CSTEDC - compute all eigenvalues and, optionally, eigen
vectors of a symmetric tridiagonal matrix using the divide
and conquer method
SYNOPSIS
SUBROUTINE CSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK,
RWORK, LRWORK, IWORK, LIWORK, INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
REAL D( * ), E( * ), RWORK( * )
COMPLEX WORK( * ), Z( LDZ, * )
PURPOSE
CSTEDC 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
complex Hermitian matrix can also be found if CHETRD or
CHPTRD or CHBTRD 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 Hermitian
matrix also. On entry, Z contains the unitary
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) COMPLEX array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the uni
tary matrix used in the reduction to tridiagonal
form. On exit, if INFO = 0, then if COMPZ = 'V',
Z contains the orthonormal eigenvectors of the
original Hermitian matrix, and if COMPZ = 'I', Z
contains the orthonormal eigenvectors of the sym
metric 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) COMPLEX 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 'I', or N <= 1, LWORK must be at least 1. If
COMPZ = 'V' and N > 1, LWORK must be at least N*N.
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.
RWORK (workspace/output) REAL array,
dimension (LRWORK) On exit, if INFO = 0, RWORK(1)
returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of the array RWORK. If COMPZ = 'N'
or N <= 1, LRWORK must be at least 1. If COMPZ =
'V' and N > 1, LRWORK must be at least 1 + 3*N +
2*N*lg N + 3*N**2 , where lg( N ) = smallest inte
ger k such that 2**k >= N. If COMPZ = 'I' and N >
1, LRWORK must be at least 1 + 4*N + 2*N**2 .
If LRWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the RWORK array, returns this value as the first
entry of the RWORK array, and no error message
related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension
(LIWORK)
LIWORK.
LIWORK (input) INTEGER
The dimension of the array IWORK. If COMPZ = 'N'
or N <= 1, LIWORK must be at least 1. If COMPZ =
'V' or N > 1, LIWORK must be at least 6 + 6*N +
5*N*lg N. If COMPZ = 'I' or N > 1, 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.
INFO (output) INTEGER
= 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
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