dppequ(l) [redhat man page]

DPPEQU(l)								 )								 DPPEQU(l)

NAME

       DPPEQU  -  compute  row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its
       condition number (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE DPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION AP( * ), S( * )

PURPOSE

       DPPEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed  storage  and  reduce  its
       condition number (with respect to the two-norm). S contains the scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with
       elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the condition number of B within a factor N of the small-
       est possible condition number over all possible diagonal scalings.

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  upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array.  The j-th column of A is stored in the
	       array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i	+  (j-1)*(2n-j)/2)  =  A(i,j)  for
	       j<=i<=n.

       S       (output) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) DOUBLE PRECISION
	       If  INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i).  If SCOND >= 0.1 and AMAX is neither too large nor too
	       small, it is not worth scaling by S.

       AMAX    (output) DOUBLE PRECISION
	       Absolute value of largest matrix element.  If AMAX is very close to overflow or very close  to  underflow,  the	matrix	should	be
	       scaled.

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value
	       > 0:  if INFO = i, the i-th diagonal element is nonpositive.

LAPACK version 3.0						   15 June 2000 							 DPPEQU(l)

dppequ.f(3)							      LAPACK							       dppequ.f(3)

NAME

       dppequ.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
	   DPPEQU

Function/Subroutine Documentation
   subroutine dppequ (characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )S, double precisionSCOND,
       double precisionAMAX, integerINFO)
       DPPEQU

       Purpose:

	    DPPEQU computes row and column scalings intended to equilibrate a
	    symmetric positive definite matrix A in packed storage and reduce
	    its condition number (with respect to the two-norm).  S contains the
	    scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
	    B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
	    This choice of S puts the condition number of B within a factor N of
	    the smallest possible condition number over all possible diagonal
	    scalings.

       Parameters:
	   UPLO

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

	   N

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

	   AP

		     AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
		     The upper or lower triangle of the symmetric matrix A, packed
		     columnwise in a linear array.  The j-th column of A is stored
		     in the array AP as follows:
		     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
		     if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

	   S

		     S is DOUBLE PRECISION array, dimension (N)
		     If INFO = 0, S contains the scale factors for A.

	   SCOND

		     SCOND is DOUBLE PRECISION
		     If INFO = 0, S contains the ratio of the smallest S(i) to
		     the largest S(i).	If SCOND >= 0.1 and AMAX is neither too
		     large nor too small, it is not worth scaling by S.

	   AMAX

		     AMAX is DOUBLE PRECISION
		     Absolute value of largest matrix element.	If AMAX is very
		     close to overflow or very close to underflow, the matrix
		     should be scaled.

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  if INFO = i, the i-th diagonal element is nonpositive.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 117 of file dppequ.f.

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

Version 3.4.2							  Tue Sep 25 2012						       dppequ.f(3)