---
name: "slaed9.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/slaed9.f"
---

# slaed9.f(3)

## NAME

SRC/slaed9.f

## SYNOPSIS

### Functions/Subroutines

subroutine **slaed9** (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info)\
 **SLAED9** used 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 (integer k, integer kstart, integer kstop, integer n, real, dimension( \* ) d, real, dimension( ldq, \* ) q, integer ldq, real rho, real, dimension( \* ) dlambda, real, dimension( \* ) w, real, dimension( lds, \* ) s, integer lds, integer info)

**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.
!>
```

*DLAMBDA*

```
!>          DLAMBDA 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.

**Contributors:**

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

Definition at line **154** of file **slaed9.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.