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# Manual Reference Pages  -  PDSTEDC (l)

### NAME

PDSTEDC - tridiagonal matrix in parallel, using the divide and conquer algorithm

Synopsis
Purpose
Arguments
Further Details

### 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/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. 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 submatrix 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

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 ScaLAPACK version 1.7 PDSTEDC (l) 13 August 2001

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