dppequ(3)

NAME

DPPEQU - compute row and column scalings intended to equi

librate 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 equi

librate 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

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 ma

trix 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 ille

gal value
> 0: if INFO = i, the i-th diagonal element is

nonpositive.

LAPACK version 3.0 15 June 2000

DPPEQU(3)