DSTEVD - compute all eigenvalues and, optionally, eigen
vectors of a real symmetric tridiagonal matrix
SYNOPSIS
SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK,
IWORK, LIWORK, INFO )
CHARACTER JOBZ
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z(
LDZ, * )
PURPOSE
DSTEVD computes all eigenvalues and, optionally, eigenvec
tors of a real symmetric tridiagonal matrix. If eigenvec
tors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assump
tions 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 with
out guard digits, but we know of none.
ARGUMENTS
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) DOUBLE PRECISION array, dimension
(N)
On entry, the n diagonal elements of the tridiago
nal matrix A. On exit, if INFO = 0, the eigenval
ues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension
(N)
On entry, the (n-1) subdiagonal elements of the
tridiagonal matrix A, stored in elements 1 to N-1
of E; E(N) need not be set, but is used by the
routine. On exit, the contents of E are
destroyed.
N)
If JOBZ = 'V', then if INFO = 0, Z contains the
orthonormal eigenvectors of the matrix A, with the
i-th column of Z holding the eigenvector associ
ated with D(i). If JOBZ = 'N', then Z is not ref
erenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1,
and if JOBZ = 'V', LDZ >= max(1,N).
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK) On exit, if INFO = 0, WORK(1)
returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If JOBZ = 'N'
or N <= 1 then LWORK must be at least 1. If JOBZ
= 'V' 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 JOBZ = 'N'
or N <= 1 then LIWORK must be at least 1. If JOBZ
= 'V' 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: if INFO = i, the algorithm failed to con
verge; i off-diagonal elements of E did not con
verge to zero.
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