svd

Computes the singular value decomposition of a matrix. More...

Functions
AFAPI void	svd (array &u, array &s, array &vt, const array &in)
	C++ Interface for SVD decomposition.
AFAPI void	svdInPlace (array &u, array &s, array &vt, array &in)
	C++ Interface for SVD decomposition (in-place)
AFAPI af_err	af_svd (af_array *u, af_array *s, af_array *vt, const af_array in)
	C Interface for SVD decomposition.
AFAPI af_err	af_svd_inplace (af_array *u, af_array *s, af_array *vt, af_array in)
	C Interface for SVD decomposition (in-place)

Detailed Description

Computes the singular value decomposition of a matrix.

This function factorizes a matrix \(A\) into two unitary matrices, \(U\) and \(V^T\), and a diagonal matrix \(S\), such that \(A = USV^T\). If \(A\) has \(M\) rows and \(N\) columns ( \(M \times N\)), then \(U\) will be \(M \times M\), \(V\) will be \(N \times N\), and \(S\) will be \(M \times N\). However, for \(S\), this function only returns the non-zero diagonal elements as a sorted (in descending order) 1D array.

To reconstruct the original matrix \(A\) from the individual factors, the following code snippet can be used:

    array U, S, Vt;
    af::svd(U, S, Vt, A);
 
    const int MN = std::min(M, N);
 
    array UU = U(span, seq(MN));
    array SS = diag(S, 0, false).as(ty);
    array VV = Vt(seq(MN), span);
 
    array AA = matmul(UU, SS, VV);

When memory is a concern, and \(A\) is dispensable, af::svdInPlace() can be used. However, this in-place version is currently limited to input arrays where \(M \geq N\).

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Function Documentation

af_svd()

AFAPI af_err af_svd	(	af_array *	u,
		af_array *	s,
		af_array *	vt,
		const af_array	in
	)

C Interface for SVD decomposition.

Parameters

[out]	u	is the output array containing U
[out]	s	is the output array containing the diagonal values of sigma, (singular values of the input matrix))
[out]	vt	is the output array containing V^H
[in]	in	is the input matrix

af_svd_inplace()

AFAPI af_err af_svd_inplace	(	af_array *	u,
		af_array *	s,
		af_array *	vt,
		af_array	in
	)

C Interface for SVD decomposition (in-place)

Parameters

[out]	u	is the output array containing U
[out]	s	is the output array containing the diagonal values of sigma, (singular values of the input matrix))
[out]	vt	is the output array containing V^H
[in,out]	in	is the input matrix that will contain random data after this operation

Note

Currently, in is limited to arrays where dim0 \(\geq\) dim1

This is best used when minimizing memory usage and in is dispensable

svd()

AFAPI void svd	(	array &	u,
		array &	s,
		array &	vt,
		const array &	in
	)

C++ Interface for SVD decomposition.

Parameters

[out]	u	is the output array containing U
[out]	s	is the output array containing the diagonal values of sigma, (singular values of the input matrix))
[out]	vt	is the output array containing V^H
[in]	in	is the input matrix

svdInPlace()

AFAPI void svdInPlace	(	array &	u,
		array &	s,
		array &	vt,
		array &	in
	)

C++ Interface for SVD decomposition (in-place)

Parameters

[out]	u	is the output array containing U
[out]	s	is the output array containing the diagonal values of sigma, (singular values of the input matrix))
[out]	vt	is the output array containing V^H
[in,out]	in	is the input matrix and will contain random data after this operation

Note

Currently, in is limited to arrays where dim0 \(\geq\) dim1

This is best used when minimizing memory usage and in is dispensable