linear_solver.hh

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#ifndef __SIM_LINEAR_SOLVER_HH__
#define __SIM_LINEAR_SOLVER_HH__

#include <cassert>
#include <sstream>
#include <string>
#include <vector>

class LinearEquation {
  public:
    LinearEquation(unsigned unknowns) {
        eq = std::vector <double> (unknowns + 1, 0);
    }

    // Add two equations
    LinearEquation operator+ (const LinearEquation& rhs) {
        assert(this->eq.size() == rhs.eq.size());

        LinearEquation res(this->eq.size() - 1);

        for (unsigned i = 0; i < res.eq.size(); i++)
            res.eq[i] = this->eq[i] + rhs.eq[i];

        return res;
    }

    // Multiply the equation by a constant
    LinearEquation & operator*= (const double cnt) {
        for (auto & c: eq)
            c *= cnt;

        return *this;
    }

    // Access a certain equation coefficient
    double & operator[] (unsigned unkw) {
        assert(unkw < eq.size());
        return eq[unkw];
    }

    // Get a string representation
    std::string toStr() const {
        std::ostringstream oss;
        for (unsigned i = 0; i < eq.size(); i++) {
            if (i)
                oss << " + ";
            oss << eq[i];
            if (i != eq.size() - 1)
                oss << "*x" << i;
        }
        oss << " = 0";
        return oss.str();
    }

    // Index for the constant term
    unsigned cnt() const { return eq.size() - 1; }

  private:

    std::vector <double> eq;
};

class LinearSystem {
  public:
    LinearSystem(unsigned unknowns) {
        for (unsigned i = 0; i < unknowns; i++)
            matrix.push_back(LinearEquation(unknowns));
    }

    LinearEquation & operator[] (unsigned eq) {
        assert(eq < matrix.size());
        return matrix[eq];
    }

    std::string toStr() const {
        std::string r;
        for (auto & eq: matrix)
            r += eq.toStr() + "\n";
        return r;
    }

    std::vector <double> solve() const;

  private:
    std::vector < LinearEquation > matrix;
};

#endif