slaeda (l) - Linux Manuals

slaeda: computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem

NAME

SLAEDA - computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem

SYNOPSIS

SUBROUTINE SLAEDA(
N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )

    
INTEGER CURLVL, CURPBM, INFO, N, TLVLS

    
INTEGER GIVCOL( 2, * ), GIVPTR( * ), PERM( * ), PRMPTR( * ), QPTR( * )

    
REAL GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )

PURPOSE

SLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem.

ARGUMENTS

N (input) INTEGER
The dimension of the symmetric tridiagonal matrix. N >= 0.
TLVLS (input) INTEGER
The total number of merging levels in the overall divide and conquer tree. CURLVL (input) INTEGER The current level in the overall merge routine, 0 <= curlvl <= tlvls. CURPBM (input) INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right). PRMPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in PERM a levelaqs permutation is stored. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem.
PERM (input) INTEGER array, dimension (N lg N)
Contains the permutations (from deflation and sorting) to be applied to each eigenblock. GIVPTR (input) INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in GIVCOL a levelaqs Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations. GIVCOL (input) INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation. GIVNUM (input) REAL array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation.
Q (input) REAL array, dimension (N**2)
Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR.
QPTR (input) INTEGER array, dimension (N+2)
Contains a list of pointers which indicate where in Q an eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block.
Z (output) REAL array, dimension (N)
On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).
ZTEMP (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.

FURTHER DETAILS

Based on contributions by

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

Pages related to slaeda

  • slaeda (3)
  • slaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
  • slaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • slaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
  • slaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
  • slaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
  • slaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
  • slaed6 (l) - computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
  • slaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • slaed8 (l) - merges the two sets of eigenvalues together into a single sorted set
  • slaed9 (l) - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP