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NAME
     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,

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( * )



     #include <sunperf.h>

     void dlagtf(int n, double *da, double  lambda,  double  *db,
               double  *dc,  double  tol, double *d, int *in, int
               *info) ;

PURPOSE
     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 tridiago-
     nal  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  ele-
               ments  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 factori-
               zation of T.

     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 factori-
               zation 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 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) 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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