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SLAGTF(3F)							    SLAGTF(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

     SUBROUTINE	SLAGTF(	N, A, LAMBDA, B, C, TOL, D, IN,	INFO )

	 INTEGER	INFO, N

	 REAL		LAMBDA,	TOL

	 INTEGER	IN( * )

	 REAL		A( * ),	B( * ),	C( * ),	D( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     N	     (input) INTEGER
	     The order of the matrix T.

     A	     (input/output) REAL 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) REAL
	     On	entry, the scalar lambda.

     B	     (input/output) REAL 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.





									Page 1






SLAGTF(3F)							    SLAGTF(3F)



     C	     (input/output) REAL 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) REAL
	     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) REAL 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
SLAGTF(3F)							    SLAGTF(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

     SUBROUTINE	SLAGTF(	N, A, LAMBDA, B, C, TOL, D, IN,	INFO )

	 INTEGER	INFO, N

	 REAL		LAMBDA,	TOL

	 INTEGER	IN( * )

	 REAL		A( * ),	B( * ),	C( * ),	D( * )

PURPOSE    [Toc]    [Back]

     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    [Toc]    [Back]

     N	     (input) INTEGER
	     The order of the matrix T.

     A	     (input/output) REAL 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) REAL
	     On	entry, the scalar lambda.

     B	     (input/output) REAL 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.





									Page 1






SLAGTF(3F)							    SLAGTF(3F)



     C	     (input/output) REAL 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) REAL
	     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) REAL 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


									PPPPaaaaggggeeee 2222
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