linear_solver.cc

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#include "sim/linear_solver.hh"
 
std::vector <double>
LinearSystem::solve() const
{
    // Solve using gauss elimination, not ideal for big matrices
    std::vector < LinearEquation > smatrix = this->matrix;
 
    unsigned order = smatrix.size();
    for (unsigned row = 0; row < order - 1; row++) {
        // Look for a non-zero row, and swap
        for (unsigned i = row; i < order; i++) {
            if (smatrix[i][row] != 0.0f) {
                if (i != row) {
                    LinearEquation tmp = smatrix[i];
                    smatrix[i] = smatrix[row];
                    smatrix[row] = tmp;
                }
                break;
            }
        }
 
        // Divide row by leading number to make it 1.0
        smatrix[row] *= (1.0f / smatrix[row][row]);
 
        // Add it (properly scaled) to the rows below
        for (unsigned i = row + 1; i < order; i++) {
            LinearEquation t = smatrix[row];
            t *= -1.0f * smatrix[i][row];
            smatrix[i] = smatrix[i] + t;
        }
    }
 
    // smatrix is now a triangular matrix with diagonal being 1
    // Just backproagate variable values from order-1 till 0
    std::vector <double> ret(order, 0.0f);
    for (int row = order - 1; row >= 0; row--) {
        // Unknown value
        ret[row] = -smatrix[row][smatrix[row].cnt()] / smatrix[row][row];
        // Propagate variable in the cnt term
        for (int i = row - 1; i >= 0; i--) {
            smatrix[i][smatrix[i].cnt()] += ret[row] * smatrix[i][row];
            smatrix[i][row] = 0.0f;
        }
    }
 
    return ret;
}