From c8842665daceabc2feea5f5b6dcc04911d6f46c7 Mon Sep 17 00:00:00 2001
From: Dennis Mannhart <dennis.mannhart@gmail.com>
Date: Mon, 23 Jul 2018 17:13:13 +0200
Subject: [PATCH] mathlib: add golden section search

---
 src/lib/mathlib/math/SearchMin.hpp | 82 ++++++++++++++++++++++++++++++
 src/lib/mathlib/mathlib.h          |  1 +
 2 files changed, 83 insertions(+)
 create mode 100644 src/lib/mathlib/math/SearchMin.hpp

diff --git a/src/lib/mathlib/math/SearchMin.hpp b/src/lib/mathlib/math/SearchMin.hpp
new file mode 100644
index 0000000000..4a02d5f9d1
--- /dev/null
+++ b/src/lib/mathlib/math/SearchMin.hpp
@@ -0,0 +1,82 @@
+/****************************************************************************
+ *
+ *   Copyright (c) 2018 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Seach.hpp
+ *
+ * - Binary Search (ToDo)
+ * - Golden Section Search
+ */
+
+#define GOLDEN_RATIO 1.6180339887 //(sqrt(5)+1)/2
+
+#pragma once
+
+#include <platforms/px4_defines.h>
+
+namespace math
+{
+
+// Type-safe abs
+template<typename _Tp>
+_Tp abs_t(_Tp val)
+{
+	return ((val > (_Tp)0) ? val : -val);
+}
+
+// golden section search to find extremeum for function with minimum
+template<typename _Tp>
+inline const _Tp goldensection(const _Tp &arg1, const _Tp &arg2, _Tp(*fun)(_Tp), const _Tp &tol)
+{
+	_Tp a = arg1;
+	_Tp b = arg2;
+	_Tp c = b - (b - a) / ((_Tp)GOLDEN_RATIO);
+	_Tp d = a + (b - a) / ((_Tp)GOLDEN_RATIO);
+
+	while (abs_t(c - d) > tol) {
+
+		if (fun(c) < fun(d)) {
+			b = d;
+
+		} else {
+			a = c;
+		}
+
+		c = b - (b - a) / ((_Tp)GOLDEN_RATIO);
+		d = a + (b - a) / ((_Tp)GOLDEN_RATIO);
+
+	}
+
+	return ((b + a) / (_Tp)2);
+}
+}
diff --git a/src/lib/mathlib/mathlib.h b/src/lib/mathlib/mathlib.h
index 40bb8f3e0b..5815e77849 100644
--- a/src/lib/mathlib/mathlib.h
+++ b/src/lib/mathlib/mathlib.h
@@ -44,5 +44,6 @@
 #include "math/Limits.hpp"
 #include "math/Functions.hpp"
 #include "math/matrix_alg.h"
+#include "math/SearchMin.hpp"
 
 #endif