Contents
slagtf - 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 SLAGTF(N, A, LAMBDA, B, C, TOL, D, IN, INFO)
INTEGER N, INFO
INTEGER IN(*)
REAL LAMBDA, TOL
REAL A(*), B(*), C(*), D(*)
SUBROUTINE SLAGTF_64(N, A, LAMBDA, B, C, TOL, D, IN, INFO)
INTEGER*8 N, INFO
INTEGER*8 IN(*)
REAL LAMBDA, TOL
REAL A(*), B(*), C(*), D(*)
F95 INTERFACE
SUBROUTINE LAGTF([N], A, LAMBDA, B, C, TOL, D, IN, [INFO])
INTEGER :: N, INFO
INTEGER, DIMENSION(:) :: IN
REAL :: LAMBDA, TOL
REAL, 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 :: LAMBDA, TOL
REAL, DIMENSION(:) :: A, B, C, D
C INTERFACE
#include <sunperf.h>
void slagtf(int n, float *a, float lambda, float *b, float
*c, float tol, float *d, int *in, int *info);
void slagtf_64(long n, float *a, float lambda, float *b,
float *c, float tol, float *d, long *in, long
*info);
slagtf 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.
N (input) The order of the matrix T.
A (input/output)
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 fac-
torization of T.
LAMBDA (input)
On entry, the scalar lambda.
B (input/output)
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 factori-
zation of T.
C (input/output)
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 factori-
zation of T.
TOL (input/output)
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 approxi-
mately 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 sup-
plied as less than eps, where eps is the relative
machine precision, then the value eps is used in
place of TOL.
D (output)
On exit, D is overwritten by the (n-2) second
super-diagonal elements of the matrix U of the
factorization of T.
IN (output)
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