# slasd8.f man page

slasd8.f —

## Synopsis

### Functions/Subroutines

subroutineslasd8(ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO)SLASD8finds 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 (integerICOMPQ, integerK, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )VF, real, dimension( * )VL, real, dimension( * )DIFL, real, dimension( lddifr, * )DIFR, integerLDDIFR, real, dimension( * )DSIGMA, real, dimension( * )WORK, integerINFO)

**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.
On exit, the elements of DSIGMA may be very slightly altered
in value.
```

*WORK*

`WORK is REAL array, dimension at least 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.

**Date:**

September 2012

**Contributors:**

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

Definition at line 166 of file slasd8.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slasd8(3) is an alias of slasd8.f(3).