dgbequ.f3

!>
!> DGBEQU 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (M)
!>          If INFO = 0, or INFO > M, R contains the row scale factors
!>          for A.
!> 

C

!>          C is DOUBLE PRECISION array, dimension (N)
!>          If INFO = 0, C contains the column scale factors for A.
!> 

ROWCND

!>          ROWCND is DOUBLE PRECISION
!>          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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION
!>          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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