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/*
* examples/blassolve.C
*
* Copyright (C) J-G Dumas
* ========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========
*/
#include <iostream>
#include "linbox/matrix/dense-matrix.h"
#include "linbox/solutions/solve.h"
#include "linbox/util/matrix-stream.h"
#include "linbox/solutions/methods.h"
using namespace LinBox;
typedef Givaro::ZRing<Givaro::Integer> Ints;
typedef DenseVector<Ints> ZVector;
int main (int argc, char **argv) {
// Usage
if (argc < 2 || argc > 4) {
std::cerr << "Usage: solve <matrix-file-in-supported-format> [<dense-vector-file>]" << std::endl;
return 0;
}
// File
std::ifstream input (argv[1]);
if (!input) { std::cerr << "Error opening matrix file " << argv[1] << std::endl; return -1; }
std::ifstream invect;
bool createB = false;
if (argc == 2) {
createB = true;
}
if (argc == 3) {
invect.open (argv[2], std::ifstream::in);
if (!invect) {
createB = true;
} else {
createB = false;
}
}
// Read Integral matrix from File
Ints ZZ;
MatrixStream< Ints > ms( ZZ, input );
DenseMatrix<Ints> A (ms);
Ints::Element d;
std::cout << "A is " << A.rowdim() << " by " << A.coldim() << std::endl;
{
// Print Matrix
// Matrix Market
// std::cout << "A is " << A << std::endl;
// Maple
A.write(std::cout << "Pretty A is ", Tag::FileFormat::Maple) << std::endl;
}
// Vectors
ZVector X(ZZ, A.coldim()),B(ZZ, A.rowdim());
if (createB) {
std::cerr << "Creating a random {-1,1} vector " << std::endl;
srand48( BaseTimer::seed() );
for(ZVector::iterator it=B.begin();
it != B.end(); ++it)
if (drand48() <0.5)
*it = -1;
else
*it = 1;
} else {
for(ZVector::iterator it=B.begin();
it != B.end(); ++it)
invect >> *it;
}
{
// Print RHS
std::cout << "B is [";
for(auto it:B) ZZ.write(std::cout, it) << " ";
std::cout << "]" << std::endl;
}
std::cout << "B is " << B.size() << "x1" << std::endl;
Timer chrono;
// DenseElimination
Method::DenseElimination M;
//M.singular(Specifier::NONSINGULAR);
chrono.start();
solve (X, d, A, B, M);
chrono.stop();
std::cout << "CPU time (seconds): " << chrono.usertime() << std::endl;
{
// Solution size
std::cout<<"Reduced solution: \n";
size_t maxbits=0;
for (size_t i=0;i<A.coldim();++i){
maxbits=(maxbits > X[i].bitsize() ? maxbits: X[i].bitsize());
}
std::cout<<" numerators of size "<<maxbits<<" bits" << std::endl
<<" denominators hold over "<<d.bitsize()<<" bits\n";
}
{
// Check Solution
if (ZZ.isZero(d))
std::cout << "**** ERROR ****\n**** Zero denominator" << std::endl;
else {
VectorDomain<Ints> VD(ZZ);
MatrixDomain<Ints> MD(ZZ);
ZVector LHS(ZZ, A.rowdim()), RHS(ZZ, B);
// check that Ax = d.b
MD.vectorMul(LHS, A, X);
VD.mulin(RHS, d);
if (VD.areEqual(LHS, RHS))
std::cout << "Ax=b : Yes" << std::endl;
else
std::cout << "Ax=b : No" << std::endl;
}
}
{
// Print Solution
std::cout << "(DenseElimination) Solution is [";
for(auto it:X) ZZ.write(std::cout, it) << " ";
std::cout << "] / ";
ZZ.write(std::cout, d)<< std::endl;
}
return 0;
}
// Local Variables:
// mode: C++
// tab-width: 4
// indent-tabs-mode: nil
// c-basic-offset: 4
// End:
// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
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