slagtf(3F)

NAME
     SLAGTF - factorize the matrix (T - lambda*I), where T is an n by n
     tridiagonal matrix and lambda is a scalar, as   T - lambda*I = PLU,

SYNOPSIS
     SUBROUTINE SLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )

         INTEGER        INFO, N

         REAL           LAMBDA, TOL

         INTEGER        IN( * )

         REAL           A( * ), B( * ), C( * ), D( * )

PURPOSE
     SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n
     tridiagonal matrix and lambda is a scalar, as

     where P is a permutation matrix, L is a unit lower tridiagonal matrix
     with at most one non-zero sub-diagonal elements per column and U is an
     upper triangular matrix with at most two non-zero super-diagonal elements
     per column.

     The factorization is obtained by Gaussian elimination with partial
     pivoting and implicit row scaling.

     The parameter LAMBDA is included in the routine so that SLAGTF may be
     used, in conjunction with SLAGTS, to obtain eigenvectors of T by inverse
     iteration.


ARGUMENTS
     N       (input) INTEGER
             The order of the matrix T.

     A       (input/output) REAL array, dimension (N)
             On entry, A must contain the diagonal elements of T.

             On exit, A is overwritten by the n diagonal elements of the upper
             triangular matrix U of the factorization of T.

     LAMBDA  (input) REAL
             On entry, the scalar lambda.

     B       (input/output) REAL array, dimension (N-1)
             On entry, B must contain the (n-1) super-diagonal elements of T.

             On exit, B is overwritten by the (n-1) super-diagonal elements of
             the matrix U of the factorization of T.
     C       (input/output) REAL array, dimension (N-1)
             On entry, C must contain the (n-1) sub-diagonal elements of T.

             On exit, C is overwritten by the (n-1) sub-diagonal elements of
             the matrix L of the factorization of T.

     TOL     (input) REAL
             On entry, a relative tolerance used to indicate whether or not
             the matrix (T - lambda*I) is nearly singular. TOL should normally
             be chose as approximately the largest relative error in the
             elements of T. For example, if the elements of T are correct to
             about 4 significant figures, then TOL should be set to about
             5*10**(-4). If TOL is supplied as less than eps, where eps is the
             relative machine precision, then the value eps is used in place
             of TOL.

     D       (output) REAL array, dimension (N-2)
             On exit, D is overwritten by the (n-2) second super-diagonal
             elements of the matrix U of the factorization of T.

     IN      (output) INTEGER array, dimension (N)
             On exit, IN contains details of the permutation matrix P. If an
             interchange occurred at the kth step of the elimination, then
             IN(k) = 1, otherwise IN(k) = 0. The element IN(n) returns the
             smallest positive integer j such that

             abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,

             where norm( A(j) ) denotes the sum of the absolute values of the
             jth row of the matrix A. If no such j exists then IN(n) is
             returned as zero. If IN(n) is returned as positive, then a
             diagonal element of U is small, indicating that (T - lambda*I) is
             singular or nearly singular,

     INFO    (output)
             = 0   : successful exit