lasd8(3)

NAME
lasd8 - lasd8: D&C step: secular equation

SYNOPSIS

  Functions

subroutine dlasd8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info)
DLASD8 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.
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.

Detailed Description

Function Documentation

  subroutine dlasd8 (integer icompq, integer k, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) vf, double precision, dimension( * ) vl, double precision, dimension( * ) difl, double precision, dimension( lddifr, * ) difr, integer lddifr, double precision, dimension( * ) dsigma, double precision, dimension( * ) work, integer info)

DLASD8 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:

    !>
    !> DLASD8 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 DLASD4, 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.
    !>
    !> DLASD8 is called from DLASD6.
    !>

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 DLASD4.  K >= 1.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension ( K )
    !>          On output, D contains the updated singular values.
    !>

    Z

    !>          Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( K )
    !>          On exit, DIFL(I) = D(I) - DSIGMA(I).
    !>

    DIFR

    !>          DIFR is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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

  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

Author

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