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sgeequ

 NAME
      SGEEQU - compute row and column scalings intended to equili-
      brate an M-by-N matrix A and reduce its condition number

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

          INTEGER        INFO, LDA, M, N

          REAL           AMAX, COLCND, ROWCND

          REAL           A( LDA, * ), C( * ), R( * )

 PURPOSE
      SGEEQU computes row and column scalings intended to equili-
      brate an M-by-N matrix A and reduce its condition number.  R
      returns the row scale factors and C the column scale fac-
      tors, chosen to try to make the largest entry in each row
      and column of the matrix B with elements
      B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

      R(i) and C(j) are restricted to be 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.

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

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

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

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

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

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

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

      AMAX    (output) REAL
              Absolute value of largest matrix element.  If AMAX
              is very close to overflow or very close to under-
              flow, 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,  and i is
              <= M:  the i-th row of A is exactly zero
              >  M:  the (i-M)-th column of A is exactly zero