# slaed9.f man page

slaed9.f —

## Synopsis

### Functions/Subroutines

subroutineslaed9(K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO)SLAED9used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

## Function/Subroutine Documentation

### subroutine slaed9 (integerK, integerKSTART, integerKSTOP, integerN, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, realRHO, real, dimension( * )DLAMDA, real, dimension( * )W, real, dimension( lds, * )S, integerLDS, integerINFO)

**SLAED9** used by sstedc. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

**Purpose:**

```
SLAED9 finds the roots of the secular equation, as defined by the
values in D, Z, and RHO, between KSTART and KSTOP. It makes the
appropriate calls to SLAED4 and then stores the new matrix of
eigenvectors for use in calculating the next level of Z vectors.
```

**Parameters:**

*K*

```
K is INTEGER
The number of terms in the rational function to be solved by
SLAED4. K >= 0.
```

*KSTART*

`KSTART is INTEGER`

*KSTOP*

```
KSTOP is INTEGER
The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
are to be computed. 1 <= KSTART <= KSTOP <= K.
```

*N*

```
N is INTEGER
The number of rows and columns in the Q matrix.
N >= K (delation may result in N > K).
```

*D*

```
D is REAL array, dimension (N)
D(I) contains the updated eigenvalues
for KSTART <= I <= KSTOP.
```

*Q*

`Q is REAL array, dimension (LDQ,N)`

*LDQ*

```
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max( 1, N ).
```

*RHO*

```
RHO is REAL
The value of the parameter in the rank one update equation.
RHO >= 0 required.
```

*DLAMDA*

```
DLAMDA is 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.
```

*W*

```
W is REAL array, dimension (K)
The first K elements of this array contain the components
of the deflation-adjusted updating vector.
```

*S*

```
S is REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which
will be stored for subsequent Z vector calculation and
multiplied by the previously accumulated eigenvectors
to update the system.
```

*LDS*

```
LDS is INTEGER
The leading dimension of S. LDS >= max( 1, K ).
```

*INFO*

```
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = 1, an eigenvalue did not converge
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Contributors:**

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 156 of file slaed9.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slaed9(3) is an alias of slaed9.f(3).