SGEEQUB(3)     LAPACK routine of NEC Numeric Library Collection     SGEEQUB(3)



NAME
       SGEEQUB

SYNOPSIS
       SUBROUTINE SGEEQUB (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)



PURPOSE
            SGEEQUB computes row and column scalings intended to equilibrate an
            M-by-N matrix A and reduce its condition number.  R returns the row
            scale factors and C the column scale factors, chosen to try to make
            the largest element in each row and column of the matrix B with
            elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
            the radix.

            R(i) and C(j) are restricted to be a power of the radix between
            SMLNUM = smallest safe number and BIGNUM = largest safe number.  Use
            of these scaling factors is not guaranteed to reduce the condition
            number of A but works well in practice.

            This routine differs from SGEEQU by restricting the scaling factors
            to a power of the radix.  Baring over- and underflow, scaling by
            these factors introduces no additional rounding errors.  However, the
            scaled entries' magnitured are no longer approximately 1 but lie
            between sqrt(radix) and 1/sqrt(radix).




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A.  N >= 0.

           A         (input)
                     A is REAL array, dimension (LDA,N)
                     The M-by-N matrix whose equilibration factors are
                     to be computed.

           LDA       (input)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           R         (output)
                     R is REAL array, dimension (M)
                     If INFO = 0 or INFO > M, R contains the row scale factors
                     for A.

           C         (output)
                     C is REAL array, dimension (N)
                     If INFO = 0,  C contains the column scale factors for A.

           ROWCND    (output)
                     ROWCND is REAL
                     If INFO = 0 or INFO > M, ROWCND contains the ratio of the
                     smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
                     AMAX is neither too large nor too small, it is not worth
                     scaling by R.

           COLCND    (output)
                     COLCND is REAL
                     If INFO = 0, COLCND contains the ratio of the smallest
                     C(i) to the largest C(i).  If COLCND >= 0.1, it is not
                     worth scaling by C.

           AMAX      (output)
                     AMAX is 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)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value
                     > 0:  if INFO = i,  and i is
                           <= M:  the i-th row of A is exactly zero
                           >  M:  the (i-M)-th column of A is exactly zero



LAPACK routine                  31 October 2017                     SGEEQUB(3)