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# Manual Reference Pages  -  ZDBTRF (l)

### NAME

ZDBTRF - compute an LU factorization of a real m-by-n band matrix A without using partial pivoting or row interchanges

Synopsis
Purpose
Arguments
Further Details

### SYNOPSIS

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

### PURPOSE

Zdbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting or 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) REAL 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. 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:

* 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.

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