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DPPCON(3F)							    DPPCON(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DPPCON(	UPLO, N, AP, ANORM, RCOND, WORK, IWORK,	INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 DOUBLE		PRECISION ANORM, RCOND

	 INTEGER	IWORK( * )

	 DOUBLE		PRECISION AP( *	), WORK( * )

PURPOSE    [Toc]    [Back]

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

     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    [Toc]    [Back]

     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

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

     AP	     (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	     The triangular factor U or	L from the Cholesky factorization A =
	     U**T*U or A = L*L**T, packed columnwise in	a linear array.	 The
	     j-th column of U or L is stored in	the array AP as	follows:  if
	     UPLO = 'U', AP(i +	(j-1)*j/2) = U(i,j) for	1<=i<=j; if UPLO =
	     'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

     ANORM   (input) DOUBLE PRECISION
	     The 1-norm	(or infinity-norm) of the symmetric 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.






									Page 1






DPPCON(3F)							    DPPCON(3F)



     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
DPPCON(3F)							    DPPCON(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DPPCON(	UPLO, N, AP, ANORM, RCOND, WORK, IWORK,	INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 DOUBLE		PRECISION ANORM, RCOND

	 INTEGER	IWORK( * )

	 DOUBLE		PRECISION AP( *	), WORK( * )

PURPOSE    [Toc]    [Back]

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

     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    [Toc]    [Back]

     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

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

     AP	     (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	     The triangular factor U or	L from the Cholesky factorization A =
	     U**T*U or A = L*L**T, packed columnwise in	a linear array.	 The
	     j-th column of U or L is stored in	the array AP as	follows:  if
	     UPLO = 'U', AP(i +	(j-1)*j/2) = U(i,j) for	1<=i<=j; if UPLO =
	     'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.

     ANORM   (input) DOUBLE PRECISION
	     The 1-norm	(or infinity-norm) of the symmetric 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.






									Page 1






DPPCON(3F)							    DPPCON(3F)



     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


									PPPPaaaaggggeeee 2222
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