NAME

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

SYNOPSIS

  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);

PURPOSE

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.

ARGUMENTS

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 elements of the upper triangular matrix U of the factorization 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 factorization 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 factorization of T.
TOL (input)
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)
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
```
.lt. 0: if INFO = -k, the kth argument had an illegal value