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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 Python.Included;
using Numpy.Models;
namespace Numpy
{
public static partial class np
{
public static partial class linalg {
/// <summary>
/// Cholesky decomposition.
///
/// Return the Cholesky decomposition, L * L.H, of the square matrix a,
/// where L is lower-triangular and .H is the conjugate transpose operator
/// (which is the ordinary transpose if a is real-valued). a must be
/// Hermitian (symmetric if real-valued) and positive-definite. Only L is
/// actually returned.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The Cholesky decomposition is often used as a fast way of solving
///
/// (when A is both Hermitian/symmetric and positive-definite).
///
/// First, we solve for in
///
/// and then for in
/// </summary>
/// <param name="a">
/// Hermitian (symmetric if all elements are real), positive-definite
/// input matrix.
/// </param>
/// <returns>
/// Upper or lower-triangular Cholesky factor of a. Returns a
/// matrix object if a is a matrix object.
/// </returns>
public static NDarray cholesky(NDarray a)
=> NumPy.Instance.linalg_cholesky(a);
}
public static partial class linalg {
/// <summary>
/// Compute the determinant of an array.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The determinant is computed via LU factorization using the LAPACK
/// routine z/dgetrf.
/// </summary>
/// <param name="a">
/// Input array to compute determinants for.
/// </param>
/// <returns>
/// Determinant of a.
/// </returns>
public static NDarray det(NDarray a)
=> NumPy.Instance.linalg_det(a);
}
public static partial class linalg {
/// <summary>
/// Compute the eigenvalues and right eigenvectors of a square array.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// This is implemented using the _geev LAPACK routines which compute
/// the eigenvalues and eigenvectors of general square arrays.
///
/// The number w is an eigenvalue of a if there exists a vector
/// v such that dot(a,v) = w * v. Thus, the arrays a, w, and
/// v satisfy the equations dot(a[:,:], v[:,i]) = w[i] * v[:,i]
/// for .
///
/// The array v of eigenvectors may not be of maximum rank, that is, some
/// of the columns may be linearly dependent, although round-off error may
/// obscure that fact. If the eigenvalues are all different, then theoretically
/// the eigenvectors are linearly independent. Likewise, the (complex-valued)
/// matrix of eigenvectors v is unitary if the matrix a is normal, i.e.,
/// if dot(a, a.H) = dot(a.H, a), where a.H denotes the conjugate
/// transpose of a.
///
/// Finally, it is emphasized that v consists of the right (as in
/// right-hand side) eigenvectors of a. A vector y satisfying
/// dot(y.T, a) = z * y.T for some number z is called a left
/// eigenvector of a, and, in general, the left and right eigenvectors
/// of a matrix are not necessarily the (perhaps conjugate) transposes
/// of each other.
///
/// References
///
/// G. Strang, Linear Algebra and Its Applications, 2nd Ed., Orlando, FL,
/// Academic Press, Inc., 1980, Various pp.
/// </summary>
/// <param name="a">
/// Matrices for which the eigenvalues and right eigenvectors will
/// be computed
/// </param>
/// <returns>
/// A tuple of:
/// w
/// The eigenvalues, each repeated according to its multiplicity.
/// The eigenvalues are not necessarily ordered. The resulting
/// array will be of complex type, unless the imaginary part is
/// zero in which case it will be cast to a real type. When a
/// is real the resulting eigenvalues will be real (0 imaginary
/// part) or occur in conjugate pairs
/// v
/// The normalized (unit “length”) eigenvectors, such that the
/// column v[:,i] is the eigenvector corresponding to the
/// eigenvalue w[i].
/// </returns>
public static (NDarray, NDarray) eig(NDarray a)
=> NumPy.Instance.linalg_eig(a);
}
public static partial class linalg {
/// <summary>
/// Return the eigenvalues and eigenvectors of a complex Hermitian
/// (conjugate symmetric) or a real symmetric matrix.
///
/// Returns two objects, a 1-D array containing the eigenvalues of a, and
/// a 2-D square array or matrix (depending on the input type) of the
/// corresponding eigenvectors (in columns).
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The eigenvalues/eigenvectors are computed using LAPACK routines _syevd,
/// _heevd
///
/// The eigenvalues of real symmetric or complex Hermitian matrices are
/// always real. [1] The array v of (column) eigenvectors is unitary
/// and a, w, and v satisfy the equations
/// dot(a, v[:, i]) = w[i] * v[:, i].
///
/// References
/// </summary>
/// <param name="a">
/// Hermitian or real symmetric matrices whose eigenvalues and
/// eigenvectors are to be computed.
/// </param>
/// <param name="UPLO">
/// Specifies whether the calculation is done with the lower triangular
/// part of a (‘L’, default) or the upper triangular part (‘U’).
/// Irrespective of this value only the real parts of the diagonal will
/// be considered in the computation to preserve the notion of a Hermitian
/// matrix. It therefore follows that the imaginary part of the diagonal
/// will always be treated as zero.
/// </param>
/// <returns>
/// A tuple of:
/// w
/// The eigenvalues in ascending order, each repeated according to
/// its multiplicity.
/// v
/// The column v[:, i] is the normalized eigenvector corresponding
/// to the eigenvalue w[i]. Will return a matrix object if a is
/// a matrix object.
/// </returns>
public static (NDarray, NDarray) eigh(NDarray a, string UPLO = "L")
=> NumPy.Instance.linalg_eigh(a, UPLO:UPLO);
}
public static partial class linalg {
/// <summary>
/// Compute the eigenvalues of a general matrix.
///
/// Main difference between eigvals and eig: the eigenvectors aren’t
/// returned.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// This is implemented using the _geev LAPACK routines which compute
/// the eigenvalues and eigenvectors of general square arrays.
/// </summary>
/// <param name="a">
/// A complex- or real-valued matrix whose eigenvalues will be computed.
/// </param>
/// <returns>
/// The eigenvalues, each repeated according to its multiplicity.
/// They are not necessarily ordered, nor are they necessarily
/// real for real matrices.
/// </returns>
public static NDarray eigvals(NDarray a)
=> NumPy.Instance.linalg_eigvals(a);
}
public static partial class linalg {
/// <summary>
/// Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
///
/// Main difference from eigh: the eigenvectors are not computed.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The eigenvalues are computed using LAPACK routines _syevd, _heevd
/// </summary>
/// <param name="a">
/// A complex- or real-valued matrix whose eigenvalues are to be
/// computed.
/// </param>
/// <param name="UPLO">
/// Specifies whether the calculation is done with the lower triangular
/// part of a (‘L’, default) or the upper triangular part (‘U’).
/// Irrespective of this value only the real parts of the diagonal will
/// be considered in the computation to preserve the notion of a Hermitian
/// matrix. It therefore follows that the imaginary part of the diagonal
/// will always be treated as zero.
/// </param>
/// <returns>
/// The eigenvalues in ascending order, each repeated according to
/// its multiplicity.
/// </returns>
public static NDarray eigvalsh(NDarray a, string UPLO = "L")
=> NumPy.Instance.linalg_eigvalsh(a, UPLO:UPLO);
}
public static partial class linalg {
/// <summary>
/// Compute the (multiplicative) inverse of a matrix.
///
/// Given a square matrix a, return the matrix ainv satisfying
/// dot(a, ainv) = dot(ainv, a) = eye(a.shape[0]).
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
/// </summary>
/// <param name="a">
/// Matrix to be inverted.
/// </param>
/// <returns>
/// (Multiplicative) inverse of the matrix a.
/// </returns>
public static NDarray inv(NDarray a)
=> NumPy.Instance.linalg_inv(a);
}
public static partial class linalg {
/// <summary>
/// Return the least-squares solution to a linear matrix equation.
