DSTEDC(1) LAPACK driver routine (version 3.2) DSTEDC(1)NAME
DSTEDC - computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer method
SYNOPSIS
SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )
CHARACTER COMPZ
INTEGER INFO, LDZ, LIWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
PURPOSE
DSTEDC computes all eigenvalues and, optionally, eigenvectors of a sym‐
metric tridiagonal matrix using the divide and conquer method. The
eigenvectors of a full or band real symmetric matrix can also be found
if DSYTRD or DSPTRD or DSBTRD 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 DLAED3 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) DOUBLE PRECISION array, dimension (N)
On entry, the diagonal elements of the tridiagonal matrix. On
exit, if INFO = 0, the eigenvalues in ascending order.
E (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the subdiagonal elements of the tridiagonal matrix.
On exit, E has been destroyed.
Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
On entry, if COMPZ = 'V', then Z contains the orthogonal 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 symmetric matrix, and if COMPZ = 'I', Z con‐
tains 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 eigenvec‐
tors are desired, then 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 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 )
= smallest integer k such that 2**k >= N. If COMPZ = 'I' and N
> 1 then LWORK must be at least ( 1 + 4*N + N**2 ). Note that
for COMPZ = 'I' or 'V', then if N is less than or equal to the
minimum divide size, usually 25, then LWORK need only be
max(1,2*(N-1)). 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 (MAX(1,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 ). Note that
for COMPZ = 'I' or 'V', then if N is less than or equal to the
minimum divide size, usually 25, then LIWORK need only be 1.
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 illegal value.
> 0: The algorithm failed to compute an eigenvalue while work‐
ing 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.
LAPACK driver routine (version 3November 2008 DSTEDC(1)
