zdbtrf(3) [debian man page]

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.

SGBTRF(l)								 )								 SGBTRF(l)

NAME

       SGBTRF - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges

SYNOPSIS

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

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

	   INTEGER	  IPIV( * )

	   REAL 	  AB( LDAB, * )

PURPOSE

       SGBTRF  computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.  This is the blocked ver-
       sion 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.

       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.

LAPACK version 3.0						   15 June 2000 							 SGBTRF(l)