306931 + ])) + + assert_equal(quat[2], np.array([0, 0, 0, 1])) + + +def test_degrees_from_rotvec(): + rotvec1 = [1.0 / np.cbrt(3), 1.0 / np.cbrt(3), 1.0 / np.cbrt(3)] + rot1 = Rotation.from_rotvec(rotvec1, degrees=True) + quat1 = rot1.as_quat() + + rotvec2 = np.deg2rad(rotvec1) + rot2 = Rotation.from_rotvec(rotvec2) + quat2 = rot2.as_quat() + + assert_allclose(quat1, quat2) + + +def test_malformed_1d_from_rotvec(): + with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'): + Rotation.from_rotvec([1, 2]) + + +def test_malformed_2d_from_rotvec(): + with pytest.raises(ValueError, match='Expected `rot_vec` to have shape'): + Rotation.from_rotvec([ + [1, 2, 3, 4], + [5, 6, 7, 8] + ]) + + +def test_as_generic_rotvec(): + quat = np.array([ + [1, 2, -1, 0.5], + [1, -1, 1, 0.0003], + [0, 0, 0, 1] + ]) + quat /= np.linalg.norm(quat, axis=1)[:, None] + + rotvec = Rotation.from_quat(quat).as_rotvec() + angle = np.linalg.norm(rotvec, axis=1) + + assert_allclose(quat[:, 3], np.cos(angle/2)) + assert_allclose(np.cross(rotvec, quat[:, :3]), np.zeros((3, 3))) + + +def test_as_rotvec_single_1d_input(): + quat = np.array([1, 2, -3, 2]) + expected_rotvec = np.array([0.5772381, 1.1544763, -1.7317144]) + + actual_rotvec = Rotation.from_quat(quat).as_rotvec() + + assert_equal(actual_rotvec.shape, (3,)) + assert_allclose(actual_rotvec, expected_rotvec) + + +def test_as_rotvec_single_2d_input(): + quat = np.array([[1, 2, -3, 2]]) + expected_rotvec = np.array([[0.5772381, 1.1544763, -1.7317144]]) + + actual_rotvec = Rotation.from_quat(quat).as_rotvec() + + assert_equal(actual_rotvec.shape, (1, 3)) + assert_allclose(actual_rotvec, expected_rotvec) + + +def test_as_rotvec_degrees(): + # x->y, y->z, z->x + mat = [[0, 0, 1], [1, 0, 0], [0, 1, 0]] + rot = Rotation.from_matrix(mat) + rotvec = rot.as_rotvec(degrees=True) + angle = np.linalg.norm(rotvec) + assert_allclose(angle, 120.0) + assert_allclose(rotvec[0], rotvec[1]) + assert_allclose(rotvec[1], rotvec[2]) + + +def test_rotvec_calc_pipeline(): + # Include small angles + rotvec = np.array([ + [0, 0, 0], + [1, -1, 2], + [-3e-4, 3.5e-4, 7.5e-5] + ]) + assert_allclose(Rotation.from_rotvec(rotvec).as_rotvec(), rotvec) + assert_allclose(Rotation.from_rotvec(rotvec, degrees=True).as_rotvec(degrees=True), + rotvec) + + +def test_from_1d_single_mrp(): + mrp = [0, 0, 1.0] + expected_quat = np.array([0, 0, 1, 0]) + result = Rotation.from_mrp(mrp) + assert_array_almost_equal(result.as_quat(), expected_quat) + + +def test_from_2d_single_mrp(): + mrp = [[0, 0, 1.0]] + expected_quat = np.array([[0, 0, 1, 0]]) + result = Rotation.from_mrp(mrp) + assert_array_almost_equal(result.as_quat(), expected_quat) + + +def test_from_generic_mrp(): + mrp = np.array([ + [1, 2, 2], + [1, -1, 0.5], + [0, 0, 0]]) + expected_quat = np.array([ + [0.2, 0.4, 0.4, -0.8], + [0.61538462, -0.61538462, 0.30769231, -0.38461538], + [0, 0, 0, 1]]) + assert_array_almost_equal(Rotation.from_mrp(mrp).as_quat(), expected_quat) + + +def test_malformed_1d_from_mrp(): + with pytest.raises(ValueError, match='Expected `mrp` to have shape'): + Rotation.from_mrp([1, 2]) + + +def test_malformed_2d_from_mrp(): + with pytest.raises(ValueError, match='Expected `mrp` to have shape'): + Rotation.from_mrp([ + [1, 2, 3, 4], + [5, 6, 7, 8] + ]) + + +def test_as_generic_mrp(): + quat = np.array([ + [1, 2, -1, 0.5], + [1, -1, 1, 0.0003], + [0, 0, 0, 1]]) + quat /= np.linalg.norm(quat, axis=1)[:, None] + + expected_mrp = np.array([ + [0.33333333, 0.66666667, -0.33333333], + [0.57725028, -0.57725028, 0.57725028], + [0, 0, 0]]) + assert_array_almost_equal(Rotation.from_quat(quat).as_mrp(), expected_mrp) + +def test_past_180_degree_rotation(): + # ensure that a > 180 degree rotation is returned as a <180 rotation in MRPs + # in this case 270 should be returned as -90 + expected_mrp = np.array([-np.tan(np.pi/2/4), 0.0, 0]) + assert_array_almost_equal( + Rotation.from_euler('xyz', [270, 0, 0], degrees=True).as_mrp(), + expected_mrp + ) + + +def test_as_mrp_single_1d_input(): + quat = np.array([1, 2, -3, 2]) + expected_mrp = np.array([0.16018862, 0.32037724, -0.48056586]) + + actual_mrp = Rotation.from_quat(quat).as_mrp() + + assert_equal(actual_mrp.shape, (3,)) + assert_allclose(actual_mrp, expected_mrp) + + +def test_as_mrp_single_2d_input(): + quat = np.array([[1, 2, -3, 2]]) + expected_mrp = np.array([[0.16018862, 0.32037724, -0.48056586]]) + + actual_mrp = Rotation.from_quat(quat).as_mrp() + + assert_equal(actual_mrp.shape, (1, 3)) + assert_allclose(actual_mrp, expected_mrp) + + +def test_mrp_calc_pipeline(): + actual_mrp = np.array([ + [0, 0, 0], + [1, -1, 2], + [0.41421356, 0, 0], + [0.1, 0.2, 0.1]]) + expected_mrp = np.array([ + [0, 0, 0], + [-0.16666667, 0.16666667, -0.33333333], + [0.41421356, 0, 0], + [0.1, 0.2, 0.1]]) + assert_allclose(Rotation.from_mrp(actual_mrp).as_mrp(), expected_mrp) + + +def test_from_euler_single_rotation(): + quat = Rotation.from_euler('z', 90, degrees=True).as_quat() + expected_quat = np.array([0, 0, 1, 1]) / np.sqrt(2) + assert_allclose(quat, expected_quat) + + +def test_single_intrinsic_extrinsic_rotation(): + extrinsic = Rotation.from_euler('z', 90, degrees=True).as_matrix() + intrinsic = Rotation.from_euler('Z', 90, degrees=True).as_matrix() + assert_allclose(extrinsic, intrinsic) + + +def test_from_euler_rotation_order(): + # Intrinsic rotation is same as extrinsic with order reversed + rnd = np.random.RandomState(0) + a = rnd.randint(low=0, high=180, size=(6, 3)) + b = a[:, ::-1] + x = Rotation.from_euler('xyz', a, degrees=True).as_quat() + y = Rotation.from_euler('ZYX', b, degrees=True).as_quat() + assert_allclose(x, y) + + +def test_from_euler_elementary_extrinsic_rotation(): + # Simple test to check if extrinsic rotations are implemented correctly + mat = Rotation.from_euler('zx', [90, 90], degrees=True).as_matrix() + expected_mat = np.array([ + [0, -1, 0], + [0, 0, -1], + [1, 0, 0] + ]) + assert_array_almost_equal(mat, expected_mat) + + +def test_from_euler_intrinsic_rotation_312(): + angles = [ + [30, 60, 45], + [30, 60, 30], + [45, 30, 60] + ] + mat = Rotation.from_euler('ZXY', angles, degrees=True).as_matrix() + + assert_array_almost_equal(mat[0], np.array([ + [0.3061862, -0.2500000, 0.9185587], + [0.8838835, 0.4330127, -0.1767767], + [-0.3535534, 0.8660254, 0.3535534] + ])) + + assert_array_almost_equal(mat[1], np.array([ + [0.5334936, -0.2500000, 0.8080127], + [0.8080127, 0.4330127, -0.3995191], + [-0.2500000, 0.8660254, 0.4330127] + ])) + + assert_array_almost_equal(mat[2], np.array([ + [0.0473672, -0.6123725, 0.7891491], + [0.6597396, 0.6123725, 0.4355958], + [-0.7500000, 0.5000000, 0.4330127] + ])) + + +def test_from_euler_intrinsic_rotation_313(): + angles = [ + [30, 60, 45], + [30, 60, 30], + [45, 30, 60] + ] + mat = Rotation.from_euler('ZXZ', angles, degrees=True).as_matrix() + + assert_array_almost_equal(mat[0], np.array([ + [0.43559574, -0.78914913, 0.4330127], + [0.65973961, -0.04736717, -0.750000], + [0.61237244, 0.61237244, 0.500000] + ])) + + assert_array_almost_equal(mat[1], np.array([ + [0.6250000, -0.64951905, 0.4330127], + [0.64951905, 0.1250000, -0.750000], + [0.4330127, 0.750000, 0.500000] + ])) + + assert_array_almost_equal(mat[2], np.array([ + [-0.1767767, -0.91855865, 0.35355339], + [0.88388348, -0.30618622, -0.35355339], + [0.4330127, 0.25000000, 0.8660254] + ])) + + +def