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RedHat 9 (Linux i386) - man page for dpbcon (redhat section l)

DPBCON(l)					)					DPBCON(l)

NAME
       DPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a real symmet-
       ric positive definite band matrix using the Cholesky factorization  A  =  U**T*U  or  A	=
       L*L**T computed by DPBTRF

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   DOUBLE	  PRECISION ANORM, RCOND

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), WORK( * )

PURPOSE
       DPBCON  estimates the reciprocal of the condition number (in the 1-norm) of a real symmet-
       ric positive definite band matrix using the Cholesky factorization  A  =  U**T*U  or  A	=
       L*L**T  computed  by DPBTRF.  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  sub-
	       diagonals if UPLO = 'L'.  KD >= 0.

       AB      (input) DOUBLE PRECISION 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) DOUBLE PRECISION
	       The 1-norm (or infinity-norm) of the symmetric band matrix A.

       RCOND   (output) DOUBLE PRECISION
	       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) DOUBLE PRECISION 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 				DPBCON(l)


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