LAPACK

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 is INTEGER


          The number of terms in the rational function to be solved


          by DLASD4.  K >= 1.



          D is DOUBLE PRECISION array, dimension ( K )


          On output, D contains the updated singular values.



          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 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 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.