CGBEQUB 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 CGEEQU 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).

M

          M is INTEGER


          The number of rows of the matrix A.  M >= 0.

N

          N is INTEGER


          The number of columns of the matrix A.  N >= 0.

KL

          KL is INTEGER


          The number of subdiagonals within the band of A.  KL >= 0.

KU

          KU is INTEGER


          The number of superdiagonals within the band of A.  KU >= 0.

AB

          AB is DOUBLE PRECISION array, dimension (LDAB,N)


          On entry, the matrix A in band storage, 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(N,j+kl)

LDAB

          LDAB is INTEGER


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

R

          R is REAL array, dimension (M)


          If INFO = 0 or INFO > M, R contains the row scale factors


          for A.

C

          C is REAL array, dimension (N)


          If INFO = 0,  C contains the column scale factors for A.

ROWCND

          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

          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

          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

          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

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NAG Ltd.

November 2011