?gesvd

Compute the SVD of a general matrix.

Interface Definition

C interface:

sgesvd_(const char *jobu, const char *jobvt, const int *m, const int *n, float *a, const int *lda, float *s, float *u, const int *ldu, float *vt,

const int *ldvt, float *work, const int *lwork, int *info);

dgesvd_(const char *jobu, const char *jobvt, const int *m, const int *n, double *a, const int *lda, double *s, double *u, const int *ldu, double *vt,

const int *ldvt, double *work, const int *lwork, int *info);

cgesvd_(const char *jobu, const char *jobvt, const int *m, const int *n, float _Complex *a, const int *lda, float *s, float _Complex *u, const int *ldu, float _Complex *vt,

const int *ldvt, float _Complex *work, const int *lwork, float *rwork, int *info);

zgesvd_(const char *jobu, const char *jobvt, const int *m, const int *n, double _Complex *a, const int *lda, double *s, double _Complex *u, const int *ldu, double _Complex *vt,

const int *ldvt, double _Complex *work, const int *lwork, double *rwork, int *info);

Fortran interface:

SGESVD(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO);

DGESVD(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO);

CGESVD(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO);

ZGESVD(JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO);

Parameters

Parameter	Type	Description	Input/Output
jobu	Character	'A': returns all columns of unitary matrix U (left singular vectors). 'S': returns the first min(m, n) columns of unitary matrix U (left singular vectors). 'O': returns the first min(m, n) columns of unitary matrix U (left singular vectors) and overwrites them to matrix a. 'N': Unitary matrix U (left singular vectors) is not computed.	Input
jobvt	Character	'A': returns all columns of VH (right singular vectors) and stores them in matrix vt. 'S': returns the first min(m, n) columns of VH (right singular vectors) and stores them in matrix vt. 'O': returns the first min(m, n) columns of VH (right singular vectors) and overwrites them to matrix a. 'N': VH (right singular vectors) is not computed.	Input
m	Integer	Number of rows in matrix a. m ≥ 0.	Input
n	Integer	Number of columns in matrix a. n ≥ 0.	Input
a	A single-precision floating-point array for sgesvd A double-precision floating-point array for dgesvd A single-precision complex array for cgesvd A double-precision complex array for zgesvd	Array with a size of ldan. On entry: Matrix a is an m x n* matrix. On exit If jobu = 'O', matrix a is overwritten by the first min(m, n) columns of unitary matrix U (left singular vectors). If jobvt = 'O', matrix a is overwritten by the first min(m, n) columns of matrix VH (right singular vectors, row-major order). If jobu != 'O' and jobvt != 'O'**, the contents of matrix a are destroyed.	Input/Output
lda	Integer	Leading dimension of matrix a. lda ≥ max(1, m).	Input
s	A single-precision floating-point array for sgesvd A double-precision floating-point array for dgesvd A single-precision floating-point array for cgesvd A double-precision floating-point array for zgesvd	Array with a size of min(m, n). On exit, it contains the singular values of matrix a sorted such that s(i) ≥ s(i+1).	Output
u	A single-precision floating-point array for sgesvd A double-precision floating-point array for dgesvd A single-precision complex array for cgesvd A double-precision complex array for zgesvd	Array with a size of *lduucol, where ucol = m if jobu = 'A' or ucol = min(m, n) if jobu = 'S'. If jobu = 'A', it is an m x m unitary matrix u. If jobu = 'S', it contains the first min(m, n) columns of matrix U (left singular vectors, column-major order). If jobu = 'N' or 'O'**, it is not used.	Output
ldu	Integer	Leading dimension of matrix u. ldu ≥ 1. If jobu = 'S' or 'A', ldu ≥ m.	Input
vt	A single-precision floating-point array for sgesvd A double-precision floating-point array for dgesvd A single-precision complex array for cgesvd A double-precision complex array for zgesvd	Array with a size of *ldvtn. If jobvt = 'A', it is an n x n unitary matrix vH. If jobvt = 'S', it contains the first min(m, n) rows of matrix vH (right singular vectors, row-major order). If jobvt = 'N' or 'O'**, it is not used.	Output
ldvt	Integer	Leading dimension of matrix vt. ldvt ≥ 1. If jobvt = 'A', ldvt ≥ n. If jobvt = 'S', ldvt ≥ min(m, n).	Input
work	A single-precision floating-point array for sgesvd A double-precision floating-point array for dgesvd A single-precision complex array for cgesvd A double-precision complex array for zgesvd	Array with a size of max(1, lwork). On exit: If info = 0, work(1) returns the optimal lwork size.	Output
lwork	Integer	Size of the work array. lwork ≥ max(1, 2min(m, n) + max(m, n)). If lwork = -1*, the function only computes the optimal size of the work array.	Input
rwork (only for complex types)	A single-precision floating-point array for cgesvd A double-precision floating-point array for zgesvd	Array with a size of 5min(m,n). If info* > 0 upon exit, rwork(1:min(m,n)-1) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal elements are stored in s.	Output
info	Integer	0: The execution is successful. Smaller than 0: If info = -i, the i-th parameter has an illegal value. Greater than 0: If ZBDSQR does not converge, info indicates the number of superdiagonal elements of an intermediate bidiagonal matrix B that did not converge to zero.	Output

