Merge commit '4ebe6417a5fce5f0994fc0c31bebf732be96a07c' as 'boost'

boost/libs/numeric/interval/examples/findroot_demo.cpp

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+/* Boost example/findroot_demo.cpp
+ * find zero points of some function by dichotomy
+ *
+ * Copyright 2000 Jens Maurer
+ * Copyright 2002-2003 Guillaume Melquiond
+ *
+ * Distributed under the Boost Software License, Version 1.0.
+ * (See accompanying file LICENSE_1_0.txt or
+ * copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ * The idea and the 2D function are based on RVInterval,
+ * which contains the following copyright notice:
+
+        This file is copyrighted 1996 by Ronald Van Iwaarden.
+
+        Permission is hereby granted, without written agreement and
+        without license or royalty fees, to use, copy, modify, and
+        distribute this software and its documentation for any
+        purpose, subject to the following conditions:
+        
+        The above license notice and this permission notice shall
+        appear in all copies or substantial portions of this software.
+        
+        The name "RVInterval" cannot be used for any modified form of
+        this software that does not originate from the authors.
+        Nevertheless, the name "RVInterval" may and should be used to
+        designate the optimization software implemented and described
+        in this package, even if embedded in any other system, as long
+        as any portion of this code remains.
+        
+        The authors specifically disclaim any warranties, including,
+        but not limited to, the implied warranties of merchantability
+        and fitness for a particular purpose.  The software provided
+        hereunder is on an "as is" basis, and the authors have no
+        obligation to provide maintenance, support, updates,
+        enhancements, or modifications.  In no event shall the authors
+        be liable to any party for direct, indirect, special,
+        incidental, or consequential damages arising out of the use of
+        this software and its documentation.      
+*/
+
+#include <boost/numeric/interval.hpp>    // must be first for <limits> workaround
+#include <list>
+#include <deque>
+#include <vector>
+#include <fstream>
+#include <iostream>
+
+
+template<class T>
+struct test_func2d
+{
+  T operator()(T x, T y) const
+  {
+    return sin(x)*cos(y) - exp(x*y)/45.0 * (pow(x+y, 2)+100.0) - 
+      cos(sin(y))*y/4.0;
+  }
+};
+
+template <class T>
+struct test_func1d
+{
+  T operator()(T x) const
+  {
+    return sin(x)/(x*x+1.0);
+  }
+};
+
+template<class T>
+struct test_func1d_2
+{
+  T operator()(T x) const
+  {
+    using std::sqrt;
+    return sqrt(x*x-1.0);
+  }
+};
+
+template<class Function, class I>
+void find_zeros(std::ostream & os, Function f, I searchrange)
+{
+  std::list<I> l, done;
+  l.push_back(searchrange);
+  while(!l.empty()) {
+    I range = l.front();
+    l.pop_front();
+    I val = f(range);
+    if (zero_in(val)) {
+      if(width(range) < 1e-6) {
+        os << range << '\n';
+        continue;
+      }
+      // there's still a solution hidden somewhere
+      std::pair<I,I> p = bisect(range);
+      l.push_back(p.first);
+      l.push_back(p.second);
+    }
+  }
+}
+
+template<class T>
+std::ostream &operator<<(std::ostream &os, const std::pair<T, T> &x) {
+  os << "(" << x.first << ", " << x.second << ")";
+  return os;
+}
+
+template<class T, class Policies>
+std::ostream &operator<<(std::ostream &os,
+                         const boost::numeric::interval<T, Policies> &x) {
+  os << "[" << x.lower() << ", " << x.upper() << "]";
+  return os;
+}
+
+static const double epsilon = 5e-3;
+
+template<class Function, class I>
+void find_zeros(std::ostream & os, Function f, I rx, I ry)
+{
+  typedef std::pair<I, I> rectangle;
+  typedef std::deque<rectangle> container;
+  container l, done;
+  // l.reserve(50);
+  l.push_back(std::make_pair(rx, ry));
+  for(int i = 1; !l.empty(); ++i) {
+    rectangle rect = l.front();
+    l.pop_front();
+    I val = f(rect.first, rect.second);
+    if (zero_in(val)) {
+      if(width(rect.first) < epsilon && width(rect.second) < epsilon) {
+        os << median(rect.first) << " " << median(rect.second) << " "
+           << lower(rect.first) << " " << upper(rect.first) << " "
+           << lower(rect.second) << " " << upper(rect.second) 
+           << '\n';
+      } else {
+        if(width(rect.first) > width(rect.second)) {
+          std::pair<I,I> p = bisect(rect.first);
+          l.push_back(std::make_pair(p.first, rect.second));
+          l.push_back(std::make_pair(p.second, rect.second));
+        } else {
+          std::pair<I,I> p = bisect(rect.second);
+          l.push_back(std::make_pair(rect.first, p.first));
+          l.push_back(std::make_pair(rect.first, p.second));
+        }
+      }
+    }
+    if(i % 10000 == 0)
+      std::cerr << "\rIteration " << i << ", l.size() = " << l.size();
+  }
+  std::cerr << '\n';
+}
+
+int main()
+{
+  using namespace boost;
+  using namespace numeric;
+  using namespace interval_lib;
+
+  typedef interval<double,
+                   policies<save_state<rounded_transc_opp<double> >,
+                            checking_base<double> > > I;
+
+  std::cout << "Zero points of sin(x)/(x*x+1)\n";
+  find_zeros(std::cout, test_func1d<I>(), I(-11, 10));
+  std::cout << "Zero points of sqrt(x*x-1)\n";
+  find_zeros(std::cout, test_func1d_2<I>(), I(-5, 6));
+  std::cout << "Zero points of Van Iwaarden's 2D function\n";
+  std::ofstream f("func2d.data");
+  find_zeros(f, test_func2d<I>(), I(-20, 20), I(-20, 20));
+  std::cout << "Use gnuplot, command 'plot \"func2d.data\" with dots'   to plot\n";
+}