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LEARN ABOUT DEBIAN

zdbtrf

ZDBTRF - compute an LU factorization of a real m-by-n band matrix
A without using partial pivoting or row  interchanges  SUBROUTINE
ZDBTRF( M, N, KL, KU, AB, LDAB, INFO )
    INTEGER INFO, KL, KU, LDAB, M, N
    COMPLEX*16	AB( LDAB, * ) 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.

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  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  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.