DragonFly On-Line Manual Pages

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NAME
       CDBTF2 - compute an LU factorization of a real m-by-n band matrix A
       without using partial pivoting with row interchanges

SYNOPSIS
       SUBROUTINE CDBTF2( M, N, KL, KU, AB, LDAB, INFO )
           INTEGER INFO, KL, KU, LDAB, M, N
           COMPLEX AB( LDAB, * )

PURPOSE
       Cdbtrf computes an LU factorization of a real m-by-n band matrix A
       without using partial pivoting with row interchanges.  This is the
       unblocked version of the algorithm, calling Level 2 BLAS.

ARGUMENTS
       M       (input) INTEGER
               The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
               The number of columns of the matrix A.  N >= 0.

       KL      (input) INTEGER
               The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
               The number of superdiagonals within the band of A.  KU >= 0.

       AB      (input/output) COMPLEX            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    (input) INTEGER
               The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.

       INFO    (output) 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.

FURTHER DETAILS
       The band storage scheme is illustrated by the following example, when M
       = N = 6, KL = 2, KU = 1:

       On entry:                       On exit:

           *   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.

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