.TH "SRC/zgesvd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zgesvd.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzgesvd\fP (jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, info)" .br .RI "\fB ZGESVD computes the singular value decomposition (SVD) for GE matrices\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zgesvd (character jobu, character jobvt, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)" .PP \fB ZGESVD computes the singular value decomposition (SVD) for GE matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZGESVD computes the singular value decomposition (SVD) of a complex !> M-by-N matrix A, optionally computing the left and/or right singular !> vectors\&. The SVD is written !> !> A = U * SIGMA * conjugate-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 unitary matrix, and !> V is an N-by-N unitary 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**H, not V\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIJOBU\fP .PP .nf !> JOBU is CHARACTER*1 !> 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\&. !> .fi .PP .br \fIJOBVT\fP .PP .nf !> JOBVT is CHARACTER*1 !> Specifies options for computing all or part of the matrix !> V**H: !> = 'A': all N rows of V**H are returned in the array VT; !> = 'S': the first min(m,n) rows of V**H (the right singular !> vectors) are returned in the array VT; !> = 'O': the first min(m,n) rows of V**H (the right singular !> vectors) are overwritten on the array A; !> = 'N': no rows of V**H (no right singular vectors) are !> computed\&. !> !> JOBVT and JOBU cannot both be 'O'\&. !> .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 COMPLEX*16 array, dimension (LDA,N) !> 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**H (the right singular vectors, !> stored rowwise); !> if JOBU \&.ne\&. 'O' and JOBVT \&.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 DOUBLE PRECISION 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 COMPLEX*16 array, dimension (LDU,UCOL) !> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'\&. !> If JOBU = 'A', U contains the M-by-M unitary 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\&. !> .fi .PP .br \fILDU\fP .PP .nf !> LDU is INTEGER !> The leading dimension of the array U\&. LDU >= 1; if !> JOBU = 'S' or 'A', LDU >= M\&. !> .fi .PP .br \fIVT\fP .PP .nf !> VT is COMPLEX*16 array, dimension (LDVT,N) !> If JOBVT = 'A', VT contains the N-by-N unitary matrix !> V**H; !> if JOBVT = 'S', VT contains the first min(m,n) rows of !> V**H (the right singular vectors, stored rowwise); !> if JOBVT = 'N' or 'O', VT is not referenced\&. !> .fi .PP .br \fILDVT\fP .PP .nf !> LDVT is INTEGER !> The leading dimension of the array VT\&. LDVT >= 1; if !> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 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 >= MAX(1,2*MIN(M,N)+MAX(M,N))\&. !> For good performance, LWORK should generally be larger\&. !> !> If LWORK = -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 LWORK is issued by XERBLA\&. !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is DOUBLE PRECISION array, dimension (5*min(M,N)) !> On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the !> unconverged superdiagonal elements of an upper bidiagonal !> matrix B whose diagonal is in S (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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit\&. !> < 0: if INFO = -i, the i-th argument had an illegal value\&. !> > 0: if ZBDSQR did not converge, INFO specifies how many !> superdiagonals of an intermediate bidiagonal form B !> did not converge to zero\&. See the description of RWORK !> above for details\&. !> .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 .PP Definition at line \fB212\fP of file \fBzgesvd\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.