test_from_euler_extrinsic_rotation_312(): + angles = [ + [30, 60, 45], + [30, 60, 30], + [45, 30, 60] + ] + mat = Rotation.from_euler('zxy', angles, degrees=True).as_matrix() + + assert_array_almost_equal(mat[0], np.array([ + [0.91855865, 0.1767767, 0.35355339], + [0.25000000, 0.4330127, -0.8660254], + [-0.30618622, 0.88388348, 0.35355339] + ])) + + assert_array_almost_equal(mat[1], np.array([ + [0.96650635, -0.0580127, 0.2500000], + [0.25000000, 0.4330127, -0.8660254], + [-0.0580127, 0.89951905, 0.4330127] + ])) + + assert_array_almost_equal(mat[2], np.array([ + [0.65973961, -0.04736717, 0.7500000], + [0.61237244, 0.61237244, -0.5000000], + [-0.43559574, 0.78914913, 0.4330127] + ])) + + +def test_from_euler_extrinsic_rotation_313(): + angles = [ + [30, 60, 45], + [30, 60, 30], + [45, 30, 60] + ] + mat = Rotation.from_euler('zxz', angles, degrees=True).as_matrix() + + assert_array_almost_equal(mat[0], np.array([ + [0.43559574, -0.65973961, 0.61237244], + [0.78914913, -0.04736717, -0.61237244], + [0.4330127, 0.75000000, 0.500000] + ])) + + assert_array_almost_equal(mat[1], np.array([ + [0.62500000, -0.64951905, 0.4330127], + [0.64951905, 0.12500000, -0.750000], + [0.4330127, 0.75000000, 0.500000] + ])) + + assert_array_almost_equal(mat[2], np.array([ + [-0.1767767, -0.88388348, 0.4330127], + [0.91855865, -0.30618622, -0.250000], + [0.35355339, 0.35355339, 0.8660254] + ])) + + +@pytest.mark.parametrize("seq_tuple", permutations("xyz")) +@pytest.mark.parametrize("intrinsic", (False, True)) +def test_as_euler_asymmetric_axes(seq_tuple, intrinsic): + # helper function for mean error tests + def test_stats(error, mean_max, rms_max): + mean = np.mean(error, axis=0) + std = np.std(error, axis=0) + rms = np.hypot(mean, std) + assert np.all(np.abs(mean) < mean_max) + assert np.all(rms < rms_max) + + rnd = np.random.RandomState(0) + n = 1000 + angles = np.empty((n, 3)) + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles[:, 1] = rnd.uniform(low=-np.pi / 2, high=np.pi / 2, size=(n,)) + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + + seq = "".join(seq_tuple) + if intrinsic: + # Extrinsic rotation (wrt to global world) at lower case + # intrinsinc (WRT the object itself) lower case. + seq = seq.upper() + rotation = Rotation.from_euler(seq, angles) + angles_quat = rotation.as_euler(seq) + angles_mat = rotation._as_euler_from_matrix(seq) + assert_allclose(angles, angles_quat, atol=0, rtol=1e-12) + assert_allclose(angles, angles_mat, atol=0, rtol=1e-12) + test_stats(angles_quat - angles, 1e-15, 1e-14) + test_stats(angles_mat - angles, 1e-15, 1e-14) + + + +@pytest.mark.parametrize("seq_tuple", permutations("xyz")) +@pytest.mark.parametrize("intrinsic", (False, True)) +def test_as_euler_symmetric_axes(seq_tuple, intrinsic): + # helper function for mean error tests + def test_stats(error, mean_max, rms_max): + mean = np.mean(error, axis=0) + std = np.std(error, axis=0) + rms = np.hypot(mean, std) + assert np.all(np.abs(mean) < mean_max) + assert np.all(rms < rms_max) + + rnd = np.random.RandomState(0) + n = 1000 + angles = np.empty((n, 3)) + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,)) + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + + # Rotation of the form A/B/A are rotation around symmetric axes + seq = "".join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + if intrinsic: + seq = seq.upper() + rotation = Rotation.from_euler(seq, angles) + angles_quat = rotation.as_euler(seq) + angles_mat = rotation._as_euler_from_matrix(seq) + assert_allclose(angles, angles_quat, atol=0, rtol=1e-13) + assert_allclose(angles, angles_mat, atol=0, rtol=1e-9) + test_stats(angles_quat - angles, 1e-16, 1e-14) + test_stats(angles_mat - angles, 1e-15, 1e-13) + + +@pytest.mark.parametrize("seq_tuple", permutations("xyz")) +@pytest.mark.parametrize("intrinsic", (False, True)) +def test_as_euler_degenerate_asymmetric_axes(seq_tuple, intrinsic): + # Since we cannot check for angle equality, we check for rotation matrix + # equality + angles = np.array([ + [45, 90, 35], + [35, -90, 20], + [35, 90, 25], + [25, -90, 15]]) + + seq = "".join(seq_tuple) + if intrinsic: + # Extrinsic rotation (wrt to global world) at lower case + # Intrinsic (WRT the object itself) upper case. + seq = seq.upper() + rotation = Rotation.from_euler(seq, angles, degrees=True) + mat_expected = rotation.as_matrix() + + with pytest.warns(UserWarning, match="Gimbal lock"): + angle_estimates = rotation.as_euler(seq, degrees=True) + mat_estimated = Rotation.from_euler(seq, angle_estimates, degrees=True).as_matrix() + + assert_array_almost_equal(mat_expected, mat_estimated) + + +@pytest.mark.parametrize("seq_tuple", permutations("xyz")) +@pytest.mark.parametrize("intrinsic", (False, True)) +def test_as_euler_degenerate_symmetric_axes(seq_tuple, intrinsic): + # Since we cannot check for angle equality, we check for rotation matrix + # equality + angles = np.array([ + [15, 0, 60], + [35, 0, 75], + [60, 180, 35], + [15, -180, 25]]) + + # Rotation of the form A/B/A are rotation around symmetric axes + seq = "".join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + if intrinsic: + # Extrinsic rotation (wrt to global world) at lower case + # Intrinsic (WRT the object itself) upper case. + seq = seq.upper() + rotation = Rotation.from_euler(seq, angles, degrees=True) + mat_expected = rotation.as_matrix() + + with pytest.warns(UserWarning, match="Gimbal lock"): + angle_estimates = rotation.as_euler(seq, degrees=True) + mat_estimated = Rotation.from_euler(seq, angle_estimates, degrees=True).as_matrix() + + assert_array_almost_equal(mat_expected, mat_estimated) + + +@pytest.mark.parametrize("seq_tuple", permutations("xyz")) +@pytest.mark.parametrize("intrinsic", (False, True)) +def test_as_euler_degenerate_compare_algorithms(seq_tuple, intrinsic): + # this test makes sure that both algorithms are doing the same choices + # in degenerate cases + + # asymmetric axes + angles = np.array([ + [45, 90, 35], + [35, -90, 20], + [35, 90, 25], + [25, -90, 15]]) + + seq = "".join(seq_tuple) + if intrinsic: + # Extrinsic rotation (wrt to global world at lower case + # Intrinsic (WRT the object itself) upper case. + seq = seq.upper() + + rot = Rotation.from_euler(seq, angles, degrees=True) + with pytest.warns(UserWarning, match="Gimbal lock"): + estimates_matrix = rot._as_euler_from_matrix(seq, degrees=True) + with pytest.warns(UserWarning, match="Gimbal lock"): + estimates_quat = rot.as_euler(seq, degrees=True) + assert_allclose( + estimates_matrix[:, [0, 2]], estimates_quat[:, [0, 2]], atol=0, rtol=1e-12 + ) + assert_allclose(estimates_matrix[:, 1], estimates_quat[:, 1], atol=0, rtol=1e-7) + + # symmetric axes + # Absolute error tolerance must be looser to directly compare the results + # from both algorithms, because of numerical loss of precision for the + # method _as_euler_from_matrix near a zero angle value + + angles = np.array([ + [15, 0, 60], + [35, 0, 75], + [60, 180, 35], + [15, -180, 25]]) + + idx = angles[:, 1] == 0 # find problematic angles indices + + # Rotation of the form A/B/A are rotation around symmetric axes + seq = "".join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + if intrinsic: + # Extrinsinc rotation (wrt to global world) at lower case + # Intrinsic (WRT the object itself) upper case. + seq = seq.upper() + + rot = Rotation.from_euler(seq, angles, degrees=True) + with pytest.warns(UserWarning, match="Gimbal lock"): + estimates_matrix = rot._as_euler_from_matrix(seq, degrees=True) + with pytest.warns(UserWarning, match="Gimbal lock"): + estimates_quat = rot.as_euler(seq, degrees=True) + assert_allclose( + estimates_matrix[:, [0, 2]], estimates_quat[:, [0, 2]], atol=0, rtol=1e-12 + ) + + assert_allclose( + estimates_matrix[~idx, 1], estimates_quat[~idx, 1], atol=0, rtol=1e-7 + ) + + assert_allclose( + estimates_matrix[idx, 1], estimates_quat[idx, 1], atol=1e-6 + ) # problematic, angles[1] = 0 + + +def test_inv(): + rnd = np.random.RandomState(0) + n = 10 + p = Rotation.random(num=n, random_state=rnd) + q = p.inv() + + p_mat = p.as_matrix() + q_mat = q.as_matrix() + result1 = np.einsum('...ij,...jk->...ik', p_mat, q_mat) + result2 = np.einsum('...ij,...jk->...ik', q_mat, p_mat) + + eye3d = np.empty((n, 3, 3)) + eye3d[:] = np.eye(3) + + assert_array_almost_equal(result1, eye3d) + assert_array_almost_equal(result2, eye3d) + + +def test_inv_single_rotation(): + rnd = np.random.RandomState(0) + p = Rotation.random(random_state=rnd) + q = p.inv() + + p_mat = p.as_matrix() + q_mat = q.as_matrix() + res1 = np.dot(p_mat, q_mat) + res2 = np.dot(q_mat, p_mat) + + eye = np.eye(3) + + assert_array_almost_equal(res1, eye) + assert_array_almost_equal(res2, eye) + + x = Rotation.random(num=1, random_state=rnd) + y = x.inv() + + x_matrix = x.as_matrix() + y_matrix = y.as_matrix() + result1 = np.einsum('...ij,...jk->...ik', x_matrix, y_matrix) + result2 = np.einsum('...ij,...jk->...ik', y_matrix, x_matrix) + + eye3d = np.empty((1, 3, 3)) + eye3d[:] = np.eye(3) + + assert_array_almost_equal(result1, eye3d) + assert_array_almost_equal(result2, eye3d) + + +def test_identity_magnitude(): + n = 10 + assert_allclose(Rotation.identity(n).magnitude(), 0) + assert_allclose(Rotation.identity(n).inv().magnitude(), 0) + + +def test_single_identity_magnitude(): + assert Rotation.identity().magnitude() == 0 + assert Rotation.identity().inv().magnitude() == 0 + + +def test_identity_invariance(): + n = 10 + p = Rotation.random(n, random_state=0) + + result = p * Rotation.identity(n) + assert_array_almost_equal(p.as_quat(), result.as_quat()) + + result = result * p.inv() + assert_array_almost_equal(result.magnitude(), np.zeros(n)) + + +def test_single_identity_invariance(): + n = 10 + p = Rotation.random(n, random_state=0) + + result = p * Rotation.identity() + assert_array_almost_equal(p.as_quat(), result.as_quat()) + + result = result * p.inv() + assert_array_almost_equal(result.magnitude(), np.zeros(n)) + + +def test_magnitude(): + r = Rotation.from_quat(np.eye(4)) + result = r.magnitude() + assert_array_almost_equal(result, [np.pi, np.pi, np.pi, 0]) + + r = Rotation.from_quat(-np.eye(4)) + result = r.magnitude() + assert_array_almost_equal(result, [np.pi, np.pi, np.pi, 0]) + + +def test_magnitude_single_rotation(): + r = Rotation.from_quat(np.eye(4)) + result1 = r[0].magnitude() + assert_allclose(result1, np.pi) + + result2 = r[3].magnitude() + assert_allclose(result2, 0) + + +def test_approx_equal(): + rng = np.random.RandomState(0) + p = Rotation.random(10, random_state=rng) + q = Rotation.random(10, random_state=rng) + r = p * q.inv() + r_mag = r.magnitude() + atol = np.median(r_mag) # ensure we get mix of Trues and Falses + assert_equal(p.approx_equal(q, atol), (r_mag < atol)) + + +def test_approx_equal_single_rotation(): + # also tests passing single argument to approx_equal + p = Rotation.from_rotvec([0, 0, 1e-9]) # less than default atol of 1e-8 + q = Rotation.from_quat(np.eye(4)) + assert p.approx_equal(q[3]) + assert not p.approx_equal(q[0]) + + # test passing atol and using degrees + assert not p.approx_equal(q[3], atol=1e-10) + assert not p.approx_equal(q[3], atol=1e-8, degrees=True) + with pytest.warns(UserWarning, match="atol must be set"): + assert p.approx_equal(q[3], degrees=True) + + +def test_mean(): + axes = np.concatenate((-np.eye(3), np.eye(3))) + thetas = np.linspace(0, np.pi / 2, 100) + for t in thetas: + r = Rotation.from_rotvec(t * axes) + assert_allclose(r.mean().magnitude(), 0, atol=1E-10) + + +def test_weighted_mean(): + # test that doubling a weight is equivalent to including a rotation twice. + axes = np.array([[0, 0, 0], [1, 0, 0], [1, 0, 0]]) + thetas = np.linspace(0, np.pi / 2, 100) + for t in thetas: + rw = Rotation.from_rotvec(t * axes[:2]) + mw = rw.mean(weights=[1, 2]) + + r = Rotation.from_rotvec(t * axes) + m = r.mean() + assert_allclose((m * mw.inv()).magnitude(), 0, atol=1E-10) + + +def test_mean_invalid_weights(): + with pytest.raises(ValueError, match="non-negative"): + r = Rotation.from_quat(np.eye(4)) + r.mean(weights=-np.ones(4)) + + +def test_reduction_no_indices(): + result = Rotation.identity().reduce(return_indices=False) + assert isinstance(result, Rotation) + + +def test_reduction_none_indices(): + result = Rotation.identity().reduce(return_indices=True) + assert type(result) == tuple + assert len(result) == 3 + + reduced, left_best, right_best = result + assert left_best is None + assert right_best is None + + +def test_reduction_scalar_calculation(): + rng = np.random.RandomState(0) + l = Rotation.random(5, random_state=rng) + r = Rotation.random(10, random_state=rng) + p = Rotation.random(7, random_state=rng) + reduced, left_best, right_best = p.reduce(l, r, return_indices=True) + + # Loop implementation of the vectorized calculation in Rotation.reduce + scalars = np.zeros((len(l), len(p), len(r))) + for i, li in enumerate(l): + for j, pj in enumerate(p): + for k, rk in enumerate(r): + scalars[i, j, k] = np.abs((li * pj * rk).as_quat()[3]) + scalars = np.reshape(np.moveaxis(scalars, 1, 0), (scalars.shape[1], -1)) + + max_ind = np.argmax(np.reshape(scalars, (len(p), -1)), axis=1) + left_best_check = max_ind // len(r) + right_best_check = max_ind % len(r) + assert (left_best == left_best_check).all() + assert (right_best == right_best_check).all() + + reduced_check = l[left_best_check] * p * r[right_best_check] + mag = (reduced.inv() * reduced_check).magnitude() + assert_array_almost_equal(mag, np.zeros(len(p))) + + +def test_apply_single_rotation_single_point(): + mat = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + r_1d = Rotation.from_matrix(mat) + r_2d = Rotation.from_matrix(np.expand_dims(mat, axis=0)) + + v_1d = np.array([1, 2, 3]) + v_2d = np.expand_dims(v_1d, axis=0) + v1d_rotated = np.array([-2, 1, 3]) + v2d_rotated = np.expand_dims(v1d_rotated, axis=0) + + assert_allclose(r_1d.apply(v_1d), v1d_rotated) + assert_allclose(r_1d.apply(v_2d), v2d_rotated) + assert_allclose(r_2d.apply(v_1d), v2d_rotated) + assert_allclose(r_2d.apply(v_2d), v2d_rotated) + + v1d_inverse = np.array([2, -1, 3]) + v2d_inverse = np.expand_dims(v1d_inverse, axis=0) + + assert_allclose(r_1d.apply(v_1d, inverse=True), v1d_inverse) + assert_allclose(r_1d.apply(v_2d, inverse=True), v2d_inverse) + assert_allclose(r_2d.apply(v_1d, inverse=True), v2d_inverse) + assert_allclose(r_2d.apply(v_2d, inverse=True), v2d_inverse) + + +def test_apply_single_rotation_multiple_points(): + mat = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + r1 = Rotation.from_matrix(mat) + r2 = Rotation.from_matrix(np.expand_dims(mat, axis=0)) + + v = np.array([[1, 2, 3], [4, 5, 6]]) + v_rotated = np.array([[-2, 1, 3], [-5, 4, 