sgesvd.f(3)

NAME
sgesvd.f -

SYNOPSIS

  Functions/Subroutines
subroutine sgesvd (JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO)
SGESVD computes the singular value decomposition (SVD) for GE matrices

Function/Subroutine Documentation

  subroutine sgesvd (characterJOBU, characterJOBVT, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )WORK, integerLWORK, integerINFO)

SGESVD computes the singular value decomposition (SVD) for GE matrices

Purpose:

     SGESVD 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.

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**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 overwritten on the array A;
              = 'N':  no rows of V**T (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 REAL 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

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

    S

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

    U

              U is REAL 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 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 REAL 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

              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 REAL 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
              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.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code):
                 - PATH 1  (M much larger than N, JOBU='N')
                 - PATH 1t (N much larger than M, JOBVT='N')
              LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths
              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

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  if SBDSQR 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.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    April 2012

Definition at line 211 of file sgesvd.f.

Author

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