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dgesvd examples
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Man Page Details
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NAME
       DGESVD - the singular value decomposition (SVD) of a real M-by-N matrix
       A, optionally computing the left and/or right singular vectors

SYNOPSIS
       SUBROUTINE DGESVD( JOBU, JOBVT, M, N, A, LDA,  S,  U,  LDU,  VT,  LDVT,
                          WORK, LWORK, INFO )

           CHARACTER      JOBU, JOBVT

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

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

PURPOSE
       DGESVD computes the singular value decomposition (SVD) of a real M-by-N
       matrix  A, optionally computing the left and/or right singular vectors.
       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 V**T, not V.


ARGUMENTS
       JOBU    (input) 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 vec-
               tors) 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   (input) CHARACTER*1
               Specifies options for computing all or part of the matrix V**T:
               = 'A':  all N rows of V**T are returned in the array VT;
               = 'S':  the first min(m,n) rows of  V**T  (the  right  singular
               vectors)  are  returned  in  the  array  VT;  = 'O':  the first
               min(m,n) rows of V**T (the right singular  vectors)  are  over-
               written  on the array A; = 'N':  no rows of V**T (no right sin-
               gular vectors) are computed.

               JOBVT and JOBU cannot both be 'O'.

       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 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**T (the right
               singular vectors, stored rowwise); if JOBU .ne. 'O'  and  JOBVT
               .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)
               (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.  If JOBU
               = 'A', U contains the M-by-M orthogonal matrix  U;  if  JOBU  =
               'S',  U contains the first min(m,n) columns of U (the left sin-
               gular vectors, stored columnwise); if JOBU = 'N' or 'O',  U  is
               not referenced.

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

       VT      (output) DOUBLE PRECISION array, dimension (LDVT,N)
               If JOBVT = 'A', VT contains the N-by-N orthogonal matrix  V**T;
               if  JOBVT  =  'S',  VT contains the first min(m,n) rows of V**T
               (the right singular vectors, stored rowwise); if JOBVT = 'N' or
               'O', VT is not referenced.

       LDVT    (input) INTEGER
               The  leading  dimension of the array VT.  LDVT >= 1; if JOBVT =
               'A', LDVT >= N; if JOBVT = '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;  if
               INFO > 0, WORK(2:MIN(M,N)) contains the unconverged superdiago-
               nal 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.

       LWORK   (input) INTEGER
               The    dimension    of    the    array    WORK.     LWORK    >=
               MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(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.

       INFO    (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an illegal value.
               > 0:  if DBDSQR did  not  converge,  INFO  specifies  how  many
               superdiagonals  of  an  intermediate  bidiagonal form B did not
               converge to  zero.  See  the  description  of  WORK  above  for
               details.

