svd

Perform Singular Value Decomposition. More...

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

Detailed Description

Perform Singular Value Decomposition.

This function factorizes a matrix A into two unitary matrices U and Vt, and a diagonal matrix S such that

\(A = U * S * Vt\)

If A has M rows and N columns, U is of the size M x M , V is of size N x N, and S is of size M x N

The arrayfire function only returns the non zero diagonal elements of S. To reconstruct the original matrix A from the individual factors, the following code snuppet can be used:

    af::array U, S, Vt;
    af::svd(U, S, Vt, A);

    const int MN = std::min(M, N);

    af::array UU = U(af::span, af::seq(MN));
    af::array SS = af::diag(S, 0, false).as(ty);
    af::array VV = Vt(af::seq(MN), af::span);

    af::array AA = matmul(UU, SS, VV);

When memory is a concern, and A is dispensible, svdInPlace() can be used

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Function Documentation

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

AFAPI af_err af_svd_inplace	(	af_array *	u,
		af_array *	s,
		af_array *	vt,
		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,out]	in	is the input matrix that will contain random data after this operation

AFAPI void af::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

Examples:

lin_algebra/svd.cpp.

AFAPI void af::svdInPlace	(	array &	u,
		array &	s,
		array &	vt,
		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,out]	in	is the input matrix and will contain random data after this operation