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slagts

SLAGTS(l)								 )								 SLAGTS(l)

NAME

       SLAGTS - may be used to solve one of the systems of equations  (T - lambda*I)*x = y or (T - lambda*I)'*x = y,

SYNOPSIS

       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( * )

PURPOSE

       SLAGTS may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T - lambda*I)'*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 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.

ARGUMENTS

       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 equa-
	       tions  (T - lambda*I)x = y  are to be solved and, if overflow would otherwise occur, the diagonal elements of  U  are  to  be  per-
	       turbed. 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.

       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 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    (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.

LAPACK version 3.0						   15 June 2000 							 SLAGTS(l)