NAME

       slagtf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO)
           SLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal
           matrix, and λ a scalar, using partial pivoting with row interchanges.

Function/Subroutine Documentation

   subroutine slagtf (integerN, real, dimension( * )A, realLAMBDA, real, dimension( * )B, real,
       dimension( * )C, realTOL, real, dimension( * )D, integer, dimension( * )IN, integerINFO)
       SLAGTF computes an LU factorization of a matrix T-λI, where T is a general tridiagonal
       matrix, and λ a scalar, using partial pivoting with row interchanges.

       Purpose:

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

               T - lambda*I = PLU,

            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.

       Parameters:
           N

                     N is INTEGER
                     The order of the matrix T.

           A

                     A is 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

                     LAMBDA is REAL
                     On entry, the scalar lambda.

           B

                     B is 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

                     C is 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

                     TOL is 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

                     D is 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

                     IN is 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

                     INFO is INTEGER
                     = 0   : successful exit
                     .lt. 0: if INFO = -k, the kth argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 157 of file slagtf.f.

Author

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