slaed8.f(3)							      LAPACK							       slaed8.f(3)

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 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 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: November 2011 Contributors: Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Definition at line 242 of file slaed8.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 slaed8.f(3)