# dlaed2.f - Man Page

SRC/dlaed2.f

## Synopsis

### Functions/Subroutines

subroutine dlaed2 (k, n, n1, d, q, ldq, indxq, rho, z, dlambda, w, q2, indx, indxc, indxp, coltyp, info)
DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

## Function/Subroutine Documentation

### subroutine dlaed2 (integer k, integer n, integer n1, double precision, dimension( * ) d, double precision, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, double precision rho, double precision, dimension( * ) z, double precision, dimension( * ) dlambda, double precision, dimension( * ) w, double precision, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) indxc, integer, dimension( * ) indxp, integer, dimension( * ) coltyp, integer info)

DLAED2 used by DSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

Purpose:

``` DLAED2 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 entry in the
Z vector.  For each such occurrence the order of the related secular
equation problem is reduced by one.```
Parameters

K

```          K is INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation. 0 <= K <=N.```

N

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

N1

```          N1 is INTEGER
The location of the last eigenvalue in the leading sub-matrix.
min(1,N) <= N1 <= N/2.```

D

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

Q

```          Q is DOUBLE PRECISION array, dimension (LDQ, N)
On entry, Q contains the eigenvectors of two submatrices in
the two square blocks with corners at (1,1), (N1,N1)
and (N1+1, N1+1), (N,N).
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 N1 added to their
values. Destroyed on exit.```

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.```

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 have been destroyed by the updating
process.```

DLAMBDA

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

W

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

Q2

```          Q2 is DOUBLE PRECISION array, dimension (N1**2+(N-N1)**2)
A copy of the first K eigenvectors which will be used by
DLAED3 in a matrix multiply (DGEMM) to solve for the new
eigenvectors.```

INDX

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

INDXC

```          INDXC is INTEGER array, dimension (N)
The permutation used to arrange the columns of the deflated
Q matrix into three groups:  the first group contains non-zero
elements only at and above N1, the second contains
non-zero elements only below N1, and the third is dense.```

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.```

COLTYP

```          COLTYP is INTEGER array, dimension (N)
During execution, a label which will indicate which of the
following types a column in the Q2 matrix is:
1 : non-zero in the upper half only;
2 : dense;
3 : non-zero in the lower half only;
4 : deflated.
On exit, COLTYP(i) is the number of columns of type i,
for i=1 to 4 only.```

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.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee

Definition at line 210 of file dlaed2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlaed2(3) is an alias of dlaed2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK