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// Copyright (c) 2019 by the SciSharp Team
// Code generated by CodeMinion: https://github.com/SciSharp/CodeMinion
using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using Python.Runtime;
using Numpy.Models;
namespace Numpy
{
public static partial class np
{
public static partial class fft {
/// <summary>
/// Compute the one-dimensional discrete Fourier Transform for real input.
///
/// This function computes the one-dimensional n-point discrete Fourier
/// Transform (DFT) of a real-valued array by means of an efficient algorithm
/// called the Fast Fourier Transform (FFT).
///
/// Notes
///
/// When the DFT is computed for purely real input, the output is
/// Hermitian-symmetric, i.e. the negative frequency terms are just the complex
/// conjugates of the corresponding positive-frequency terms, and the
/// negative-frequency terms are therefore redundant. This function does not
/// compute the negative frequency terms, and the length of the transformed
/// axis of the output is therefore n//2 + 1.
///
/// When A = rfft(a) and fs is the sampling frequency, A[0] contains
/// the zero-frequency term 0*fs, which is real due to Hermitian symmetry.
///
/// If n is even, A[-1] contains the term representing both positive
/// and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely
/// real. If n is odd, there is no term at fs/2; A[-1] contains
/// the largest positive frequency (fs/2*(n-1)/n), and is complex in the
/// general case.
///
/// If the input a contains an imaginary part, it is silently discarded.
/// </summary>
/// <param name="a">
/// Input array
/// </param>
/// <param name="n">
/// Number of points along transformation axis in the input to use.
/// If n is smaller than the length of the input, the input is cropped.
/// If it is larger, the input is padded with zeros. If n is not given,
/// the length of the input along the axis specified by axis is used.
/// </param>
/// <param name="axis">
/// Axis over which to compute the FFT. If not given, the last axis is
/// used.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axis
/// indicated by axis, or the last one if axis is not specified.
/// If n is even, the length of the transformed axis is (n/2)+1.
/// If n is odd, the length is (n+1)/2.
/// </returns>
public static NDarray rfft(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_rfft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the inverse of the n-point DFT for real input.
///
/// This function computes the inverse of the one-dimensional n-point
/// discrete Fourier Transform of real input computed by rfft.
/// In other words, irfft(rfft(a), len(a)) == a to within numerical
/// accuracy. (See Notes below for why len(a) is necessary here.)
///
/// The input is expected to be in the form returned by rfft, i.e. the
/// real zero-frequency term followed by the complex positive frequency terms
/// in order of increasing frequency. Since the discrete Fourier Transform of
/// real input is Hermitian-symmetric, the negative frequency terms are taken
/// to be the complex conjugates of the corresponding positive frequency terms.
///
/// Notes
///
/// Returns the real valued n-point inverse discrete Fourier transform
/// of a, where a contains the non-negative frequency terms of a
/// Hermitian-symmetric sequence. n is the length of the result, not the
/// input.
///
/// If you specify an n such that a must be zero-padded or truncated, the
/// extra/removed values will be added/removed at high frequencies. One can
/// thus resample a series to m points via Fourier interpolation by:
/// a_resamp = irfft(rfft(a), m).
/// </summary>
/// <param name="a">
/// The input array.
/// </param>
/// <param name="n">
/// Length of the transformed axis of the output.
/// For n output points, n//2+1 input points are necessary. If the
/// input is longer than this, it is cropped. If it is shorter than this,
/// it is padded with zeros. If n is not given, it is determined from
/// the length of the input along the axis specified by axis.
/// </param>
/// <param name="axis">
/// Axis over which to compute the inverse FFT. If not given, the last
/// axis is used.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axis
/// indicated by axis, or the last one if axis is not specified.
/// The length of the transformed axis is n, or, if n is not given,
/// 2*(m-1) where m is the length of the transformed axis of the
/// input. To get an odd number of output points, n must be specified.
/// </returns>
public static NDarray irfft(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_irfft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the 2-dimensional FFT of a real array.
///
/// Notes
///
/// This is really just rfftn with different default behavior.
/// For more details see rfftn.
/// </summary>
/// <param name="a">
/// Input array, taken to be real.
/// </param>
/// <param name="s">
/// Shape of the FFT.
/// </param>
/// <param name="axes">
/// Axes over which to compute the FFT.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The result of the real 2-D FFT.
