ZGBTRF(3f)

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

SYNOPSIS

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

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

INTEGER
    IPIV( * )

COMPLEX*16
    AB( LDAB, * )

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.

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*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    (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.