PDSTEDC(l) ) PDSTEDC(l)NAME
PDSTEDC - tridiagonal matrix in parallel, using the divide and conquer
algorithm
SYNOPSIS
SUBROUTINE PDSTEDC( COMPZ, N, D, E, Q, IQ, JQ, DESCQ, WORK, LWORK,
IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, IQ, JQ, LIWORK, LWORK, N
INTEGER DESCQ( * ), IWORK( * )
DOUBLE PRECISION D( * ), E( * ), Q( * ), WORK( * )
PURPOSE
symmetric tridiagonal matrix in parallel, using the divide and conquer
algorithm. This code makes very mild assumptions about floating point
arithmetic. It will work on machines with a guard digit in add/sub‐
tract, 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 conceiv‐
ably fail on hexadecimal or decimal machines without guard digits, but
we know of none. See DLAED3 for details.
ARGUMENTS
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only. (NOT IMPLEMENTED YET)
= 'I': Compute eigenvectors of tridiagonal matrix also.
= 'V': Compute eigenvectors of original dense symmetric matrix
also. On entry, Z contains the orthogonal matrix used to
reduce the original matrix to tridiagonal form. (NOT
IMPLEMENTED YET)
N (global input) INTEGER
The order of the tridiagonal matrix T. N >= 0.
D (global input/output) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in descending order.
E (global input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Q (local output) DOUBLE PRECISION array,
local dimension ( LLD_Q, LOCc(JQ+N-1)) Q contains the
orthonormal eigenvectors of the symmetric tridiagonal matrix.
On output, Q is distributed across the P processes in block
cyclic format.
IQ (global input) INTEGER
Q's global row index, which points to the beginning of the sub‐
matrix which is to be operated on.
JQ (global input) INTEGER
Q's global column index, which points to the beginning of the
submatrix which is to be operated on.
DESCQ (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix Z.
WORK (local workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On output, WORK(1) returns the workspace
needed.
LWORK (local input/output) INTEGER,
the dimension of the array WORK. LWORK = 6*N + 2*NP*NQ NP =
NUMROC( N, NB, MYROW, DESCQ( RSRC_ ), NPROW ) NQ = NUMROC( N,
NB, MYCOL, DESCQ( CSRC_ ), NPCOL )
If LWORK = -1, the LWORK is global input and a workspace query
is assumed; the routine only calculates the minimum size for
the WORK array. The required workspace is returned as the
first element of WORK and no error message is issued by
PXERBLA.
IWORK (local workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK. LIWORK = 2 + 7*N + 8*NPCOL
INFO (global output) INTEGER
= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had an
illegal value, then INFO = -(i*100+j), if the i-th argument is
a scalar and had an illegal value, then INFO = -i. > 0: The
algorithm failed to compute the INFO/(N+1) th eigenvalue while
working on the submatrix lying in global rows and columns
mod(INFO,N+1).
FURTHER DETAILS
Contributed by Francoise Tisseur, University of Manchester.
Reference: F. Tisseur and J. Dongarra, "A Parallel Divide and
Conquer Algorithm for the Symmetric Eigenvalue Problem
on Distributed Memory Architectures",
SIAM J. Sci. Comput., 6:20 (1999), pp. 2223--2236.
(see also LAPACK Working Note 132)
http://www.netlib.org/lapack/lawns/lawn132.ps
ScaLAPACK version 1.7 13 August 2001 PDSTEDC(l)
