sptcon(l) [redhat man page]

SPTCON(l)								 )								 SPTCON(l)

NAME

       SPTCON  - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the
       factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF

SYNOPSIS

       SUBROUTINE SPTCON( N, D, E, ANORM, RCOND, WORK, INFO )

	   INTEGER	  INFO, N

	   REAL 	  ANORM, RCOND

	   REAL 	  D( * ), E( * ), WORK( * )

PURPOSE

       SPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix	using  the
       factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF.  Norm(inv(A)) is computed by a direct method, and the reciprocal of the con-
       dition number is computed as
		    RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       D       (input) REAL array, dimension (N)
	       The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by SPTTRF.

       E       (input) REAL array, dimension (N-1)
	       The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A,  as computed by SPTTRF.

       ANORM   (input) REAL
	       The 1-norm of the original matrix A.

       RCOND   (output) REAL
	       The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM),	where  AINVNM  is  the	1-norm	of
	       inv(A) computed in this routine.

       WORK    (workspace) REAL array, dimension (N)

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS

       The method used is described in Nicholas J. Higham, "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM
       J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

LAPACK version 3.0						   15 June 2000 							 SPTCON(l)

sptcon.f(3)							      LAPACK							       sptcon.f(3)

NAME

       sptcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sptcon (N, D, E, ANORM, RCOND, WORK, INFO)
	   SPTCON

Function/Subroutine Documentation
   subroutine sptcon (integerN, real, dimension( * )D, real, dimension( * )E, realANORM, realRCOND, real, dimension( * )WORK, integerINFO)
       SPTCON

       Purpose:

	    SPTCON computes the reciprocal of the condition number (in the
	    1-norm) of a real symmetric positive definite tridiagonal matrix
	    using the factorization A = L*D*L**T or A = U**T*D*U computed by
	    SPTTRF.

	    Norm(inv(A)) is computed by a direct method, and the reciprocal of
	    the condition number is computed as
			 RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   D

		     D is REAL array, dimension (N)
		     The n diagonal elements of the diagonal matrix D from the
		     factorization of A, as computed by SPTTRF.

	   E

		     E is REAL array, dimension (N-1)
		     The (n-1) off-diagonal elements of the unit bidiagonal factor
		     U or L from the factorization of A,  as computed by SPTTRF.

	   ANORM

		     ANORM is REAL
		     The 1-norm of the original matrix A.

	   RCOND

		     RCOND is REAL
		     The reciprocal of the condition number of the matrix A,
		     computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
		     1-norm of inv(A) computed in this routine.

	   WORK

		     WORK is REAL array, dimension (N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Further Details:

	     The method used is described in Nicholas J. Higham, "Efficient
	     Algorithms for Computing the Condition Number of a Tridiagonal
	     Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

       Definition at line 119 of file sptcon.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sptcon.f(3)