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slagtf

 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 tridiago-
      nal 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 factoriza-
              tion 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 factoriza-
              tion of T.

      C       (input/output) REAL array, dimension (N-1)
              On entry, C must contain the (n-1) sub-diagonal ele-
              ments 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 approxi-
              mately 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 fac-
              torization 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
              < 0: if INFO = -k, the kth argument had an illegal
              value