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sgbequ

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

 SYNOPSIS
      SUBROUTINE SGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND,
                         COLCND, AMAX, INFO )

          INTEGER        INFO, KL, KU, LDAB, M, N

          REAL           AMAX, COLCND, ROWCND

          REAL           AB( LDAB, * ), C( * ), R( * )

 PURPOSE
      SGBEQU computes row and column scalings intended to equili-
      brate an M by N band 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 absolute value 1.

      R(i) and C(j) *  are restricted to be between SMLNUM = smal-
      lest safe number and BIGNUM = largest safe number.  Use of
      these scaling factors is not guaranteed to reduce the condi-
      tion 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.

      KL      (input) INTEGER
              The number of subdiagonals within the band of A.  KL
              >= 0.

      KU      (input) INTEGER
              The number of superdiagonals within the band of A.
              KU >= 0.

      AB      (input) REAL array, dimension (LDAB,N)
              The band matrix A, stored in rows 1 to KL+KU+1.  The
              j-th column of A is stored in the j-th column of the
              array AB as follows: AB(ku+1+i-j,j) = A(i,j) for
              max(1,j-ku)<=i<=min(m,j+kl).

      LDAB    (input) INTEGER
              The leading dimension of the array AB.  LDAB >=

              KL+KU+1.

      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