Add gradient descent test

src/test_gradient_descent.cpp

+#define CATCH_CONFIG_MAIN // This tells Catch to provide a main() - only do this
+                          // in one cpp file
+#include "catch.hpp"
+#include "differentiator.h"
+#include "optimizer.h"
+#include "sample_functions.h"
+#define _USE_MATH_DEFINES
+#include <cmath>
+#include <cstdint>
+#include <fstream>
+#include <iomanip>
+#include <string>
+#include <vector>
+
+TEST_CASE("Gradient Descent on functions with one dimensional argument",
+          "[gradient_descent]") {
+    using namespace numerics;
+    using std::cerr;
+    using std::cout;
+    using std::endl;
+    FivePointDifferentiator fp;
+    double step = 1e-4;
+    GradientDescent optimizer(step);
+
+    Coordinate<double> position1(1), position2(2), ref2(2), res1(1), res2(2);
+
+    double precision = 1e-9;
+    double error = 1e-5;
+
+    using funct = Function<Coordinate<double>, double>;
+
+    SECTION("Testing 1D parabola") {
+        funct& parabola = functions::parabola_1d;
+        cerr << "Tested function: " << functions::parabola_1d << endl;
+        position1[0] = 10;
+        res1 = optimizer.optimize(parabola, position1, precision);
+        REQUIRE(res1.l2Norm() < error);
+        REQUIRE(std::abs(parabola(res1)) < error);
+    }
+    SECTION("Testing 1D higher-order parabola") {
+        double ref_pos = sqrt(4.6 / 4);
+
+        funct& higher_parabola = functions::higher_parabola_1d;
+        cerr << "Tested function: " << functions::higher_parabola_1d << endl;
+        position1[0] = 10;
+        res1 = optimizer.optimize(higher_parabola, position1, precision);
+        REQUIRE(std::abs(res1[0] - ref_pos) < error);
+
+        position1[0] = -ref_pos + 0.5;
+        res1 = optimizer.optimize(higher_parabola, position1, precision);
+        REQUIRE(std::abs(res1[0] - ref_pos) < error);
+    }
+    SECTION("Testing 1D reference Polynomial") {
+        funct& reference_polynomial = functions::ref_polynomial_1d;
+        cerr << "Tested function: " << functions::ref_polynomial_1d << endl;
+        position1[0] = 20;
+        res1 = optimizer.optimize(reference_polynomial, position1, precision);
+        REQUIRE(std::abs(reference_polynomial(res1)) < error);
+    }
+
+    SECTION("Testing narrow 1d Lennard Jones potential") {
+        double rm = functions::narrow_LJ.get_rm();
+
+        funct& narrow_LJ = functions::narrow_LJ;
+        position1[0] = rm * 3;
+        res1 = optimizer.optimize(narrow_LJ, position1, precision);
+        REQUIRE(std::abs(res1[0] - rm) < error);
+
+        position1[0] = rm / 2.0;
+        res1 = optimizer.optimize(narrow_LJ, position1, precision);
+        REQUIRE(std::abs(res1[0] - rm) < error);
+    }
+
+    SECTION("Testing wide 1d Lennard Jones potential") {
+        double rm = functions::wide_LJ.get_rm();
+        funct& wide_LJ = functions::wide_LJ;
+        position1[0] = rm * 3;
+        res1 = optimizer.optimize(wide_LJ, position1, precision);
+        REQUIRE(std::abs(res1[0] - rm) < error);
+
+        position1[0] = rm / 2.0;
+        res1 = optimizer.optimize(wide_LJ, position1, precision);
+        REQUIRE(std::abs(res1[0] - rm) < error);
+    }
+
+    SECTION("Testing 2D parabola") {
+        funct& parabola2d = functions::parabola_2d;
+        position2[0] = 10;
+        position2[1] = -123.0;
+        res2 = optimizer.optimize(parabola2d, position2, precision);
+        REQUIRE(res2.l2Norm() < error);
+        REQUIRE(std::abs(parabola2d(res2)) < error);
+        position2[0] = -133;
+        position2[1] = -0.1;
+        res2 = optimizer.optimize(parabola2d, position2, precision);
+        REQUIRE(res2.l2Norm() < error);
+        REQUIRE(std::abs(parabola2d(res2)) < error);
+    }
+    SECTION("Testing 2D parabola") {
+        funct& periodic_wave = functions::periodic_wave_2d;
+        uint32_t k = 13;
+        uint32_t l = 31;
+
+        ref2[0] = (2 * k - 0.5) * M_PI;
+        ref2[1] = (2 * l + 1.0) * M_PI;
+        position2[0] = ref2[0] + 0.5;
+        position2[1] = ref2[1] - 0.2;
+        res2 = optimizer.optimize(periodic_wave, position2, precision);
+        REQUIRE((res2 - ref2).l2Norm() < error);
+        k = -4;
+        l = 5;
+
+        ref2[0] = (2 * k - 0.5) * M_PI;
+        ref2[1] = (2 * l + 1.0) * M_PI;
+        position2[0] = ref2[0] - 0.3;
+        position2[1] = ref2[1] + 0.4;
+        res2 = optimizer.optimize(periodic_wave, position2, precision);
+        REQUIRE((res2 - ref2).l2Norm() < error);
+    }
+}