/// </returns>
public static NDarray rfft2(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_rfft2(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the 2-dimensional inverse FFT of a real array.
///
/// Notes
///
/// This is really irfftn with different defaults.
/// For more details see irfftn.
/// </summary>
/// <param name="a">
/// The input array
/// </param>
/// <param name="s">
/// Shape of the inverse FFT.
/// </param>
/// <param name="axes">
/// The axes over which to compute the inverse fft.
/// Default is the last two axes.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The result of the inverse real 2-D FFT.
/// </returns>
public static NDarray irfft2(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_irfft2(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the N-dimensional discrete Fourier Transform for real input.
///
/// This function computes the N-dimensional discrete Fourier Transform over
/// any number of axes in an M-dimensional real array by means of the Fast
/// Fourier Transform (FFT). By default, all axes are transformed, with the
/// real transform performed over the last axis, while the remaining
/// transforms are complex.
///
/// Notes
///
/// The transform for real input is performed over the last transformation
/// axis, as by rfft, then the transform over the remaining axes is
/// performed as by fftn. The order of the output is as for rfft for the
/// final transformation axis, and as for fftn for the remaining
/// transformation axes.
///
/// See fft for details, definitions and conventions used.
/// </summary>
/// <param name="a">
/// Input array, taken to be real.
/// </param>
/// <param name="s">
/// Shape (length along each transformed axis) to use from the input.
/// (s[0] refers to axis 0, s[1] to axis 1, etc.).
/// The final element of s corresponds to n for rfft(x, n), while
/// for the remaining axes, it corresponds to n for fft(x, n).
/// Along any axis, if the given shape is smaller than that of the input,
/// the input is cropped. If it is larger, the input is padded with zeros.
/// if s is not given, the shape of the input along the axes specified
/// by axes is used.
/// </param>
/// <param name="axes">
/// Axes over which to compute the FFT. If not given, the last len(s)
/// axes are used, or all axes if s is also not specified.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axes
/// indicated by axes, or by a combination of s and a,
/// as explained in the parameters section above.
/// The length of the last axis transformed will be s[-1]//2+1,
/// while the remaining transformed axes will have lengths according to
/// s, or unchanged from the input.
/// </returns>
public static NDarray rfftn(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_rfftn(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the inverse of the N-dimensional FFT of real input.
///
/// This function computes the inverse of the N-dimensional discrete
/// Fourier Transform for real input over any number of axes in an
/// M-dimensional array by means of the Fast Fourier Transform (FFT). In
/// other words, irfftn(rfftn(a), a.shape) == a to within numerical
/// accuracy. (The a.shape is necessary like len(a) is for irfft,
/// and for the same reason.)
///
/// The input should be ordered in the same way as is returned by rfftn,
/// i.e. as for irfft for the final transformation axis, and as for ifftn
/// along all the other axes.
///
/// Notes
///
/// See fft for definitions and conventions used.
///
/// See rfft for definitions and conventions used for real input.
/// </summary>
/// <param name="a">
/// Input array.
/// </param>
/// <param name="s">
/// Shape (length of each transformed axis) of the output
/// (s[0] refers to axis 0, s[1] to axis 1, etc.). s is also the
/// number of input points used along this axis, except for the last axis,
/// where s[-1]//2+1 points of the input are used.
/// Along any axis, if the shape indicated by s is smaller than that of
/// the input, the input is cropped. If it is larger, the input is padded
/// with zeros. If s is not given, the shape of the input along the
/// axes specified by axes is used.
/// </param>
/// <param name="axes">
/// Axes over which to compute the inverse FFT. If not given, the last
/// len(s) axes are used, or all axes if s is also not specified.
/// Repeated indices in axes means that the inverse transform over that
/// axis is performed multiple times.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axes
/// indicated by axes, or by a combination of s or a,
/// as explained in the parameters section above.
/// The length of each transformed axis is as given by the corresponding
/// element of s, or the length of the input in every axis except for the
/// last one if s is not given. In the final transformed axis the length
/// of the output when s is not given is 2*(m-1) where m is the
/// length of the final transformed axis of the input. To get an odd
/// number of output points in the final axis, s must be specified.
/// </returns>
public static NDarray irfftn(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_irfftn(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the FFT of a signal that has Hermitian symmetry, i.e., a real
/// spectrum.
