void i_vti_v(RBlackbox& Res, DenseMatrix<Rationals >& M, DVector& den, Integer& detPrec)
{
detPrec=1;
Rationals Q;
int n = M.coldim();
//DVector denV(n,1);
for (int i=0; i < den.size();++i) den[i]=1;
for (int i=0; i < n; ++i) {
for (int j=0; j <=i ; ++j) {
Integer q_num =0;
Integer q_den =1;
for (int k=0; k < n; ++k) {
Integer deno_ik, nume_ik, deno_jk, nume_jk, deno, nume;
Q.get_den (deno_ik, M.getEntry(k,i));
Q.get_num (nume_ik, M.getEntry(k,i));
Q.get_den (deno_jk, M.getEntry(k,j));
Q.get_num (nume_jk, M.getEntry(k,j));
if (i==k) {
nume_ik = deno_ik-nume_ik;
}
else {
nume_ik = -nume_ik;
}
if (j==k) {
nume_jk = deno_jk-nume_jk;
}
else {
nume_jk = -nume_jk;
}
//cout << nume_ik << nume_jk;
deno = deno_ik*deno_jk;
nume = nume_ik*nume_jk;
//cout << q_num << "/" << q_den << " " ;
//cout << nume << "/" << deno << " " ;
if (deno==q_den) q_num+=nume;
else {
if (nume != 0) {
Integer g = gcd(q_den, deno);
q_num = q_num*deno/g+nume*q_den/g;
q_den = q_den*deno/g;
}
}
//cout << q_num << "/" << q_den << " " ;
}
if (q_num != 0) {
Quotient q(q_num,q_den);
if (i!=j) {
den[i]=lcm(den[i], q_den);
den[j]=lcm(den[j], q_den);
Res.setEntry(i,j,q);
Res.setEntry(j,i,q);
cout << i << " " << j << " " << q_num << "/" << q_den << "\n";
cout << j << " " << i << " " << q_num << "/" << q_den << "\n";
}
else {
den[i]=lcm(den[i], q_den);
Res.setEntry(i,j,q);
cout << i << " " << j << " " << q_num << "/" << q_den << "\n";
}
}
}
}
Integer d = 1;
for (int i=0; i < den.size(); ++i) {
detPrec *=den[i];
d = lcm(d, den[i]);
}
den[den.size()-1]=d;
for (int i=den.size()-2; i >=0; --i) {
den[i]=d*den[i+1];
}
}
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;
// BlasElimination
Method::BlasElimination 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
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 << "(BlasElimination) Solution is [";
for(auto it:X) ZZ.write(std::cout, it) << " ";
std::cout << "] / ";
ZZ.write(std::cout, d)<< std::endl;
}
return 0;
}