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
SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO) INTEGER N, INFO INTEGER IN(*) DOUBLE PRECISION LAMBDA, TOL DOUBLE PRECISION A(*), B(*), C(*), D(*)
SUBROUTINE DLAGTF_64( N, A, LAMBDA, B, C, TOL, D, IN, INFO) INTEGER*8 N, INFO INTEGER*8 IN(*) DOUBLE PRECISION LAMBDA, TOL DOUBLE PRECISION A(*), B(*), C(*), D(*)
SUBROUTINE LAGTF( [N], A, LAMBDA, B, C, TOL, D, IN, [INFO]) INTEGER :: N, INFO INTEGER, DIMENSION(:) :: IN REAL(8) :: LAMBDA, TOL REAL(8), DIMENSION(:) :: A, B, C, D
SUBROUTINE LAGTF_64( [N], A, LAMBDA, B, C, TOL, D, IN, [INFO]) INTEGER(8) :: N, INFO INTEGER(8), DIMENSION(:) :: IN REAL(8) :: LAMBDA, TOL REAL(8), DIMENSION(:) :: A, B, C, D
#include <sunperf.h>
void dlagtf(int n, double *a, double lambda, double *b, double *c, double tol, double *d, int *in, int *info);
void dlagtf_64(long n, double *a, double lambda, double *b, double *c, double tol, double *d, long *in, long *info);
dlagtf 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 SLAGTF may be used, in conjunction with SLAGTS, to obtain eigenvectors of T by inverse iteration.
On exit, A is overwritten by the n diagonal elements of the upper triangular matrix U of the factorization of T.
On exit, B is overwritten by the (n-1) super-diagonal elements of the matrix U of the factorization of T.
On exit, C is overwritten by the (n-1) sub-diagonal elements of the matrix L of the factorization of T.
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,
= 0 : successful exit
.lt. 0: if INFO = -k, the kth argument had an illegal value