6]]) + + assert_allclose(r1.apply(v), v_rotated) + assert_allclose(r2.apply(v), v_rotated) + + v_inverse = np.array([[2, -1, 3], [5, -4, 6]]) + + assert_allclose(r1.apply(v, inverse=True), v_inverse) + assert_allclose(r2.apply(v, inverse=True), v_inverse) + + +def test_apply_multiple_rotations_single_point(): + mat = np.empty((2, 3, 3)) + mat[0] = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + mat[1] = np.array([ + [1, 0, 0], + [0, 0, -1], + [0, 1, 0] + ]) + r = Rotation.from_matrix(mat) + + v1 = np.array([1, 2, 3]) + v2 = np.expand_dims(v1, axis=0) + + v_rotated = np.array([[-2, 1, 3], [1, -3, 2]]) + + assert_allclose(r.apply(v1), v_rotated) + assert_allclose(r.apply(v2), v_rotated) + + v_inverse = np.array([[2, -1, 3], [1, 3, -2]]) + + assert_allclose(r.apply(v1, inverse=True), v_inverse) + assert_allclose(r.apply(v2, inverse=True), v_inverse) + + +def test_apply_multiple_rotations_multiple_points(): + mat = np.empty((2, 3, 3)) + mat[0] = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + mat[1] = np.array([ + [1, 0, 0], + [0, 0, -1], + [0, 1, 0] + ]) + r = Rotation.from_matrix(mat) + + v = np.array([[1, 2, 3], [4, 5, 6]]) + v_rotated = np.array([[-2, 1, 3], [4, -6, 5]]) + assert_allclose(r.apply(v), v_rotated) + + v_inverse = np.array([[2, -1, 3], [4, 6, -5]]) + assert_allclose(r.apply(v, inverse=True), v_inverse) + + +def test_getitem(): + mat = np.empty((2, 3, 3)) + mat[0] = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + mat[1] = np.array([ + [1, 0, 0], + [0, 0, -1], + [0, 1, 0] + ]) + r = Rotation.from_matrix(mat) + + assert_allclose(r[0].as_matrix(), mat[0], atol=1e-15) + assert_allclose(r[1].as_matrix(), mat[1], atol=1e-15) + assert_allclose(r[:-1].as_matrix(), np.expand_dims(mat[0], axis=0), atol=1e-15) + + +def test_getitem_single(): + with pytest.raises(TypeError, match='not subscriptable'): + Rotation.identity()[0] + + +def test_setitem_single(): + r = Rotation.identity() + with pytest.raises(TypeError, match='not subscriptable'): + r[0] = Rotation.identity() + + +def test_setitem_slice(): + rng = np.random.RandomState(seed=0) + r1 = Rotation.random(10, random_state=rng) + r2 = Rotation.random(5, random_state=rng) + r1[1:6] = r2 + assert_equal(r1[1:6].as_quat(), r2.as_quat()) + + +def test_setitem_integer(): + rng = np.random.RandomState(seed=0) + r1 = Rotation.random(10, random_state=rng) + r2 = Rotation.random(random_state=rng) + r1[1] = r2 + assert_equal(r1[1].as_quat(), r2.as_quat()) + + +def test_setitem_wrong_type(): + r = Rotation.random(10, random_state=0) + with pytest.raises(TypeError, match='Rotation object'): + r[0] = 1 + + +def test_n_rotations(): + mat = np.empty((2, 3, 3)) + mat[0] = np.array([ + [0, -1, 0], + [1, 0, 0], + [0, 0, 1] + ]) + mat[1] = np.array([ + [1, 0, 0], + [0, 0, -1], + [0, 1, 0] + ]) + r = Rotation.from_matrix(mat) + + assert_equal(len(r), 2) + assert_equal(len(r[:-1]), 1) + + +def test_random_rotation_shape(): + rnd = np.random.RandomState(0) + assert_equal(Rotation.random(random_state=rnd).as_quat().shape, (4,)) + assert_equal(Rotation.random(None, random_state=rnd).as_quat().shape, (4,)) + + assert_equal(Rotation.random(1, random_state=rnd).as_quat().shape, (1, 4)) + assert_equal(Rotation.random(5, random_state=rnd).as_quat().shape, (5, 4)) + + +def test_align_vectors_no_rotation(): + x = np.array([[1, 2, 3], [4, 5, 6]]) + y = x.copy() + + r, rssd = Rotation.align_vectors(x, y) + assert_array_almost_equal(r.as_matrix(), np.eye(3)) + assert_allclose(rssd, 0, atol=1e-6) + + +def test_align_vectors_no_noise(): + rnd = np.random.RandomState(0) + c = Rotation.random(random_state=rnd) + b = rnd.normal(size=(5, 3)) + a = c.apply(b) + + est, rssd = Rotation.align_vectors(a, b) + assert_allclose(c.as_quat(), est.as_quat()) + assert_allclose(rssd, 0, atol=1e-7) + + +def test_align_vectors_improper_rotation(): + # Tests correct logic for issue #10444 + x = np.array([[0.89299824, -0.44372674, 0.0752378], + [0.60221789, -0.47564102, -0.6411702]]) + y = np.array([[0.02386536, -0.82176463, 0.5693271], + [-0.27654929, -0.95191427, -0.1318321]]) + + est, rssd = Rotation.align_vectors(x, y) + assert_allclose(x, est.apply(y), atol=1e-6) + assert_allclose(rssd, 0, atol=1e-7) + + +def test_align_vectors_rssd_sensitivity(): + rssd_expected = 0.141421356237308 + sens_expected = np.array([[0.2, 0. , 0.], + [0. , 1.5, 1.], + [0. , 1. , 1.]]) + atol = 1e-6 + a = [[0, 1, 0], [0, 1, 1], [0, 1, 1]] + b = [[1, 0, 0], [1, 1.1, 0], [1, 0.9, 0]] + rot, rssd, sens = Rotation.align_vectors(a, b, return_sensitivity=True) + assert np.isclose(rssd, rssd_expected, atol=atol) + assert np.allclose(sens, sens_expected, atol=atol) + + +def test_align_vectors_scaled_weights(): + n = 10 + a = Rotation.random(n, random_state=0).apply([1, 0, 0]) + b = Rotation.random(n, random_state=1).apply([1, 0, 0]) + scale = 2 + + est1, rssd1, cov1 = Rotation.align_vectors(a, b, np.ones(n), True) + est2, rssd2, cov2 = Rotation.align_vectors(a, b, scale * np.ones(n), True) + + assert_allclose(est1.as_matrix(), est2.as_matrix()) + assert_allclose(np.sqrt(scale) * rssd1, rssd2, atol=1e-6) + assert_allclose(cov1, cov2) + + +def test_align_vectors_noise(): + rnd = np.random.RandomState(0) + n_vectors = 100 + rot = Rotation.random(random_state=rnd) + vectors = rnd.normal(size=(n_vectors, 3)) + result = rot.apply(vectors) + + # The paper adds noise as independently distributed angular errors + sigma = np.deg2rad(1) + tolerance = 1.5 * sigma + noise = Rotation.from_rotvec( + rnd.normal( + size=(n_vectors, 3), + scale=sigma + ) + ) + + # Attitude errors must preserve norm. Hence apply individual random + # rotations to each vector. + noisy_result = noise.apply(result) + + est, rssd, cov = Rotation.align_vectors(noisy_result, vectors, + return_sensitivity=True) + + # Use rotation compositions to find out closeness + error_vector = (rot * est.inv()).as_rotvec() + assert_allclose(error_vector[0], 0, atol=tolerance) + assert_allclose(error_vector[1], 0, atol=tolerance) + assert_allclose(error_vector[2], 0, atol=tolerance) + + # Check error bounds using covariance matrix + cov *= sigma + assert_allclose(cov[0, 0], 0, atol=tolerance) + assert_allclose(cov[1, 1], 0, atol=tolerance) + assert_allclose(cov[2, 2], 0, atol=tolerance) + + assert_allclose(rssd, np.sum((noisy_result - est.apply(vectors))**2)**0.5) + + +def test_align_vectors_invalid_input(): + with pytest.raises(ValueError, match="Expected input `a` to have shape"): + Rotation.align_vectors([1, 2, 3, 4], [1, 2, 3]) + + with pytest.raises(ValueError, match="Expected input `b` to have shape"): + Rotation.align_vectors([1, 2, 3], [1, 2, 3, 4]) + + with pytest.raises(ValueError, match="Expected inputs `a` and `b` " + "to have same shapes"): + Rotation.align_vectors([[1, 2, 3],[4, 5, 6]], [[1, 2, 3]]) + + with pytest.raises(ValueError, + match="Expected `weights` to be 1 dimensional"): + Rotation.align_vectors([[1, 2, 3]], [[1, 2, 3]], weights=[[1]]) + + with pytest.raises(ValueError, + match="Expected `weights` to have number of values"): + Rotation.align_vectors([[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]], + weights=[1, 2, 3]) + + with pytest.raises(ValueError, + match="`weights` may not contain negative values"): + Rotation.align_vectors([[1, 2, 3]], [[1, 2, 3]], weights=[-1]) + + with pytest.raises(ValueError, + match="Only one infinite weight is