?gesvdx

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?gesvdx

Computes the SVD and left and right singular vectors for a matrix.

Syntax

lapack_int LAPACKE_sgesvdx (int matrix_layout, char jobu, char jobvt, char range, lapack_int m, lapack_int n, float * a, lapack_int lda, float vl, float vu, lapack_int il, lapack_int iu, lapack_int * ns, float * s, float * u, lapack_int ldu, float * vt, lapack_int ldvt, lapack_int * superb);

lapack_int LAPACKE_dgesvdx (int matrix_layout, char jobu, char jobvt, char range, lapack_int m, lapack_int n, double * a, lapack_int lda, double vl, double vu, lapack_int il, lapack_int iu, lapack_int *ns, double * s, double * u, lapack_int ldu, double * vt, lapack_int ldvt, lapack_int * superb);

lapack_int LAPACKE_cgesvdx (int matrix_layout, char jobu, char jobvt, char range, lapack_int m, lapack_int n, lapack_complex_float * a, lapack_int lda, float vl, float vu, lapack_int il, lapack_int iu, lapack_int * ns, float * s, lapack_complex_float * u, lapack_int ldu, lapack_complex_float * vt, lapack_int ldvt, lapack_int * superb);

lapack_int LAPACKE_zgesvdx (int matrix_layout, char jobu, char jobvt, char range, lapack_int m, lapack_int n, lapack_complex_double * a, lapack_int lda, double vl, double vu, lapack_int il, lapack_int iu, lapack_int * ns, double * s, lapack_complex_double * u, lapack_int ldu, lapack_complex_double * vt, lapack_int ldvt, lapack_int * superb);

Include Files

mkl.h

Description

?gesvdx computes the singular value decomposition (SVD) of a real or complex m-by-n matrix A, optionally computing the left and right singular vectors. The SVD is written

A = U * Σ * transpose(V)

where Σ is an m-by-n matrix which is zero except for its min(m,n) diagonal elements, U is an m-by-m matrix, and V is an n-by-n matrix. The matrices U and V are orthogonal for real A, and unitary for complex A. The diagonal elements of Σ are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m,n) columns of U and V are the left and right singular vectors of A.

?gesvdx uses an eigenvalue problem for obtaining the SVD, which allows for the computation of a subset of singular values and vectors. See ?bdsvdx for details.

Note that the routine returns V^T, not V.

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

jobu

Specifies options for computing all or part of the matrix U:

= 'V': the first min(m,n) columns of U (the left singular vectors) or as specified by range are returned in the array u;

= 'N': no columns of U (no left singular vectors) are computed.

jobvt

Specifies options for computing all or part of the matrix V^T:

= 'V': the first min(m,n) rows of V^T (the right singular vectors) or as specified by range are returned in the array vt;

= 'N': no rows of V^T (no right singular vectors) are computed.

range

= 'A': find all singular values.

= 'V': all singular values in the half-open interval (vl,vu] are found.

= 'I': the il-th through iu-th singular values are found.

m

The number of rows of the input matrix A. m≥ 0.

n

The number of columns of the input matrix A. n≥ 0.

a

Array, size lda*n

On entry, the m-by-n matrix A.

lda

The leading dimension of the array a.

lda≥ max(1,m).

vl

vl≥0.

vu

If range='V', the lower and upper bounds of the interval to be searched for singular values. vu > vl. Not referenced if range = 'A' or 'I'.

il

iu

If range='I', the indices (in ascending order) of the smallest and largest singular values to be returned. 1 ≤il≤iu≤ min(m,n), if min(m,n) > 0. Not referenced if range = 'A' or 'V'.

ldu

The leading dimension of the array u. ldu≥ 1; if jobu = 'V', ldu≥m.

ldvt

The leading dimension of the array vt. ldvt≥ 1; if jobvt = 'V', ldvt≥ns (see above).

Output Parameters

a	On exit, the contents of a are destroyed.
ns	The total number of singular values found, 0 ≤ns≤ min(m, n). If range = 'A', ns = min(m, n); if range = 'I', ns = iu - il + 1.
s	Array, size (min(m,n)) The singular values of `A`, sorted so that `s[i]`≥`s[i + 1]`.
u	Array, size ldu*`ucol` If jobu = 'V', u contains columns of `U` (the left singular vectors, stored columnwise) as specified by range; if jobu = 'N', u is not referenced. NOTE: Make sure that `ucol`≥ns; if range = 'V', the exact value of ns is not known in advance and an upper bound must be used.
vt	Array, size ldvt*n If jobvt = 'V', vt contains the rows of `V`^T (the right singular vectors, stored rowwise) as specified by range; if jobvt = 'N', vt is not referenced. NOTE: Make sure that ldvt≥ns; if range = 'V', the exact value of ns is not known in advance and an upper bound must be used.
superb	Array, size (12*min(m, n)). If info = 0, the first ns elements of superb are zero. If info > 0, then superb contains the indices of the eigenvectors that failed to converge in ?bdsvdx/?stevx.

Return Values

This function returns a value info.

= 0: successful exit.

< 0: if info = -i, the i-th argument had an illegal value.

> 0: if info = i, then i eigenvectors failed to converge in ?bdsvdx/?stevx. if info = n*2 + 1, an internal error occurred in ?bdsvdx.

Parent topic: Singular Value Decomposition: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?gesvdx