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)

DPBEQU(l)								 )								 DPBEQU(l)

NAME

       DPBEQU  - compute row and column scalings intended to equilibrate a symmetric positive definite band matrix A and reduce its condition num-
       ber (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE DPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, KD, LDAB, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION AB( LDAB, * ), S( * )

PURPOSE

       DPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band matrix A 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 pos-
       sible condition number over all possible diagonal scalings.

ARGUMENTS

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

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

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
	       The  upper  or  lower triangle of the symmetric band matrix A, stored in the first KD+1 rows of the array.  The j-th column of A is
	       stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO =  'L',
	       AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

       LDAB	(input) INTEGER
		The leading dimension of the array A.  LDAB >= KD+1.

       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 							 DPBEQU(l)