Created starter files for the project.

venv/Lib/site-packages/numpy/fft/helper.py

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+"""
+Discrete Fourier Transforms - helper.py
+
+"""
+from numpy.compat import integer_types
+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 = integer_types + (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