.TH "SRC/sgesdd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/sgesdd.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBsgesdd\fP (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)" .br .RI "\fBSGESDD\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "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)" .PP \fBSGESDD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBZ\fP .PP .nf !> 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\&. !> .fi .PP .br \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the input matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the input matrix A\&. N >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fIS\fP .PP .nf !> S is REAL array, dimension (min(M,N)) !> The singular values of A, sorted so that S(i) >= S(i+1)\&. !> .fi .PP .br \fIU\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDU\fP .PP .nf !> 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\&. !> .fi .PP .br \fIVT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDVT\fP .PP .nf !> 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)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK; !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIIWORK\fP .PP .nf !> IWORK is INTEGER array, dimension (8*min(M,N)) !> .fi .PP .br \fIINFO\fP .PP .nf !> 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\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA .RE .PP .PP Definition at line \fB211\fP of file \fBsgesdd\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.