SRC/zgbtrf.f(3)            Library Functions Manual            SRC/zgbtrf.f(3)

NAME
       SRC/zgbtrf.f

SYNOPSIS
   Functions/Subroutines
       subroutine zgbtrf (m, n, kl, ku, ab, ldab, ipiv, info)
           ZGBTRF

Function/Subroutine Documentation
   subroutine zgbtrf (integer m, integer n, integer kl, integer ku,
       complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(
       * ) ipiv, integer info)
       ZGBTRF

       Purpose:


           !>
           !> ZGBTRF 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.
           !>

       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.

       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 143 of file zgbtrf.f.

Author
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LAPACK                          Version 3.12.0                 SRC/zgbtrf.f(3)