/* -*- mode: C++; tab-width: 4; indent-tabs-mode: t; c-basic-offset: 4 -*- */
// vim:sts=4:sw=4:ts=4:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/*
 * Copyright (C) 2014 FFLAS-FFACK group
 *
 * Written by Clement Pernet <Clement.Pernet@imag.fr>
 * Brice Boyer (briceboyer) <boyer.brice@gmail.com>
 *
 *
 * ========LICENCE========
 * This file is part of the library FFLAS-FFPACK.
 *
 * FFLAS-FFPACK 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 __FFLASFFPACK_ffpack_invert_INL
#define __FFLASFFPACK_ffpack_invert_INL


namespace FFPACK {
template <class Field>
	typename Field::Element_ptr
	Invert (const Field& F, const size_t M,
		typename Field::Element_ptr A, const size_t lda,
		int& nullity)
	{
        FFLASFFPACK_check(lda >= M);

		Checker_invert<Field> checker(F,M,A,lda);

		if (M == 0) {
			nullity = 0 ;
			return NULL ;
		}
		size_t * P = FFLAS::fflas_new<size_t>(M);
		size_t * Q = FFLAS::fflas_new<size_t>(M);
		size_t R =  ReducedColumnEchelonForm (F, M, M, A, lda, P, Q, true);
		nullity = (int)(M - R);
		applyP (F, FFLAS::FflasLeft, FFLAS::FflasTrans,
			M, 0, (int)R, A, lda, P);
		delete [] P;
		delete [] Q;

		checker.check(A,nullity);
		return A;
	}

	template <class Field>
	typename Field::Element_ptr
	Invert (const Field& F, const size_t M,
		typename Field::ConstElement_ptr A, const size_t lda,
		typename Field::Element_ptr X, const size_t ldx,
		int& nullity)
	{
		FFLASFFPACK_check(lda >= M);
		FFLASFFPACK_check(ldx >= M);
		if (M == 0) {
			nullity = 0 ;
			return NULL ;
		}
		FFLAS::fassign(F,M,M,A,lda,X,ldx);
		Invert (F, M, X, ldx, nullity);
		return X;
	}

	template <class Field>
	typename Field::Element_ptr
	Invert2( const Field& F, const size_t M,
		 typename Field::Element_ptr A, const size_t lda,
		 typename Field::Element_ptr X, const size_t ldx,
		 int& nullity)
	{
		FFLASFFPACK_check(lda >= M);
		FFLASFFPACK_check(ldx >= M);

		if (M == 0) {
			nullity = 0 ;
			return NULL ;
		}

		size_t *P = FFLAS::fflas_new<size_t>(M);
		size_t *rowP = FFLAS::fflas_new<size_t>(M);


		nullity = int(M - LUdivine( F, FFLAS::FflasNonUnit, FFLAS::FflasNoTrans, M, M, A, lda, P, rowP));

		if (nullity > 0){
			FFLAS::fflas_delete( P);
			FFLAS::fflas_delete( rowP);
			return NULL;
		}
		else {
			// Initializing X to 0
#if 0/*  timer remnants */
			t1.clear();
			t1.start();
#endif
			//! @todo this init is not all necessary (done after ftrtri)
			FFLAS::fzero(F,M,M,X,ldx);

			// X = L^-1 in n^3/3
			ftrtri (F, FFLAS::FflasLower, FFLAS::FflasUnit, M, A, lda);
			for (size_t i=0; i<M; ++i){
				for (size_t j=i; j<M; ++j)
					F.assign(*(X +i*ldx+j), F.zero);
				F.assign (*(X+i*(ldx+1)), F.one);
			}
			for (size_t i=1; i<M; ++i)
				FFLAS::fassign (F, i, (A+i*lda), 1, (X+i*ldx), 1);

			ftrsm( F, FFLAS::FflasLeft, FFLAS::FflasUpper, FFLAS::FflasNoTrans, FFLAS::FflasNonUnit,
			       M, M, F.one, A, lda , X, ldx);

			// X = P^-1.X
			applyP( F, FFLAS::FflasLeft, FFLAS::FflasTrans,
				M, 0,(int) M, X, ldx, P );

			FFLAS::fflas_delete( P);
			FFLAS::fflas_delete( rowP);
			return X;
		}
	}

} // FFPACK

#endif // __FFLASFFPACK_ffpack_invert_INL
