dgbtrf man page on IRIX

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DGBTRF(3F)							    DGBTRF(3F)

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

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

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

	 INTEGER	IPIV( * )

	 DOUBLE		PRECISION AB( LDAB, * )

PURPOSE
     DGBTRF computes an LU factorization of a real m-by-n band matrix A using
     partial pivoting 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) DOUBLE PRECISION 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).

									Page 1

DGBTRF(3F)							    DGBTRF(3F)

     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.

									Page 2

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