dlaed8-f(3)

dlaed8.f –

Synopsis

Functions/Subroutines

subroutine dlaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

subroutine dlaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, double precision, dimension( * )D, double precision, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, double precisionRHO, integerCUTPNT, double precision, dimension( * )Z, double precision, dimension( * )DLAMDA, double precision, dimension( ldq2, * )Q2, integerLDQ2, double precision, dimension( * )W, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( 2, * )GIVCOL, double precision, dimension( 2, * )GIVNUM, integer, dimension( * )INDXP, integer, dimension( * )INDX, integerINFO)

DLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Purpose:

 DLAED8 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.

Parameters:

ICOMPQ

 ICOMPQ is 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 is INTEGER
 The number of non-deflated eigenvalues, and the order of the
 related secular equation.

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

QSIZ

 QSIZ is INTEGER
 The dimension of the orthogonal matrix used to reduce
 the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.

 D is DOUBLE PRECISION 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.

 Q is DOUBLE PRECISION 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

 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 CUTPNT added to
 their values in order to be accurate.

RHO

 RHO is DOUBLE PRECISION
 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
 DLAED3.

CUTPNT

 CUTPNT is INTEGER
 The location of the last eigenvalue in the leading
 sub-matrix. min(1,N) <= CUTPNT <= N.

 Z is DOUBLE PRECISION 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

 DLAMDA is DOUBLE PRECISION array, dimension (N)
 A copy of the first K eigenvalues which will be used by
 DLAED3 to form the secular equation.

 Q2 is DOUBLE PRECISION array, dimension (LDQ2,N)
 If ICOMPQ = 0, Q2 is not referenced. Otherwise,
 a copy of the first K eigenvectors which will be used by
 DLAED7 in a matrix multiply (DGEMM) to update the new
 eigenvectors.

LDQ2

 LDQ2 is INTEGER
 The leading dimension of the array Q2. LDQ2 >= max(1,N).

 W is DOUBLE PRECISION array, dimension (N)
 The first k values of the final deflation-altered z-vector and
 will be passed to DLAED3.

PERM

 PERM is INTEGER array, dimension (N)
 The permutations (from deflation and sorting) to be applied
 to each eigenblock.

GIVPTR

 GIVPTR is INTEGER
 The number of Givens rotations which took place in this
 subproblem.

GIVCOL

 GIVCOL is INTEGER array, dimension (2, N)
 Each pair of numbers indicates a pair of columns to take place
 in a Givens rotation.

GIVNUM

 GIVNUM is DOUBLE PRECISION array, dimension (2, N)
 Each number indicates the S value to be used in the
 corresponding Givens rotation.

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.

INDX

 INDX is INTEGER array, dimension (N)
 The permutation used to sort the contents of D into ascending
 order.

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.

Date:

September 2012

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Definition at line 242 of file dlaed8.f.

Author

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