CLARRV(l) ) CLARRV(l)
CLARRV - compute the eigenvectors of the tridiagonal matrix T = L D L^T given L, D and the
eigenvalues of L D L^T
SUBROUTINE CLARRV( N, D, L, ISPLIT, M, W, IBLOCK, GERSCH, TOL, Z, LDZ, ISUPPZ, WORK,
IWORK, INFO )
INTEGER INFO, LDZ, M, N
INTEGER IBLOCK( * ), ISPLIT( * ), ISUPPZ( * ), IWORK( * )
REAL D( * ), GERSCH( * ), L( * ), W( * ), WORK( * )
COMPLEX Z( LDZ, * )
CLARRV 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.
N (input) INTEGER
The order of the matrix. N >= 0.
D (input/output) REAL array, dimension (N)
On entry, the n diagonal elements of the diagonal matrix D. On exit, D may be
L (input/output) REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the unit bidiagonal matrix L in ele-
ments 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) REAL
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 precision
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) REAL 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 SLARRE 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 eigenvalues 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) COMPLEX array, dimension (LDZ, max(1,M) )
If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain 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) col-
umns 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 >=
ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
The support of the eigenvectors in Z, i.e., the indices indicating the nonzero
elements in Z. The i-th eigenvector is nonzero only in elements ISUPPZ( 2*i-1 )
through ISUPPZ( 2*i ).
WORK (workspace) REAL 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 SLARRB if INFO = 2, internal error in CSTEIN
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
Ken Stanley, Computer Science Division, University of
California at Berkeley, USA
LAPACK version 3.0 15 June 2000 CLARRV(l)