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## zgbequ()

subroutine zgbequ | ( | integer | m,
|  | integer | n,
|  | integer | kl,
|  | integer | ku,
|  | complex*16, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | double precision, dimension( * ) | r,
|  | double precision, dimension( * ) | c,
|  | double precision | rowcnd,
|  | double precision | colcnd,
|  | double precision | amax,
|  | integer | info )

ZGBEQU

Download ZGBEQU + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZGBEQU 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.
      !>

Parameters

  [in]

  M

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

  [in]

  N

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

  [in]

  KL

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

  [in]

  KU

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

  [in]

  AB

      !>          AB is COMPLEX*16 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).
      !>

  [in]

  LDAB

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

  [out]

  R

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

  [out]

  C

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

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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.
      !>

  [out]

  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
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.