first commit

projecten1/lib/python3.6/site-packages/numpy/fft/__init__.py

@@ -0,0 +1,11 @@
+from __future__ import division, absolute_import, print_function
+
+# To get sub-modules
+from .info import __doc__
+
+from .fftpack import *
+from .helper import *
+
+from numpy.testing import _numpy_tester
+test = _numpy_tester().test
+bench = _numpy_tester().bench

projecten1/lib/python3.6/site-packages/numpy/fft/helper.py

@@ -0,0 +1,323 @@
+"""
+Discrete Fourier Transforms - helper.py
+
+"""
+from __future__ import division, absolute_import, print_function
+
+import collections
+import threading
+
+from numpy.compat import integer_types
+from numpy.core import (
+        asarray, concatenate, arange, take, integer, empty
+        )
+
+# Created by Pearu Peterson, September 2002
+
+__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq']
+
+integer_types = integer_types + (integer,)
+
+
+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.,  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.]])
+
+    """
+    tmp = asarray(x)
+    ndim = tmp.ndim
+    if axes is None:
+        axes = list(range(ndim))
+    elif isinstance(axes, integer_types):
+        axes = (axes,)
+    y = tmp
+    for k in axes:
+        n = tmp.shape[k]
+        p2 = (n+1)//2
+        mylist = concatenate((arange(p2, n), arange(p2)))
+        y = take(y, mylist, k)
+    return y
+
+
+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.]])
+
+    """
+    tmp = asarray(x)
+    ndim = tmp.ndim
+    if axes is None:
+        axes = list(range(ndim))
+    elif isinstance(axes, integer_types):
+        axes = (axes,)
+    y = tmp
+    for k in axes:
+        n = tmp.shape[k]
+        p2 = n-(n+1)//2
+        mylist = concatenate((arange(p2, n), arange(p2)))
+        y = take(y, mylist, k)
+    return y
+
+
+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, -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
+    #return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d)
+
+
+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.,  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
+
+
+class _FFTCache(object):
+    """
+    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.
+    """
+    def __init__(self, max_size_in_mb, max_item_count):
+        self._max_size_in_bytes = max_size_in_mb * 1024 ** 2
+        self._max_item_count = max_item_count
+        self._dict = collections.OrderedDict()
+        self._lock = threading.Lock()
+
+    def put_twiddle_factors(self, n, factors):
+        """
+        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.
+        """
+        with self._lock:
+            # Pop + later add to move it to the end for LRU behavior.
+            # Internally everything is stored in a dictionary whose values are
+            # lists.
+            try:
+                value = self._dict.pop(n)
+            except KeyError:
+                value = []
+            value.append(factors)
+            self._dict[n] = value
+            self._prune_cache()
+
+    def pop_twiddle_factors(self, n):
+        """
+        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.
+        """
+        with self._lock:
+            if n not in self._dict or not self._dict[n]:
+                return None
+            # Pop + later add to move it to the end for LRU behavior.
+            all_values = self._dict.pop(n)
+            value = all_values.pop()
+            # Only put pack if there are still some arrays left in the list.
+            if all_values:
+                self._dict[n] = all_values
+            return value
+
+    def _prune_cache(self):
+        # Always keep at least one item.
+        while len(self._dict) > 1 and (
+                len(self._dict) > self._max_item_count or self._check_size()):
+            self._dict.popitem(last=False)
+
+    def _check_size(self):
+        item_sizes = [sum(_j.nbytes for _j in _i)
+                      for _i in self._dict.values() if _i]
+        if not item_sizes:
+            return False
+        max_size = max(self._max_size_in_bytes, 1.5 * max(item_sizes))
+        return sum(item_sizes) > max_size

