#include "krylov/types/common.hpp"
#include <cassert>
#include <cmath>

static bool approx(double a, double b, double eps = 1e-10) {
    return std::abs(a - b) < eps;
}

int main() {
    using krylov::Matrix;
    using krylov::Vector;
    using MatrixXd = Matrix;
    using VectorXd = Vector;

    // 1) 基本矩阵 / 向量运算
    MatrixXd A(2, 2);
    A << 4, 1,
         2, 3;
    VectorXd b(2);
    b << 1, 2;

    VectorXd Ab = A * b;
    assert(approx(Ab(0), 4 * 1 + 1 * 2));
    assert(approx(Ab(1), 2 * 1 + 3 * 2));

    // 2) 行列式 / 逆
    assert(approx(A.determinant(), 4 * 3 - 1 * 2));
    MatrixXd I = A * A.inverse();
    assert(approx(I(0, 0), 1.0));
    assert(approx(I(1, 1), 1.0));
    assert(approx(I(0, 1), 0.0));
    assert(approx(I(1, 0), 0.0));

    // 3) 线性方程求解 A x = b
    VectorXd x = A.colPivHouseholderQr().solve(b);
    VectorXd r = A * x - b;
    assert(r.norm() < 1e-10);

    // 4) 范数
    VectorXd v(3);
    v << 3, 0, 4;
    assert(approx(v.norm(), 5.0));
    assert(approx(v.squaredNorm(), 25.0));

    // 5) 稀疏矩阵基础
    krylov::SparseMatrix S(3, 3);
    S.insert(0, 0) = 1.0;
    S.insert(1, 1) = 2.0;
    S.insert(2, 2) = 3.0;
    S.makeCompressed();
    VectorXd y(3);
    y << 1, 1, 1;
    VectorXd Sy = S * y;
    assert(approx(Sy(0), 1.0));
    assert(approx(Sy(1), 2.0));
    assert(approx(Sy(2), 3.0));

    return 0;
}