- 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( * )
PURPOSESLAED2 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.
- 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 DETAILSBased on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.