///
/// Notes
///
/// hfft/ihfft are a pair analogous to rfft/irfft, but for the
/// opposite case: here the signal has Hermitian symmetry in the time
/// domain and is real in the frequency domain. So here it’s hfft for
/// which you must supply the length of the result if it is to be odd.
/// </summary>
/// <param name="a">
/// The input array.
/// </param>
/// <param name="n">
/// Length of the transformed axis of the output. For n output
/// points, n//2 + 1 input points are necessary. If the input is
/// longer than this, it is cropped. If it is shorter than this, it is
/// padded with zeros. If n is not given, it is determined from the
/// length of the input along the axis specified by axis.
/// </param>
/// <param name="axis">
/// Axis over which to compute the FFT. If not given, the last
/// axis is used.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axis
/// indicated by axis, or the last one if axis is not specified.
/// The length of the transformed axis is n, or, if n is not given,
/// 2*m - 2 where m is the length of the transformed axis of
/// the input. To get an odd number of output points, n must be
/// specified, for instance as 2*m - 1 in the typical case,
/// </returns>
public static NDarray hfft(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_hfft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the inverse FFT of a signal that has Hermitian symmetry.
///
/// Notes
///
/// hfft/ihfft are a pair analogous to rfft/irfft, but for the
/// opposite case: here the signal has Hermitian symmetry in the time
/// domain and is real in the frequency domain. So here it’s hfft for
/// which you must supply the length of the result if it is to be odd:
/// </summary>
/// <param name="a">
/// Input array.
/// </param>
/// <param name="n">
/// Length of the inverse FFT, the number of points along
/// transformation axis in the input to use. If n is smaller than
/// the length of the input, the input is cropped. If it is larger,
/// the input is padded with zeros. If n is not given, the length of
/// the input along the axis specified by axis is used.
/// </param>
/// <param name="axis">
/// Axis over which to compute the inverse FFT. If not given, the last
/// axis is used.
/// </param>
/// <param name="norm">
/// Normalization mode (see numpy.fft). Default is None.
/// </param>
/// <returns>
/// The truncated or zero-padded input, transformed along the axis
/// indicated by axis, or the last one if axis is not specified.
/// The length of the transformed axis is n//2 + 1.
/// </returns>
public static NDarray ihfft(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_ihfft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// 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:
/// </summary>
/// <param name="n">
/// Window length.
/// </param>
/// <param name="d">
/// Sample spacing (inverse of the sampling rate). Defaults to 1.
/// </param>
/// <returns>
/// Array of length n containing the sample frequencies.
/// </returns>
public static NDarray fftfreq(int n, float? d = 1.0f)
=> NumPy.Instance.fft_fftfreq(n, d:d);
}
public static partial class fft {
/// <summary>
/// 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:
///
/// Unlike fftfreq (but like scipy.fftpack.rfftfreq)
/// the Nyquist frequency component is considered to be positive.
/// </summary>
/// <param name="n">
/// Window length.
/// </param>
/// <param name="d">
/// Sample spacing (inverse of the sampling rate). Defaults to 1.
/// </param>
/// <returns>
/// Array of length n//2 + 1 containing the sample frequencies.
/// </returns>
public static NDarray rfftfreq(int n, float? d = 1.0f)
=> NumPy.Instance.fft_rfftfreq(n, d:d);
}
public static partial class fft {
/// <summary>
/// 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.
/// </summary>
/// <param name="x">
/// Input array.
/// </param>
/// <param name="axes">
/// Axes over which to shift. Default is None, which shifts all axes.
/// </param>
/// <returns>
/// The shifted array.
/// </returns>
public static NDarray fftshift(NDarray x, int[] axes = null)
=> NumPy.Instance.fft_fftshift(x, axes:axes);
}
public static partial class fft {
/// <summary>
/// The inverse of fftshift. Although identical for even-length x, the
/// functions differ by one sample for odd-length x.
/// </summary>
/// <param name="x">
/// Input array.
/// </param>
/// <param name="axes">
/// Axes over which to calculate. Defaults to None, which shifts all axes.
/// </param>
/// <returns>
/// The shifted array.
/// </returns>
public static NDarray ifftshift(NDarray x, int[] axes = null)
=> NumPy.Instance.fft_ifftshift(x, axes:axes);
}
}
}