dlagtf-f(3)

dlagtf.f –

Synopsis

Functions/Subroutines

subroutine dlagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO)
DLAGTF 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 dlagtf (integerN, double precision, dimension( * )A, double precisionLAMBDA, double precision, dimension( * )B, double precision, dimension( * )C, double precisionTOL, double precision, dimension( * )D, integer, dimension( * )IN, integerINFO)

DLAGTF 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:

 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 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 eigenvectors of T by
 inverse iteration.

Parameters:

 N is INTEGER
 The order of the matrix T.

 A is 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

 LAMBDA is DOUBLE PRECISION
 On entry, the scalar lambda.

 B is 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 is 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

 TOL is 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 is 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 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 dlagtf.f.

Author

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