SYNOPSIS

SUBROUTINE SLAEDA(

N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )

    

INTEGER CURLVL, CURPBM, INFO, N, TLVLS

    

INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), PRMPTR( * ), QPTR( * )

    

REAL GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )

PURPOSE

SLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem.

ARGUMENTS

N (input) INTEGER

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

TLVLS (input) INTEGER

The total number of merging levels in the overall divide and conquer tree. CURLVL (input) INTEGER The current level in the overall merge routine, 0 <= curlvl <= tlvls. CURPBM (input) INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right). PRMPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in PERM a level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem.

PERM (input) INTEGER array, dimension (N lg N)

Contains the permutations (from deflation and sorting) to be applied to each eigenblock. GIVPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in GIVCOL a level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations. GIVCOL (input) INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. GIVNUM (input) REAL array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.

Q (input) REAL array, dimension (N**2)

Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR.

QPTR (input) INTEGER array, dimension (N+2)

Contains a list of pointers which indicate where in Q an eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block.

Z (output) REAL array, dimension (N)

On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).

ZTEMP (workspace) REAL array, dimension (N)

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