# laed9 - Man Page

laed9: D&C step: secular equation

## Synopsis

### Functions

subroutine dlaed9 (k, kstart, kstop, n, d, q, ldq, rho, dlambda, w, s, lds, info)
DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.
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 Documentation

### subroutine dlaed9 (integer k, integer kstart, integer kstop, integer n, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, double precision rho, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( lds, * ) s, integer lds, integer info)

DLAED9 used by DSTEDC. Finds the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense.

Purpose:

``` DLAED9 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 DLAED4 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
DLAED4.  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 DOUBLE PRECISION array, dimension (N)
D(I) contains the updated eigenvalues
for KSTART <= I <= KSTOP.```

Q

`          Q is DOUBLE PRECISION array, dimension (LDQ,N)`

LDQ

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

RHO

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

DLAMBDA

```          DLAMBDA is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components

S

```          S is DOUBLE PRECISION 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

NAG Ltd.

Contributors:

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

Definition at line 154 of file dlaed9.f.

### 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

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

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.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK