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Man Pages


Manual Reference Pages  -  PSLAED3 (l)

NAME

PSLAED3 - find the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K

CONTENTS

Synopsis
Purpose
Arguments

SYNOPSIS

SUBROUTINE PSLAED3( ICTXT, K, N, NB, D, DROW, DCOL, RHO, DLAMDA, W, Z, U, LDU, BUF, INDX, INDCOL, INDROW, INDXR, INDXC, CTOT, NPCOL, INFO )
    INTEGER DCOL, DROW, ICTXT, INFO, K, LDU, N, NB, NPCOL
    REAL RHO
    INTEGER CTOT( 0: NPCOL-1, 4 ), INDCOL( * ), INDROW( * ), INDX( * ), INDXC( * ), INDXR( * )
    REAL BUF( * ), D( * ), DLAMDA( * ), U( LDU, * ), W( * ), Z( * )

PURPOSE

PSLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to SLAED4

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

ARGUMENTS

ICTXT (global input) INTEGER
  The BLACS context handle, indicating the global context of the operation on the matrix. The context itself is global.
K (output) INTEGER
  The number of non-deflated eigenvalues, and the order of the related secular equation. 0 <= K <=N.
N (input) INTEGER
  The dimension of the symmetric tridiagonal matrix. N >= 0.
NB (global input) INTEGER
  The blocking factor used to distribute the columns of the matrix. NB >= 1.
D (input/output) REAL array, dimension (N)
  On entry, D contains the eigenvalues of the two submatrices to be combined. On exit, D contains the trailing (N-K) updated eigenvalues (those which were deflated) sorted into increasing order.
DROW (global input) INTEGER
  The process row over which the first row of the matrix D is distributed. 0 <= DROW < NPROW.
DCOL (global input) INTEGER
  The process column over which the first column of the matrix D is distributed. 0 <= DCOL < NPCOL.
Q (input/output) REAL array, dimension (LDQ, N)
  On entry, Q contains the eigenvectors of two submatrices in the two square blocks with corners at (1,1), (N1,N1) and (N1+1, N1+1), (N,N). On exit, Q contains the trailing (N-K) updated eigenvectors (those which were deflated) in its last N-K columns.
LDQ (input) INTEGER
  The leading dimension of the array Q. LDQ >= max(1,NQ).
RHO (global input/output) 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 PSLAED3.

DLAMDA (global output) REAL array, dimension (N) A copy of the first K eigenvalues which will be used by SLAED3 to form the secular equation.

W (global output) REAL array, dimension (N)
  The first k values of the final deflation-altered z-vector which will be passed to SLAED3.
Z (global input) 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 have been destroyed by the updating process.
U (global output) REAL array
  global dimension (N, N), local dimension (LDU, NQ). Q contains the orthonormal eigenvectors of the symmetric tridiagonal matrix.
LDU (input) INTEGER
  The leading dimension of the array U.
QBUF (workspace) REAL array, dimension 3*N
INDX (workspace) INTEGER array, dimension (N)
  The permutation used to sort the contents of DLAMDA into ascending order.

INDCOL (workspace) INTEGER array, dimension (N)

INDROW (workspace) INTEGER array, dimension (N)

INDXR (workspace) INTEGER array, dimension (N)

INDXC (workspace) INTEGER array, dimension (N)

CTOT (workspace) INTEGER array, dimension( NPCOL, 4)
NPCOL (global input) INTEGER
  The total number of columns over which the distributed submatrix is distributed.
INFO (output) INTEGER
  = 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute the ith eigenvalue.
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ScaLAPACK version 1.7 PSLAED3 (l) 13 August 2001

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