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boost/numeric/odeint.hpp
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#include <boost/numeric/odeint/stepper/generation.hpp>
#include <boost/numeric/odeint/iterator/const_step_iterator.hpp>
#include <boost/numeric/odeint/iterator/const_step_time_iterator.hpp>
#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
#include <boost/numeric/odeint/iterator/adaptive_time_iterator.hpp>
#endif // BOOST_NUMERIC_ODEINT_HPP_INCLUDED

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@ -25,6 +23,7 @@
functions</a></span></dt>
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@ -10,8 +10,6 @@
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@ -152,7 +150,7 @@
<span class="identifier">rk</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys1</span> <span class="special">,</span> <span class="identifier">in</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">out</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">);</span> <span class="comment">// Out-of-place transformation</span>
<span class="identifier">rk</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys1</span> <span class="special">,</span> <span class="identifier">inout</span> <span class="special">,</span> <span class="identifier">dxdtin</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">);</span> <span class="comment">// In-place tranformation of inout</span>
<span class="identifier">rk</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys1</span> <span class="special">,</span> <span class="identifier">in</span> <span class="special">,</span> <span class="identifier">dxdtin</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">out</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">);</span> <span class="comment">// Out-of-place transformation</span>
</pre>
</pre>
<p>
</p>
<p>
@ -2004,8 +2002,8 @@
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">deriv_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">deriv_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">time_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span> <span class="identifier">order_type</span><span class="special">;</span>
@ -2091,7 +2089,7 @@
<p>
</p>
<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">static</span> <span class="identifier">size_t</span> <span class="identifier">N</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<span class="keyword">struct</span> <span class="identifier">ornstein_det</span>
<span class="special">{</span>
@ -2103,8 +2101,8 @@
<span class="keyword">struct</span> <span class="identifier">ornstein_stoch</span>
<span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">mt19937</span> <span class="identifier">m_rng</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">m_dist</span><span class="special">;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">mt19937</span> <span class="identifier">m_rng</span><span class="special">;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">m_dist</span><span class="special">;</span>
<span class="identifier">ornstein_stoch</span><span class="special">(</span> <span class="keyword">double</span> <span class="identifier">sigma</span> <span class="special">)</span> <span class="special">:</span> <span class="identifier">m_rng</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">m_dist</span><span class="special">(</span> <span class="number">0.0</span> <span class="special">,</span> <span class="identifier">sigma</span> <span class="special">)</span> <span class="special">{</span> <span class="special">}</span>
@ -2281,14 +2279,12 @@ c3 = 2/3, a31 = 0 , a32 = 2/3
</p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="number">3</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span> <span class="keyword">double</span> <span class="special">,</span> <span class="number">3</span> <span class="special">&gt;</span> <span class="identifier">state_type</span><span class="special">;</span>
<span class="identifier">heun</span><span class="special">&lt;</span> <span class="identifier">state_type</span> <span class="special">&gt;</span> <span class="identifier">h</span><span class="special">;</span>
<span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span>
<span class="identifier">integrate_const</span><span class="special">(</span> <span class="identifier">h</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">100.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">,</span>
<span class="special">[](</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&amp;</span><span class="identifier">_x</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">_t</span> <span class="special">)</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">_t</span> <span class="special">&lt;&lt;</span> <span class="string">"\t"</span> <span class="special">&lt;&lt;</span> <span class="identifier">_x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">&lt;&lt;</span> <span class="string">"\t"</span> <span class="special">&lt;&lt;</span> <span class="identifier">_x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">&lt;&lt;</span> <span class="string">"\t"</span> <span class="special">&lt;&lt;</span> <span class="identifier">_x</span><span class="special">[</span><span class="number">2</span><span class="special">]</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="special">});</span>
<span class="identifier">streaming_observer</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">)</span> <span class="special">);</span>
</pre>
<p>
</p>

2
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@ -10,8 +10,6 @@
<link rel="next" href="../concepts.html" title="Concepts">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
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2
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@ -10,8 +10,6 @@
<link rel="next" href="using_boost__range.html" title="Using boost::range">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
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</div>

2
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@ -10,8 +10,6 @@
<link rel="next" href="tutorial/harmonic_oscillator.html" title="Harmonic oscillator">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="getting_started/short_example.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="tutorial/harmonic_oscillator.html"><img src="../images/next.png" alt="Next"></a>
</div>

2
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@ -10,8 +10,6 @@
<link rel="next" href="references.html" title="References">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
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</div>

