---
name: "dgesdd"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dgesdd/3lapack"
---

# dgesdd(3lapack)

computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors

## NAME

DGESDD - computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and right singular vectors

## SYNOPSIS

- SUBROUTINE DGESDD(

  JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO )

- CHARACTER

  JOBZ

- INTEGER

  INFO, LDA, LDU, LDVT, LWORK, M, N

- INTEGER

  IWORK( \* )

- DOUBLE

  PRECISION A( LDA, \* ), S( \* ), U( LDU, \* ), VT( LDVT, \* ), WORK( \* )

## PURPOSE

DGESDD 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.\
 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.\

## ARGUMENTS

- JOBZ (input) 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 (input) INTEGER

  The number of rows of the input matrix A.  M \>= 0.

- N (input) INTEGER

  The number of columns of the input matrix A.  N \>= 0.

- A (input/output) DOUBLE PRECISION 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 (input) INTEGER

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

- S (output) DOUBLE PRECISION array, dimension (min(M,N))

  The singular values of A, sorted so that S(i) \>= S(i+1).

- U (output) DOUBLE PRECISION 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 (input) INTEGER

  The leading dimension of the array U.  LDU \>= 1; if JOBZ = 'S' or 'A' or JOBZ = 'O' and M \< N, LDU \>= M.

- VT (output) DOUBLE PRECISION 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 (input) 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 (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

  On exit, if INFO = 0, WORK(1) returns the optimal LWORK;

- LWORK (input) INTEGER

  The dimension of the array WORK. LWORK \>= 1. If JOBZ = 'N', LWORK \>= 3\*min(M,N) + max(max(M,N),7\*min(M,N)). If JOBZ = 'O', LWORK \>= 3\*min(M,N)\*min(M,N) +  max(max(M,N),5\*min(M,N)\*min(M,N)+4\*min(M,N)). If JOBZ = 'S' or 'A' LWORK \>= 3\*min(M,N)\*min(M,N) + max(max(M,N),4\*min(M,N)\*min(M,N)+4\*min(M,N)). For good performance, LWORK should generally be larger. If LWORK = -1 but other input arguments are legal, WORK(1) returns the optimal LWORK.

- IWORK (workspace) INTEGER array, dimension (8\*min(M,N))

  - INFO (output) INTEGER

  \= 0:  successful exit.\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.\
   \> 0:  DBDSDC did not converge, updating process failed.

## FURTHER DETAILS

Based on contributions by\
\
    Ming Gu and Huan Ren, Computer Science Division, University of\
    California at Berkeley, USA\