CDBTRF ‐ compute an LU factorization of a real m‐by‐n band matrix
A without using partial pivoting or row interchanges SUBROUTINE
CDBTRF( M, N, KL, KU, AB, LDAB, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
COMPLEX AB( LDAB, * ) Cdbtrf 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.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 num‐
ber of superdiagonals within the band of A. KU >= 0. AB
(input/output) REAL array, dimension (LDAB,N) On entry, the ma‐
trix 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 toKL+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 de‐
tails. LDAB (input) INTEGER The leading dimension of the ar‐
ray AB. LDAB >= 2*KL+KU+1. INFO (output) INTEGER = 0: suc‐
cessful 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 divi‐
sion by zero will occur if it is used to solve a system of equa‐
tions. 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.
