共役勾配法

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int CGSolver(const vector< vector<double> > &A, const vector<double> &b, vector<double> &x, int n, int &max_iter, double &eps)
{
    if(n <= 0) return 0;
 
    vector<double> r(n), p(n), y(n);
    x.assign(n, 0.0);
 
        for(int i = 0; i < n; ++i){
        double ax = 0.0;
        for(int j = 0; j < n; ++j){
            ax += A[i][j]*x[j];
        }
        r[i] = b[i]-ax;
        p[i] = r[i];
    }
 
    double rr0 = dot(r, r, n), rr1;
    double alpha, beta;
 
    double e = 0.0;
    int k;
    for(k = 0; k < max_iter; ++k){
                for(int i = 0; i < n; ++i){
            y[i] = dot(A[i], p, n);
        }
 
                alpha = rr0/dot(p, y, n);
 
                for(int i = 0; i < n; ++i){
            x[i] += alpha*p[i];
            r[i] -= alpha*y[i];
        }
 
                rr1 = dot(r, r, n);
 
                e = sqrt(rr1);
        if(e < eps){
            k++;
            break;
        }
 
                beta = rr1/rr0;
        for(int i = 0; i < n; ++i){
            p[i] = r[i]+beta*p[i];
        }
 
                rr0 = rr1;
    }
 
    max_iter = k+1;
    eps = e;
 
    return 1;
}