SLAED7 (3)  Linux Man Pages
NAME
slaed7.f 
SYNOPSIS
Functions/Subroutines
subroutine slaed7 (ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO)
SLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix. Used when the original matrix is dense.
Function/Subroutine Documentation
subroutine slaed7 (integerICOMPQ, integerN, integerQSIZ, integerTLVLS, integerCURLVL, integerCURPBM, real, dimension( * )D, real, dimension( ldq, * )Q, integerLDQ, integer, dimension( * )INDXQ, realRHO, integerCUTPNT, real, dimension( * )QSTORE, integer, dimension( * )QPTR, integer, dimension( * )PRMPTR, integer, dimension( * )PERM, integer, dimension( * )GIVPTR, integer, dimension( 2, * )GIVCOL, real, dimension( 2, * )GIVNUM, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
SLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix. Used when the original matrix is dense.
Purpose:

SLAED7 computes the updated eigensystem of a diagonal matrix after modification by a rankone symmetric matrix. This routine is used only for the eigenproblem which requires all eigenvalues and optionally eigenvectors of a dense symmetric matrix that has been reduced to tridiagonal form. SLAED1 handles the case in which all eigenvalues and eigenvectors of a symmetric tridiagonal matrix are desired. T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out) where Z = Q**Tu, u is a vector of length N with ones in the CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. The eigenvectors of the original matrix are stored in Q, and the eigenvalues are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero in the Z vector. For each such occurence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine SLAED8. The second stage consists of calculating the updated eigenvalues. This is done by finding the roots of the secular equation via the routine SLAED4 (as called by SLAED9). This routine also calculates the eigenvectors of the current problem. The final stage consists of computing the updated eigenvectors directly using the updated eigenvalues. The eigenvectors for the current problem are multiplied with the eigenvectors from the overall problem.
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.
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.
TLVLSTLVLS is INTEGER The total number of merging levels in the overall divide and conquer tree.
CURLVLCURLVL is INTEGER The current level in the overall merge routine, 0 <= CURLVL <= TLVLS.
CURPBMCURPBM is INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right).
DD is REAL array, dimension (N) On entry, the eigenvalues of the rank1perturbed matrix. On exit, the eigenvalues of the repaired matrix.
QQ is REAL array, dimension (LDQ, N) On entry, the eigenvectors of the rank1perturbed matrix. On exit, the eigenvectors of the repaired tridiagonal matrix.
LDQLDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).
INDXQINDXQ is INTEGER array, dimension (N) The permutation which will reintegrate the subproblem just solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) will be in ascending order.
RHORHO is REAL The subdiagonal element used to create the rank1 modification.
CUTPNTCUTPNT is INTEGER Contains the location of the last eigenvalue in the leading submatrix. min(1,N) <= CUTPNT <= N.
QSTOREQSTORE is REAL array, dimension (N**2+1) Stores eigenvectors of submatrices encountered during divide and conquer, packed together. QPTR points to beginning of the submatrices.
QPTRQPTR is INTEGER array, dimension (N+2) List of indices pointing to beginning of submatrices stored in QSTORE. The submatrices are numbered starting at the bottom left of the divide and conquer tree, from left to right and bottom to top.
PRMPTRPRMPTR is 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 also the size of the full, nondeflated problem.
PERMPERM is INTEGER array, dimension (N lg N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock.
GIVPTRGIVPTR is 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.
GIVCOLGIVCOL is INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
GIVNUMGIVNUM is REAL array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.
WORKWORK is REAL array, dimension (3*N+2*QSIZ*N)
IWORKIWORK is INTEGER array, dimension (4*N)
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = 1, an eigenvalue did not converge
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 258 of file slaed7.f.
Author
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