slasda.f(3)

NAME
slasda.f -

SYNOPSIS

  Functions/Subroutines
subroutine slasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Function/Subroutine Documentation

  subroutine slasda (integerICOMPQ, integerSMLSIZ, integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real, dimension( ldu, * )U, integerLDU, real, dimension( ldu, * )VT, integer, dimension( * )K, real, dimension( ldu, * )DIFL, real, dimension( ldu, * )DIFR, real, dimension( ldu, * )Z, real, dimension( ldu, * )POLES, integer, dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer, dimension( ldgcol, * )PERM, real, dimension( ldu, * )GIVNUM, real, dimension( * )C, real, dimension( * )S, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

Purpose:

     Using a divide and conquer approach, SLASDA computes the singular
     value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
     B with diagonal D and offdiagonal E, where M = N + SQRE. The
     algorithm computes the singular values in the SVD B = U * S * VT.
     The orthogonal matrices U and VT are optionally computed in
     compact form.
     A related subroutine, SLASD0, computes the singular values and
     the singular vectors in explicit form.

Parameters:
    ICOMPQ

              ICOMPQ is INTEGER
             Specifies whether singular vectors are to be computed
             in compact form, as follows
             = 0: Compute singular values only.
             = 1: Compute singular vectors of upper bidiagonal
                  matrix in compact form.

    SMLSIZ

              SMLSIZ is INTEGER
             The maximum size of the subproblems at the bottom of the
             computation tree.

    N

              N is INTEGER
             The row dimension of the upper bidiagonal matrix. This is
             also the dimension of the main diagonal array D.

    SQRE

              SQRE is INTEGER
             Specifies the column dimension of the bidiagonal matrix.
             = 0: The bidiagonal matrix has column dimension M = N;
             = 1: The bidiagonal matrix has column dimension M = N + 1.

    D

              D is REAL array, dimension ( N )
             On entry D contains the main diagonal of the bidiagonal
             matrix. On exit D, if INFO = 0, contains its singular values.

    E

              E is REAL array, dimension ( M-1 )
             Contains the subdiagonal entries of the bidiagonal matrix.
             On exit, E has been destroyed.

    U

              U is REAL array,
             dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
             if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
             singular vector matrices of all subproblems at the bottom
             level.

    LDU

              LDU is INTEGER, LDU = > N.
             The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
             GIVNUM, and Z.

    VT

              VT is REAL array,
             dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
             if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
             singular vector matrices of all subproblems at the bottom
             level.

    K

              K is INTEGER array, dimension ( N )
             if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
             If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
             secular equation on the computation tree.

    DIFL

              DIFL is REAL array, dimension ( LDU, NLVL ),
             where NLVL = floor(log_2 (N/SMLSIZ))).

    DIFR

              DIFR is REAL array,
                      dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
                      dimension ( N ) if ICOMPQ = 0.
             If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
             record distances between singular values on the I-th
             level and singular values on the (I -1)-th level, and
             DIFR(1:N, 2 * I ) contains the normalizing factors for
             the right singular vector matrix. See SLASD8 for details.

    Z

              Z is REAL array,
                      dimension ( LDU, NLVL ) if ICOMPQ = 1 and
                      dimension ( N ) if ICOMPQ = 0.
             The first K elements of Z(1, I) contain the components of
             the deflation-adjusted updating row vector for subproblems
             on the I-th level.

    POLES

              POLES is REAL array,
             dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
             if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
             POLES(1, 2*I) contain  the new and old singular values
             involved in the secular equations on the I-th level.

    GIVPTR

              GIVPTR is INTEGER array,
             dimension ( N ) if ICOMPQ = 1, and not referenced if
             ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
             the number of Givens rotations performed on the I-th
             problem on the computation tree.

    GIVCOL

              GIVCOL is INTEGER array,
             dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
             referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
             GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
             of Givens rotations performed on the I-th level on the
             computation tree.

    LDGCOL

              LDGCOL is INTEGER, LDGCOL = > N.
             The leading dimension of arrays GIVCOL and PERM.

    PERM

              PERM is INTEGER array, dimension ( LDGCOL, NLVL )
             if ICOMPQ = 1, and not referenced
             if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
             permutations done on the I-th level of the computation tree.

    GIVNUM

              GIVNUM is REAL array,
             dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
             referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
             GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
             values of Givens rotations performed on the I-th level on
             the computation tree.

    C

              C is REAL array,
             dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
             If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
             C( I ) contains the C-value of a Givens rotation related to
             the right null space of the I-th subproblem.

    S

              S is REAL array, dimension ( N ) if
             ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
             and the I-th subproblem is not square, on exit, S( I )
             contains the S-value of a Givens rotation related to
             the right null space of the I-th subproblem.

    WORK

              WORK is REAL array, dimension
             (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

    IWORK

              IWORK is INTEGER array, dimension (7*N).

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              > 0:  if INFO = 1, a singular value did not converge

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

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

Definition at line 272 of file slasda.f.

Author

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