cppequ(3)

NAME

CPPEQU - compute row and column scalings intended to equi

librate 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 equi

librate 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.

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 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) 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 ille

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

nonpositive.

LAPACK version 3.0 15 June 2000

CPPEQU(3)