init: 初始化krylov复现项目

tests/test_eigen.cpp

@@ -0,0 +1,59 @@
+#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;
+}