slasd2.f(3)

NAME
slasd2.f -

SYNOPSIS

  Functions/Subroutines
subroutine slasd2 (NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2, VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO)
SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.

Function/Subroutine Documentation

  subroutine slasd2 (integerNL, integerNR, integerSQRE, integerK, real, dimension( * )D, real, dimension( * )Z, realALPHA, realBETA, real, dimension( ldu, * )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )DSIGMA, real, dimension( ldu2, * )U2, integerLDU2, real, dimension( ldvt2, * )VT2, integerLDVT2, integer, dimension( * )IDXP, integer, dimension( * )IDX, integer, dimension( * )IDXC, integer, dimension( * )IDXQ, integer, dimension( * )COLTYP, integerINFO)

SLASD2 merges the two sets of singular values together into a single sorted set. Used by sbdsdc.

Purpose:

     SLASD2 merges the two sets of singular values together into a single
     sorted set.  Then it tries to deflate the size of the problem.
     There are two ways in which deflation can occur:  when two or more
     singular values are close together or if there is a tiny entry in the
     Z vector.  For each such occurrence the order of the related secular
     equation problem is reduced by one.
     SLASD2 is called from SLASD1.

Parameters:
    NL

              NL is INTEGER
             The row dimension of the upper block.  NL >= 1.

    NR

              NR is INTEGER
             The row dimension of the lower block.  NR >= 1.

    SQRE

              SQRE is INTEGER
             = 0: the lower block is an NR-by-NR square matrix.
             = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
             The bidiagonal matrix has N = NL + NR + 1 rows and
             M = N + SQRE >= N columns.

    K

              K is INTEGER
             Contains the dimension of the non-deflated matrix,
             This is the order of the related secular equation. 1 <= K <=N.

    D

              D is REAL array, dimension (N)
             On entry D contains the singular values of the two submatrices
             to be combined.  On exit D contains the trailing (N-K) updated
             singular values (those which were deflated) sorted into
             increasing order.

    Z

              Z is REAL array, dimension (N)
             On exit Z contains the updating row vector in the secular
             equation.

    ALPHA

              ALPHA is REAL
             Contains the diagonal element associated with the added row.

    BETA

              BETA is REAL
             Contains the off-diagonal element associated with the added
             row.

    U

              U is REAL array, dimension (LDU,N)
             On entry U contains the left singular vectors of two
             submatrices in the two square blocks with corners at (1,1),
             (NL, NL), and (NL+2, NL+2), (N,N).
             On exit U contains the trailing (N-K) updated left singular
             vectors (those which were deflated) in its last N-K columns.

    LDU

              LDU is INTEGER
             The leading dimension of the array U.  LDU >= N.

    VT

              VT is REAL array, dimension (LDVT,M)
             On entry VT**T contains the right singular vectors of two
             submatrices in the two square blocks with corners at (1,1),
             (NL+1, NL+1), and (NL+2, NL+2), (M,M).
             On exit VT**T contains the trailing (N-K) updated right singular
             vectors (those which were deflated) in its last N-K columns.
             In case SQRE =1, the last row of VT spans the right null
             space.

    LDVT

              LDVT is INTEGER
             The leading dimension of the array VT.  LDVT >= M.

    DSIGMA

              DSIGMA is REAL array, dimension (N)
             Contains a copy of the diagonal elements (K-1 singular values
             and one zero) in the secular equation.

    U2

              U2 is REAL array, dimension (LDU2,N)
             Contains a copy of the first K-1 left singular vectors which
             will be used by SLASD3 in a matrix multiply (SGEMM) to solve
             for the new left singular vectors. U2 is arranged into four
             blocks. The first block contains a column with 1 at NL+1 and
             zero everywhere else; the second block contains non-zero
             entries only at and above NL; the third contains non-zero
             entries only below NL+1; and the fourth is dense.

    LDU2

              LDU2 is INTEGER
             The leading dimension of the array U2.  LDU2 >= N.

    VT2

              VT2 is REAL array, dimension (LDVT2,N)
             VT2**T contains a copy of the first K right singular vectors
             which will be used by SLASD3 in a matrix multiply (SGEMM) to
             solve for the new right singular vectors. VT2 is arranged into
             three blocks. The first block contains a row that corresponds
             to the special 0 diagonal element in SIGMA; the second block
             contains non-zeros only at and before NL +1; the third block
             contains non-zeros only at and after  NL +2.

    LDVT2

              LDVT2 is INTEGER
             The leading dimension of the array VT2.  LDVT2 >= M.

    IDXP

              IDXP is INTEGER array, dimension (N)
             This will contain the permutation used to place deflated
             values of D at the end of the array. On output IDXP(2:K)
             points to the nondeflated D-values and IDXP(K+1:N)
             points to the deflated singular values.

    IDX

              IDX is INTEGER array, dimension (N)
             This will contain the permutation used to sort the contents of
             D into ascending order.

    IDXC

              IDXC is INTEGER array, dimension (N)
             This will contain the permutation used to arrange the columns
             of the deflated U matrix into three groups:  the first group
             contains non-zero entries only at and above NL, the second
             contains non-zero entries only below NL+2, and the third is
             dense.

    IDXQ

              IDXQ is INTEGER array, dimension (N)
             This contains the permutation which separately sorts the two
             sub-problems in D into ascending order.  Note that entries in
             the first hlaf of this permutation must first be moved one
             position backward; and entries in the second half
             must first have NL+1 added to their values.

    COLTYP

              COLTYP is INTEGER array, dimension (N)
             As workspace, this will contain a label which will indicate
             which of the following types a column in the U2 matrix or a
             row in the VT2 matrix is:
             1 : non-zero in the upper half only
             2 : non-zero in the lower half only
             3 : dense
             4 : deflated
             On exit, it is an array of dimension 4, with COLTYP(I) being
             the dimension of the I-th type columns.

    INFO

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

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 268 of file slasd2.f.

Author

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