projecten1/lib/python3.6/site-packages/numpy/fft/info.py

@@ -0,0 +1,187 @@
+"""
+Discrete Fourier Transform (:mod:`numpy.fft`)
+=============================================
+
+.. currentmodule:: numpy.fft
+
+Standard FFTs
+-------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fft       Discrete Fourier transform.
+   ifft      Inverse discrete Fourier transform.
+   fft2      Discrete Fourier transform in two dimensions.
+   ifft2     Inverse discrete Fourier transform in two dimensions.
+   fftn      Discrete Fourier transform in N-dimensions.
+   ifftn     Inverse discrete Fourier transform in N dimensions.
+
+Real FFTs
+---------
+
+.. autosummary::
+   :toctree: generated/
+
+   rfft      Real discrete Fourier transform.
+   irfft     Inverse real discrete Fourier transform.
+   rfft2     Real discrete Fourier transform in two dimensions.
+   irfft2    Inverse real discrete Fourier transform in two dimensions.
+   rfftn     Real discrete Fourier transform in N dimensions.
+   irfftn    Inverse real discrete Fourier transform in N dimensions.
+
+Hermitian FFTs
+--------------
+
+.. autosummary::
+   :toctree: generated/
+
+   hfft      Hermitian discrete Fourier transform.
+   ihfft     Inverse Hermitian discrete Fourier transform.
+
+Helper routines
+---------------
+
+.. autosummary::
+   :toctree: generated/
+
+   fftfreq   Discrete Fourier Transform sample frequencies.
+   rfftfreq  DFT sample frequencies (for usage with rfft, irfft).
+   fftshift  Shift zero-frequency component to center of spectrum.
+   ifftshift Inverse of fftshift.
+
+
+Background information
+----------------------
+
+Fourier analysis is fundamentally a method for expressing a function as a
+sum of periodic components, and for recovering the function from those
+components.  When both the function and its Fourier transform are
+replaced with discretized counterparts, it is called the discrete Fourier
+transform (DFT).  The DFT has become a mainstay of numerical computing in
+part because of a very fast algorithm for computing it, called the Fast
+Fourier Transform (FFT), which was known to Gauss (1805) and was brought
+to light in its current form by Cooley and Tukey [CT]_.  Press et al. [NR]_
+provide an accessible introduction to Fourier analysis and its
+applications.
+
+Because the discrete Fourier transform separates its input into
+components that contribute at discrete frequencies, it has a great number
+of applications in digital signal processing, e.g., for filtering, and in
+this context the discretized input to the transform is customarily
+referred to as a *signal*, which exists in the *time domain*.  The output
+is called a *spectrum* or *transform* and exists in the *frequency
+domain*.
+
+Implementation details
+----------------------
+
+There are many ways to define the DFT, varying in the sign of the
+exponent, normalization, etc.  In this implementation, the DFT is defined
+as
+
+.. math::
+   A_k =  \\sum_{m=0}^{n-1} a_m \\exp\\left\\{-2\\pi i{mk \\over n}\\right\\}
+   \\qquad k = 0,\\ldots,n-1.
+
+The DFT is in general defined for complex inputs and outputs, and a
+single-frequency component at linear frequency :math:`f` is
+represented by a complex exponential
+:math:`a_m = \\exp\\{2\\pi i\\,f m\\Delta t\\}`, where :math:`\\Delta t`
+is the sampling interval.
+
+The values in the result follow so-called "standard" order: If ``A =
+fft(a, n)``, then ``A[0]`` contains the zero-frequency term (the sum of
+the signal), which is always purely real for real inputs. Then ``A[1:n/2]``
+contains the positive-frequency terms, and ``A[n/2+1:]`` contains the
+negative-frequency terms, in order of decreasingly negative frequency.
+For an even number of input points, ``A[n/2]`` represents both positive and
+negative Nyquist frequency, and is also purely real for real input.  For
+an odd number of input points, ``A[(n-1)/2]`` contains the largest positive
+frequency, while ``A[(n+1)/2]`` contains the largest negative frequency.
+The routine ``np.fft.fftfreq(n)`` returns an array giving the frequencies
+of corresponding elements in the output.  The routine
+``np.fft.fftshift(A)`` shifts transforms and their frequencies to put the
+zero-frequency components in the middle, and ``np.fft.ifftshift(A)`` undoes
+that shift.
+
+When the input `a` is a time-domain signal and ``A = fft(a)``, ``np.abs(A)``
+is its amplitude spectrum and ``np.abs(A)**2`` is its power spectrum.
+The phase spectrum is obtained by ``np.angle(A)``.
+
+The inverse DFT is defined as
+
+.. math::
+   a_m = \\frac{1}{n}\\sum_{k=0}^{n-1}A_k\\exp\\left\\{2\\pi i{mk\\over n}\\right\\}
+   \\qquad m = 0,\\ldots,n-1.
+
+It differs from the forward transform by the sign of the exponential
+argument and the default normalization by :math:`1/n`.
+
+Normalization
+-------------
+The default normalization has the direct transforms unscaled and the inverse
+transforms are scaled by :math:`1/n`. It is possible to obtain unitary
+transforms by setting the keyword argument ``norm`` to ``"ortho"`` (default is
+`None`) so that both direct and inverse transforms will be scaled by
+:math:`1/\\sqrt{n}`.
+
+Real and Hermitian transforms
+-----------------------------
+
+When the input is purely real, its transform is Hermitian, i.e., the
+component at frequency :math:`f_k` is the complex conjugate of the
+component at frequency :math:`-f_k`, which means that for real
+inputs there is no information in the negative frequency components that
+is not already available from the positive frequency components.
+The family of `rfft` functions is
+designed to operate on real inputs, and exploits this symmetry by
+computing only the positive frequency components, up to and including the
+Nyquist frequency.  Thus, ``n`` input points produce ``n/2+1`` complex
+output points.  The inverses of this family assumes the same symmetry of
+its input, and for an output of ``n`` points uses ``n/2+1`` input points.
+
+Correspondingly, when the spectrum is purely real, the signal is
+Hermitian.  The `hfft` family of functions exploits this symmetry by
+using ``n/2+1`` complex points in the input (time) domain for ``n`` real
+points in the frequency domain.
+
+In higher dimensions, FFTs are used, e.g., for image analysis and
+filtering.  The computational efficiency of the FFT means that it can
+also be a faster way to compute large convolutions, using the property
+that a convolution in the time domain is equivalent to a point-by-point
+multiplication in the frequency domain.
+
+Higher dimensions
+-----------------
+
+In two dimensions, the DFT is defined as
+
+.. math::
+   A_{kl} =  \\sum_{m=0}^{M-1} \\sum_{n=0}^{N-1}
+   a_{mn}\\exp\\left\\{-2\\pi i \\left({mk\\over M}+{nl\\over N}\\right)\\right\\}
+   \\qquad k = 0, \\ldots, M-1;\\quad l = 0, \\ldots, N-1,
+
+which extends in the obvious way to higher dimensions, and the inverses
+in higher dimensions also extend in the same way.
+
+References
+----------
+
+.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
+        machine calculation of complex Fourier series," *Math. Comput.*
+        19: 297-301.
+
+.. [NR] Press, W., Teukolsky, S., Vetterline, W.T., and Flannery, B.P.,
+        2007, *Numerical Recipes: The Art of Scientific Computing*, ch.
+        12-13.  Cambridge Univ. Press, Cambridge, UK.
+
+Examples
+--------
+
+For examples, see the various functions.
+
+"""
+from __future__ import division, absolute_import, print_function
+
+depends = ['core']

