dlagtf(3)

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 tridi

agonal 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

DLAGTF may be used, in conjunction with DLAGTS, to obtain eigen

vectors 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 ele

ments 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-diag

onal 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-diago

nal 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 su

per-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 elim

ination, 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(3)