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 in packed storage and reduce its condition number (with respect  to  the
       two-norm)

SYNOPSIS

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

           CHARACTER      UPLO

           INTEGER        INFO, N

           REAL           AMAX, SCOND

           REAL           AP( * ), S( * )

PURPOSE

       SPPEQU  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

        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) REAL 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) 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 illegal value
                > 0:  if INFO = i, the i-th diagonal element is nonpositive.

 LAPACK routine (version 3.2)               April 2011                            SPPEQU(3lapack)