projecten1/lib/python3.6/site-packages/numpy/fft/setup.py

@@ -0,0 +1,19 @@
+from __future__ import division, print_function
+
+
+def configuration(parent_package='',top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    config = Configuration('fft', parent_package, top_path)
+
+    config.add_data_dir('tests')
+
+    # Configure fftpack_lite
+    config.add_extension('fftpack_lite',
+                         sources=['fftpack_litemodule.c', 'fftpack.c']
+                         )
+
+    return config
+
+if __name__ == '__main__':
+    from numpy.distutils.core import setup
+    setup(configuration=configuration)

projecten1/lib/python3.6/site-packages/numpy/fft/tests/test_fftpack.py

@@ -0,0 +1,190 @@
+from __future__ import division, absolute_import, print_function
+
+import numpy as np
+from numpy.random import random
+from numpy.testing import (
+        run_module_suite, assert_array_almost_equal, assert_array_equal,
+        assert_raises,
+        )
+import threading
+import sys
+if sys.version_info[0] >= 3:
+    import queue
+else:
+    import Queue as queue
+
+
+def fft1(x):
+    L = len(x)
+    phase = -2j*np.pi*(np.arange(L)/float(L))
+    phase = np.arange(L).reshape(-1, 1) * phase
+    return np.sum(x*np.exp(phase), axis=1)
+
+
+class TestFFTShift(object):
+
+    def test_fft_n(self):
+        assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
+
+
+class TestFFT1D(object):
+
+    def test_fft(self):
+        x = random(30) + 1j*random(30)
+        assert_array_almost_equal(fft1(x), np.fft.fft(x))
+        assert_array_almost_equal(fft1(x) / np.sqrt(30),
+                                  np.fft.fft(x, norm="ortho"))
+
+    def test_ifft(self):
+        x = random(30) + 1j*random(30)
+        assert_array_almost_equal(x, np.fft.ifft(np.fft.fft(x)))
+        assert_array_almost_equal(
+            x, np.fft.ifft(np.fft.fft(x, norm="ortho"), norm="ortho"))
+
+    def test_fft2(self):
+        x = random((30, 20)) + 1j*random((30, 20))
+        assert_array_almost_equal(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
+                                  np.fft.fft2(x))
+        assert_array_almost_equal(np.fft.fft2(x) / np.sqrt(30 * 20),
+                                  np.fft.fft2(x, norm="ortho"))
+
+    def test_ifft2(self):
+        x = random((30, 20)) + 1j*random((30, 20))
+        assert_array_almost_equal(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
+                                  np.fft.ifft2(x))
+        assert_array_almost_equal(np.fft.ifft2(x) * np.sqrt(30 * 20),
+                                  np.fft.ifft2(x, norm="ortho"))
+
+    def test_fftn(self):
+        x = random((30, 20, 10)) + 1j*random((30, 20, 10))
+        assert_array_almost_equal(
+            np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
+            np.fft.fftn(x))
+        assert_array_almost_equal(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
+                                  np.fft.fftn(x, norm="ortho"))
+
+    def test_ifftn(self):
+        x = random((30, 20, 10)) + 1j*random((30, 20, 10))
+        assert_array_almost_equal(
+            np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
+            np.fft.ifftn(x))
+        assert_array_almost_equal(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
+                                  np.fft.ifftn(x, norm="ortho"))
+
+    def test_rfft(self):
+        x = random(30)
+        for n in [x.size, 2*x.size]:
+            for norm in [None, 'ortho']:
+                assert_array_almost_equal(
+                    np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
+                    np.fft.rfft(x, n=n, norm=norm))
+            assert_array_almost_equal(np.fft.rfft(x, n=n) / np.sqrt(n),
+                                      np.fft.rfft(x, n=n, norm="ortho"))
+
+    def test_irfft(self):
+        x = random(30)
+        assert_array_almost_equal(x, np.fft.irfft(np.fft.rfft(x)))
+        assert_array_almost_equal(
+            x, np.fft.irfft(np.fft.rfft(x, norm="ortho"), norm="ortho"))
