Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes row and column scalings intended to equilibrate a symmetric positive
       definite matrix A and reduce its condition number (with respect to the two-norm)

SYNOPSIS

       SUBROUTINE DPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )

           IMPLICIT        NONE

           INTEGER         INFO, LDA, N

           DOUBLE          PRECISION AMAX, SCOND

           DOUBLE          PRECISION A( LDA, * ), S( * )

PURPOSE

       DPOEQU computes row and column scalings  intended  to  equilibrate  a  symmetric  positive
       definite  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 possible condition number over all possible diagonal
        scalings.

ARGUMENTS

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

        A       (input) DOUBLE PRECISION array, dimension (LDA,N)
                The N-by-N symmetric positive definite matrix whose scaling
                factors are to be computed.  Only the diagonal elements of A
                are referenced.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,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 routine (version 3.2)            April 2011                           DPOEQUB(3lapack)