SLAGTS(3F) SLAGTS(3F)
SLAGTS - may be used to solve one of the systems of equations (T -
lambda*I)*x = y or (T - lambda*I)'*x = y,
SUBROUTINE SLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
INTEGER INFO, JOB, N
REAL TOL
INTEGER IN( * )
REAL A( * ), B( * ), C( * ), D( * ), Y( * )
SLAGTS may be used to solve one of the systems of equations
where T is an n by n tridiagonal matrix, for x, following the
factorization of (T - lambda*I) as
(T - lambda*I) = P*L*U ,
by routine SLAGTF. The choice of equation to be solved is controlled by
the argument JOB, and in each case there is an option to perturb zero or
very small diagonal elements of U, this option being intended for use in
applications such as inverse iteration.
JOB (input) INTEGER
Specifies the job to be performed by SLAGTS as follows:
= 1: The equations (T - lambda*I)x = y are to be solved, but
diagonal elements of U are not to be perturbed. = -1: The
equations (T - lambda*I)x = y are to be solved and, if overflow
would otherwise occur, the diagonal elements of U are to be
perturbed. See argument TOL below. = 2: The equations (T -
lambda*I)'x = y are to be solved, but diagonal elements of U are
not to be perturbed. = -2: The equations (T - lambda*I)'x = y
are to be solved and, if overflow would otherwise occur, the
diagonal elements of U are to be perturbed. See argument TOL
below.
N (input) INTEGER
The order of the matrix T.
A (input) REAL array, dimension (N)
On entry, A must contain the diagonal elements of U as returned
from SLAGTF.
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SLAGTS(3F) SLAGTS(3F)
B (input) REAL array, dimension (N-1)
On entry, B must contain the first super-diagonal elements of U
as returned from SLAGTF.
C (input) REAL array, dimension (N-1)
On entry, C must contain the sub-diagonal elements of L as
returned from SLAGTF.
D (input) REAL array, dimension (N-2)
On entry, D must contain the second super-diagonal elements of U
as returned from SLAGTF.
IN (input) INTEGER array, dimension (N)
On entry, IN must contain details of the matrix P as returned
from SLAGTF.
Y (input/output) REAL array, dimension (N)
On entry, the right hand side vector y. On exit, Y is
overwritten by the solution vector x.
TOL (input/output) REAL
On entry, with JOB .lt. 0, TOL should be the minimum
perturbation to be made to very small diagonal elements of U.
TOL should normally be chosen as about eps*norm(U), where eps is
the relative machine precision, but if TOL is supplied as nonpositive,
then it is reset to eps*max( abs( u(i,j) ) ). If JOB
.gt. 0 then TOL is not referenced.
On exit, TOL is changed as described above, only if TOL is nonpositive
on entry. Otherwise TOL is unchanged.
INFO (output) INTEGER
= 0 : successful exit
element of the solution vector x. This can only occur when JOB is
supplied as positive and either means that a diagonal element of
U is very small, or that the elements of the right-hand side
vector y are very large.
SLAGTS(3F) SLAGTS(3F)
SLAGTS - may be used to solve one of the systems of equations (T -
lambda*I)*x = y or (T - lambda*I)'*x = y,
SUBROUTINE SLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
INTEGER INFO, JOB, N
REAL TOL
INTEGER IN( * )
REAL A( * ), B( * ), C( * ), D( * ), Y( * )
SLAGTS may be used to solve one of the systems of equations
where T is an n by n tridiagonal matrix, for x, following the
factorization of (T - lambda*I) as
(T - lambda*I) = P*L*U ,
by routine SLAGTF. The choice of equation to be solved is controlled by
the argument JOB, and in each case there is an option to perturb zero or
very small diagonal elements of U, this option being intended for use in
applications such as inverse iteration.
JOB (input) INTEGER
Specifies the job to be performed by SLAGTS as follows:
= 1: The equations (T - lambda*I)x = y are to be solved, but
diagonal elements of U are not to be perturbed. = -1: The
equations (T - lambda*I)x = y are to be solved and, if overflow
would otherwise occur, the diagonal elements of U are to be
perturbed. See argument TOL below. = 2: The equations (T -
lambda*I)'x = y are to be solved, but diagonal elements of U are
not to be perturbed. = -2: The equations (T - lambda*I)'x = y
are to be solved and, if overflow would otherwise occur, the
diagonal elements of U are to be perturbed. See argument TOL
below.
N (input) INTEGER
The order of the matrix T.
A (input) REAL array, dimension (N)
On entry, A must contain the diagonal elements of U as returned
from SLAGTF.
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SLAGTS(3F) SLAGTS(3F)
B (input) REAL array, dimension (N-1)
On entry, B must contain the first super-diagonal elements of U
as returned from SLAGTF.
C (input) REAL array, dimension (N-1)
On entry, C must contain the sub-diagonal elements of L as
returned from SLAGTF.
D (input) REAL array, dimension (N-2)
On entry, D must contain the second super-diagonal elements of U
as returned from SLAGTF.
IN (input) INTEGER array, dimension (N)
On entry, IN must contain details of the matrix P as returned
from SLAGTF.
Y (input/output) REAL array, dimension (N)
On entry, the right hand side vector y. On exit, Y is
overwritten by the solution vector x.
TOL (input/output) REAL
On entry, with JOB .lt. 0, TOL should be the minimum
perturbation to be made to very small diagonal elements of U.
TOL should normally be chosen as about eps*norm(U), where eps is
the relative machine precision, but if TOL is supplied as nonpositive,
then it is reset to eps*max( abs( u(i,j) ) ). If JOB
.gt. 0 then TOL is not referenced.
On exit, TOL is changed as described above, only if TOL is nonpositive
on entry. Otherwise TOL is unchanged.
INFO (output) INTEGER
= 0 : successful exit
element of the solution vector x. This can only occur when JOB is
supplied as positive and either means that a diagonal element of
U is very small, or that the elements of the right-hand side
vector y are very large.
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