psgbtrf(3) [debian man page]

PSGBTRF(l)						   LAPACK routine (version 1.5) 						PSGBTRF(l)

NAME

       PSGBTRF - compute a LU factorization of an N-by-N real banded distributed matrix with bandwidth BWL, BWU

SYNOPSIS

       SUBROUTINE PSGBTRF( N, BWL, BWU, A, JA, DESCA, IPIV, AF, LAF, WORK, LWORK, INFO )

	   INTEGER	   BWL, BWU, INFO, JA, LAF, LWORK, N

	   INTEGER	   DESCA( * ), IPIV( * )

	   REAL 	   A( * ), AF( * ), WORK( * )

PURPOSE

       PSGBTRF	computes a LU factorization of an N-by-N real banded distributed matrix with bandwidth BWL, BWU: A(1:N, JA:JA+N-1).  Reordering is
       used to increase parallelism in the factorization.  This reordering results in factors that are DIFFERENT from those produced by equivalent
       sequential codes. These factors cannot be used directly by users; however, they can be used in
       subsequent calls to PSGBTRS to solve linear systems.

       The factorization has the form

	       P A(1:N, JA:JA+N-1) Q = L U

       where U is a banded upper triangular matrix and L is banded lower triangular, and P and Q are permutation matrices.
       The matrix Q represents reordering of columns
       for parallelism's sake, while P represents
       reordering of rows for numerical stability using
       classic partial pivoting.

LAPACK version 1.5						    12 May 1997 							PSGBTRF(l)

SGETF2(l)								 )								 SGETF2(l)

NAME

       SGETF2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges

SYNOPSIS

       SUBROUTINE SGETF2( M, N, A, LDA, IPIV, INFO )

	   INTEGER	  INFO, LDA, M, N

	   INTEGER	  IPIV( * )

	   REAL 	  A( LDA, * )

PURPOSE

       SGETF2  computes  an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges.  The factorization has the
       form
	  A = P * L * U
       where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper	triangular
       (upper trapezoidal if m < n).

       This is the right-looking Level 2 BLAS version of the algorithm.

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.

       A       (input/output) REAL array, dimension (LDA,N)
	       On  entry, the m by n matrix to be factored.  On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal ele-
	       ments of L are not stored.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,M).

       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 = -k, the k-th argument had an illegal value
	       > 0: if INFO = k, U(k,k) 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.

LAPACK version 3.0						   15 June 2000 							 SGETF2(l)