SLAED8 (3) Linux Manual Page

slaed8.f –

Synopsis

Functions/Subroutines

subroutine slaed8 (ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2, W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO)
SLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

Function/Subroutine Documentation

subroutine slaed8 (integerICOMPQ, integerK, integerN, integerQSIZ, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, realRHO, integerCUTPNT, real, dimension( * )Z, real, dimension( * )DLAMDA, real, dimension( ldq2, * )Q2, integerLDQ2, real, dimension( * )W, integer, dimension( * )PERM, integerGIVPTR, integer, dimension( 2, * )GIVCOL, real, dimension( 2, * )GIVNUM, integer, dimension( * )INDXP, integer, dimension( * )INDX, integerINFO)

SLAED8 used by sstedc. Merges eigenvalues and deflates secular equation. Used when the original matrix is dense.

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.

 

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

 K is INTEGER

 The number of non-deflated eigenvalues, and the order of the

 related secular equation.

N

 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

 D is 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.

Q

 Q is 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

 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 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

 CUTPNT is INTEGER

 The location of the last eigenvalue in the leading

 sub-matrix. min(1,N) <= CUTPNT <= N.

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 are destroyed by the updating

 process.

DLAMDA

 DLAMDA is REAL array, dimension (N)

 A copy of the first K eigenvalues which will be used by

 SLAED3 to form the secular equation.

Q2

 Q2 is 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

 LDQ2 is INTEGER

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

W

 W is REAL array, dimension (N)

 The first k values of the final deflation-altered z-vector and

 will be passed to SLAED3.

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 REAL 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 slaed8.f.

Author

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