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RedHat 9 (Linux i386) - man page for dlagtf (redhat section l)

DLAGTF(l)					)					DLAGTF(l)

NAME
       DLAGTF  - 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 DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION LAMBDA, TOL

	   INTEGER	  IN( * )

	   DOUBLE	  PRECISION A( * ), B( * ), C( * ), D( * )

PURPOSE
       DLAGTF 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 col-
       umn.

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

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

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

       A       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
	       On entry, the scalar lambda.

       B       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
	       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) DOUBLE PRECISION 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) INTEGER
	       = 0   : successful exit

LAPACK version 3.0			   15 June 2000 				DLAGTF(l)


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