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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( * )



     #include <sunperf.h>

     void sgbequ(int m, int n, int kl, int ku,  float  *sab,  int
               ldab,  float  *r,  float *sc, float *rowcnd, float
               *colcnd, float *amax, int *info);

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 = 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.

     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
               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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