///
/// Solves the equation a x = b by computing a vector x that
/// minimizes the Euclidean 2-norm || b - a x ||^2. The equation may
/// be under-, well-, or over- determined (i.e., the number of
/// linearly independent rows of a can be less than, equal to, or
/// greater than its number of linearly independent columns). If a
/// is square and of full rank, then x (but for round-off error) is
/// the “exact” solution of the equation.
///
/// Notes
///
/// If b is a matrix, then all array results are returned as matrices.
/// </summary>
/// <param name="a">
/// “Coefficient” matrix.
/// </param>
/// <param name="b">
/// Ordinate or “dependent variable” values. If b is two-dimensional,
/// the least-squares solution is calculated for each of the K columns
/// of b.
/// </param>
/// <param name="rcond">
/// Cut-off ratio for small singular values of a.
/// For the purposes of rank determination, singular values are treated
/// as zero if they are smaller than rcond times the largest singular
/// value of a.
/// </param>
/// <returns>
/// A tuple of:
/// x
/// Least-squares solution. If b is two-dimensional,
/// the solutions are in the K columns of x.
/// residuals
/// Sums of residuals; squared Euclidean 2-norm for each column in
/// b - a*x.
/// If the rank of a is < N or M <= N, this is an empty array.
/// If b is 1-dimensional, this is a (1,) shape array.
/// Otherwise the shape is (K,).
/// rank
/// Rank of matrix a.
/// s
/// Singular values of a.
/// </returns>
public static (NDarray, NDarray, int, NDarray) lstsq(NDarray a, NDarray b, float? rcond = null)
=> NumPy.Instance.linalg_lstsq(a, b, rcond:rcond);
}
public static partial class linalg {
/// <summary>
/// Compute the (Moore-Penrose) pseudo-inverse of a matrix.
///
/// Calculate the generalized inverse of a matrix using its
/// singular-value decomposition (SVD) and including all
/// large singular values.
///
/// Notes
///
/// The pseudo-inverse of a matrix A, denoted , is
/// defined as: “the matrix that ‘solves’ [the least-squares problem]
/// ,” i.e., if is said solution, then
/// is that matrix such that .
///
/// It can be shown that if is the singular
/// value decomposition of A, then
/// , where are
/// orthogonal matrices, is a diagonal matrix consisting
/// of A’s so-called singular values, (followed, typically, by
/// zeros), and then is simply the diagonal matrix
/// consisting of the reciprocals of A’s singular values
/// (again, followed by zeros). [1]
///
/// References
/// </summary>
/// <param name="a">
/// Matrix or stack of matrices to be pseudo-inverted.
/// </param>
/// <param name="rcond">
/// Cutoff for small singular values.
/// Singular values smaller (in modulus) than
/// rcond * largest_singular_value (again, in modulus)
/// are set to zero. Broadcasts against the stack of matrices
/// </param>
/// <returns>
/// The pseudo-inverse of a. If a is a matrix instance, then so
/// is B.
/// </returns>
public static NDarray pinv(NDarray a, float rcond = 1e-15f)
=> NumPy.Instance.linalg_pinv(a, rcond);
}
public static partial class linalg {
/// <summary>
/// Solve a linear matrix equation, or system of linear scalar equations.
///
/// Computes the “exact” solution, x, of the well-determined, i.e., full
/// rank, linear matrix equation ax = b.
///
/// Notes
///
/// Broadcasting rules apply, see the numpy.linalg documentation for
/// details.
///
/// The solutions are computed using LAPACK routine _gesv
///
/// a must be square and of full-rank, i.e., all rows (or, equivalently,
/// columns) must be linearly independent; if either is not true, use
/// lstsq for the least-squares best “solution” of the
/// system/equation.
///
/// References
/// </summary>
/// <param name="a">
/// Coefficient matrix.
/// </param>
/// <param name="b">
/// Ordinate or “dependent variable” values.
