ZLARRV(3S)ZLARRV(3S)NAME
ZLARRV - 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 ZLARRV( 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( *
)
COMPLEX*16 Z( LDZ, * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSE
ZLARRV 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.
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ZLARRV(3S)ZLARRV(3S)
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
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) 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
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*16 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)
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
indicating the nonzero elements in Z. The i-th eigenvector is
nonzero only in elements ISUPPZ( 2*i-1 ) through ISUPPZ( 2*i ).
GERSCH (workspace) DOUBLE PRECISION array, dimension (2*N)
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ZLARRV(3S)ZLARRV(3S)
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, internal
error in ZSTEIN
FURTHER DETAILS
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
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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