SLAED8 (3)  Linux Manuals
NAME
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.
KK is INTEGER The number of nondeflated eigenvalues, and the order of the related secular equation.
NN is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
QSIZQSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1.
DD is REAL array, dimension (N) On entry, the eigenvalues of the two submatrices to be combined. On exit, the trailing (NK) updated eigenvalues (those which were deflated) sorted into increasing order.
QQ 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 (NK) updated eigenvectors (those which were deflated) in its last NK columns.
LDQLDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).
INDXQINDXQ is INTEGER array, dimension (N) The permutation which separately sorts the two subproblems 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.
RHORHO is REAL On entry, the offdiagonal element associated with the rank1 cut which originally split the two submatrices which are now being recombined. On exit, RHO has been modified to the value required by SLAED3.
CUTPNTCUTPNT is INTEGER The location of the last eigenvalue in the leading submatrix. min(1,N) <= CUTPNT <= N.
ZZ is REAL array, dimension (N) On entry, Z contains the updating vector (the last row of the first subeigenvector matrix and the first row of the second subeigenvector matrix). On exit, the contents of Z are destroyed by the updating process.
DLAMDADLAMDA is REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation.
Q2Q2 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.
LDQ2LDQ2 is INTEGER The leading dimension of the array Q2. LDQ2 >= max(1,N).
WW is REAL array, dimension (N) The first k values of the final deflationaltered zvector and will be passed to SLAED3.
PERMPERM is INTEGER array, dimension (N) The permutations (from deflation and sorting) to be applied to each eigenblock.
GIVPTRGIVPTR is INTEGER The number of Givens rotations which took place in this subproblem.
GIVCOLGIVCOL is INTEGER array, dimension (2, N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
GIVNUMGIVNUM is REAL array, dimension (2, N) Each number indicates the S value to be used in the corresponding Givens rotation.
INDXPINDXP 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 Dvalues and INDXP(K+1:N) points to the deflated eigenvalues.
INDXINDX is INTEGER array, dimension (N) The permutation used to sort the contents of D into ascending order.
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith 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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