/// </param>
/// <returns>
/// Solution to the system a x = b. Returned shape is identical to b.
/// </returns>
public static NDarray solve(NDarray a, NDarray b)
=> NumPy.Instance.linalg_solve(a, b);
}
public static partial class linalg {
/// <summary>
/// Singular Value Decomposition.
///
/// When a is a 2D array, it is factorized as u @ np.diag(s) @ vh
/// = (u * s) @ vh, where u and vh are 2D unitary arrays and s is a 1D
/// array of a’s singular values. When a is higher-dimensional, SVD is
/// applied in stacked mode as explained below.
///
/// Notes
///
/// The decomposition is performed using LAPACK routine _gesdd.
///
/// SVD is usually described for the factorization of a 2D matrix .
/// The higher-dimensional case will be discussed below. In the 2D case, SVD is
/// written as , where , ,
/// and . The 1D array s
/// contains the singular values of a and u and vh are unitary. The rows
/// of vh are the eigenvectors of and the columns of u are
/// the eigenvectors of . In both cases the corresponding
/// (possibly non-zero) eigenvalues are given by s**2.
///
/// If a has more than two dimensions, then broadcasting rules apply, as
/// explained in Linear algebra on several matrices at once. This means that SVD is
/// working in “stacked” mode: it iterates over all indices of the first
/// a.ndim - 2 dimensions and for each combination SVD is applied to the
/// last two indices. The matrix a can be reconstructed from the
/// decomposition with either (u * s[..., None, :]) @ vh or
/// u @ (s[..., None] * vh). (The @ operator can be replaced by the
/// function np.matmul for python versions below 3.5.)
///
/// If a is a matrix object (as opposed to an ndarray), then so are
/// all the return values.
/// </summary>
/// <param name="a">
/// A real or complex array with a.ndim >= 2.
/// </param>
/// <param name="full_matrices">
/// If True (default), u and vh have the shapes (..., M, M) and
/// (..., N, N), respectively. Otherwise, the shapes are
/// (..., M, K) and (..., K, N), respectively, where
/// K = min(M, N).
/// </param>
/// <param name="compute_uv">
/// Whether or not to compute u and vh in addition to s. True
/// by default.
/// </param>
/// <returns>
/// A tuple of:
/// u
/// Unitary array(s). The first a.ndim - 2 dimensions have the same
/// size as those of the input a. The size of the last two dimensions
/// depends on the value of full_matrices. Only returned when
/// compute_uv is True.
/// s
/// Vector(s) with the singular values, within each vector sorted in
/// descending order. The first a.ndim - 2 dimensions have the same
/// size as those of the input a.
/// vh
/// Unitary array(s). The first a.ndim - 2 dimensions have the same
/// size as those of the input a. The size of the last two dimensions
/// depends on the value of full_matrices. Only returned when
/// compute_uv is True.
/// </returns>
public static (NDarray, NDarray, NDarray) svd(NDarray a, bool? full_matrices = true, bool? compute_uv = true)
=> NumPy.Instance.linalg_svd(a, full_matrices:full_matrices, compute_uv:compute_uv);
}
public static partial class fft {
/// <summary>
/// Compute the one-dimensional discrete Fourier Transform.
///
/// This function computes the one-dimensional n-point discrete Fourier
/// Transform (DFT) with the efficient Fast Fourier Transform (FFT)
/// algorithm [CT].
///
/// Notes
///
/// FFT (Fast Fourier Transform) refers to a way the discrete Fourier
/// Transform (DFT) can be calculated efficiently, by using symmetries in the
/// calculated terms. The symmetry is highest when n is a power of 2, and
/// the transform is therefore most efficient for these sizes.
///
/// The DFT is defined, with the conventions used in this implementation, in
/// the documentation for the numpy.fft module.
///
/// References
/// </summary>
/// <param name="a">
/// Input array, can be complex.
/// </param>
/// <param name="n">
/// Length of the transformed axis of the output.
