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CPBCON(1)		 LAPACK routine (version 3.2)		     CPBCON(1)

NAME
       CPBCON  -  estimates  the  reciprocal  of  the condition number (in the
       1-norm) of a complex Hermitian positive definite band matrix using  the
       Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF

SYNOPSIS
       SUBROUTINE CPBCON( UPLO,	 N,  KD,  AB, LDAB, ANORM, RCOND, WORK, RWORK,
			  INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   REAL		  ANORM, RCOND

	   REAL		  RWORK( * )

	   COMPLEX	  AB( LDAB, * ), WORK( * )

PURPOSE
       CPBCON estimates the reciprocal of the condition number (in the 1-norm)
       of a complex Hermitian positive definite band matrix using the Cholesky
       factorization A = U**H*U or A = L*L**H computed by CPBTRF.  An estimate
       is  obtained for norm(inv(A)), and the reciprocal of the condition num‐
       ber 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) COMPLEX array, dimension (LDAB,N)
	       The  triangular factor U or L from the Cholesky factorization A
	       = U**H*U or A = L*L**H 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 Hermitian band matrix A.

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

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (N)

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

 LAPACK routine (version 3.2)	 November 2008			     CPBCON(1)
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