Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  an LU factorization of a complex m-by-n band matrix A using partial
       pivoting with row interchanges

SYNOPSIS

       SUBROUTINE CGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )

           INTEGER        INFO, KL, KU, LDAB, M, N

           INTEGER        IPIV( * )

           COMPLEX        AB( LDAB, * )

PURPOSE

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

        IPIV    (output) 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    (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:
            *    *    *    +    +    +       *    *    *   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.

 LAPACK routine (version 3.2)               April 2011                            CGBTRF(3lapack)