3
doc/boost_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html
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@ -10,8 +10,6 @@
<link rel="next" href="stiff_systems.html" title="Stiff systems">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="solar_system.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="stiff_systems.html"><img src="../../images/next.png" alt="Next"></a>
</div>
@ -131,7 +129,6 @@
<span class="identifier">lorenz</span><span class="special">()(</span> <span class="identifier">x</span> <span class="special">,</span> <span class="identifier">dxdt</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">);</span>
<span class="special">...</span>
<span class="special">}</span>
</pre>
<p>
This works fine and <code class="computeroutput"><span class="identifier">lorenz_with_lyap</span></code>

24
doc/boost_numeric_odeint/tutorial/harmonic_oscillator.html
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@ -10,8 +10,6 @@
<link rel="next" href="solar_system.html" title="Solar system">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../tutorial.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="solar_system.html"><img src="../../images/next.png" alt="Next"></a>
</div>
@ -29,6 +27,8 @@
with Constant Step Size</a></span></dt>
<dt><span class="section"><a href="harmonic_oscillator.html#boost_numeric_odeint.tutorial.harmonic_oscillator.integration_with_adaptive_step_size">Integration
with Adaptive Step Size</a></span></dt>
<dt><span class="section"><a href="harmonic_oscillator.html#boost_numeric_odeint.tutorial.harmonic_oscillator.using_iterators">Using
iterators</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
@ -1448,6 +1448,26 @@
works.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numeric_odeint.tutorial.harmonic_oscillator.using_iterators"></a><a class="link" href="harmonic_oscillator.html#boost_numeric_odeint.tutorial.harmonic_oscillator.using_iterators" title="Using iterators">Using
iterators</a>
</h4></div></div></div>
<p>
odeint supports iterators for solving ODEs. That is you instantiate a pair
of iterators and instead of using the integrate routines with an appropriate
observer you put the iterators in one of the algorithm from the C++ standard
library or from Boost.Range. An example is
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span> <span class="identifier">make_adaptive_iterator_begin</span><span class="special">(</span> <span class="identifier">controlled_stepper</span> <span class="special">,</span> <span class="identifier">harmonic_oscillator</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span>
<span class="identifier">make_adaptive_iterator_end</span><span class="special">(</span> <span class="identifier">controlled_stepper</span> <span class="special">,</span> <span class="identifier">harmonic_oscillator</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span>
<span class="identifier">write_state</span><span class="special">()</span> <span class="special">);</span>
</pre>
<p>
</p>
</div>
<p>
The full cpp file for this example can be found here: <a href="https://github.com/headmyshoulder/odeint-v2/tree/master/libs/numeric/odeint/examples/harmonic_oscillator.cpp" target="_top">harmonic_oscillator.cpp</a>
</p>

2
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@ -10,8 +10,6 @@
<link rel="next" href="../odeint_in_detail.html" title="odeint in detail">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
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<a accesskey="p" href="all_examples.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="../odeint_in_detail.html"><img src="../../images/next.png" alt="Next"></a>
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4
doc/boost_numeric_odeint/tutorial/solar_system.html
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@ -10,8 +10,6 @@
<link rel="next" href="chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="harmonic_oscillator.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="chaotic_systems_and_lyapunov_exponents.html"><img src="../../images/next.png" alt="Next"></a>
</div>
@ -140,7 +138,7 @@ p<sub>&#8203;i</sub><sup>2</sup> / (2m<sub>&#8203;i</sub>) + H<sub>&#8203;q</sub
<span class="comment">//...</span>
<span class="comment">// more operators</span>
</pre>
</pre>
<p>
</p>
<p>

4
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@ -10,8 +10,6 @@
<link rel="next" href="using_cuda_and_thrust.html" title="Using Cuda and Thrust">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
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</div>
@ -435,8 +433,6 @@
<span class="identifier">integrate_const</span><span class="special">(</span> <span class="identifier">runge_kutta4</span><span class="special">&lt;</span> <span class="identifier">container_type</span> <span class="special">&gt;()</span> <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">(</span> <span class="identifier">ensemble</span> <span class="special">)</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">100.0</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">(</span> <span class="identifier">obs</span> <span class="special">)</span> <span class="special">);</span>
<span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">epsilon</span> <span class="special">&lt;&lt;</span> <span class="string">"\t"</span> <span class="special">&lt;&lt;</span> <span class="identifier">obs</span><span class="special">.</span><span class="identifier">get_K_mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
</p>

2
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@ -10,8 +10,6 @@
<link rel="next" href="special_topics.html" title="Special topics">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
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@ -10,8 +10,6 @@
<link rel="next" href="using_opencl_and_vexcl.html" title="Using OpenCL and VexCL">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
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</div>
@ -178,8 +176,8 @@
<span class="keyword">static</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span> <span class="identifier">value_type</span> <span class="special">,</span> <span class="identifier">value_type</span> <span class="special">&gt;</span> <span class="identifier">get_mean</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&amp;</span><span class="identifier">x</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">value_type</span> <span class="identifier">sin_sum</span> <span class="special">=</span> <span class="identifier">thrust</span><span class="special">::</span><span class="identifier">reduce</span><span class="special">(</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">sin_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">,</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">sin_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">);</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">sin_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">,</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">sin_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">);</span>
<span class="identifier">value_type</span> <span class="identifier">cos_sum</span> <span class="special">=</span> <span class="identifier">thrust</span><span class="special">::</span><span class="identifier">reduce</span><span class="special">(</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">cos_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">,</span>
<span class="identifier">thrust</span><span class="special">::</span><span class="identifier">make_transform_iterator</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">cos_functor</span><span class="special">()</span> <span class="special">)</span> <span class="special">);</span>

7
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@ -8,8 +8,6 @@
<link rel="next" href="boost_numeric_odeint/getting_started.html" title="Getting started">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
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<div class="chapter">
<div class="titlepage"><div>
@ -24,7 +22,7 @@
<div><p class="copyright">Copyright &#169; 2009-2011 Karsten Ahnert
and Mario Mulansky</p></div>
<div><div class="legalnotice">
<a name="id533358"></a><p>
<a name="odeint.legal"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
@ -65,6 +63,7 @@
functions</a></span></dt>
<dt><span class="section"><a href="boost_numeric_odeint/odeint_in_detail/integrate_functions.html">Integrate
functions</a></span></dt>
<dt><span class="section"><a href="boost_numeric_odeint/odeint_in_detail/iterators.html">Iterators</a></span></dt>
<dt><span class="section"><a href="boost_numeric_odeint/odeint_in_detail/state_types__algebras_and_operations.html">State
types, algebras and operations</a></span></dt>
<dt><span class="section"><a href="boost_numeric_odeint/odeint_in_detail/using_boost__ref.html">Using
@ -95,7 +94,7 @@
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</div>
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85
libs/numeric/odeint/doc/details_iterators.qbk
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@ -1,20 +1,91 @@
[section ODE Iterators]
[section Iterators]
odeint supports iterators for iterating throught an ordinary differential equation. They offer you an alternative to the integrate functions. Furthermore, many of the standard algorithms in the C++ standard library and Boost.Range can be used with the odeint't iterators.
odeint supports iterators for iterating through an ordinary differential equation. They offer you an alternative to the integrate functions. Furthermore, many of the standard algorithms in the C++ standard library and Boost.Range can be used with the odeint't iterators.
[warning odeint's iterators do not satisfy the iterator concepts defined in the standard completely. In detail the iterator transitivity is violated in some rare cases. But this is not relevant for all algorithms in the C++ standard library and in Boost.Range.]
odeint provides for four new iterators.
[import ../examples/const_step_iterator.cpp]
Four iterators are provided. They are all single pass iterators. The first one is a iterator which solves the odeint with constant step size. An example is
[const_step_iterator_accumulate]
In this example all x-values of the solution are accumulated. The iterator itself does not occur directly in this example but it is generated by the factory functions `make_const_step_iterator_begin` and `make_const_step_iterator_end`. odeint also supports Boost.Range, that is you write the above example in a shortified form with the factory function `make_const_step_range`
[const_step_iterator_accumulate_range]
The second iterator type is also a iterator with const step size. But the value type of this iterator consists here of a pair of the time and the state of the solution of the ODE. An example is
[const_step_time_iterator_accumulate_range]
The factory functions are now `make_const_step_time_iterator_begin`, `make_const_step_time_iterator_end` and `make_const_step_time_range`.
[import ../examples/adaptive_iterator.cpp]
The other two iterator types adaptive iterators which are completely analogous to the const step iterators. Examples are
[adaptive_iterator_accumulate_range]
[adaptive_time_iterator_accumulate_range]
[section const_step_iterator]
* Definition: `const_step_iterator< Stepper , System >`
* `value_type` is `Stepper::state_type`
* Factory functions
* `make_const_step_iterator_begin( stepper , system , state , t_start , dt )`
* `make_const_step_iterator_end( stepper , system , state , t_end , dt )`
* `make_const_step_range( stepper , system , state , t_start , t_end , dt )`
* This stepper works with all steppers fullfilling the Stepper concept or the DenseOutputStepper concept.
[endsect]
[section const_step_time_iterator]
* Definition: `const_step_iterator< Stepper , System >`
* `value_type` is `std::pair< Stepper::state_type& , Stepper::time_type >`
* Factory functions
* `make_const_step_time_iterator_begin( stepper , system , state , t_start , dt )`
* `make_const_step_time_iterator_end( stepper , system , state , t_end , dt )`
* `make_const_step_time_range( stepper , system , state , t_start , t_end , dt )`
* This stepper works with all steppers fullfilling the Stepper concept or the DenseOutputStepper concept.
[endsect]
[section adaptive_step_iterator]
* Definition: `adaptive_iterator< Stepper , System >`
* `value_type` is `Stepper::state_type`
* Factory functions
* `make_adaptive_iterator_begin( stepper , system , state , t_start , dt )`
* `make_adaptive_iterator_end( stepper , system , state , t_end , dt )`
* `make_adaptive_range( stepper , system , state , t_start , t_end , dt )`
* This stepper works with all steppers fullfilling the ControlledStepper concept or the DenseOutputStepper concept.
[endsect]
[section adaptive_step_time_iterator]
* Definition: `adaptive_iterator< Stepper , System >`
* `value_type` is `std::pair< Stepper::state_type& , Stepper::time_type >`
* Factory functions
* `make_adaptive_time_iterator_begin( stepper , system , state , t_start , dt )`
* `make_adaptive_time_iterator_end( stepper , system , state , t_end , dt )`
* `make_adaptive_time_range( stepper , system , state , t_start , t_end , dt )`
* This stepper works with all steppers fullfilling the ControlledStepper concept or the DenseOutputStepper concept.
[endsect]
const step iterator, factory functions
const step time iterator, factory functions
adaptive iterator, factory functions
adaptive time iterator, factory functions
[endsect]