Dependencies

#include "klapack.h"

Examples

C interface:

const char jobu = 'A';
const char jobvt = 'A';
const int m = 5;
const int n = 5;
const int lda = 5;
const int ldu = 5;
const int ldvt = 5;

double a[] = {72.1673, 66.1857, 64.7644, 28.0199, 91.4151,
              6.5180,  62.8483, 72.4323, 46.5760, 8.6928,
              28.9821, 42.1828, 18.6437, 99.8612, 35.6972,
              67.9812, 5.0880,  85.5035, 79.2945, 54.5920,
              28.6869, 49.7512, 7.5186,  28.6929, 84.6041};

double *s = (double*)malloc(m * sizeof(double));
double *u = (double*)malloc(ldu*m * sizeof(double));
double *vt = (double*)malloc(ldvt*n * sizeof(double));

double qwork;
int lwork = -1;
int info = 0;

dgesvd_(&jobu, &jobvt, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &qwork, &lwork, &info);
if (info != 0) {
    printf("Error, info = %d\n", info);
    return info;
}

lwork = (int)qwork;
double *work = (double*)malloc(lwork * sizeof(double));

dgesvd_(&jobu, &jobvt, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, &info);
if (info != 0) {
    printf("Error, info = %d\n", info);
    return info;
}
/* output */
* s
* 254.071516      87.547400       67.835073       64.370735       14.897476
* u
* -0.395825       -0.377874       -0.458327       -0.488090       -0.502234       -0.155273       -0.217110       0.348128        0.628260        -0.642534       * -0.312281       0.362918        -0.694714       0.528618        0.093312        -0.399962       0.761762        0.321232        -0.289476       -0.269743    
* -0.749482       -0.313183       0.287969        0.061841        0.503430
* vt
* -0.562230       -0.504441       -0.297298       0.148954        -0.564680       -0.340949       0.391046        -0.060652       0.818829        0.238069        * -0.403926       0.372759        0.728616      -0.186514        -0.363629       -0.527964       0.375181        -0.468379       -0.520847       0.299721        * -0.354610       -0.559386       0.397083        -0.035531       0.634351

Fortran interface:

CHARACTER :: jobu = "A"
CHARACTER :: jobvt = "A"
PARAMETER (m = 5)
PARAMETER (n = 5) 
PARAMETER (lda = 5) 
PARAMETER (ldu = 5)
PARAMETER (ldvt = 5)
INTEGER :: info = 0 
REAL(8) :: a(lad, n)
REAL(8) :: s(m) 
REAL(8) :: u(ldu, m)
REAL(8) :: vt(ldvt, n)
REAL(8), ALLOCATABLE :: work(:) 
INTEGER :: lwork = -1 
REAL(8) :: qwork
  
DATA a / 72.1673, 66.1857, 64.7644, 28.0199, 91.4151,
         6.5180,  62.8483, 72.4323, 46.5760, 8.6928,
         28.9821, 42.1828, 18.6437, 99.8612, 35.6972,
         67.9812, 5.0880,  85.5035, 79.2945, 54.5920,
         28.6869, 49.7512, 7.5186,  28.6929, 84.6041/ 
EXTERNAL DGESVD
CALL DGESVD(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, qwork, lwork, info);
lwork = (int)qwork; 
work = (double *)malloc(sizeof(double) * lwork);
CALL DGESVD(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, info);
* 
* Output: 
* s
* 254.071516      87.547400       67.835073       64.370735       14.897476
* u
* -0.395825       -0.377874       -0.458327       -0.488090       -0.502234       -0.155273       -0.217110       0.348128        0.628260        -0.642534       * -0.312281       0.362918        -0.694714       0.528618        0.093312        -0.399962       0.761762        0.321232        -0.289476       -0.269743    
* -0.749482       -0.313183       0.287969        0.061841        0.503430
* vt
* -0.562230       -0.504441       -0.297298       0.148954        -0.564680       -0.340949       0.391046        -0.060652       0.818829        0.238069        * -0.403926       0.372759        0.728616      -0.186514        -0.363629       -0.527964       0.375181        -0.468379       -0.520847       0.299721        * -0.354610       -0.559386       0.397083        -0.035531       0.634351

Parent topic: SVD Functions