SSTEDC - compute all eigenvalues and, optionally, eigen
vectors of a symmetric tridiagonal matrix using the divide
and conquer method
SYNOPSIS
SUBROUTINE SSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
PURPOSE
SSTEDC computes all eigenvalues and, optionally, eigenvec
tors of a symmetric tridiagonal matrix using the divide
and conquer method. The eigenvectors of a full or band
real symmetric matrix can also be found if SSYTRD or SSP
TRD or SSBTRD has been used to reduce this matrix to
tridiagonal form.
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 SLAED3 for details.
ARGUMENTS
COMPZ (input) CHARACTER*1
= 'N': Compute eigenvalues only.
= '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.
N (input) INTEGER
The dimension of the symmetric tridiagonal matrix.
N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the diagonal elements of the tridiagonal
matrix. On exit, if INFO = 0, the eigenvalues in
ascending order.
On entry, the subdiagonal elements of the tridiag
onal matrix. On exit, E has been destroyed.
Z (input/output) REAL array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the
orthogonal matrix used in the reduction to tridi
agonal form. On exit, if INFO = 0, then if COMPZ
= 'V', Z contains the orthonormal eigenvectors of
the original symmetric matrix, and if COMPZ = 'I',
Z contains the orthonormal eigenvectors of the
symmetric tridiagonal matrix. If COMPZ = 'N',
then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1.
If eigenvectors are desired, then LDZ >= max(1,N).
WORK (workspace/output) REAL array,
dimension (LWORK) On exit, if INFO = 0, WORK(1)
returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If COMPZ = 'N'
or N <= 1 then LWORK must be at least 1. If COMPZ
= 'V' and N > 1 then LWORK must be at least ( 1 +
3*N + 2*N*lg N + 3*N**2 ), where lg( N ) = small
est integer k such that 2**k >= N. If COMPZ = 'I'
and N > 1 then LWORK must be at least ( 1 + 4*N +
N**2 ).
If LWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension
(LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal
LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK. If COMPZ = 'N'
or N <= 1 then LIWORK must be at least 1. If
COMPZ = 'V' and N > 1 then LIWORK must be at least
( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I' and N > 1
then LIWORK must be at least ( 3 + 5*N ).
If LIWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the IWORK array, returns this value as the first
entry of the IWORK array, and no error message
related to LIWORK is issued by XERBLA.
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
> 0: The algorithm failed to compute an eigen
value while working on the submatrix lying in rows
and columns INFO/(N+1) through mod(INFO,N+1).
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of
California
at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee.
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