allowed"): + Rotation.align_vectors([[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]], + weights=[np.inf, np.inf]) + + with pytest.raises(ValueError, + match="Cannot align zero length primary vectors"): + Rotation.align_vectors([[0, 0, 0]], [[1, 2, 3]]) + + with pytest.raises(ValueError, + match="Cannot return sensitivity matrix"): + Rotation.align_vectors([[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]], + return_sensitivity=True, weights=[np.inf, 1]) + + with pytest.raises(ValueError, + match="Cannot return sensitivity matrix"): + Rotation.align_vectors([[1, 2, 3]], [[1, 2, 3]], + return_sensitivity=True) + + +def test_align_vectors_align_constrain(): + # Align the primary +X B axis with the primary +Y A axis, and rotate about + # it such that the +Y B axis (residual of the [1, 1, 0] secondary b vector) + # is aligned with the +Z A axis (residual of the [0, 1, 1] secondary a + # vector) + atol = 1e-12 + b = [[1, 0, 0], [1, 1, 0]] + a = [[0, 1, 0], [0, 1, 1]] + m_expected = np.array([[0, 0, 1], + [1, 0, 0], + [0, 1, 0]]) + R, rssd = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + assert_allclose(R.apply(b), a, atol=atol) # Pri and sec align exactly + assert np.isclose(rssd, 0, atol=atol) + + # Do the same but with an inexact secondary rotation + b = [[1, 0, 0], [1, 2, 0]] + rssd_expected = 1.0 + R, rssd = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + assert_allclose(R.apply(b)[0], a[0], atol=atol) # Only pri aligns exactly + assert np.isclose(rssd, rssd_expected, atol=atol) + a_expected = [[0, 1, 0], [0, 1, 2]] + assert_allclose(R.apply(b), a_expected, atol=atol) + + # Check random vectors + b = [[1, 2, 3], [-2, 3, -1]] + a = [[-1, 3, 2], [1, -1, 2]] + rssd_expected = 1.3101595297515016 + R, rssd = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.apply(b)[0], a[0], atol=atol) # Only pri aligns exactly + assert np.isclose(rssd, rssd_expected, atol=atol) + + +def test_align_vectors_near_inf(): + # align_vectors should return near the same result for high weights as for + # infinite weights. rssd will be different with floating point error on the + # exactly aligned vector being multiplied by a large non-infinite weight + n = 100 + mats = [] + for i in range(6): + mats.append(Rotation.random(n, random_state=10 + i).as_matrix()) + + for i in range(n): + # Get random pairs of 3-element vectors + a = [1*mats[0][i][0], 2*mats[1][i][0]] + b = [3*mats[2][i][0], 4*mats[3][i][0]] + + R, _ = Rotation.align_vectors(a, b, weights=[1e10, 1]) + R2, _ = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.as_matrix(), R2.as_matrix(), atol=1e-4) + + for i in range(n): + # Get random triplets of 3-element vectors + a = [1*mats[0][i][0], 2*mats[1][i][0], 3*mats[2][i][0]] + b = [4*mats[3][i][0], 5*mats[4][i][0], 6*mats[5][i][0]] + + R, _ = Rotation.align_vectors(a, b, weights=[1e10, 2, 1]) + R2, _ = Rotation.align_vectors(a, b, weights=[np.inf, 2, 1]) + assert_allclose(R.as_matrix(), R2.as_matrix(), atol=1e-4) + + +def test_align_vectors_parallel(): + atol = 1e-12 + a = [[1, 0, 0], [0, 1, 0]] + b = [[0, 1, 0], [0, 1, 0]] + m_expected = np.array([[0, 1, 0], + [-1, 0, 0], + [0, 0, 1]]) + R, _ = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + R, _ = Rotation.align_vectors(a[0], b[0]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + assert_allclose(R.apply(b[0]), a[0], atol=atol) + + b = [[1, 0, 0], [1, 0, 0]] + m_expected = np.array([[1, 0, 0], + [0, 1, 0], + [0, 0, 1]]) + R, _ = Rotation.align_vectors(a, b, weights=[np.inf, 1]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + R, _ = Rotation.align_vectors(a[0], b[0]) + assert_allclose(R.as_matrix(), m_expected, atol=atol) + assert_allclose(R.apply(b[0]), a[0], atol=atol) + + +def test_align_vectors_primary_only(): + atol = 1e-12 + mats_a = Rotation.random(100, random_state=0).as_matrix() + mats_b = Rotation.random(100, random_state=1).as_matrix() + for mat_a, mat_b in zip(mats_a, mats_b): + # Get random 3-element unit vectors + a = mat_a[0] + b = mat_b[0] + + # Compare to align_vectors with primary only + R, rssd = Rotation.align_vectors(a, b) + assert_allclose(R.apply(b), a, atol=atol) + assert np.isclose(rssd, 0, atol=atol) + + +def test_slerp(): + rnd = np.random.RandomState(0) + + key_rots = Rotation.from_quat(rnd.uniform(size=(5, 4))) + key_quats = key_rots.as_quat() + + key_times = [0, 1, 2, 3, 4] + interpolator = Slerp(key_times, key_rots) + + times = [0, 0.5, 0.25, 1, 1.5, 2, 2.75, 3, 3.25, 3.60, 4] + interp_rots = interpolator(times) + interp_quats = interp_rots.as_quat() + + # Dot products are affected by sign of quaternions + interp_quats[interp_quats[:, -1] < 0] *= -1 + # Checking for quaternion equality, perform same operation + key_quats[key_quats[:, -1] < 0] *= -1 + + # Equality at keyframes, including both endpoints + assert_allclose(interp_quats[0], key_quats[0]) + assert_allclose(interp_quats[3], key_quats[1]) + assert_allclose(interp_quats[5], key_quats[2]) + assert_allclose(interp_quats[7], key_quats[3]) + assert_allclose(interp_quats[10], key_quats[4]) + + # Constant angular velocity between keyframes. Check by equating + # cos(theta) between quaternion pairs with equal time difference. + cos_theta1 = np.sum(interp_quats[0] * interp_quats[2]) + cos_theta2 = np.sum(interp_quats[2] * interp_quats[1]) + assert_allclose(cos_theta1, cos_theta2) + + cos_theta4 = np.sum(interp_quats[3] * interp_quats[4]) + cos_theta5 = np.sum(interp_quats[4] * interp_quats[5]) + assert_allclose(cos_theta4, cos_theta5) + + # theta1: 0 -> 0.25, theta3 : 0.5 -> 1 + # Use double angle formula for double the time difference + cos_theta3 = np.sum(interp_quats[1] * interp_quats[3]) + assert_allclose(cos_theta3, 2 * (cos_theta1**2) - 1) + + # Miscellaneous checks + assert_equal(len(interp_rots), len(times)) + + +def test_slerp_rot_is_rotation(): + with pytest.raises(TypeError, match="must be a `Rotation` instance"): + r = np.array([[1,2,3,4], + [0,0,0,1]]) + t = np.array([0, 1]) + Slerp(t, r) + + +def test_slerp_single_rot(): + msg = "must be a sequence of at least 2 rotations" + with pytest.raises(ValueError, match=msg): + r = Rotation.from_quat([1, 2, 3, 4]) + Slerp([1], r) + + +def test_slerp_rot_len1(): + msg = "must be a sequence of at least 2 rotations" + with pytest.raises(ValueError, match=msg): + r = Rotation.from_quat([[1, 2, 3, 4]]) + Slerp([1], r) + + +def test_slerp_time_dim_mismatch(): + with pytest.raises(ValueError, + match="times to be specified in a 1 dimensional array"): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(2, 4))) + t = np.array([[1], + [2]]) + Slerp(t, r) + + +def test_slerp_num_rotations_mismatch(): + with pytest.raises(ValueError, match="number of rotations to be equal to " + "number of timestamps"): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(5, 4))) + t = np.arange(7) + Slerp(t, r) + + +def test_slerp_equal_times(): + with pytest.raises(ValueError, match="strictly increasing order"): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(5, 4))) + t = [0, 1, 2, 2, 4] + Slerp(t, r) + + +def test_slerp_decreasing_times(): + with pytest.raises(ValueError, match="strictly increasing order"): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(5, 4))) + t = [0, 1, 3, 2, 4] + Slerp(t, r) + + +def test_slerp_call_time_dim_mismatch(): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(5, 