cppequ.f(3) [centos man page]

cppequ.f(3)							      LAPACK							       cppequ.f(3)

NAME

       cppequ.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cppequ (UPLO, N, AP, S, SCOND, AMAX, INFO)
	   CPPEQU

Function/Subroutine Documentation
   subroutine cppequ (characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )S, realSCOND, realAMAX, integerINFO)
       CPPEQU

       Purpose:

	    CPPEQU computes row and column scalings intended to equilibrate a
	    Hermitian 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 COMPLEX array, dimension (N*(N+1)/2)
		     The upper or lower triangle of the Hermitian 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 REAL array, dimension (N)
		     If INFO = 0, S contains the scale factors for A.

	   SCOND

		     SCOND is REAL
		     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 REAL
		     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 118 of file cppequ.f.

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

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

Check Out this Related Man Page

CPPEQU(l)								 )								 CPPEQU(l)

NAME

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

SYNOPSIS

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   REAL 	  AMAX, SCOND

	   REAL 	  S( * )

	   COMPLEX	  AP( * )

PURPOSE

       CPPEQU computes row and column scalings intended to equilibrate a Hermitian 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) COMPLEX array, dimension (N*(N+1)/2)
	       The  upper or lower triangle of the Hermitian 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) REAL array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) REAL
	       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) REAL
	       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 							 CPPEQU(l)

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cppequ.f(3) [centos man page]

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