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## cla_gbrpvgrw()

real function cla_gbrpvgrw | ( | integer | n,
|  | integer | kl,
|  | integer | ku,
|  | integer | ncols,
|  | complex, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | complex, dimension( ldafb, * ) | afb,
|  | integer | ldafb )

CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

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

Purpose:

      !>
      !> CLA_GBRPVGRW computes the reciprocal pivot growth factor
      !> norm(A)/norm(U). The  norm is used. If this is
      !> much less than 1, the stability of the LU factorization of the
      !> (equilibrated) matrix A could be poor. This also means that the
      !> solution X, estimated condition numbers, and error bounds could be
      !> unreliable.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>     The number of linear equations, i.e., the order 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]

  NCOLS

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

  [in]

  AB

      !>          AB is COMPLEX 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)
      !>

  [in]

  LDAB

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

  [in]

  AFB

      !>          AFB is COMPLEX array, dimension (LDAFB,N)
      !>     Details of the LU factorization of the band matrix A, as
      !>     computed by CGBTRF.  U is stored as an upper triangular
      !>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
      !>     and the multipliers used during the factorization are stored
      !>     in rows KL+KU+2 to 2*KL+KU+1.
      !>

  [in]

  LDAFB

      !>          LDAFB is INTEGER
      !>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
      !>

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