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""" Discrete Fourier Transforms - helper.py
"""
except ImportError: import dummy_threading as threading
# Created by Pearu Peterson, September 2002
return (x,)
""" 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., 4., -5., -4., -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.]])
""" elif isinstance(axes, integer_types): shift = x.shape[axes] // 2 else: shift = [x.shape[ax] // 2 for ax in axes]
""" 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)
""" 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, -5. , -3.75, -2.5 , -1.25])
""" raise ValueError("n should be an integer")
""" 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., 40., -50., -40., -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
""" Cache for the FFT twiddle factors as an LRU (least recently used) cache.
Parameters ---------- max_size_in_mb : int Maximum memory usage of the cache before items are being evicted. max_item_count : int Maximum item count of the cache before items are being evicted.
Notes ----- Items will be evicted if either limit has been reached upon getting and setting. The maximum memory usages is not strictly the given ``max_size_in_mb`` but rather ``max(max_size_in_mb, 1.5 * size_of_largest_item)``. Thus the cache will never be completely cleared - at least one item will remain and a single large item can cause the cache to retain several smaller items even if the given maximum cache size has been exceeded. """
""" Store twiddle factors for an FFT of length n in the cache.
Putting multiple twiddle factors for a certain n will store it multiple times.
Parameters ---------- n : int Data length for the FFT. factors : ndarray The actual twiddle values. """ # Pop + later add to move it to the end for LRU behavior. # Internally everything is stored in a dictionary whose values are # lists.
""" Pop twiddle factors for an FFT of length n from the cache.
Will return None if the requested twiddle factors are not available in the cache.
Parameters ---------- n : int Data length for the FFT.
Returns ------- out : ndarray or None The retrieved twiddle factors if available, else None. """ # Pop + later add to move it to the end for LRU behavior. # Only put pack if there are still some arrays left in the list. self._dict[n] = all_values
# Always keep at least one item. len(self._dict) > self._max_item_count or self._check_size()): self._dict.popitem(last=False)
for _i in self._dict.values() if _i] return False |