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

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 )
INTEGER INFO, KL, KU, LDAB, M, N
INTEGER IPIV( * )
COMPLEX*16 AB( LDAB, * )

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) 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.