void SolutionSlau QRalgo std vector std vector double std vector std v

void SolutionSlau::QRalgo(std::vector <std::vector <double>> &Q,
    std::vector <std::vector <double>> &R, std::vector <double> &x)
{
    int size = A.size();
    R = A;
    std::vector<std::vector<double> > E(size, std::vector<double>(size, 0));
    for (int i = 0; i < size; ++i)
        E[i][i] = 1;
    for (int k = 0; k < size - 1; ++k)
    {
        double sum = 0;
        for (int i = k; i < size; ++i)
        {
            sum += R[i][k] * R[i][k];
        }
        double betta = sign(-R[k][k])*sqrt(sum);
        double mu = 1 / sqrt(2 * betta*(betta - R[k][k]));
        std::vector<double> w;
        for (int i = 0; i < size; ++i)
        {
            if (i < k)
                w.push_back(0);
            else if (i == k)
                w.push_back(R[i][i] - betta);
            else
                w.push_back(R[i][k]);
        }
        std::vector<std::vector<double> > H(size, std::vector<double>(size, 0));

        for (int i = 0; i < size; ++i)
        {
            for (int j = 0; j < size; ++j)
            {
                H[i][j] = E[i][j] - w[i] * w[j] * 2 * mu*mu;
            }
        }
        std::vector<std::vector<double> > res(size, std::vector<double>(size, 0));
        multiply(H, R, res);
        R = res;
    }
    std::vector<std::vector<double> > temp(size, std::vector<double>(size, 0));
    obrMatrix(A, E);
    multiply(R, E, Q);
    //transposition(Q);
    std::vector<double> y(size);
    for (int i = 0; i < size; ++i)
    {
        y[i] = 0;
        for (int j = 0; j < size; ++j)
            y[i] += Q[i][j] * b[j];
    }

    for (int i = size - 1; i >= 0; --i)
    {
        for (int j = i + 1; j < size; ++j)
        {
            y[i] -= R[i][j] * x[j];
        }
        x[i] = y[i] / R[i][i];
    }
}