dlagts-f(3)

dlagts.f –

Synopsis

Functions/Subroutines

subroutine dlagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO)
DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Function/Subroutine Documentation

subroutine dlagts (integerJOB, integerN, double precision, dimension( * )A, double precision, dimension( * )B, double precision, dimension( * )C, double precision, dimension( * )D, integer, dimension( * )IN, double precision, dimension( * )Y, double precisionTOL, integerINFO)

DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Purpose:

 DLAGTS may be used to solve one of the systems of equations
 (T - lambda*I)*x = y or (T - lambda*I)**T*x = y,
 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 DLAGTF. 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.

 

Parameters:

JOB

 JOB is INTEGER
 Specifies the job to be performed by DLAGTS 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)**Tx = y are to be solved,
 but diagonal elements of U are not to be perturbed.
 = -2: The equations (T - lambda*I)**Tx = 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

 N is INTEGER
 The order of the matrix T.

A

 A is DOUBLE PRECISION array, dimension (N)
 On entry, A must contain the diagonal elements of U as
 returned from DLAGTF.

B

 B is DOUBLE PRECISION array, dimension (N-1)
 On entry, B must contain the first super-diagonal elements of
 U as returned from DLAGTF.

C

 C is DOUBLE PRECISION array, dimension (N-1)
 On entry, C must contain the sub-diagonal elements of L as
 returned from DLAGTF.

D

 D is DOUBLE PRECISION array, dimension (N-2)
 On entry, D must contain the second super-diagonal elements
 of U as returned from DLAGTF.

IN

 IN is INTEGER array, dimension (N)
 On entry, IN must contain details of the matrix P as returned
 from DLAGTF.

Y

 Y is DOUBLE PRECISION array, dimension (N)
 On entry, the right hand side vector y.
 On exit, Y is overwritten by the solution vector x.

TOL

 TOL is DOUBLE PRECISION
 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
 non-positive, 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
 non-positive on entry. Otherwise TOL is unchanged.

INFO

 INFO is INTEGER
 = 0 : successful exit
 .lt. 0: if INFO = -i, the i-th argument had an illegal value
 .gt. 0: overflow would occur when computing the INFO(th)
 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.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 162 of file dlagts.f.

Author

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