dppcon(l) [redhat man page]

DPPCON(l)								 )								 DPPCON(l)

NAME

       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

       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

       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

       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.

       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 							 DPPCON(l)

DSPCON(l)								 )								 DSPCON(l)

NAME

       DSPCON  -  estimate  the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A =
       U*D*U**T or A = L*D*L**T computed by DSPTRF

SYNOPSIS

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION ANORM, RCOND

	   INTEGER	  IPIV( * ), IWORK( * )

	   DOUBLE	  PRECISION AP( * ), WORK( * )

PURPOSE

       DSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using  the  factorization  A  =
       U*D*U**T  or A = L*D*L**T computed by DSPTRF.  An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is com-
       puted as RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.  =  'U':	Upper  triangular,
	       form is A = U*D*U**T;
	       = 'L':  Lower triangular, form is A = L*D*L**T.

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

       AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	       The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangu-
	       lar matrix.

       IPIV    (input) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D as determined by DSPTRF.

       ANORM   (input) DOUBLE PRECISION
	       The 1-norm of the original 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 (2*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 							 DSPCON(l)