# dlaed8.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine dlaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

## Function/Subroutine Documentation

### subroutine dlaed8 (integer ICOMPQ, integer K, integer N, integer QSIZ, double precision, dimension( * ) D, double precision, dimension( ldq, * ) Q, integer LDQ, integer, dimension( * ) INDXQ, double precision RHO, integer CUTPNT, double precision, dimension( * ) Z, double precision, dimension( * ) DLAMDA, double precision, dimension( ldq2, * ) Q2, integer LDQ2, double precision, dimension( * ) W, integer, dimension( * ) PERM, integer GIVPTR, integer, dimension( 2, * ) GIVCOL, double precision, dimension( 2, * ) GIVNUM, integer, dimension( * ) INDXP, integer, dimension( * ) INDX, integer INFO)

DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Purpose:

``` DLAED8 merges the two sets of eigenvalues together into a single
sorted set.  Then it tries to deflate the size of the problem.
There are two ways in which deflation can occur:  when two or more
eigenvalues are close together or if there is a tiny element in the
Z vector.  For each such occurrence the order of the related secular
equation problem is reduced by one.```
Parameters:

ICOMPQ

```          ICOMPQ is INTEGER
= 0:  Compute eigenvalues only.
= 1:  Compute eigenvectors of original dense symmetric matrix
also.  On entry, Q contains the orthogonal matrix used
to reduce the original matrix to tridiagonal form.```

K

```          K is INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation.```

N

```          N is INTEGER
The dimension of the symmetric tridiagonal matrix.  N >= 0.```

QSIZ

```          QSIZ is INTEGER
The dimension of the orthogonal matrix used to reduce
the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.```

D

```          D is DOUBLE PRECISION array, dimension (N)
On entry, the eigenvalues of the two submatrices to be
combined.  On exit, the trailing (N-K) updated eigenvalues
(those which were deflated) sorted into increasing order.```

Q

```          Q is DOUBLE PRECISION array, dimension (LDQ,N)
If ICOMPQ = 0, Q is not referenced.  Otherwise,
on entry, Q contains the eigenvectors of the partially solved
system which has been previously updated in matrix
multiplies with other partially solved eigensystems.
On exit, Q contains the trailing (N-K) updated eigenvectors
(those which were deflated) in its last N-K columns.```

LDQ

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

INDXQ

```          INDXQ is INTEGER array, dimension (N)
The permutation which separately sorts the two sub-problems
in D into ascending order.  Note that elements in the second
half of this permutation must first have CUTPNT added to
their values in order to be accurate.```

RHO

```          RHO is DOUBLE PRECISION
On entry, the off-diagonal element associated with the rank-1
cut which originally split the two submatrices which are now
being recombined.
On exit, RHO has been modified to the value required by
DLAED3.```

CUTPNT

```          CUTPNT is INTEGER
The location of the last eigenvalue in the leading
sub-matrix.  min(1,N) <= CUTPNT <= N.```

Z

```          Z is DOUBLE PRECISION array, dimension (N)
On entry, Z contains the updating vector (the last row of
the first sub-eigenvector matrix and the first row of the
second sub-eigenvector matrix).
On exit, the contents of Z are destroyed by the updating
process.```

DLAMDA

```          DLAMDA is DOUBLE PRECISION array, dimension (N)
A copy of the first K eigenvalues which will be used by
DLAED3 to form the secular equation.```

Q2

```          Q2 is DOUBLE PRECISION array, dimension (LDQ2,N)
If ICOMPQ = 0, Q2 is not referenced.  Otherwise,
a copy of the first K eigenvectors which will be used by
DLAED7 in a matrix multiply (DGEMM) to update the new
eigenvectors.```

LDQ2

```          LDQ2 is INTEGER
The leading dimension of the array Q2.  LDQ2 >= max(1,N).```

W

```          W is DOUBLE PRECISION array, dimension (N)
The first k values of the final deflation-altered z-vector and
will be passed to DLAED3.```

PERM

```          PERM is INTEGER array, dimension (N)
The permutations (from deflation and sorting) to be applied
to each eigenblock.```

GIVPTR

```          GIVPTR is INTEGER
The number of Givens rotations which took place in this
subproblem.```

GIVCOL

```          GIVCOL is INTEGER array, dimension (2, N)
Each pair of numbers indicates a pair of columns to take place
in a Givens rotation.```

GIVNUM

```          GIVNUM is DOUBLE PRECISION array, dimension (2, N)
Each number indicates the S value to be used in the
corresponding Givens rotation.```

INDXP

```          INDXP is INTEGER array, dimension (N)
The permutation used to place deflated values of D at the end
of the array.  INDXP(1:K) points to the nondeflated D-values
and INDXP(K+1:N) points to the deflated eigenvalues.```

INDX

```          INDX is INTEGER array, dimension (N)
The permutation used to sort the contents of D into ascending
order.```

INFO

```          INFO is INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Contributors:

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

Definition at line 245 of file dlaed8.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaed8(3) is an alias of dlaed8.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK