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DPPEQU(3F)							    DPPEQU(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

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

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 DOUBLE		PRECISION AMAX,	SCOND

	 DOUBLE		PRECISION AP( *	), S( *	)

PURPOSE    [Toc]    [Back]

     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.

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 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



									Page 1






DPPEQU(3F)							    DPPEQU(3F)



	     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.
DPPEQU(3F)							    DPPEQU(3F)


NAME    [Toc]    [Back]

     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    [Toc]    [Back]

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

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 DOUBLE		PRECISION AMAX,	SCOND

	 DOUBLE		PRECISION AP( *	), S( *	)

PURPOSE    [Toc]    [Back]

     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.

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 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



									Page 1






DPPEQU(3F)							    DPPEQU(3F)



	     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.


									PPPPaaaaggggeeee 2222
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