---
name: "slaed2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slaed2/3lapack"
---

# slaed2(3lapack)

merges the two sets of eigenvalues together into a single sorted set

## NAME

SLAED2 - merges the two sets of eigenvalues together into a single sorted set

## SYNOPSIS

- SUBROUTINE SLAED2(

  K, N, N1, D, Q, LDQ, INDXQ, RHO, Z, DLAMDA, W, Q2, INDX, INDXC, INDXP, COLTYP, INFO )

- INTEGER

  INFO, K, LDQ, N, N1

- REAL

  RHO

- INTEGER

  COLTYP( \* ), INDX( \* ), INDXC( \* ), INDXP( \* ), INDXQ( \* )

- REAL

  D( \* ), DLAMDA( \* ), Q( LDQ, \* ), Q2( \* ), W( \* ), Z( \* )

## PURPOSE

SLAED2 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.\

## ARGUMENTS

- K (output) INTEGER

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

- N (input) INTEGER

  The dimension of the symmetric tridiagonal matrix.  N \>= 0.

- N1 (input) INTEGER

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

- D (input/output) REAL 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 (input/output) REAL 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 (input) INTEGER

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

- INDXQ (input/output) 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 (input/output) REAL

  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 SLAED3.

- Z (input) REAL 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. DLAMDA (output) REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation.

- W (output) REAL array, dimension (N)

  The first k values of the final deflation-altered z-vector which will be passed to SLAED3.

- Q2 (output) REAL array, dimension (N1\*\*2+(N-N1)\*\*2)

  A copy of the first K eigenvectors which will be used by SLAED3 in a matrix multiply (SGEMM) to solve for the new eigenvectors.

- INDX (workspace) INTEGER array, dimension (N)

  The permutation used to sort the contents of DLAMDA into ascending order.

- INDXC (output) 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 (workspace) 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 (workspace/output) 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 (output) INTEGER

  \= 0:  successful exit.\
   \< 0:  if INFO = -i, the i-th argument had an illegal value.

## FURTHER DETAILS

Based on contributions by\
\
    Jeff Rutter, Computer Science Division, University of California\
    at Berkeley, USA\
 Modified by Francoise Tisseur, University of Tennessee.\