DSTEVD(1) LAPACK driver routine (version 3.2) DSTEVD(1)NAME
DSTEVD - computes all eigenvalues and, optionally, eigenvectors 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, eigenvectors of a real
symmetric tridiagonal matrix. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm 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 dig‐
its, 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 tridiagonal matrix A.
On exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A, stored in elements 1 to N-1 of E. On exit, the con‐
tents of E are destroyed.
Z (output) DOUBLE PRECISION array, dimension (LDZ, 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 associated with D(i). If JOBZ = 'N', then Z is
not referenced.
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 sizes of the WORK and IWORK arrays, returns these val‐
ues as the first entries of the WORK and IWORK arrays, and no
error message related to LWORK or LIWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (MAX(1,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 sizes of the WORK and IWORK arrays, returns these val‐
ues as the first entries of the WORK and IWORK arrays, and no
error message related to LWORK or LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the algorithm failed to converge; i off-
diagonal elements of E did not converge to zero.
LAPACK driver routine (version 3November 2008 DSTEVD(1)
