Пример #1
0
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];
	}

}
Пример #2
0
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;
}