DLARRV(l) ) DLARRV(l)NAME
DLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T
given L, D and the eigenvalues of L D L^T
SYNOPSIS
SUBROUTINE DLARRV( N, D, L, ISPLIT, M, W, IBLOCK, GERSCH, TOL, Z, LDZ,
ISUPPZ, WORK, IWORK, INFO )
INTEGER INFO, LDZ, M, N
DOUBLE PRECISION TOL
INTEGER IBLOCK( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * )
DOUBLE PRECISION D( * ), GERSCH( * ), L( * ), W( * ), WORK(
* ), Z( LDZ, * )
PURPOSE
DLARRV computes the eigenvectors of the tridiagonal matrix T = L D L^T
given L, D and the eigenvalues of L D L^T. The input eigenvalues should
have high relative accuracy with respect to the entries of L and D. The
desired accuracy of the output can be specified by the input parameter
TOL.
ARGUMENTS
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 diagonal matrix D. On
exit, D may be overwritten.
L (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the unit bidiagonal
matrix L in elements 1 to N-1 of L. L(N) need not be set. On
exit, L is overwritten.
ISPLIT (input) INTEGER array, dimension (N)
The splitting points, at which T breaks up into submatrices.
The first submatrix consists of rows/columns 1 to ISPLIT( 1 ),
the second of rows/columns ISPLIT( 1 )+1 through ISPLIT( 2 ),
etc.
TOL (input) DOUBLE PRECISION
The absolute error tolerance for the eigenvalues/eigenvectors.
Errors in the input eigenvalues must be bounded by TOL. The
eigenvectors output have residual norms bounded by TOL, and the
dot products between different eigenvectors are bounded by TOL.
TOL must be at least N*EPS*|T|, where EPS is the machine preci‐
sion and |T| is the 1-norm of the tridiagonal matrix.
M (input) INTEGER
The total number of eigenvalues found. 0 <= M <= N. If RANGE
= 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (input) DOUBLE PRECISION array, dimension (N)
The first M elements of W contain the eigenvalues for which
eigenvectors are to be computed. The eigenvalues should be
grouped by split-off block and ordered from smallest to largest
within the block ( The output array W from DLARRE is expected
here ). Errors in W must be bounded by TOL (see above).
IBLOCK (input) INTEGER array, dimension (N)
The submatrix indices associated with the corresponding eigen‐
values in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to the
first submatrix from the top, =2 if W(i) belongs to the second
submatrix, etc.
Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
If JOBZ = 'V', then if INFO = 0, the first M columns of Z con‐
tain the orthonormal eigenvectors of the matrix T corresponding
to the selected eigenvalues, with the i-th column of Z holding
the eigenvector associated with W(i). If JOBZ = 'N', then Z is
not referenced. Note: the user must ensure that at least
max(1,M) columns are supplied in the array Z; if RANGE = 'V',
the exact value of M is not known in advance and an upper bound
must be used.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ =
'V', LDZ >= max(1,N).
ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
The support of the eigenvectors in Z, i.e., the indices indi‐
cating the nonzero elements in Z. The i-th eigenvector is
nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ).
WORK (workspace) DOUBLE PRECISION array, dimension (13*N)
IWORK (workspace) INTEGER array, dimension (6*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = 1, internal error in DLARRB if INFO = 2, inter‐
nal error in DSTEIN
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
LAPACK version 3.0 15 June 2000 DLARRV(l)