11
libs/numeric/odeint/doc/tutorial_harmonic_oscillator.qbk
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@ -91,6 +91,15 @@ When using `make_controlled` or `make_dense_output` one should be aware which ex
[endsect]
The full cpp file for this example can be found here: [github_link libs/numeric/odeint/examples/harmonic_oscillator.cpp harmonic_oscillator.cpp]
[section Using iterators]
odeint supports iterators for solving ODEs. That is you instantiate a pair of iterators and instead of using the integrate routines with an appropriate observer you put the iterators in one of the algorithm from the C++ standard library or from Boost.Range. An example is
[harm_iterator_const_step]
[endsect]
The full cpp file for this example can be found here: [github_link libs/numeric/odeint/examples/harmonic_oscillator.cpp harmonic_oscillator.cpp]
[endsect]

4
libs/numeric/odeint/examples/adaptive_iterator.cpp
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@ -146,12 +146,14 @@ int main( int argc , char **argv )
// boost::range::accumulate
{
//[adaptive_time_iterator_accumulate_range
auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
[]( double sum , const pair< state_type& , double > &x ) {
return sum + x.first[0]; } );
cout << res << endl;
//]
}
@ -310,12 +312,14 @@ int main( int argc , char **argv )
// boost::range::accumulate
{
//[adaptive_iterator_accumulate_range
auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
[]( double sum , const state_type& x ) {
return sum + x[0]; } );
cout << res << endl;
//]
}

6
libs/numeric/odeint/examples/const_step_iterator.cpp
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@ -74,6 +74,7 @@ int main( int argc , char **argv )
// std::accumulate
{
//[ const_step_iterator_accumulate
runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = std::accumulate( make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 0.01 ) ,
@ -82,6 +83,7 @@ int main( int argc , char **argv )
[]( double sum , const state_type &x ) {
return sum + x[0]; } );
cout << res << endl;
//]
}
@ -162,22 +164,26 @@ int main( int argc , char **argv )
// boost::range::accumulate
{
//[const_step_iterator_accumulate_range
runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_const_step_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
[]( double sum , const state_type &x ) {
return sum + x[0]; } );
cout << res << endl;
//]
}
// boost::range::accumulate with time iterator
{
//[const_step_time_iterator_accumulate_range
runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_const_step_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
[]( double sum , const std::pair< state_type &, double > &x ) {
return sum + x.first[0]; } );
cout << res << endl;
//]
}

15
libs/numeric/odeint/examples/harmonic_oscillator.cpp
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@ -61,6 +61,14 @@ struct push_back_state_and_time
};
//]
struct write_state
{
void operator()( const state_type &x ) const
{
std::cout << x[0] << "\t" << x[1] << "\n";
}
};
int main(int /* argc */ , char** /* argv */ )
{
@ -166,4 +174,11 @@ int main(int /* argc */ , char** /* argv */ )
harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
//]
//[harm_iterator_const_step
std::for_each( make_adaptive_iterator_begin( controlled_stepper , harmonic_oscillator , x , 0.0 , 0.01 ) ,
make_adaptive_iterator_end( controlled_stepper , harmonic_oscillator , x , 0.0 , 0.01 ) ,
write_state() );
//]
}