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

NAME

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

SYNOPSIS

       SUBROUTINE SSYEQUB( UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO )

           IMPLICIT        NONE

           INTEGER         INFO, LDA, N

           REAL            AMAX, SCOND

           CHARACTER       UPLO

           REAL            A( LDA, * ), S( * ), WORK( * )

PURPOSE

       SSYEQUB computes row and column scalings intended to equilibrate a symmetric 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

        UPLO    (input) CHARACTER*1
                Specifies whether the details of the factorization are stored
                as an upper or lower triangular matrix.
                = 'U':  Upper triangular, form is A = U*D*U**T;
                = 'L':  Lower triangular, form is A = L*D*L**T.

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

        A       (input) REAL array, dimension (LDA,N)
                The N-by-N symmetric 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) 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.

        WORK    (workspace) REAL array, dimension (3*N)

        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.

FURTHER DETAILS

        Reference: Livne, O.E. and Golub, G.H., "Scaling by Binormalization",
        Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
        DOI 10.1023/B:NUMA.0000016606.32820.69
        Tech report version: http://ruready.utah.edu/archive/papers/bin.pdf

    LAPACK routine (version 3.2.2)          April 2011                           SSYEQUB(3lapack)