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## dgbtrf()

subroutine dgbtrf | ( | integer | m,
|  | integer | n,
|  | integer | kl,
|  | integer | ku,
|  | double precision, dimension( ldab, * ) | ab,
|  | integer | ldab,
|  | integer, dimension( * ) | ipiv,
|  | integer | info )

DGBTRF

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

Purpose:

      !>
      !> DGBTRF computes an LU factorization of a real m-by-n band matrix A
      !> using partial pivoting with row interchanges.
      !>
      !> This is the blocked version of the algorithm, calling Level 3 BLAS.
      !>

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,out]

  AB

      !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
      !>          On entry, the matrix A in band storage, in rows KL+1 to
      !>          2*KL+KU+1; rows 1 to KL of the array need not be set.
      !>          The j-th column of A is stored in the j-th column of the
      !>          array AB as follows:
      !>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
      !>
      !>          On exit, details of the factorization: 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.
      !>          See below for further details.
      !>

  [in]

  LDAB

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

  [out]

  IPIV

      !>          IPIV is INTEGER array, dimension (min(M,N))
      !>          The pivot indices; for 1 <= i <= min(M,N), row i of the
      !>          matrix was interchanged with row IPIV(i).
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0: successful exit
      !>          < 0: if INFO = -i, the i-th argument had an illegal value
      !>          > 0: if INFO = +i, U(i,i) is exactly zero. The factorization
      !>               has been completed, but the factor U is exactly
      !>               singular, and division by zero will occur if it is used
      !>               to solve a system of equations.
      !>

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

Further Details:

      !>
      !>  The band storage scheme is illustrated by the following example, when
      !>  M = N = 6, KL = 2, KU = 1:
      !>
      !>  On entry:                       On exit:
      !>
      !>      *    *    *    +    +    +       *    *    *   u14  u25  u36
      !>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
      !>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
      !>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
      !>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
      !>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
      !>
      !>  Array elements marked * are not used by the routine; elements marked
      !>  + need not be set on entry, but are required by the routine to store
      !>  elements of U because of fill-in resulting from the row interchanges.
      !>