| lasd8(3) | LAPACK | lasd8(3) |
lasd8 - lasd8: D&C step: secular equation
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.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
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