4))) + t = np.arange(5) + s = Slerp(t, r) + + with pytest.raises(ValueError, + match="`times` must be at most 1-dimensional."): + interp_times = np.array([[3.5], + [4.2]]) + s(interp_times) + + +def test_slerp_call_time_out_of_range(): + rnd = np.random.RandomState(0) + r = Rotation.from_quat(rnd.uniform(size=(5, 4))) + t = np.arange(5) + 1 + s = Slerp(t, r) + + with pytest.raises(ValueError, match="times must be within the range"): + s([0, 1, 2]) + with pytest.raises(ValueError, match="times must be within the range"): + s([1, 2, 6]) + + +def test_slerp_call_scalar_time(): + r = Rotation.from_euler('X', [0, 80], degrees=True) + s = Slerp([0, 1], r) + + r_interpolated = s(0.25) + r_interpolated_expected = Rotation.from_euler('X', 20, degrees=True) + + delta = r_interpolated * r_interpolated_expected.inv() + + assert_allclose(delta.magnitude(), 0, atol=1e-16) + + +def test_multiplication_stability(): + qs = Rotation.random(50, random_state=0) + rs = Rotation.random(1000, random_state=1) + for q in qs: + rs *= q * rs + assert_allclose(np.linalg.norm(rs.as_quat(), axis=1), 1) + + +def test_pow(): + atol = 1e-14 + p = Rotation.random(10, random_state=0) + p_inv = p.inv() + # Test the short-cuts and other integers + for n in [-5, -2, -1, 0, 1, 2, 5]: + # Test accuracy + q = p ** n + r = Rotation.identity(10) + for _ in range(abs(n)): + if n > 0: + r = r * p + else: + r = r * p_inv + ang = (q * r.inv()).magnitude() + assert np.all(ang < atol) + + # Test shape preservation + r = Rotation.from_quat([0, 0, 0, 1]) + assert (r**n).as_quat().shape == (4,) + r = Rotation.from_quat([[0, 0, 0, 1]]) + assert (r**n).as_quat().shape == (1, 4) + + # Large angle fractional + for n in [-1.5, -0.5, -0.0, 0.0, 0.5, 1.5]: + q = p ** n + r = Rotation.from_rotvec(n * p.as_rotvec()) + assert_allclose(q.as_quat(), r.as_quat(), atol=atol) + + # Small angle + p = Rotation.from_rotvec([1e-12, 0, 0]) + n = 3 + q = p ** n + r = Rotation.from_rotvec(n * p.as_rotvec()) + assert_allclose(q.as_quat(), r.as_quat(), atol=atol) + + +def test_pow_errors(): + p = Rotation.random(random_state=0) + with pytest.raises(NotImplementedError, match='modulus not supported'): + pow(p, 1, 1) + + +def test_rotation_within_numpy_array(): + single = Rotation.random(random_state=0) + multiple = Rotation.random(2, random_state=1) + + array = np.array(single) + assert_equal(array.shape, ()) + + array = np.array(multiple) + assert_equal(array.shape, (2,)) + assert_allclose(array[0].as_matrix(), multiple[0].as_matrix()) + assert_allclose(array[1].as_matrix(), multiple[1].as_matrix()) + + array = np.array([single]) + assert_equal(array.shape, (1,)) + assert_equal(array[0], single) + + array = np.array([multiple]) + assert_equal(array.shape, (1, 2)) + assert_allclose(array[0, 0].as_matrix(), multiple[0].as_matrix()) + assert_allclose(array[0, 1].as_matrix(), multiple[1].as_matrix()) + + array = np.array([single, multiple], dtype=object) + assert_equal(array.shape, (2,)) + assert_equal(array[0], single) + assert_equal(array[1], multiple) + + array = np.array([multiple, multiple, multiple]) + assert_equal(array.shape, (3, 2)) + + +def test_pickling(): + r = Rotation.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]) + pkl = pickle.dumps(r) + unpickled = pickle.loads(pkl) + assert_allclose(r.as_matrix(), unpickled.as_matrix(), atol=1e-15) + + +def test_deepcopy(): + r = Rotation.from_quat([0, 0, np.sin(np.pi/4), np.cos(np.pi/4)]) + r1 = copy.deepcopy(r) + assert_allclose(r.as_matrix(), r1.as_matrix(), atol=1e-15) + + +def test_as_euler_contiguous(): + r = Rotation.from_quat([0, 0, 0, 1]) + e1 = r.as_euler('xyz') # extrinsic euler rotation + e2 = r.as_euler('XYZ') # intrinsic + assert e1.flags['C_CONTIGUOUS'] is True + assert e2.flags['C_CONTIGUOUS'] is True + assert all(i >= 0 for i in e1.strides) + assert all(i >= 0 for i in e2.strides) + + +def test_concatenate(): + rotation = Rotation.random(10, random_state=0) + sizes = [1, 2, 3, 1, 3] + starts = [0] + list(np.cumsum(sizes)) + split = [rotation[i:i + n] for i, n in zip(starts, sizes)] + result = Rotation.concatenate(split) + assert_equal(rotation.as_quat(), result.as_quat()) + + +def test_concatenate_wrong_type(): + with pytest.raises(TypeError, match='Rotation objects only'): + Rotation.concatenate([Rotation.identity(), 1, None]) + + +# Regression test for gh-16663 +def test_len_and_bool(): + rotation_multi_empty = Rotation(np.empty((0, 4))) + rotation_multi_one = Rotation([[0, 0, 0, 1]]) + rotation_multi = Rotation([[0, 0, 0, 1], [0, 0, 0, 1]]) + rotation_single = Rotation([0, 0, 0, 1]) + + assert len(rotation_multi_empty) == 0 + assert len(rotation_multi_one) == 1 + assert len(rotation_multi) == 2 + with pytest.raises(TypeError, match="Single rotation has no len()."): + len(rotation_single) + + # Rotation should always be truthy. See gh-16663 + assert rotation_multi_empty + assert rotation_multi_one + assert rotation_multi + assert rotation_single + + +def test_from_davenport_single_rotation(): + axis = [0, 0, 1] + quat = Rotation.from_davenport(axis, 'extrinsic', 90, + degrees=True).as_quat() + expected_quat = np.array([0, 0, 1, 1]) / np.sqrt(2) + assert_allclose(quat, expected_quat) + + +def test_from_davenport_one_or_two_axes(): + ez = [0, 0, 1] + ey = [0, 1, 0] + + # Single rotation, single axis, axes.shape == (3, ) + rot = Rotation.from_rotvec(np.array(ez) * np.pi/4) + rot_dav = Rotation.from_davenport(ez, 'e', np.pi/4) + assert_allclose(rot.as_quat(canonical=True), + rot_dav.as_quat(canonical=True)) + + # Single rotation, single axis, axes.shape == (1, 3) + rot = Rotation.from_rotvec([np.array(ez) * np.pi/4]) + rot_dav = Rotation.from_davenport([ez], 'e', [np.pi/4]) + assert_allclose(rot.as_quat(canonical=True), + rot_dav.as_quat(canonical=True)) + + # Single rotation, two axes, axes.shape == (2, 3) + rot = Rotation.from_rotvec([np.array(ez) * np.pi/4, + np.array(ey) * np.pi/6]) + rot = rot[0] * rot[1] + rot_dav = Rotation.from_davenport([ey, ez], 'e', [np.pi/6, np.pi/4]) + assert_allclose(rot.as_quat(canonical=True), + rot_dav.as_quat(canonical=True)) + + # Two rotations, single axis, axes.shape == (3, ) + rot = Rotation.from_rotvec([np.array(ez) * np.pi/6, + np.array(ez) * np.pi/4]) + rot_dav = Rotation.from_davenport([ez], 'e', [np.pi/6, np.pi/4]) + assert_allclose(rot.as_quat(canonical=True), + rot_dav.as_quat(canonical=True)) + + +def test_from_davenport_invalid_input(): + ez = [0, 0, 1] + ey = [0, 1, 0] + ezy = [0, 1, 1] + with pytest.raises(ValueError, match="must be orthogonal"): + Rotation.from_davenport([ez, ezy], 'e', [0, 0]) + with pytest.raises(ValueError, match="must be orthogonal"): + Rotation.from_davenport([ez, ey, ezy], 'e', [0, 0, 0]) + with pytest.raises(ValueError, match="order should be"): + Rotation.from_davenport([ez], 'xyz', [0]) + with pytest.raises(ValueError, match="Expected `angles`"): + Rotation.from_davenport([ez, ey, ez], 'e', [0, 1, 2, 3]) + + +def test_as_davenport(): + rnd = np.random.RandomState(0) + n = 100 + angles = np.empty((n, 3)) + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles_middle = rnd.uniform(low=0, high=np.pi, size=(n,)) + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + lambdas = rnd.uniform(low=0, high=np.pi, size=(20,)) + + e1 = np.array([1, 0, 0]) + e2 = np.array([0, 1, 0]) + + for lamb in lambdas: + ax_lamb = [e1, e2, Rotation.from_rotvec(lamb*e2).apply(e1)] + angles[:, 1] = angles_middle - lamb + for order in ['extrinsic', 'intrinsic']: + ax = ax_lamb if order == 'intrinsic' else ax_lamb[::-1] + rot = Rotation.from_davenport(ax, order, angles) + angles_dav = rot.as_davenport(ax, order) + assert_allclose(angles_dav, angles) + + +def test_as_davenport_degenerate(): + # Since we cannot check for angle equality, we check for rotation matrix + # equality + rnd = np.random.RandomState(0) + n = 5 + angles = np.empty((n, 3)) + + # symmetric sequences + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles_middle = [rnd.choice([0, np.pi]) for i in range(n)] + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + lambdas = rnd.uniform(low=0, high=np.pi, size=(5,)) + + e1 = np.array([1, 0, 0]) + e2 = np.array([0, 1, 0]) + + for lamb in lambdas: + ax_lamb = [e1, e2, Rotation.from_rotvec(lamb*e2).apply(e1)] + angles[:, 1] = angles_middle - lamb + for order in ['extrinsic', 'intrinsic']: + ax = ax_lamb if order == 'intrinsic' else ax_lamb[::-1] + rot = Rotation.from_davenport(ax, order, angles) + with pytest.warns(UserWarning, match="Gimbal lock"): + angles_dav = rot.as_davenport(ax, order) + mat_expected = rot.as_matrix() + mat_estimated = Rotation.from_davenport(ax, order, angles_dav).as_matrix() + assert_array_almost_equal(mat_expected, mat_estimated) + + +def test_compare_from_davenport_from_euler(): + rnd = np.random.RandomState(0) + n = 100 + angles = np.empty((n, 3)) + + # symmetric sequences + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,)) + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + for order in ['extrinsic', 'intrinsic']: + for seq_tuple in permutations('xyz'): + seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + ax = [basis_vec(i) for i in seq] + if order == 'intrinsic': + seq = seq.upper() + eul = Rotation.from_euler(seq, angles) + dav = Rotation.from_davenport(ax, order, angles) + assert_allclose(eul.as_quat(canonical=True), dav.as_quat(canonical=True), + rtol=1e-12) + + # asymmetric sequences + angles[:, 1] -= np.pi / 2 + for order in ['extrinsic', 'intrinsic']: + for seq_tuple in permutations('xyz'): + seq = ''.join(seq_tuple) + ax = [basis_vec(i) for i in seq] + if order == 'intrinsic': + seq = seq.upper() + eul = Rotation.from_euler(seq, angles) + dav = Rotation.from_davenport(ax, order, angles) + assert_allclose(eul.as_quat(), dav.as_quat(), rtol=1e-12) + + +def test_compare_as_davenport_as_euler(): + rnd = np.random.RandomState(0) + n = 100 + angles = np.empty((n, 3)) + + # symmetric sequences + angles[:, 0] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + angles[:, 1] = rnd.uniform(low=0, high=np.pi, size=(n,)) + angles[:, 2] = rnd.uniform(low=-np.pi, high=np.pi, size=(n,)) + for order in ['extrinsic', 'intrinsic']: + for seq_tuple in permutations('xyz'): + seq = ''.join([seq_tuple[0], seq_tuple[1], seq_tuple[0]]) + ax = [basis_vec(i) for i in seq] + if order == 'intrinsic': + seq = seq.upper() + rot = Rotation.from_euler(seq, angles) + eul = rot.as_euler(seq) + dav = rot.as_davenport(ax, order) + assert_allclose(eul, dav, rtol=1e-12) + + # asymmetric sequences + angles[:, 1] -= np.pi / 2 + for order in ['extrinsic', 'intrinsic']: + for seq_tuple in permutations('xyz'): + seq = ''.join(seq_tuple) + ax = [basis_vec(i) for i in seq] + if order == 'intrinsic': + seq = seq.upper() + rot = Rotation.from_euler(seq, angles) + eul = rot.as_euler(seq) + dav = rot.as_davenport(ax, order) + assert_allclose(eul, dav, rtol=1e-12) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py new file mode 100644 index 0000000000000000000000000000000000000000..befe60c13c5a5863a2ae50f9d20e6d054795f6b9 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_groups.py @@ -0,0 +1,169 @@ +import pytest + +import numpy as np +from numpy.testing import assert_array_almost_equal +from scipy.spatial.transform import Rotation +from scipy.optimize import linear_sum_assignment +from scipy.spatial.distance import cdist +from scipy.constants import golden as phi +from scipy.spatial import cKDTree + + +TOL = 1E-12 +NS = range(1, 13) +NAMES = ["I", "O", "T"] + ["C%d" % n for n in NS] + ["D%d" % n for n in NS] +SIZES = [60, 24, 12] + list(NS) + [2 * n for n in NS] + + +def _calculate_rmsd(P, Q): + """Calculates the root-mean-square distance between the points of P and Q. + The distance is taken as the minimum over all possible matchings. It is + zero if P and Q are identical and non-zero if not. + """ + distance_matrix = cdist(P, Q, metric='sqeuclidean') + matching = linear_sum_assignment(distance_matrix) + return np.sqrt(distance_matrix[matching].sum()) + + +def _generate_pyramid(n, axis): + thetas = np.linspace(0, 2 * np.pi, n + 1)[:-1] + P = np.vstack([np.zeros(n), np.cos(thetas), np.sin(thetas)]).T + P = np.concatenate((P, [[1, 0, 0]])) + return np.roll(P, axis, axis=1) + + +def _generate_prism(n, axis): + thetas = np.linspace(0, 2 * np.pi, n + 1)[:-1] + bottom = np.vstack([-np.ones(n), np.cos(thetas), np.sin(thetas)]).T + top = np.vstack([+np.ones(n), np.cos(thetas), np.sin(thetas)]).T + P = np.concatenate((bottom, top)) + return np.roll(P, axis, axis=1) + + +def _generate_icosahedron(): + x = np.array([[0, -1, -phi], + [0, -1, +phi], + [0, +1, -phi], + [0, +1, +phi]]) + return np.concatenate([np.roll(x, i, axis=1) for i in range(3)]) + + +def _generate_octahedron(): + return np.array([[-1, 0, 0], [+1, 0, 0], [0, -1, 0], + [0, +1, 0], [0, 0, -1], [0, 0, +1]]) + + +def _generate_tetrahedron(): + return np.array([[1, 1, 1], [1, -1, -1], [-1, 1, -1], [-1, -1, 1]]) + + +@pytest.mark.parametrize("name", [-1, None, True, np.array(['C3'])]) +def test_group_type(name): + with pytest.raises(ValueError, + match="must be a string"): + Rotation.create_group(name) + + +@pytest.mark.parametrize("name", ["Q", " ", "CA", "C ", "DA", "D ", "I2", ""]) +def test_group_name(name): + with pytest.raises(ValueError, + match="must be one of 'I', 'O', 'T', 'Dn', 'Cn'"): + Rotation.create_group(name) + + +@pytest.mark.parametrize("name", ["C0", "D0"]) +def test_group_order_positive(name): + with pytest.raises(ValueError, + match="Group order must be positive"): + Rotation.create_group(name) + + +@pytest.mark.parametrize("axis", ['A', 'b', 0, 1, 2, 4, False, None]) +def test_axis_valid(axis): + with pytest.raises(ValueError, + match="`axis` must be one of"): + Rotation.create_group("C1", axis) + + +def test_icosahedral(): + """The icosahedral group fixes the rotations of an icosahedron. Here we + test that the icosahedron is invariant after application of the elements + of the rotation group.""" + P = _generate_icosahedron() + for g in Rotation.create_group("I"): + g = Rotation.from_quat(g.as_quat()) + assert _calculate_rmsd(P, g.apply(P)) < TOL + + +def test_octahedral(): + """Test that the octahedral group correctly fixes the rotations of an + octahedron.""" + P = _generate_octahedron() + for g in Rotation.create_group("O"): + assert _calculate_rmsd(P, g.apply(P)) < TOL + + +def test_tetrahedral(): + """Test that the tetrahedral group correctly fixes the rotations of a + tetrahedron.""" + P = _generate_tetrahedron() + for g in Rotation.create_group("T"): + assert _calculate_rmsd(P, g.apply(P)) < TOL + + +@pytest.mark.parametrize("n", NS) +@pytest.mark.parametrize("axis", 'XYZ') +def test_dicyclic(n, axis): + """Test that the dicyclic group