sgesdd.f - Man Page
SRC/sgesdd.f
Synopsis
Functions/Subroutines
subroutine sgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
SGESDD
Function/Subroutine Documentation
subroutine sgesdd (character jobz, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)
SGESDD
Purpose:
SGESDD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors. If singular vectors are desired, it uses a divide-and-conquer algorithm. The SVD is written A = 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 VT = V**T, not V.
- Parameters
JOBZ
JOBZ is CHARACTER*1 Specifies options for computing all or part of the matrix U: = 'A': all M columns of U and all N rows of V**T are returned in the arrays U and VT; = 'S': the first min(M,N) columns of U and the first min(M,N) rows of V**T are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten on the array A and all rows of V**T are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**T are overwritten in the array A; = 'N': no columns of U or rows of V**T are computed.
M
M is INTEGER The number of rows of the input matrix A. M >= 0.
N
N is INTEGER The number of columns of the input matrix A. N >= 0.
A
A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if JOBZ = 'O', A is overwritten with the first N columns of U (the left singular vectors, stored columnwise) if M >= N; A is overwritten with the first M rows of V**T (the right singular vectors, stored rowwise) otherwise. if JOBZ .ne. 'O', the contents of A are destroyed.
LDA
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
S
S is REAL array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).
U
U is REAL array, dimension (LDU,UCOL) UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; UCOL = min(M,N) if JOBZ = 'S'. If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M orthogonal matrix U; if JOBZ = 'S', U contains the first min(M,N) columns of U (the left singular vectors, stored columnwise); if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
LDU
LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
VT
VT is REAL array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S', VT contains the first min(M,N) rows of V**T (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
LDVT
LDVT is INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; if JOBZ = 'S', LDVT >= min(M,N).
WORK
WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK;
LWORK
LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1, a workspace query is assumed. The optimal size for the WORK array is calculated and stored in WORK(1), and no other work except argument checking is performed. Let mx = max(M,N) and mn = min(M,N). If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ). If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ). If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn. If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx. These are not tight minimums in all cases; see comments inside code. For good performance, LWORK should generally be larger; a query is recommended.
IWORK
IWORK is INTEGER array, dimension (8*min(M,N))
INFO
INFO is INTEGER < 0: if INFO = -i, the i-th argument had an illegal value. = -4: if A had a NAN entry. > 0: SBDSDC did not converge, updating process failed. = 0: successful exit.
- Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
- Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 211 of file sgesdd.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Referenced By
The man page sgesdd(3) is an alias of sgesdd.f(3).
Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK