# zgesdd.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **zgesdd** (JOBZ, M, **N**, A, **LDA**, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)**ZGESDD**

## Function/Subroutine Documentation

### subroutine zgesdd (character JOBZ, 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, dimension( * ) IWORK, integer INFO)

**ZGESDD**

**Purpose:**

ZGESDD computes the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method. 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 VT = V**H, not V. The divide and conquer algorithm makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

**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**H 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**H are returned in the arrays U and VT; = 'O': If M >= N, the first N columns of U are overwritten in the array A and all rows of V**H are returned in the array VT; otherwise, all columns of U are returned in the array U and the first M rows of V**H are overwritten in the array A; = 'N': no columns of U or rows of V**H 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 COMPLEX*16 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**H (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 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) 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 unitary 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 COMPLEX*16 array, dimension (LDVT,N) If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the N-by-N unitary matrix V**H; if JOBZ = 'S', VT contains the first min(M,N) rows of V**H (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 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 >= 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 >= 2*mn + mx. If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx. If JOBZ = 'S', LWORK >= mn*mn + 3*mn. If JOBZ = 'A', LWORK >= mn*mn + 2*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.

*RWORK*RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) Let mx = max(M,N) and mn = min(M,N). If JOBZ = 'N', LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn); else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn; else LRWORK >= max( 5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn ).

*IWORK*IWORK is INTEGER array, dimension (8*min(M,N))

*INFO*INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The updating process of DBDSDC did not converge.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**June 2016

**Contributors:**Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 228 of file zgesdd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK