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RedHat 9 (Linux i386) - man page for cgbtrf (redhat section l)

CGBTRF(l)					)					CGBTRF(l)

NAME
       CGBTRF  - compute an LU factorization of a complex m-by-n band matrix A using partial piv-
       oting with row interchanges

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

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

	   INTEGER	  IPIV( * )

	   COMPLEX	  AB( LDAB, * )

PURPOSE
       CGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivot-
       ing  with 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) COMPLEX 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 				CGBTRF(l)


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