DragonFly On-Line Manual Pages

PSLAED3(l)                             )                            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

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.

ScaLAPACK version 1.7           13 August 2001                      PSLAED3(l)