spbcon(l) [redhat man page]

SPBCON(l)								 )								 SPBCON(l)

NAME

       SPBCON  -  estimate  the  reciprocal  of  the  condition number (in the 1-norm) of a real symmetric positive definite band matrix using the
       Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF

SYNOPSIS

       SUBROUTINE SPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL 	  ANORM, RCOND

	   INTEGER	  IWORK( * )

	   REAL 	  AB( LDAB, * ), WORK( * )

PURPOSE

       SPBCON estimates the reciprocal of the condition number (in the 1-norm) of a  real  symmetric  positive	definite  band	matrix	using  the
       Cholesky  factorization	A  = U**T*U or A = L*L**T computed by SPBTRF.  An estimate is obtained for norm(inv(A)), and the reciprocal of the
       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangular factor stored in AB;
	       = 'L':  Lower triangular factor stored in AB.

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

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

       AB      (input) REAL array, dimension (LDAB,N)
	       The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A,  stored  in	the  first
	       KD+1  rows  of  the  array.   The  j-th	column	of  U  or L is stored in the j-th column of the array AB as follows: if UPLO ='U',
	       AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       ANORM   (input) REAL
	       The 1-norm (or infinity-norm) of the symmetric band matrix A.

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

       WORK    (workspace) REAL array, dimension (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

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

LAPACK version 3.0						   15 June 2000 							 SPBCON(l)

spbcon.f(3)							      LAPACK							       spbcon.f(3)

NAME

       spbcon.f -

SYNOPSIS

   Functions/Subroutines
       subroutine spbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO)
	   SPBCON

Function/Subroutine Documentation
   subroutine spbcon (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, realANORM, realRCOND, real, dimension( *
       )WORK, integer, dimension( * )IWORK, integerINFO)
       SPBCON

       Purpose:

	    SPBCON estimates the reciprocal of the condition number (in the
	    1-norm) of a real symmetric positive definite band matrix using the
	    Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF.

	    An estimate is obtained for norm(inv(A)), and the reciprocal of the
	    condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangular factor stored in AB;
		     = 'L':  Lower triangular factor stored in AB.

	   N

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

	   KD

		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

	   AB

		     AB is REAL array, dimension (LDAB,N)
		     The triangular factor U or L from the Cholesky factorization
		     A = U**T*U or A = L*L**T of the band matrix A, stored in the
		     first KD+1 rows of the array.  The j-th column of U or L is
		     stored in the j-th column of the array AB as follows:
		     if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
		     if UPLO ='L', AB(1+i-j,j)	  = L(i,j) for j<=i<=min(n,j+kd).

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   ANORM

		     ANORM is REAL
		     The 1-norm (or infinity-norm) of the symmetric band 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 an
		     estimate of the 1-norm of inv(A) computed in this routine.

	   WORK

		     WORK is REAL array, dimension (3*N)

	   IWORK

		     IWORK is INTEGER 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:
	   November 2011

       Definition at line 132 of file spbcon.f.

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

Version 3.4.1							  Sun May 26 2013						       spbcon.f(3)