SRC/sgesvdx.f(3)

NAME
SRC/sgesvdx.f

SYNOPSIS

  Functions/Subroutines
subroutine sgesvdx (jobu, jobvt, range, m, n, a, lda, vl, vu, il, iu, ns, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
SGESVDX computes the singular value decomposition (SVD) for GE matrices

Function/Subroutine Documentation

  subroutine sgesvdx (character jobu, character jobvt, character range, integer m, integer n, real, dimension( lda, * ) a, integer lda, real vl, real vu, integer il, integer iu, integer ns, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

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

Purpose:

      SGESVDX 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.
      SGESVDX uses an eigenvalue problem for obtaining the SVD, which
      allows for the computation of a subset of singular values and
      vectors. See SBDSVDX for details.
      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:
              = 'V':  the first min(m,n) columns of U (the left singular
                      vectors) or as specified by RANGE are returned in
                      the array U;
              = '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:
               = 'V':  the first min(m,n) rows of V**T (the right singular
                       vectors) or as specified by RANGE are returned in
                       the array VT;
               = 'N':  no rows of V**T (no right singular vectors) are
                       computed.

    RANGE

              RANGE is CHARACTER*1
              = 'A': all singular values will be found.
              = 'V': all singular values in the half-open interval (VL,VU]
                     will be found.
              = 'I': the IL-th through IU-th singular values will be found.

    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, the contents of A are destroyed.

    LDA

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

    VL

              VL is REAL
              If RANGE='V', the lower bound of the interval to
              be searched for singular values. VU > VL.
              Not referenced if RANGE = 'A' or 'I'.

    VU

              VU is REAL
              If RANGE='V', the upper bound of the interval to
              be searched for singular values. VU > VL.
              Not referenced if RANGE = 'A' or 'I'.

    IL

              IL is INTEGER
              If RANGE='I', the index of the
              smallest singular value to be returned.
              1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
              Not referenced if RANGE = 'A' or 'V'.

    IU

              IU is INTEGER
              If RANGE='I', the index of the
              largest singular value to be returned.
              1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
              Not referenced if RANGE = 'A' or 'V'.

    NS

              NS is INTEGER
              The total number of singular values found,
              0 <= NS <= min(M,N).
              If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.

    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)
              If JOBU = 'V', U contains columns of U (the left singular
              vectors, stored columnwise) as specified by RANGE; if
              JOBU = 'N', U is not referenced.
              Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
              the exact value of NS is not known in advance and an upper
              bound must be used.

    LDU

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

    VT

              VT is REAL array, dimension (LDVT,N)
              If JOBVT = 'V', VT contains the rows of V**T (the right singular
              vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
              VT is not referenced.
              Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
              the exact value of NS is not known in advance and an upper
              bound must be used.

    LDVT

              LDVT is INTEGER
              The leading dimension of the array VT.  LDVT >= 1; if
              JOBVT = 'V', LDVT >= NS (see above).

    WORK

              WORK is REAL 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,MIN(M,N)*(MIN(M,N)+4)) for the paths (see
              comments inside the code):
                 - PATH 1  (M much larger than N)
                 - PATH 1t (N much larger than M)
              LWORK >= MAX(1,MIN(M,N)*2+MAX(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.

    IWORK

              IWORK is INTEGER array, dimension (12*MIN(M,N))
              If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
              then IWORK contains the indices of the eigenvectors that failed
              to converge in SBDSVDX/SSTEVX.

    INFO

         INFO is INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an illegal value
               > 0:  if INFO = i, then i eigenvectors failed to converge
                     in SBDSVDX/SSTEVX.
                     if INFO = N*2 + 1, an internal error occurred in
                     SBDSVDX

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 260 of file sgesvdx.f.

Author

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