DLARRE(3S)DLARRE(3S)NAME
DLARRE - the tridiagonal matrix T, DLARRE sets "small" off-diagonal
elements to zero, and for each unreduced block T_i, it finds (i) the
numbers sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T
representations and (iii) eigenvalues of each L_i D_i L_i^T
SYNOPSIS
SUBROUTINE DLARRE( N, D, E, TOL, NSPLIT, ISPLIT, M, W, WOFF, GERSCH,
WORK, INFO )
INTEGER INFO, M, N, NSPLIT
DOUBLE PRECISION TOL
INTEGER ISPLIT( * )
DOUBLE PRECISION D( * ), E( * ), GERSCH( * ), W( * ), WOFF( *
), WORK( * )
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
Given the tridiagonal matrix T, DLARRE sets "small" off-diagonal elements
to zero, and for each unreduced block T_i, it finds (i) the numbers
sigma_i (ii) the base T_i - sigma_i I = L_i D_i L_i^T representations and
(iii) eigenvalues of each L_i D_i L_i^T. The representations and
eigenvalues found are then used by DSTEGR to compute the eigenvectors of
a symmetric tridiagonal matrix. Currently, the base representations are
limited to being positive or negative definite, and the eigenvalues of
the definite matrices are found by the dqds algorithm (subroutine
DLASQ2). As an added benefit, DLARRE also outputs the n Gerschgorin
intervals for each L_i D_i L_i^T.
ARGUMENTS
N (input) INTEGER
The order of the matrix.
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix T.
On exit, the n diagonal elements of the diagonal matrices D_i.
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DLARRE(3S)DLARRE(3S)
E (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix T; E(N) need not be set. On exit, the subdiagonal
elements of the unit bidiagonal matrices L_i.
TOL (input) DOUBLE PRECISION
The threshold for splitting. If on input |E(i)| < TOL, then the
matrix T is split into smaller blocks.
NSPLIT (input) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.
ISPLIT (output) INTEGER array, dimension (2*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., and
the NSPLIT-th consists of rows/columns ISPLIT(NSPLIT-1)+1 through
ISPLIT(NSPLIT)=N.
M (output) INTEGER
The total number of eigenvalues (of all the L_i D_i L_i^T) found.
W (output) DOUBLE PRECISION array, dimension (N)
The first M elements contain the eigenvalues. The eigenvalues of
each of the blocks, L_i D_i L_i^T, are sorted in ascending order.
WOFF (output) DOUBLE PRECISION array, dimension (N)
The NSPLIT base points sigma_i.
GERSCH (output) DOUBLE PRECISION array, dimension (2*N)
The n Gerschgorin intervals.
WORK (input) DOUBLE PRECISION array, dimension (4*N???)
Workspace.
INFO (output) INTEGER
Output error code from DLASQ2
FURTHER DETAILS
Based on contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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