/// 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.
/// </returns>
public static NDarray fft_(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_fft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the 2-dimensional discrete Fourier Transform
///
/// This function computes the n-dimensional discrete Fourier Transform
/// over any axes in an M-dimensional array by means of the
/// Fast Fourier Transform (FFT). By default, the transform is computed over
/// the last two axes of the input array, i.e., a 2-dimensional FFT.
///
/// Notes
///
/// fft2 is just fftn with a different default for axes.
///
/// The output, analogously to fft, contains the term for zero frequency in
/// the low-order corner of the transformed axes, the positive frequency terms
/// in the first half of these axes, the term for the Nyquist frequency in the
/// middle of the axes and the negative frequency terms in the second half of
/// the axes, in order of decreasingly negative frequency.
///
/// See fftn for details and a plotting example, and numpy.fft for
/// definitions and conventions used.
/// </summary>
/// <param name="a">
/// Input array, can be complex
/// </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.).
/// This corresponds to n for fft(x, n).
/// Along each 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 two
/// axes are used. A repeated index in axes means the transform over
/// that axis is performed multiple times. A one-element sequence means
/// that a one-dimensional FFT is performed.
/// </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 the last two axes if axes is not given.
/// </returns>
public static NDarray fft2(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_fft2(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the N-dimensional discrete Fourier Transform.
///
/// This function computes the N-dimensional discrete Fourier Transform over
/// any number of axes in an M-dimensional array by means of the Fast Fourier
/// Transform (FFT).
///
/// Notes
///
/// The output, analogously to fft, contains the term for zero frequency in
/// the low-order corner of all axes, the positive frequency terms in the
/// first half of all axes, the term for the Nyquist frequency in the middle
/// of all axes and the negative frequency terms in the second half of all
/// axes, in order of decreasingly negative frequency.
///
/// See numpy.fft for details, definitions and conventions used.
/// </summary>
/// <param name="a">
/// Input array, can be complex.
/// </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.).
/// This 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.
/// Repeated indices in axes means that the 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 and a,
/// as explained in the parameters section above.
/// </returns>
public static NDarray fftn(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_fftn(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the one-dimensional inverse discrete Fourier Transform.
///
/// This function computes the inverse of the one-dimensional n-point
/// discrete Fourier transform computed by fft. In other words,
/// ifft(fft(a)) == a to within numerical accuracy.
/// For a general description of the algorithm and definitions,
/// see numpy.fft.
///
/// The input should be ordered in the same way as is returned by fft,
/// i.e.,
///
/// For an even number of input points, A[n//2] represents the sum of
/// the values at the positive and negative Nyquist frequencies, as the two
/// are aliased together. See numpy.fft for details.
///
/// Notes
///
/// If the input parameter n is larger than the size of the input, the input
/// is padded by appending zeros at the end. Even though this is the common
/// approach, it might lead to surprising results. If a different padding is
/// desired, it must be performed before calling ifft.
/// </summary>
/// <param name="a">
/// Input array, can be complex.
/// </param>
/// <param name="n">
/// Length of the transformed axis of the output.
/// 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.
/// See notes about padding issues.
/// </param>
/// <param name="axis">
/// Axis over which to compute the inverse DFT. 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.
/// </returns>
public static NDarray ifft(NDarray a, int? n = null, int? axis = -1, string norm = null)
=> NumPy.Instance.fft_ifft(a, n:n, axis:axis, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the 2-dimensional inverse discrete Fourier Transform.
///
/// This function computes the inverse of the 2-dimensional discrete Fourier
/// Transform over any number of axes in an M-dimensional array by means of
/// the Fast Fourier Transform (FFT). In other words, ifft2(fft2(a)) == a
/// to within numerical accuracy. By default, the inverse transform is
/// computed over the last two axes of the input array.
