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.

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

 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.

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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