DLAGTF(3F)DLAGTF(3F)NAMEDLAGTF - 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( * )
PURPOSEDLAGTF 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 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.
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.
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DLAGTF(3F)DLAGTF(3F)
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)
= 0 : successful exit
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