///
/// The input, analogously to ifft, should be ordered in the same way as is
/// returned by fft2, i.e. it should have the term for zero frequency
/// in the low-order corner of the two axes, the positive frequency terms in
/// the first half of these axes, the term for the Nyquist frequency in the
/// middle of the axes and the negative frequency terms in the second half of
/// both axes, in order of decreasingly negative frequency.
///
/// Notes
///
/// ifft2 is just ifftn with a different default for axes.
///
/// See ifftn for details and a plotting example, and numpy.fft for
/// definition and conventions used.
///
/// Zero-padding, analogously with ifft, is performed by appending zeros to
/// the input along the specified dimension. Although this is the common
/// approach, it might lead to surprising results. If another form of zero
/// padding is desired, it must be performed before ifft2 is called.
/// </summary>
/// <param name="a">
/// Input array, can be complex.
/// </param>
/// <param name="s">
/// Shape (length of each axis) of the output (s[0] refers to axis 0,
/// s[1] to axis 1, etc.). This corresponds to n for ifft(x, n).
/// Along each 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. See notes for issue on ifft zero padding.
/// </param>
/// <param name="axes">
/// Axes over which to compute the FFT. If not given, the last two
/// axes are used. A repeated index in axes means the transform over
/// that axis is performed multiple times. A one-element sequence means
/// that a one-dimensional FFT is performed.
/// </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 the last two axes if axes is not given.
/// </returns>
public static NDarray ifft2(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_ifft2(a, s:s, axes:axes, norm:norm);
}
public static partial class fft {
/// <summary>
/// Compute the N-dimensional inverse discrete Fourier Transform.
///
/// This function computes the inverse of the N-dimensional discrete
/// Fourier Transform over any number of axes in an M-dimensional array by
/// means of the Fast Fourier Transform (FFT). In other words,
/// ifftn(fftn(a)) == a to within numerical accuracy.
/// For a description of the definitions and conventions used, see numpy.fft.
///
/// The input, analogously to ifft, should be ordered in the same way as is
/// returned by fftn, i.e. it should have the term for zero frequency
/// in all axes in the low-order corner, the positive frequency terms in the
/// first half of all axes, the term for the Nyquist frequency in the middle
/// of all axes and the negative frequency terms in the second half of all
/// axes, in order of decreasingly negative frequency.
///
/// Notes
///
/// See numpy.fft for definitions and conventions used.
///
/// Zero-padding, analogously with ifft, is performed by appending zeros to
/// the input along the specified dimension. Although this is the common
/// approach, it might lead to surprising results. If another form of zero
/// padding is desired, it must be performed before ifftn is called.
/// </summary>
/// <param name="a">
/// Input array, can be complex.
/// </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.).
/// This corresponds to n for ifft(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. See notes for issue on ifft zero padding.
/// </param>
/// <param name="axes">
/// Axes over which to compute the IFFT. 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.
/// </returns>
public static NDarray ifftn(NDarray a, int[] s = null, int[] axes = null, string norm = null)
=> NumPy.Instance.fft_ifftn(a, s:s, axes:axes, norm:norm);
}
/// <summary>
/// Modified Bessel function of the first kind, order 0.
///
/// Usually denoted . This function does broadcast, but will not
/// “up-cast” int dtype arguments unless accompanied by at least one float or
/// complex dtype argument (see Raises below).
///
/// Notes
///
/// We use the algorithm published by Clenshaw [1] and referenced by
/// Abramowitz and Stegun [2], for which the function domain is
/// partitioned into the two intervals [0,8] and (8,inf), and Chebyshev
/// polynomial expansions are employed in each interval. Relative error on
/// the domain [0,30] using IEEE arithmetic is documented [3] as having a
/// peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).
///
/// References
/// </summary>
/// <param name="x">
/// Argument of the Bessel function.
/// </param>
/// <returns>
/// The modified Bessel function evaluated at each of the elements of x.
/// </returns>
public static NDarray i0(NDarray x)
=> NumPy.Instance.i0(x);
}
}