Dixon System Solving via Lifting using dense LU or sparse LU.
#include <iostream>
#include <omp.h>
#include "linbox/solutions/methods.h"
#include "linbox/solutions/solve.h"
#include "linbox/util/args-parser.h"
#include "linbox/util/error.h"
#include "linbox/util/matrix-stream.h"
#include <givaro/givrandom.h>
typedef Givaro::ZRing<Givaro::Integer> Ints;
typedef DenseVector<Ints> ZVector;
template<typename _Matrix, typename _EliminationMethod>
int test(_Matrix A, std::string vector_file, bool inv, bool pp, bool sparse_elim) {
std::cout << "A is " << A.rowdim() << " by " << A.coldim() << std::endl;
if (pp)
{
A.write(std::cout << "A:=", Tag::FileFormat::Maple) << ';' << std::endl;
}
Ints ZZ;
std::ifstream invect;
ZVector B(ZZ, A.rowdim());
bool createB = vector_file.empty();
if (!createB) {
invect.open (vector_file, std::ifstream::in);
if (!invect) {
createB = true;
} else {
for(ZVector::iterator it=B.begin(); it != B.end(); ++it)
invect >> *it;
}
}
ZVector X(ZZ, A.coldim());
if (createB) {
ZVector U(ZZ, A.coldim());
Givaro::GivRandom bgen( BaseTimer::seed() );
if (inv) {
std::cerr << "Creating a random {-1,1} vector " << std::endl;
for(auto& it:B) it = (bgen.brand()?1:-1);
} else {
std::cerr << "Creating a random consistant {-1,1} vector " << std::endl;
A.apply(B,U);
}
}
if(pp)
{
B.write(std::cout << "B:=", Tag::FileFormat::Maple) << ';' << std::endl;
}
std::cout << "B is " << B.size() << "x1" << std::endl;
Timer chrono;
_EliminationMethod M;
if (inv){
M.singularity = Singularity::NonSingular;
}
Ints::Element d;
Method::Dixon m(M);
typedef Givaro::Modular<double> Field;
std::cout << "Using: " << *fixedprime << " as the fixed p-adic." << std::endl;
chrono.start();
if (!sparse_elim){
if (inv)
{
std::cout << "Solving using Dense Elimination for non singular system" << std::endl;
if (ss != SS_OK) {
std::cerr << "Error during solveNonsingular (possibly singular matrix or p-adic precision too small)" << std::endl;
exit(-1);
}
}
else
{
std::cout << "Solving using Dense Elimination for any system" << std::endl;
if (ss == SS_FAILED){
std::cerr << "Error during solve (all primes used were bad)" << std::endl;
exit(-1);
}
if (ss == SS_INCONSISTENT){
std::cerr << "Error: system appeared inconsistent" << std::endl;
exit(-1);
}
}
} else {
try
{
std::cout << "Solving using Sparse Elimination for any system" << std::endl;
rsolve.
solve(X, d, A, B);
}
{
std::cerr << e << '\n';
exit(-1);
}
}
chrono.stop();
std::cout << "CPU time (seconds): " << chrono.usertime() << std::endl;
{
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";
}
{
VectorDomain<Ints> VD(ZZ);
ZVector LHS(ZZ, A.rowdim()), RHS(ZZ, B);
MD.vectorMul(LHS, A, X);
VD.mulin(RHS, d);
if (VD.areEqual(LHS, RHS))
std::cout << "Ax=d.b : Yes" << std::endl;
else
std::cout << "Ax=d.b : No" << std::endl;
}
{
std::cout << "Solution is [";
for(auto it:X) ZZ.write(std::cout, it) << " ";
std::cout << "] / ";
ZZ.write(std::cout, d)<< std::endl;
}
return 0;
}
int main (int argc, char **argv) {
std::string matrix_file = "";
std::string vector_file = "";
bool inv = false;
bool pp = false;
bool sparse_elim = false;
Argument as[] = {
{ 'm', "-m FILE", "Set the input file for the matrix.", TYPE_STR , &matrix_file },
{ 'v', "-v FILE", "Set the input file for the vector.", TYPE_STR , &vector_file },
{ 'i', "-i" , "whether the matrix is known to be invertible.", TYPE_BOOL , &inv },
{ 'p', "-p" , "whether you want to pretty print the matrix.", TYPE_BOOL , &pp },
{ 's', "-s" , "whether to use sparse elimination.", TYPE_BOOL , &sparse_elim },
END_OF_ARGUMENTS
};
FFLAS::parseArguments(argc,argv,as);
if (matrix_file.empty()) {
std::cerr << "You must specify an input file for the matrix with -m" << std::endl;
exit(-1);
}
std::ifstream input (matrix_file);
if (!input) { std::cerr << "Error opening matrix file " << argv[1] << std::endl; exit(-1); }
Ints ZZ;
if (sparse_elim){
SparseMatrix<Ints> A(ms);
return test<SparseMatrix<Ints>,Method::SparseElimination>
(A, vector_file, inv , pp, sparse_elim);
} else {
return test<DenseMatrix<Ints>,Method::DenseElimination>
(A, vector_file, inv , pp, sparse_elim);
}
}
Dense matrix representation.
Definition: blas-matrix.h:62
Interface for the different specialization of p-adic lifting based solvers.
Definition: rational-solver.h:134
SolverReturnStatus solve(Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, const bool side, int maxPrimes=5) const
Solve a linear system Ax=b over quotient field of a ring giving a random solution if the system is si...
SolverReturnStatus solveNonsingular(Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=5) const
Solve a nonsingular linear system Ax=b over quotient field of a ring, giving the unique solution of t...
Adaptor class to make a single prime number behave like a PrimeIterator.
Definition: random-prime.h:322
base class for execption handling in LinBox
Definition: error.h:37
Class of matrix arithmetic functions.
Definition: matrixdomain/matrix-domain.h:82
MatrixStream.
Definition: matrix-stream.h:200
Prime Iterator.
Definition: random-prime.h:76
Givaro::Integer integer
Integers in LinBox.
Definition: integer.h:55
SolverReturnStatus
define the different return status of the p-adic based solver's computation.
Definition: rational-solver.h:88
Namespace in which all linbox code resides.
Definition: alt-blackbox-block-container.h:4
Generates random positive prime Integers.
Rational solving (Dixon, Wiedemann,...)
A SparseMatrix<_Field, _Storage> ....
FieldTrait.
Definition: field-traits.h:123