zgbtf2.f(3)

NAME
zgbtf2.f -

SYNOPSIS

  Functions/Subroutines
subroutine zgbtf2 (M, N, KL, KU, AB, LDAB, IPIV, INFO)
ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Function/Subroutine Documentation

  subroutine zgbtf2 (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, integerINFO)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

Purpose:

     ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
     A using partial pivoting with row interchanges.
     This is the unblocked version of the algorithm, calling Level 2 BLAS.

Parameters:
    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*16 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.

    LDAB

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

    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).

    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.

Date:
    September 2012

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.

Definition at line 146 of file zgbtf2.f.

Author

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