/* Copyright (C) 2003 LinBox
 * Written by Zhendong Wan
 *
 * modified by Pascal Giorgi 1/07/04
 * put the Field as template parameter
 * and add Field F as a parameter
 *
 * ========LICENCE========
 * This file is part of the library LinBox.
 *
  * LinBox is free software: you can redistribute it and/or modify
 * it under the terms of the  GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 * ========LICENCE========
 */


#ifndef __LINBOX_matrix_inverse_H
#define __LINBOX_matrix_inverse_H

#include "linbox/util/debug.h"
#include "linbox/util/error.h"
#include <vector>
#include <algorithm>

namespace LinBox
{
	class MatrixInverse {

	public:

		/** \brief compute the inverse of a dense matrix, by Gaussian elimination.
		 *  The matrix should support ColIterator and RowIterator.
		 *  It returns 0, if an inverse is found, and
		 *  returns 1, otherwise.
		 */
		template<class Field, class AnyDenseMatrix>
		static  long matrixInverseIn(const Field& F, AnyDenseMatrix& A)
		{

			// check if A is a square matrix
			linbox_check(A.rowdim() == A. coldim());

			// PG 1/07/04
			//typedef typename AnyDenseMatrix::Field Field;

			// step1 PLU Inplcae, actually, LPA = U.
			// XXX Permutation
			std::vector<std::pair<int,int> > P;
			P.reserve (A.rowdim());

			typename AnyDenseMatrix::RowIterator cur_r, tmp_r;
			typename AnyDenseMatrix::ColIterator cur_c, tmp_c;
			typename AnyDenseMatrix::Row::iterator cur_rp, tmp_rp;
			typename AnyDenseMatrix::Col::iterator cur_cp, tmp_cp;

			std::vector<typename Field::Element> tmp_v (A.rowdim());

			typename Field::Element tmp_e;

			// PG 1/07/04
			//const Field F = A. field();

			int offset = 0;

			cur_r = A. rowBegin();
			cur_c = A. colBegin();
			for( ; cur_r != A. rowEnd(); ++ cur_r, ++ cur_c, ++ offset) {
				//for(cur_r = A. rowBegin(), cur_c = A. colBegin(); cur_r != A. rowEnd(); ++ cur_r, ++ cur_c, ++ offset)

				//try to find the pivot.
				tmp_r = cur_r;

				tmp_cp = cur_c -> begin() + offset;

				while ((tmp_cp != cur_c -> end()) && F.isZero(*tmp_cp)) {
					++ tmp_cp;
					++ tmp_r;
				}

				if (tmp_cp == cur_c -> end()) return 1;

				//if swicth two row if nessary. Each row in dense matrix is stored in contiguous space
				if (tmp_r != cur_r) {
					P.push_back(std::pair<int,int>(offset, (int)(tmp_cp - cur_c -> begin()) ) );

					std::copy (tmp_r -> begin(), tmp_r -> end(), tmp_v.begin());

					std::copy (cur_r -> begin(), cur_r -> end(), tmp_r -> begin());

					std::copy (tmp_v.begin(), tmp_v.end(), cur_r -> begin());
				}

				// continue gauss elimination

				for(tmp_r = cur_r + 1; tmp_r != A.rowEnd(); ++ tmp_r) {

					//see if need to update the row
					if (!F.isZero(*(tmp_r -> begin() + offset ))) {

						F.div (tmp_e, *(tmp_r -> begin() + offset), *(cur_r -> begin() + offset));

						F.negin(tmp_e);

						for ( cur_rp = cur_r ->begin(),tmp_rp =  tmp_r -> begin();
						      tmp_rp != tmp_r -> end(); ++ tmp_rp, ++ cur_rp )

							F.axpyin ( *tmp_rp, *cur_rp, tmp_e);

						F.assign(*(tmp_r -> begin() + offset), tmp_e);
					}
				}

			}


			//second compute inverse of A.
			AnyDenseMatrix tmp(A);


			//2a compute inverse of PA, by solving upper-triangeular system, PA = U^{-1} L.

			offset = 0;
			for(cur_c = A.colBegin();cur_c != A. colEnd(); ++ cur_c, ++ offset) {

				for (cur_cp = cur_c -> begin();
				     cur_cp != cur_c -> begin() + offset; ++ cur_cp)
					F.assign (*cur_cp, F.zero);

				F.assign(*cur_cp, F.mOne); ++ cur_cp;

				for (; cur_cp != cur_c -> end(); ++ cur_cp)
					F.negin(*cur_cp);

				//matrix is indexed by 0, instead of 1.

				for (cur_cp = cur_c -> begin() + (ptrdiff_t)(A.rowdim() - 1),
				     tmp_r = tmp.rowBegin() + ( (int)A.rowdim() - 1);
				     cur_cp != cur_c -> begin() - 1;
				     -- cur_cp, -- tmp_r) {

					F.assign (tmp_e, *cur_cp);

					for(tmp_cp = cur_c -> begin() + (ptrdiff_t) (A.rowdim() - 1), tmp_rp = tmp_r -> begin() + (ptrdiff_t) ( A.rowdim() -1);
					    tmp_cp != cur_cp; -- tmp_cp, -- tmp_rp)
						F.axpyin(tmp_e, *tmp_cp, *tmp_rp);

					F. div(*cur_cp, tmp_e, *tmp_rp);

					F.negin(*cur_cp);

				}

			}



			// 2b, compute inverse of A, A^{-1} = (PA)^{-1} P
			std::vector<std::pair<int, int> >::reverse_iterator v_p;

			for(v_p = P.rbegin(); v_p != P.rend(); ++ v_p) {

				cur_c = A.colBegin() + v_p -> first;

				tmp_c = A.colBegin() + v_p -> second;

				std::copy (cur_c -> begin(), cur_c -> end(), tmp_v.begin());

				std::copy (tmp_c -> begin(), tmp_c -> end(), cur_c -> begin());

				std::copy (tmp_v.begin(), tmp_v.end(), tmp_c -> begin());

			}


			return 0;
		}
	};

	template<>
	inline long MatrixInverse::matrixInverseIn(const MultiModDouble& F, BlasMatrix<MultiModDouble>& A) {
		throw LinboxError("LinBox ERROR: use of MultiModDouble with too large moduli is not allowed at this time\n");
		return 0;
	}

} // namespace LinBox


#endif //__LINBOX_matrix_inverse_H

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