# zgesvd.f man page

zgesvd.f —

## Synopsis

### Functions/Subroutines

subroutine **zgesvd** (JOBU, JOBVT, M, **N**, A, **LDA**, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, INFO)**ZGESVD computes the singular value decomposition (SVD) for GE matrices**

## Function/Subroutine Documentation

### 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)

**ZGESVD computes the singular value decomposition (SVD) for GE matrices**

**Purpose:**

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.

**Parameters:**-
*JOBU*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.

*JOBVT*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'.

*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 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.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*S*S is DOUBLE PRECISION array, dimension (min(M,N)) The singular values of A, sorted so that S(i) >= S(i+1).

*U*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.

*LDU*LDU is INTEGER The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.

*VT*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.

*LDVT*LDVT is INTEGER The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).

*WORK*WORK is COMPLEX*16 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 >= 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.

*RWORK*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.

*INFO*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.

**Author:**-
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**April 2012

Definition at line 216 of file zgesvd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgesvd(3) is an alias of zgesvd.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK