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/* Copyright (c) 1997-2015
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program 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 General Public License for more details.
--------------------------------------------------------------------------------
*/
#ifndef POLYMAKE_HERMITE_NORMAL_FORM_H
#define POLYMAKE_HERMITE_NORMAL_FORM_H
#include <iostream>
#include "polymake/client.h"
#include "polymake/pair.h"
#include "polymake/SparseMatrix.h"
#include "polymake/Bitset.h"
#include "polymake/Array.h"
#include "polymake/linalg.h"
#include "polymake/numerical_functions.h"
#include "polymake/list"
#include "polymake/GenericStruct.h"
namespace polymake { namespace common {
template <typename MatrixTop, typename E>
std::pair<Matrix<E>, SparseMatrix<E> > hermite_normal_form(const GenericMatrix<MatrixTop, E>& M, bool reduced = true){
SparseMatrix2x2<E> U;
SparseMatrix<E> R, S;
Matrix<E> N(M);
const int rows = M.rows();
const int cols = M.cols();
R = unit_matrix<E>(cols);
int current_row = 0, current_col = 0;
for(int i = 0; i<rows; i++){
bool nonzero = true;
// cout << N(i,current_col) << endl;
// Find a non-zero entry and move it to here.
if(N(i,current_col) == 0){
nonzero = false;
for(int j = current_col; j<cols; j++){
if(N(i,j) != 0){
nonzero = true;
U.i = current_col;
U.j = j;
U.a_ii = 0;
U.a_ij = 1;
U.a_ji = 1;
U.a_jj = 0;
R.multiply_from_right(U);
N.multiply_from_right(U);
}
}
}
// cout << pm::Matrix<E>(N) << endl;
if(!nonzero){
// cout << "Continueing" << endl;
current_row++;
continue;
}
// GCD part of algorithm.
for(int j = current_col+1; j<cols; j++){
// cout << " " << i << " " << j << endl;
if(N(i,j) != 0){
U.i = current_col;
U.j = j;
ExtGCD<E> egcd = ext_gcd(N(i,current_col), N(i,j));
U.a_ii = egcd.p;
U.a_ji = egcd.q;
U.a_ij = egcd.k2;
U.a_jj = -egcd.k1;
R.multiply_from_right(U);
N.multiply_from_right(U);
// cout << U.i<<": "<<U.a_ii <<" " << U.a_ij<<endl<<U.j <<": " <<U.a_ji<<" " << U.a_jj << endl;
}
// cout << pm::Matrix<E>(N) << endl;
}
if(N(i,current_col)<0){
S = unit_matrix<E>(cols);
S(current_col,current_col) = -1;
R = R*S;
N = N*S;
}
if(reduced){
for(int j=0; j<current_col; j++){
U.i = j;
U.j = current_col;
E factor = N(i,j) % N(i,current_col);
if(factor < 0) factor += N(i,current_col);
factor = (N(i,j) - factor)/N(i,current_col);
U.a_ii = 1;
U.a_ji = -factor;
U.a_ij = 0;
U.a_jj = 1;
R.multiply_from_right(U);
N.multiply_from_right(U);
}
}
current_col++;
if(current_col == cols){
break;
}
// cout << i << " " << current_row << endl;
}
return std::pair<Matrix<E>, SparseMatrix<E> >(N, R);
}
}
}
#endif
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