correctly fixes the rotations of a + prism.""" + P = _generate_prism(n, axis='XYZ'.index(axis)) + for g in Rotation.create_group("D%d" % n, axis=axis): + assert _calculate_rmsd(P, g.apply(P)) < TOL + + +@pytest.mark.parametrize("n", NS) +@pytest.mark.parametrize("axis", 'XYZ') +def test_cyclic(n, axis): + """Test that the cyclic group correctly fixes the rotations of a + pyramid.""" + P = _generate_pyramid(n, axis='XYZ'.index(axis)) + for g in Rotation.create_group("C%d" % n, axis=axis): + assert _calculate_rmsd(P, g.apply(P)) < TOL + + +@pytest.mark.parametrize("name, size", zip(NAMES, SIZES)) +def test_group_sizes(name, size): + assert len(Rotation.create_group(name)) == size + + +@pytest.mark.parametrize("name, size", zip(NAMES, SIZES)) +def test_group_no_duplicates(name, size): + g = Rotation.create_group(name) + kdtree = cKDTree(g.as_quat()) + assert len(kdtree.query_pairs(1E-3)) == 0 + + +@pytest.mark.parametrize("name, size", zip(NAMES, SIZES)) +def test_group_symmetry(name, size): + g = Rotation.create_group(name) + q = np.concatenate((-g.as_quat(), g.as_quat())) + distance = np.sort(cdist(q, q)) + deltas = np.max(distance, axis=0) - np.min(distance, axis=0) + assert (deltas < TOL).all() + + +@pytest.mark.parametrize("name", NAMES) +def test_reduction(name): + """Test that the elements of the rotation group are correctly + mapped onto the identity rotation.""" + g = Rotation.create_group(name) + f = g.reduce(g) + assert_array_almost_equal(f.magnitude(), np.zeros(len(g))) + + +@pytest.mark.parametrize("name", NAMES) +def test_single_reduction(name): + g = Rotation.create_group(name) + f = g[-1].reduce(g) + assert_array_almost_equal(f.magnitude(), 0) + assert f.as_quat().shape == (4,) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py new file mode 100644 index 0000000000000000000000000000000000000000..6441431f2fb54a95edd6364c4671bc55a2ce2b8f --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/spatial/transform/tests/test_rotation_spline.py @@ -0,0 +1,162 @@ +from itertools import product +import numpy as np +from numpy.testing import assert_allclose +from pytest import raises +from scipy.spatial.transform import Rotation, RotationSpline +from scipy.spatial.transform._rotation_spline import ( + _angular_rate_to_rotvec_dot_matrix, + _rotvec_dot_to_angular_rate_matrix, + _matrix_vector_product_of_stacks, + _angular_acceleration_nonlinear_term, + _create_block_3_diagonal_matrix) + + +def test_angular_rate_to_rotvec_conversions(): + np.random.seed(0) + rv = np.random.randn(4, 3) + A = _angular_rate_to_rotvec_dot_matrix(rv) + A_inv = _rotvec_dot_to_angular_rate_matrix(rv) + + # When the rotation vector is aligned with the angular rate, then + # the rotation vector rate and angular rate are the same. + assert_allclose(_matrix_vector_product_of_stacks(A, rv), rv) + assert_allclose(_matrix_vector_product_of_stacks(A_inv, rv), rv) + + # A and A_inv must be reciprocal to each other. + I_stack = np.empty((4, 3, 3)) + I_stack[:] = np.eye(3) + assert_allclose(np.matmul(A, A_inv), I_stack, atol=1e-15) + + +def test_angular_rate_nonlinear_term(): + # The only simple test is to check that the term is zero when + # the rotation vector + np.random.seed(0) + rv = np.random.rand(4, 3) + assert_allclose(_angular_acceleration_nonlinear_term(rv, rv), 0, + atol=1e-19) + + +def test_create_block_3_diagonal_matrix(): + np.random.seed(0) + A = np.empty((4, 3, 3)) + A[:] = np.arange(1, 5)[:, None, None] + + B = np.empty((4, 3, 3)) + B[:] = -np.arange(1, 5)[:, None, None] + d = 10 * np.arange(10, 15) + + banded = _create_block_3_diagonal_matrix(A, B, d) + + # Convert the banded matrix to the full matrix. + k, l = list(zip(*product(np.arange(banded.shape[0]), + np.arange(banded.shape[1])))) + k = np.asarray(k) + l = np.asarray(l) + + i = k - 5 + l + j = l + values = banded.ravel() + mask = (i >= 0) & (i < 15) + i = i[mask] + j = j[mask] + values = values[mask] + full = np.zeros((15, 15)) + full[i, j] = values + + zero = np.zeros((3, 3)) + eye = np.eye(3) + + # Create the reference full matrix in the most straightforward manner. + ref = np.block([ + [d[0] * eye, B[0], zero, zero, zero], + [A[0], d[1] * eye, B[1], zero, zero], + [zero, A[1], d[2] * eye, B[2], zero], + [zero, zero, A[2], d[3] * eye, B[3]], + [zero, zero, zero, A[3], d[4] * eye], + ]) + + assert_allclose(full, ref, atol=1e-19) + + +def test_spline_2_rotations(): + times = [0, 10] + rotations = Rotation.from_euler('xyz', [[0, 0, 0], [10, -20, 30]], + degrees=True) + spline = RotationSpline(times, rotations) + + rv = (rotations[0].inv() * rotations[1]).as_rotvec() + rate = rv / (times[1] - times[0]) + times_check = np.array([-1, 5, 12]) + dt = times_check - times[0] + rv_ref = rate * dt[:, None] + + assert_allclose(spline(times_check).as_rotvec(), rv_ref) + assert_allclose(spline(times_check, 1), np.resize(rate, (3, 3))) + assert_allclose(spline(times_check, 2), 0, atol=1e-16) + + +def test_constant_attitude(): + times = np.arange(10) + rotations = Rotation.from_rotvec(np.ones((10, 3))) + spline = RotationSpline(times, rotations) + + times_check = np.linspace(-1, 11) + assert_allclose(spline(times_check).as_rotvec(), 1, rtol=1e-15) + assert_allclose(spline(times_check, 1), 0, atol=1e-17) + assert_allclose(spline(times_check, 2), 0, atol=1e-17) + + assert_allclose(spline(5.5).as_rotvec(), 1, rtol=1e-15) + assert_allclose(spline(5.5, 1), 0, atol=1e-17) + assert_allclose(spline(5.5, 2), 0, atol=1e-17) + + +def test_spline_properties(): + times = np.array([0, 5, 15, 27]) + angles = [[-5, 10, 27], [3, 5, 38], [-12, 10, 25], [-15, 20, 11]] + + rotations = Rotation.from_euler('xyz', angles, degrees=True) + spline = RotationSpline(times, rotations) + + assert_allclose(spline(times).as_euler('xyz', degrees=True), angles) + assert_allclose(spline(0).as_euler('xyz', degrees=True), angles[0]) + + h = 1e-8 + rv0 = spline(times).as_rotvec() + rvm = spline(times - h).as_rotvec() + rvp = spline(times + h).as_rotvec() + # rtol bumped from 1e-15 to 1.5e-15 in gh18414 for linux 32 bit + assert_allclose(rv0, 0.5 * (rvp + rvm), rtol=1.5e-15) + + r0 = spline(times, 1) + rm = spline(times - h, 1) + rp = spline(times + h, 1) + assert_allclose(r0, 0.5 * (rm + rp), rtol=1e-14) + + a0 = spline(times, 2) + am = spline(times - h, 2) + ap = spline(times + h, 2) + assert_allclose(a0, am, rtol=1e-7) + assert_allclose(a0, ap, rtol=1e-7) + + +def test_error_handling(): + raises(ValueError, RotationSpline, [1.0], Rotation.random()) + + r = Rotation.random(10) + t = np.arange(10).reshape(5, 2) + raises(ValueError, RotationSpline, t, r) + + t = np.arange(9) + raises(ValueError, RotationSpline, t, r) + + t = np.arange(10) + t[5] = 0 + raises(ValueError, RotationSpline, t, r) + + t = np.arange(10) + + s = RotationSpline(t, r) + raises(ValueError, s, 10, -1) + + raises(ValueError, s, np.arange(10).reshape(5, 2)) diff --git a/env-llmeval/lib/python3.10/site-packages/scipy/special/tests/data/gsl.npz b/env-llmeval/lib/python3.10/site-packages/scipy/special/tests/data/gsl.npz new file mode 100644 index 0000000000000000000000000000000000000000..b090dae17b5b0403f7c4919c46a464a09509aeab --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/scipy/special/tests/data/gsl.npz @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:acab700208cbb301ee51eb1f512cb1c27e7b4e7533fc5a5f5cd5c5d6aa197dd8 +size 51433