+
+    def test_rfft2(self):
+        x = random((30, 20))
+        assert_array_almost_equal(np.fft.fft2(x)[:, :11], np.fft.rfft2(x))
+        assert_array_almost_equal(np.fft.rfft2(x) / np.sqrt(30 * 20),
+                                  np.fft.rfft2(x, norm="ortho"))
+
+    def test_irfft2(self):
+        x = random((30, 20))
+        assert_array_almost_equal(x, np.fft.irfft2(np.fft.rfft2(x)))
+        assert_array_almost_equal(
+            x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"), norm="ortho"))
+
+    def test_rfftn(self):
+        x = random((30, 20, 10))
+        assert_array_almost_equal(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x))
+        assert_array_almost_equal(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
+                                  np.fft.rfftn(x, norm="ortho"))
+
+    def test_irfftn(self):
+        x = random((30, 20, 10))
+        assert_array_almost_equal(x, np.fft.irfftn(np.fft.rfftn(x)))
+        assert_array_almost_equal(
+            x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"), norm="ortho"))
+
+    def test_hfft(self):
+        x = random(14) + 1j*random(14)
+        x_herm = np.concatenate((random(1), x, random(1)))
+        x = np.concatenate((x_herm, x[::-1].conj()))
+        assert_array_almost_equal(np.fft.fft(x), np.fft.hfft(x_herm))
+        assert_array_almost_equal(np.fft.hfft(x_herm) / np.sqrt(30),
+                                  np.fft.hfft(x_herm, norm="ortho"))
+
+    def test_ihttf(self):
+        x = random(14) + 1j*random(14)
+        x_herm = np.concatenate((random(1), x, random(1)))
+        x = np.concatenate((x_herm, x[::-1].conj()))
+        assert_array_almost_equal(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)))
+        assert_array_almost_equal(
+            x_herm, np.fft.ihfft(np.fft.hfft(x_herm, norm="ortho"),
+                                 norm="ortho"))
+
+    def test_all_1d_norm_preserving(self):
+        # verify that round-trip transforms are norm-preserving
+        x = random(30)
+        x_norm = np.linalg.norm(x)
+        n = x.size * 2
+        func_pairs = [(np.fft.fft, np.fft.ifft),
+                      (np.fft.rfft, np.fft.irfft),
+                      # hfft: order so the first function takes x.size samples
+                      #       (necessary for comparison to x_norm above)
+                      (np.fft.ihfft, np.fft.hfft),
+                      ]
+        for forw, back in func_pairs:
+            for n in [x.size, 2*x.size]:
+                for norm in [None, 'ortho']:
+                    tmp = forw(x, n=n, norm=norm)
+                    tmp = back(tmp, n=n, norm=norm)
+                    assert_array_almost_equal(x_norm,
+                                              np.linalg.norm(tmp))
+
+class TestFFTThreadSafe(object):
+    threads = 16
+    input_shape = (800, 200)
+
+    def _test_mtsame(self, func, *args):
+        def worker(args, q):
+            q.put(func(*args))
+
+        q = queue.Queue()
+        expected = func(*args)
+
+        # Spin off a bunch of threads to call the same function simultaneously
+        t = [threading.Thread(target=worker, args=(args, q))
+             for i in range(self.threads)]
+        [x.start() for x in t]
+
+        [x.join() for x in t]
+        # Make sure all threads returned the correct value
+        for i in range(self.threads):
+            assert_array_equal(q.get(timeout=5), expected,
+                'Function returned wrong value in multithreaded context')
+
+    def test_fft(self):
+        a = np.ones(self.input_shape) * 1+0j
+        self._test_mtsame(np.fft.fft, a)
+
+    def test_ifft(self):
+        a = np.ones(self.input_shape) * 1+0j
+        self._test_mtsame(np.fft.ifft, a)
+
+    def test_rfft(self):
+        a = np.ones(self.input_shape)
+        self._test_mtsame(np.fft.rfft, a)
+
+    def test_irfft(self):
+        a = np.ones(self.input_shape) * 1+0j
+        self._test_mtsame(np.fft.irfft, a)
+
+
+if __name__ == "__main__":
+    run_module_suite()

