[T] added test for regula falsi

Tests/MathLib/TestNonlinear1D.cpp

+/**
+ * \copyright
+ * Copyright (c) 2012-2016, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#include <limits>
+#include <type_traits>
+#include <gtest/gtest.h>
+#include <logog/include/logog.hpp>
+#include "MathLib/Nonlinear/Root1D.h"
+
+double f(double x)
+{
+    return x*x-1;
+}
+
+template <typename T>
+class MathLibRegulaFalsi : public ::testing::Test
+{
+};
+
+namespace NL = MathLib::Nonlinear;
+using RegulaFalsiTypes = ::testing::Types<NL::Unmodified, NL::Illinois, NL::Pegasus, NL::AndersonBjorck>;
+
+TYPED_TEST_CASE(MathLibRegulaFalsi, RegulaFalsiTypes);
+
+TYPED_TEST(MathLibRegulaFalsi, QuadraticFunction)
+{
+    auto rf = NL::makeRegulaFalsi<TypeParam>(f, -0.1, 1.1);
+    double old_range = rf.getRange();
+
+    DBUG(" 0 -- x ~ %23.16g, range = %23.16g", rf.getResult(), old_range);
+
+    for (unsigned n=0; n<10; ++n)
+    {
+        rf.step(1);
+        double range = rf.getRange();
+        // expect that the interval of the root search shrinks
+        EXPECT_GT(old_range, range);
+        old_range = range;
+        DBUG("%2i -- x ~ %23.16g, range = %23.16g", n+1, rf.getResult(), range);
+
+        if (range < std::numeric_limits<double>::epsilon()) break;
+    }
+
+    auto const error = std::abs(f(rf.getResult()));
+
+    if (!std::is_same<NL::Unmodified, TypeParam>::value) {
+        EXPECT_GT(std::numeric_limits<double>::epsilon(), old_range);
+        EXPECT_GT(std::numeric_limits<double>::epsilon(), error);
+    } else {
+        // The unmodified regula falsi method converges very slowly.
+        EXPECT_GT(100.0*std::numeric_limits<double>::epsilon(), error);
+    }
+}