svd

Perform singular value decomposition. More...

Functions
AFAPI void	svd (array &u, array &s, array &vt, const array &in)
	C++ Interface to perform singular value decomposition. More...
AFAPI void	svdInPlace (array &u, array &s, array &vt, array &in)
	C++ Interface to perform in-place singular value decomposition. More...
AFAPI af_err	af_svd (af_array *u, af_array *s, af_array *vt, const af_array in)
	C Interface to perform singular value decomposition. More...
AFAPI af_err	af_svd_inplace (af_array *u, af_array *s, af_array *vt, af_array in)
	C Interface to perform in-place singular value decomposition. More...

Detailed Description

Perform singular value decomposition.

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 to perform singular value decomposition.

Parameters

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

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

af_svd_inplace()

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

C Interface to perform in-place singular value decomposition.

This function minimizes memory usage if in is dispensable. Input array in is limited to arrays where dim0 \(\geq\) dim1.

Parameters

[out]	u	U
[out]	s	diagonal values of sigma (singular values of the input matrix)
[out]	vt	V^H
[in,out]	in	input array; contains random data after the operation this operation

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

svd()

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

C++ Interface to perform singular value decomposition.

Parameters

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

svdInPlace()

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

C++ Interface to perform in-place singular value decomposition.

This function minimizes memory usage if in is dispensable. Input array in is limited to arrays where dim0 \(\geq\) dim1.

Parameters

[out]	u	U
[out]	s	diagonal values of sigma (singular values of the input matrix)
[out]	vt	V^H
[in,out]	in	input array; contains random data after the operation this operation