---
name: "dlasd8.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dlasd8.f"
---

# dlasd8.f(3)

## NAME

SRC/dlasd8.f

## SYNOPSIS

### Functions/Subroutines

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.

## Function/Subroutine 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

Definition at line **162** of file **dlasd8.f**.

## Author

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