# slaed2.f - Man Page

SRC/slaed2.f

## Synopsis

### Functions/Subroutines

subroutine **slaed2** (k, n, n1, d, q, ldq, indxq, rho, z, dlambda, w, q2, indx, indxc, indxp, coltyp, info)**SLAED2** used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

## Function/Subroutine Documentation

### subroutine slaed2 (integer k, integer n, integer n1, real, dimension( * ) d, real, dimension( ldq, * ) q, integer ldq, integer, dimension( * ) indxq, real rho, real, dimension( * ) z, real, dimension( * ) dlambda, real, dimension( * ) w, real, dimension( * ) q2, integer, dimension( * ) indx, integer, dimension( * ) indxc, integer, dimension( * ) indxp, integer, dimension( * ) coltyp, integer info)

**SLAED2** used by SSTEDC. Merges eigenvalues and deflates secular equation. Used when the original matrix is tridiagonal.

**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.

**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 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*Q is 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*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 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*Z is 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.

*DLAMBDA*DLAMBDA is REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation.

*W*W is REAL array, dimension (N) The first k values of the final deflation-altered z-vector which will be passed to SLAED3.

*Q2*Q2 is 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*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

Univ. of Colorado Denver

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 **slaed2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slaed2(3) is an alias of slaed2.f(3).