CGBEQU computes row and column scalings intended to equilibrate 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.

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 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

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KL+KU+1.

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011