GNU/Linux man pages
Livre :
Expressions régulières,
Syntaxe et mise en oeuvre :
GNU/Linux |
CentOS 4.8 |
i386 |
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slarre(l) |
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SLARRE - the tridiagonal matrix T, SLARRE 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
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SUBROUTINE SLARRE( |
N, D, E, TOL, NSPLIT, ISPLIT, M, W, WOFF, GERSCH, WORK, INFO ) | ||
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INTEGER |
INFO, M, N, NSPLIT | ||
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REAL |
TOL | ||
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INTEGER |
ISPLIT( * ) | ||
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REAL |
D( * ), E( * ), GERSCH( * ), W( * ), WOFF( * ), WORK( * ) |
Given the
tridiagonal matrix T, SLARRE 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 SSTEGR 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
SLASQ2). As an added benefit, SLARRE also outputs the n
Gerschgorin
intervals for each L_i D_i L_i^T.
N (input) INTEGER
The order of the matrix.
D (input/output) REAL 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.
E (input/output) REAL 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) REAL
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) REAL 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) REAL array, dimension (N)
The NSPLIT base points sigma_i.
GERSCH (output) REAL array, dimension (2*N)
The n Gerschgorin intervals.
WORK (input) REAL array, dimension (4*N???)
Workspace.
INFO (output) INTEGER
Output error code from SLASQ2
Based on
contributions by
Inderjit Dhillon, IBM Almaden, USA
Osni Marques, LBNL/NERSC, USA
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slarre(l) | |