Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       SLASD9 - find the square roots of the roots of the secular equation,

```

#### SYNOPSIS

```       SUBROUTINE SLASD9( ICOMPQ, LDU, K, D, Z, VF, VL, DIFL, DIFR, DSIGMA, WORK, INFO )

INTEGER        ICOMPQ, INFO, K, LDU

REAL           D( * ), DIFL( * ), DIFR( LDU, * ), DSIGMA( * ), VF( * ), VL( * ), WORK(
* ), Z( * )

```

#### PURPOSE

```       SLASD9 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.

SLASD9 is called from SLASD7.

```

#### ARGUMENTS

```       ICOMPQ  (input) INTEGER
Specifies  whether  singular  vectors  are  to be computed in factored form in the
calling routine:

ICOMPQ = 0             Compute singular values only.

ICOMPQ = 1             Compute singular vector matrices in factored form also.   K
(input)  INTEGER  The  number  of  terms  in the rational function to be solved by
SLASD4.  K >= 1.

D       (output) REAL array, dimension(K)
D(I) contains the updated singular values.

DSIGMA  (input) REAL array, dimension(K)
The first K elements of this array contain the old roots of the deflated  updating
problem.  These are the poles of the secular equation.

Z       (input) REAL array, dimension (K)
The  first  K  elements  of  this  array  contain the components of the deflation-

VF      (input/output) REAL array, dimension(K)
On entry, VF contains  information passed through SBEDE8.f On  exit,  VF  contains
the  first  K  components of the first components of all right singular vectors of
the bidiagonal matrix.

VL      (input/output) REAL array, dimension(K)
On entry, VL contains  information passed through SBEDE8.f On  exit,  VL  contains
the first K components of the last components of all right singular vectors of the
bidiagonal matrix.

DIFL    (output) REAL array, dimension (K).
On exit, DIFL(I) = D(I) - DSIGMA(I).

DIFR    (output) REAL array,
dimension (LDU, 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.

WORK    (workspace) REAL array,
dimension at least (3 * K) Workspace.

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = 1, an singular value did not converge

```

#### FURTHERDETAILS

```       Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
```