projecten1/lib/python3.6/site-packages/numpy/fft/tests/test_helper.py

@@ -0,0 +1,158 @@
+"""Test functions for fftpack.helper module
+
+Copied from fftpack.helper by Pearu Peterson, October 2005
+
+"""
+from __future__ import division, absolute_import, print_function
+
+import numpy as np
+from numpy.testing import (
+        run_module_suite, assert_array_almost_equal, assert_equal,
+        )
+from numpy import fft
+from numpy import pi
+from numpy.fft.helper import _FFTCache
+
+
+class TestFFTShift(object):
+
+    def test_definition(self):
+        x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
+        y = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
+        assert_array_almost_equal(fft.fftshift(x), y)
+        assert_array_almost_equal(fft.ifftshift(y), x)
+        x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
+        y = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]
+        assert_array_almost_equal(fft.fftshift(x), y)
+        assert_array_almost_equal(fft.ifftshift(y), x)
+
+    def test_inverse(self):
+        for n in [1, 4, 9, 100, 211]:
+            x = np.random.random((n,))
+            assert_array_almost_equal(fft.ifftshift(fft.fftshift(x)), x)
+
+    def test_axes_keyword(self):
+        freqs = [[0, 1, 2], [3, 4, -4], [-3, -2, -1]]
+        shifted = [[-1, -3, -2], [2, 0, 1], [-4, 3, 4]]
+        assert_array_almost_equal(fft.fftshift(freqs, axes=(0, 1)), shifted)
+        assert_array_almost_equal(fft.fftshift(freqs, axes=0),
+                fft.fftshift(freqs, axes=(0,)))
+        assert_array_almost_equal(fft.ifftshift(shifted, axes=(0, 1)), freqs)
+        assert_array_almost_equal(fft.ifftshift(shifted, axes=0),
+                fft.ifftshift(shifted, axes=(0,)))
+
+
+class TestFFTFreq(object):
+
+    def test_definition(self):
+        x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
+        assert_array_almost_equal(9*fft.fftfreq(9), x)
+        assert_array_almost_equal(9*pi*fft.fftfreq(9, pi), x)
+        x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
+        assert_array_almost_equal(10*fft.fftfreq(10), x)
+        assert_array_almost_equal(10*pi*fft.fftfreq(10, pi), x)
+
+
+class TestRFFTFreq(object):
+
+    def test_definition(self):
+        x = [0, 1, 2, 3, 4]
+        assert_array_almost_equal(9*fft.rfftfreq(9), x)
+        assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
+        x = [0, 1, 2, 3, 4, 5]
+        assert_array_almost_equal(10*fft.rfftfreq(10), x)
+        assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x)
+
+
+class TestIRFFTN(object):
+
+    def test_not_last_axis_success(self):
+        ar, ai = np.random.random((2, 16, 8, 32))
+        a = ar + 1j*ai
+
+        axes = (-2,)
+
+        # Should not raise error
+        fft.irfftn(a, axes=axes)
+
+
+class TestFFTCache(object):
+
+    def test_basic_behaviour(self):
+        c = _FFTCache(max_size_in_mb=1, max_item_count=4)
+
+        # Put
+        c.put_twiddle_factors(1, np.ones(2, dtype=np.float32))
+        c.put_twiddle_factors(2, np.zeros(2, dtype=np.float32))
+
+        # Get
+        assert_array_almost_equal(c.pop_twiddle_factors(1),
+                                  np.ones(2, dtype=np.float32))
+        assert_array_almost_equal(c.pop_twiddle_factors(2),
+                                  np.zeros(2, dtype=np.float32))
+
+        # Nothing should be left.
+        assert_equal(len(c._dict), 0)
+
+        # Now put everything in twice so it can be retrieved once and each will
+        # still have one item left.
+        for _ in range(2):
+            c.put_twiddle_factors(1, np.ones(2, dtype=np.float32))
+            c.put_twiddle_factors(2, np.zeros(2, dtype=np.float32))
+        assert_array_almost_equal(c.pop_twiddle_factors(1),
+                                  np.ones(2, dtype=np.float32))
+        assert_array_almost_equal(c.pop_twiddle_factors(2),
+                                  np.zeros(2, dtype=np.float32))
+        assert_equal(len(c._dict), 2)
+
+    def test_automatic_pruning(self):
+        # That's around 2600 single precision samples.
+        c = _FFTCache(max_size_in_mb=0.01, max_item_count=4)
+
+        c.put_twiddle_factors(1, np.ones(200, dtype=np.float32))
+        c.put_twiddle_factors(2, np.ones(200, dtype=np.float32))
+        assert_equal(list(c._dict.keys()), [1, 2])
+
+        # This is larger than the limit but should still be kept.
+        c.put_twiddle_factors(3, np.ones(3000, dtype=np.float32))
+        assert_equal(list(c._dict.keys()), [1, 2, 3])
+        # Add one more.
+        c.put_twiddle_factors(4, np.ones(3000, dtype=np.float32))
+        # The other three should no longer exist.
+        assert_equal(list(c._dict.keys()), [4])
+
+        # Now test the max item count pruning.
+        c = _FFTCache(max_size_in_mb=0.01, max_item_count=2)
+        c.put_twiddle_factors(2, np.empty(2))
+        c.put_twiddle_factors(1, np.empty(2))
+        # Can still be accessed.
+        assert_equal(list(c._dict.keys()), [2, 1])
+
+        c.put_twiddle_factors(3, np.empty(2))
+        # 1 and 3 can still be accessed - c[2] has been touched least recently
+        # and is thus evicted.
+        assert_equal(list(c._dict.keys()), [1, 3])
+
+        # One last test. We will add a single large item that is slightly
+        # bigger then the cache size. Some small items can still be added.
+        c = _FFTCache(max_size_in_mb=0.01, max_item_count=5)
+        c.put_twiddle_factors(1, np.ones(3000, dtype=np.float32))
+        c.put_twiddle_factors(2, np.ones(2, dtype=np.float32))
+        c.put_twiddle_factors(3, np.ones(2, dtype=np.float32))
+        c.put_twiddle_factors(4, np.ones(2, dtype=np.float32))
+        assert_equal(list(c._dict.keys()), [1, 2, 3, 4])
+
+        # One more big item. This time it is 6 smaller ones but they are
+        # counted as one big item.
+        for _ in range(6):
+            c.put_twiddle_factors(5, np.ones(500, dtype=np.float32))
+        # '1' no longer in the cache. Rest still in the cache.
+        assert_equal(list(c._dict.keys()), [2, 3, 4, 5])
+
+        # Another big item - should now be the only item in the cache.
+        c.put_twiddle_factors(6, np.ones(4000, dtype=np.float32))
+        assert_equal(list(c._dict.keys()), [6])
+
+
+if __name__ == "__main__":
+    run_module_suite()