CGBEQU - compute row and column scalings intended to equi­
       librate an M-by-N band matrix A and reduce  its  condition
       number


SYNOPSIS

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

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

           REAL           AMAX, COLCND, ROWCND

           REAL           C( * ), R( * )

           COMPLEX        AB( LDAB, * )


PURPOSE

       CGBEQU computes row and column scalings intended to  equi­
       librate  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 = small­
       est safe number and BIGNUM = largest safe number.  Use  of
       these scaling factors is not guaranteed to reduce the con­
       dition 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) COMPLEX 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 >=


       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
               smallest 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 ille­
               gal 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


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