From b5e25f44cfcc251f3e47c24bdebb455f2fd601bd Mon Sep 17 00:00:00 2001
From: Krishna Vedala <7001608+kvedala@users.noreply.github.com>
Date: Sun, 21 Jun 2020 00:09:09 -0400
Subject: [PATCH] added minima algorithm using golden section search

---
 numerical_methods/golden_search_extrema.cpp | 128 ++++++++++++++++++++
 1 file changed, 128 insertions(+)
 create mode 100644 numerical_methods/golden_search_extrema.cpp

diff --git a/numerical_methods/golden_search_extrema.cpp b/numerical_methods/golden_search_extrema.cpp
new file mode 100644
index 000000000..2d4611561
--- /dev/null
+++ b/numerical_methods/golden_search_extrema.cpp
@@ -0,0 +1,128 @@
+/**
+ * \file
+ * \brief Find extrema of a univariate real function in a given interval using
+ * [golden section search
+ * algorithm](https://en.wikipedia.org/wiki/Golden-section_search).
+ *
+ * \author [Krishna Vedala](https://github.com/kvedala)
+ */
+#define _USE_MATH_DEFINES  //< required for MS Visual C++
+#include <cassert>
+#include <cmath>
+#include <ctime>
+#include <functional>
+#include <iostream>
+#include <limits>
+
+#define EPSILON 1e-7  ///< solution accuracy limit
+#define M_GOLDEN_RATIO \
+    static_cast<double>(1.618033988749894848204586834)  ///< golden ratio value
+
+/**
+ * @brief Get the minima of a function in the given interval. To get the maxima,
+ * simply negate the function.
+ *
+ * @param f function to get minima for
+ * @param lim_a lower limit of search window
+ * @param lim_b upper limit of search window
+ * @return local minima found in the interval
+ */
+double get_minima(const std::function<double(double)> &f, double lim_a,
+                  double lim_b) {
+    double c, d;
+    double prev_mean, mean = std::numeric_limits<double>::infinity();
+
+    do {
+        prev_mean = mean;
+
+        c = lim_b - (lim_b - lim_a) / M_GOLDEN_RATIO;
+        d = lim_a + (lim_b - lim_a) / M_GOLDEN_RATIO;
+
+        if (f(c) < f(d)) {
+            lim_b = d;
+        } else {
+            lim_a = c;
+        }
+
+        mean = (lim_a + lim_b) * 0.5f;
+    } while (std::abs(mean - prev_mean) > EPSILON);
+
+    return mean;
+}
+
+/**
+ * @brief Test function to find minima for the function
+ * \f$f(x)= (x-2)^2\f$
+ * in the interval \f$[1,5]\f$
+ * \n Expected result = 2
+ */
+void test1() {
+    // define the function to minimize as a lambda function
+    std::function<double(double)> f1 = [](double x) {
+        return (x - 2) * (x - 2);
+    };
+
+    std::cout << "Test 1.... ";
+
+    double minima = get_minima(f1, 1, 5);
+
+    std::cout << minima << "...";
+
+    assert(std::abs(minima - 2) < EPSILON);
+    std::cout << "passed\n";
+}
+
+/**
+ * @brief Test function to find *maxima* for the function
+ * \f$f(x)= x^{\frac{1}{x}}\f$
+ * in the interval \f$[-2,10]\f$
+ * \n Expected result: \f$e\approx 2.71828182845904509\f$
+ */
+void test2() {
+    // define the function to maximize as a lambda function
+    // since we are maximixing, we negated the function return value
+    std::function<double(double)> func = [](double x) {
+        return -std::pow(x, 1.f / x);
+    };
+
+    std::cout << "Test 2.... ";
+
+    double minima = get_minima(func, -2, 10);
+
+    std::cout << minima << " (" << M_E << ")...";
+
+    assert(std::abs(minima - M_E) < EPSILON);
+    std::cout << "passed\n";
+}
+
+/**
+ * @brief Test function to find *maxima* for the function
+ * \f$f(x)= \cos x\f$
+ * in the interval \f$[0,12]\f$
+ * \n Expected result: \f$\pi\approx 3.14159265358979312\f$
+ */
+void test3() {
+    // define the function to maximize as a lambda function
+    // since we are maximixing, we negated the function return value
+    std::function<double(double)> func = [](double x) { return std::cos(x); };
+
+    std::cout << "Test 3.... ";
+
+    double minima = get_minima(func, 0, 12);
+
+    std::cout << minima << " (" << M_PI << ")...";
+
+    assert(std::abs(minima - M_PI) < EPSILON);
+    std::cout << "passed\n";
+}
+
+/** Main function */
+int main() {
+    std::cout.precision(18);
+
+    test1();
+    test2();
+    test3();
+
+    return 0;
+}