SLAED8(3F)SLAED8(3F)NAME
SLAED8 - merge the two sets of eigenvalues together into a single sorted
set
SYNOPSIS
SUBROUTINE SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z,
DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM,
INDXP, INDX, INFO )
INTEGER CUTPNT, GIVPTR, ICOMPQ, INFO, K, LDQ, LDQ2, N, QSIZ
REAL RHO
INTEGER GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ( * ),
PERM( * )
REAL D( * ), DLAMDA( * ), GIVNUM( 2, * ), Q( LDQ, * ), Q2(
LDQ2, * ), W( * ), Z( * )
PURPOSE
SLAED8 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 element in the Z vector. For each
such occurrence the order of the related secular equation problem is
reduced by one.
ARGUMENTS
ICOMPQ (input) INTEGER
= 0: Compute eigenvalues only.
= 1: Compute eigenvectors of original dense symmetric matrix
also. On entry, Q contains the orthogonal matrix used to reduce
the original matrix to tridiagonal form.
K (output) INTEGER
The number of non-deflated eigenvalues, and the order of the
related secular equation.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
QSIZ (input) INTEGER
The dimension of the orthogonal matrix used to reduce the full
matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
D (input/output) REAL array, dimension (N)
On entry, the eigenvalues of the two submatrices to be combined.
On exit, the trailing (N-K) updated eigenvalues (those which were
deflated) sorted into increasing order.
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SLAED8(3F)SLAED8(3F)
Q (input/output) REAL array, dimension (LDQ,N)
If ICOMPQ = 0, Q is not referenced. Otherwise, on entry, Q
contains the eigenvectors of the partially solved system which has
been previously updated in matrix multiplies with other partially
solved eigensystems. 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) 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 CUTPNT added to their values in
order to be accurate.
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.
CUTPNT (input) INTEGER The location of the last eigenvalue in the
leading sub-matrix. min(1,N) <= CUTPNT <= N.
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 are 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.
Q2 (output) REAL array, dimension (LDQ2,N)
If ICOMPQ = 0, Q2 is not referenced. Otherwise, a copy of the
first K eigenvectors which will be used by SLAED7 in a matrix
multiply (SGEMM) to update the new eigenvectors.
LDQ2 (input) INTEGER
The leading dimension of the array Q2. LDQ2 >= max(1,N).
W (output) REAL array, dimension (N)
The first k values of the final deflation-altered z-vector and
will be passed to SLAED3.
PERM (output) INTEGER array, dimension (N)
The permutations (from deflation and sorting) to be applied to
each eigenblock.
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SLAED8(3F)SLAED8(3F)
GIVPTR (output) INTEGER The number of Givens rotations which took
place in this subproblem.
GIVCOL (output) INTEGER array, dimension (2, N) Each pair of
numbers indicates a pair of columns to take place in a Givens
rotation.
GIVNUM (output) REAL array, dimension (2, N) Each number indicates
the S value to be used in the corresponding Givens rotation.
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.
INDX (workspace) INTEGER array, dimension (N)
The permutation used to sort the contents of D into ascending
order.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
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