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Diffstat (limited to '.venv/lib/python3.12/site-packages/numpy/fft/helper.py')
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diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/helper.py b/.venv/lib/python3.12/site-packages/numpy/fft/helper.py new file mode 100644 index 00000000..927ee1af --- /dev/null +++ b/.venv/lib/python3.12/site-packages/numpy/fft/helper.py @@ -0,0 +1,221 @@ +""" +Discrete Fourier Transforms - helper.py + +""" +from numpy.core import integer, empty, arange, asarray, roll +from numpy.core.overrides import array_function_dispatch, set_module + +# Created by Pearu Peterson, September 2002 + +__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq'] + +integer_types = (int, integer) + + +def _fftshift_dispatcher(x, axes=None): + return (x,) + + +@array_function_dispatch(_fftshift_dispatcher, module='numpy.fft') +def fftshift(x, axes=None): + """ + Shift the zero-frequency component to the center of the spectrum. + + This function swaps half-spaces for all axes listed (defaults to all). + Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even. + + Parameters + ---------- + x : array_like + Input array. + axes : int or shape tuple, optional + Axes over which to shift. Default is None, which shifts all axes. + + Returns + ------- + y : ndarray + The shifted array. + + See Also + -------- + ifftshift : The inverse of `fftshift`. + + Examples + -------- + >>> freqs = np.fft.fftfreq(10, 0.1) + >>> freqs + array([ 0., 1., 2., ..., -3., -2., -1.]) + >>> np.fft.fftshift(freqs) + array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.]) + + Shift the zero-frequency component only along the second axis: + + >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) + >>> freqs + array([[ 0., 1., 2.], + [ 3., 4., -4.], + [-3., -2., -1.]]) + >>> np.fft.fftshift(freqs, axes=(1,)) + array([[ 2., 0., 1.], + [-4., 3., 4.], + [-1., -3., -2.]]) + + """ + x = asarray(x) + if axes is None: + axes = tuple(range(x.ndim)) + shift = [dim // 2 for dim in x.shape] + elif isinstance(axes, integer_types): + shift = x.shape[axes] // 2 + else: + shift = [x.shape[ax] // 2 for ax in axes] + + return roll(x, shift, axes) + + +@array_function_dispatch(_fftshift_dispatcher, module='numpy.fft') +def ifftshift(x, axes=None): + """ + The inverse of `fftshift`. Although identical for even-length `x`, the + functions differ by one sample for odd-length `x`. + + Parameters + ---------- + x : array_like + Input array. + axes : int or shape tuple, optional + Axes over which to calculate. Defaults to None, which shifts all axes. + + Returns + ------- + y : ndarray + The shifted array. + + See Also + -------- + fftshift : Shift zero-frequency component to the center of the spectrum. + + Examples + -------- + >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) + >>> freqs + array([[ 0., 1., 2.], + [ 3., 4., -4.], + [-3., -2., -1.]]) + >>> np.fft.ifftshift(np.fft.fftshift(freqs)) + array([[ 0., 1., 2.], + [ 3., 4., -4.], + [-3., -2., -1.]]) + + """ + x = asarray(x) + if axes is None: + axes = tuple(range(x.ndim)) + shift = [-(dim // 2) for dim in x.shape] + elif isinstance(axes, integer_types): + shift = -(x.shape[axes] // 2) + else: + shift = [-(x.shape[ax] // 2) for ax in axes] + + return roll(x, shift, axes) + + +@set_module('numpy.fft') +def fftfreq(n, d=1.0): + """ + Return the Discrete Fourier Transform sample frequencies. + + The returned float array `f` contains the frequency bin centers in cycles + per unit of the sample spacing (with zero at the start). For instance, if + the sample spacing is in seconds, then the frequency unit is cycles/second. + + Given a window length `n` and a sample spacing `d`:: + + f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even + f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd + + Parameters + ---------- + n : int + Window length. + d : scalar, optional + Sample spacing (inverse of the sampling rate). Defaults to 1. + + Returns + ------- + f : ndarray + Array of length `n` containing the sample frequencies. + + Examples + -------- + >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) + >>> fourier = np.fft.fft(signal) + >>> n = signal.size + >>> timestep = 0.1 + >>> freq = np.fft.fftfreq(n, d=timestep) + >>> freq + array([ 0. , 1.25, 2.5 , ..., -3.75, -2.5 , -1.25]) + + """ + if not isinstance(n, integer_types): + raise ValueError("n should be an integer") + val = 1.0 / (n * d) + results = empty(n, int) + N = (n-1)//2 + 1 + p1 = arange(0, N, dtype=int) + results[:N] = p1 + p2 = arange(-(n//2), 0, dtype=int) + results[N:] = p2 + return results * val + + +@set_module('numpy.fft') +def rfftfreq(n, d=1.0): + """ + Return the Discrete Fourier Transform sample frequencies + (for usage with rfft, irfft). + + The returned float array `f` contains the frequency bin centers in cycles + per unit of the sample spacing (with zero at the start). For instance, if + the sample spacing is in seconds, then the frequency unit is cycles/second. + + Given a window length `n` and a sample spacing `d`:: + + f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even + f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd + + Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`) + the Nyquist frequency component is considered to be positive. + + Parameters + ---------- + n : int + Window length. + d : scalar, optional + Sample spacing (inverse of the sampling rate). Defaults to 1. + + Returns + ------- + f : ndarray + Array of length ``n//2 + 1`` containing the sample frequencies. + + Examples + -------- + >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float) + >>> fourier = np.fft.rfft(signal) + >>> n = signal.size + >>> sample_rate = 100 + >>> freq = np.fft.fftfreq(n, d=1./sample_rate) + >>> freq + array([ 0., 10., 20., ..., -30., -20., -10.]) + >>> freq = np.fft.rfftfreq(n, d=1./sample_rate) + >>> freq + array([ 0., 10., 20., 30., 40., 50.]) + + """ + if not isinstance(n, integer_types): + raise ValueError("n should be an integer") + val = 1.0/(n*d) + N = n//2 + 1 + results = arange(0, N, dtype=int) + return results * val |