A high-performance general-purpose compute library

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);
const array as(dtype type) const
Casts the array into another data type.
AFAPI void svd(array &u, array &s, array &vt, const array &in)
C++ Interface to perform singular value decomposition.

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 \(M \geq N\).


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]uU
[out]sdiagonal values of sigma (singular values of the input matrix)
[out]vtV^H
[in]ininput 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]uU
[out]sdiagonal values of sigma (singular values of the input matrix)
[out]vtV^H
[in,out]ininput 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]uU
[out]sdiagonal values of sigma (singular values of the input matrix)
[out]vtV^H
[in]ininput 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]uU
[out]sdiagonal values of sigma (singular values of the input matrix)
[out]vtV^H
[in,out]ininput array; contains random data after the operation this operation