NAME

sgesvd - compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors

SYNOPSIS

  SUBROUTINE SGESVD( JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT, 
 *      LDVT, WORK, LDWORK, INFO)
  CHARACTER * 1 JOBU, JOBVT
  INTEGER M, N, LDA, LDU, LDVT, LDWORK, INFO
  REAL A(LDA,*), SING(*), U(LDU,*), VT(LDVT,*), WORK(*)

  SUBROUTINE SGESVD_64( JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT, 
 *      LDVT, WORK, LDWORK, INFO)
  CHARACTER * 1 JOBU, JOBVT
  INTEGER*8 M, N, LDA, LDU, LDVT, LDWORK, INFO
  REAL A(LDA,*), SING(*), U(LDU,*), VT(LDVT,*), WORK(*)

F95 INTERFACE

  SUBROUTINE GESVD( JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU], 
 *       VT, [LDVT], [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: JOBU, JOBVT
  INTEGER :: M, N, LDA, LDU, LDVT, LDWORK, INFO
  REAL, DIMENSION(:) :: SING, WORK
  REAL, DIMENSION(:,:) :: A, U, VT

  SUBROUTINE GESVD_64( JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU], 
 *       VT, [LDVT], [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: JOBU, JOBVT
  INTEGER(8) :: M, N, LDA, LDU, LDVT, LDWORK, INFO
  REAL, DIMENSION(:) :: SING, WORK
  REAL, DIMENSION(:,:) :: A, U, VT

C INTERFACE

#include <sunperf.h>

void sgesvd(char jobu, char jobvt, int m, int n, float *a, int lda, float *sing, float *u, int ldu, float *vt, int ldvt, int *info);

void sgesvd_64(char jobu, char jobvt, long m, long n, float *a, long lda, float *sing, float *u, long ldu, float *vt, long ldvt, long *info);

PURPOSE

sgesvd computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written = U * SIGMA * transpose(V)

where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA 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.

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

ARGUMENTS

JOBU (input)
Specifies options for computing all or part of the matrix U:

 = 'A':  all M columns of U are returned in array U:

 = 'S':  the first min(m,n) columns of U (the left singular
vectors) are returned in the array U;
 = 'O':  the first min(m,n) columns of U (the left singular
vectors) are overwritten on the array A;
 = 'N':  no columns of U (no left singular vectors) are
computed.

JOBVT (input)
Specifies options for computing all or part of the matrix V**T:

 = 'A':  all N rows of V**T are returned in the array VT;

 = 'S':  the first min(m,n) rows of V**T (the right singular
vectors) are returned in the array VT;
 = 'O':  the first min(m,n) rows of V**T (the right singular
vectors) are overwritten on the array A;
 = 'N':  no rows of V**T (no right singular vectors) are
computed.

JOBVT and JOBU cannot both be 'O'.

M (input)
The number of rows of the input matrix A. M > = 0.
N (input)
The number of columns of the input matrix A. N > = 0.
A (input/output)
On entry, the M-by-N matrix A. On exit, if JOBU = 'O', A is overwritten with the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBVT = 'O', A is overwritten with the first min(m,n) rows of V**T (the right singular vectors, stored rowwise); if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A are destroyed.
LDA (input)
The leading dimension of the array A. LDA > = max(1,M).
SING (output)
The singular values of A, sorted so that SING(i) > = SING(i+1).
U (output)
(LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the M-by-M orthogonal matrix U; if JOBU = 'S', U contains the first min(m,n) columns of U (the left singular vectors, stored columnwise); if JOBU = 'N' or 'O', U is not referenced.
LDU (input)
The leading dimension of the array U. LDU > = 1; if JOBU = 'S' or 'A', LDU > = M.
VT (output)
If JOBVT = 'A', VT contains the N-by-N orthogonal matrix V**T; if JOBVT = 'S', VT contains the first min(m,n) rows of V**T (the right singular vectors, stored rowwise); if JOBVT = 'N' or 'O', VT is not referenced.
LDVT (input)
The leading dimension of the array VT. LDVT > = 1; if JOBVT = 'A', LDVT > = N; if JOBVT = 'S', LDVT > = min(M,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK; if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiagonal elements of an upper bidiagonal matrix B whose diagonal is in SING (not necessarily sorted). B satisfies A = U * B * VT, so it has the same singular values as A, and singular vectors related by U and VT.
LDWORK (input)
The dimension of the array WORK. LDWORK > = 1. LDWORK > = MAX(3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). For good performance, LDWORK should generally be larger.
If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LDWORK is issued by XERBLA.

INFO (output)

 = 0:  successful exit.

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

 > 0:  if SBDSQR did not converge, INFO specifies how many
superdiagonals of an intermediate bidiagonal form B
did not converge to zero. See the description of WORK
above for details.