SRC/slasd8.f(3)

NAME
SRC/slasd8.f

SYNOPSIS

  Functions/Subroutines
subroutine slasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info)
SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.

Function/Subroutine Documentation

  subroutine slasd8 (integer icompq, integer k, real, dimension( * ) d, real, dimension( * ) z, real, dimension( * ) vf, real, dimension( * ) vl, real, dimension( * ) difl, real, dimension( lddifr, * ) difr, integer lddifr, real, dimension( * ) dsigma, real, dimension( * ) work, integer info)

SLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.

Purpose:

     SLASD8 finds the square roots of the roots of the secular equation,
     as defined by the values in DSIGMA and Z. It makes the appropriate
     calls to SLASD4, and stores, for each  element in D, the distance
     to its two nearest poles (elements in DSIGMA). It also updates
     the arrays VF and VL, the first and last components of all the
     right singular vectors of the original bidiagonal matrix.
     SLASD8 is called from SLASD6.

Parameters
    ICOMPQ

              ICOMPQ is INTEGER
              Specifies whether singular vectors are to be computed in
              factored form in the calling routine:
              = 0: Compute singular values only.
              = 1: Compute singular vectors in factored form as well.

    K

              K is INTEGER
              The number of terms in the rational function to be solved
              by SLASD4.  K >= 1.

    D

              D is REAL array, dimension ( K )
              On output, D contains the updated singular values.

    Z

              Z is REAL array, dimension ( K )
              On entry, the first K elements of this array contain the
              components of the deflation-adjusted updating row vector.
              On exit, Z is updated.

    VF

              VF is REAL array, dimension ( K )
              On entry, VF contains  information passed through DBEDE8.
              On exit, VF contains the first K components of the first
              components of all right singular vectors of the bidiagonal
              matrix.

    VL

              VL is REAL array, dimension ( K )
              On entry, VL contains  information passed through DBEDE8.
              On exit, VL contains the first K components of the last
              components of all right singular vectors of the bidiagonal
              matrix.

    DIFL

              DIFL is REAL array, dimension ( K )
              On exit, DIFL(I) = D(I) - DSIGMA(I).

    DIFR

              DIFR is REAL array,
                       dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and
                       dimension ( K ) if ICOMPQ = 0.
              On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not
              defined and will not be referenced.
              If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
              normalizing factors for the right singular vector matrix.

    LDDIFR

              LDDIFR is INTEGER
              The leading dimension of DIFR, must be at least K.

    DSIGMA

              DSIGMA is REAL array, dimension ( K )
              On entry, the first K elements of this array contain the old
              roots of the deflated updating problem.  These are the poles
              of the secular equation.

    WORK

              WORK is REAL array, dimension (3*K)

    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.

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

Definition at line 162 of file slasd8.f.

Author

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