mirror of https://github.com/triqs/dft_tools
99 lines
3.6 KiB
Python
99 lines
3.6 KiB
Python
class function_template():
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def old_fft(name, state=None):
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"""This function does something.
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:param name: The name to use.
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:type name: str.
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:param state: Current state to be in.
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:type state: bool.
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:returns: int -- the return code.
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:raises: AttributeError, KeyError
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"""
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return 0
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def fft(a, n=None, axis=-1):
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"""
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Compute the one-dimensional discrete Fourier Transform.
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This function computes the one-dimensional *n*-point discrete Fourier
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Transform (DFT) with the efficient Fast Fourier Transform (FFT)
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algorithm [CT].
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Parameters
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----------
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a : array_like
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Input array, can be complex.
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n : int, optional
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Length of the transformed axis of the output.
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If `n` is smaller than the length of the input, the input is cropped.
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If it is larger, the input is padded with zeros. If `n` is not given,
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the length of the input along the axis specified by `axis` is used.
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axis : int, optional
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Axis over which to compute the FFT. If not given, the last axis is
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used.
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Returns
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-------
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out : complex ndarray
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The truncated or zero-padded input, transformed along the axis
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indicated by `axis`, or the last one if `axis` is not specified.
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Raises
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------
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IndexError
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if `axes` is larger than the last axis of `a`.
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See Also
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--------
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numpy.fft : for definition of the DFT and conventions used.
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ifft : The inverse of `fft`.
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fft2 : The two-dimensional FFT.
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fftn : The *n*-dimensional FFT.
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rfftn : The *n*-dimensional FFT of real input.
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fftfreq : Frequency bins for given FFT parameters.
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Notes
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-----
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FFT (Fast Fourier Transform) refers to a way the discrete Fourier
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Transform (DFT) can be calculated efficiently, by using symmetries in the
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calculated terms. The symmetry is highest when `n` is a power of 2, and
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the transform is therefore most efficient for these sizes.
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The DFT is defined, with the conventions used in this implementation, in
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the documentation for the `numpy.fft` module.
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References
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----------
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.. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the
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machine calculation of complex Fourier series," *Math. Comput.*
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19: 297-301.
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Examples
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--------
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>>> np.fft.fft(np.exp(2j * np.pi * np.arange(8) / 8))
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array([ -3.44505240e-16 +1.14383329e-17j,
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8.00000000e+00 -5.71092652e-15j,
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2.33482938e-16 +1.22460635e-16j,
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1.64863782e-15 +1.77635684e-15j,
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9.95839695e-17 +2.33482938e-16j,
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0.00000000e+00 +1.66837030e-15j,
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1.14383329e-17 +1.22460635e-16j,
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-1.64863782e-15 +1.77635684e-15j])
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>>> import matplotlib.pyplot as plt
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>>> t = np.arange(256)
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>>> sp = np.fft.fft(np.sin(t))
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>>> freq = np.fft.fftfreq(t.shape[-1])
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>>> plt.plot(freq, sp.real, freq, sp.imag)
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[<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at
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0x...>]
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>>> plt.show()
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In this example, real input has an FFT which is Hermitian, i.e., symmetric
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in the real part and anti-symmetric in the imaginary part, as described in
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the `numpy.fft` documentation.
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"""
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return 0
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