NAME

zgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges

SYNOPSIS

  SUBROUTINE ZGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO)
  DOUBLE COMPLEX AB(LDAB,*)
  INTEGER M, N, KL, KU, LDAB, INFO
  INTEGER IPIV(*)

  SUBROUTINE ZGBTF2_64( M, N, KL, KU, AB, LDAB, IPIV, INFO)
  DOUBLE COMPLEX AB(LDAB,*)
  INTEGER*8 M, N, KL, KU, LDAB, INFO
  INTEGER*8 IPIV(*)

F95 INTERFACE

  SUBROUTINE GBTF2( [M], [N], KL, KU, AB, [LDAB], IPIV, [INFO])
  COMPLEX(8), DIMENSION(:,:) :: AB
  INTEGER :: M, N, KL, KU, LDAB, INFO
  INTEGER, DIMENSION(:) :: IPIV

  SUBROUTINE GBTF2_64( [M], [N], KL, KU, AB, [LDAB], IPIV, [INFO])
  COMPLEX(8), DIMENSION(:,:) :: AB
  INTEGER(8) :: M, N, KL, KU, LDAB, INFO
  INTEGER(8), DIMENSION(:) :: IPIV

C INTERFACE

#include <sunperf.h>

void zgbtf2(int m, int n, int kl, int ku, doublecomplex *ab, int ldab, int *ipiv, int *info);

void zgbtf2_64(long m, long n, long kl, long ku, doublecomplex *ab, long ldab, long *ipiv, long *info);

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.

ARGUMENTS

M (input)
The number of rows of the matrix A. M > = 0.
N (input)
The number of columns of the matrix A. N > = 0.
KL (input)
The number of subdiagonals within the band of A. KL > = 0.
KU (input)
The number of superdiagonals within the band of A. KU > = 0.
AB (input/output)
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)
The leading dimension of the array AB. LDAB > = 2*KL+KU+1.
IPIV (output)
The pivot indices; for 1 < = i < = min(M,N), row i of the matrix was interchanged with row IPIV(i).

INFO (output)

 = 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.