mirror of
https://github.com/boostorg/odeint.git
synced 2025-05-09 23:24:01 +00:00
boost::range detail documentation
This commit is contained in:
Karsten Ahnert
parent
83c55a4632
commit
b6bbedde4f
@ -22,18 +22,206 @@
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
Most steppers in odeint also accept the state give as a range. A range is
|
||||
sequence of values modelled by a range concept, see <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>
|
||||
for an overview over existing concepts and examples of ranges.
|
||||
sequence of values modelled by a range concept. See <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>
|
||||
for an overview over existing concepts and examples of ranges. This means
|
||||
that the <code class="computeroutput"><span class="identifier">state_type</span></code> of the
|
||||
stepper must not necessarily used to call the <code class="computeroutput"><span class="identifier">do_step</span></code>
|
||||
method.
|
||||
</p>
|
||||
<p>
|
||||
state type mus not necessary be used in the steppers
|
||||
One use case for <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>
|
||||
in odeint has been shown in <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic
|
||||
system</a> where the state consists of two parts: one for the original
|
||||
state and one for the perturbations. The ranges are used to initialize (solve)
|
||||
only the system part where the perturbation part is not touched. After that
|
||||
the complete state including also the perturbations is solved. Another use
|
||||
case is a system consisting of coupled units where you want to initialize
|
||||
each unit separately with the ODE of the uncoupled unit. An example is a
|
||||
chain of coupled van-der-Pol-oscillators which are initialized uniformily
|
||||
from the uncoupled van-der-Pol-oscillator. Then you can use <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>
|
||||
to solve only one individual oscillator in the chain.
|
||||
</p>
|
||||
<p>
|
||||
example
|
||||
An example was given in <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic
|
||||
system</a> tutorial. Using Boost.Range usually means that your system
|
||||
function needs to adapt to the iterators of Boost.Range. That is, your function
|
||||
is called with a range and you need to get the iterators from that range.
|
||||
This can easily be done. You have to implement your system as a class or
|
||||
a struct and you have to templatize the <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>. Then you can use the <code class="computeroutput"><span class="identifier">range_iterator</span></code>-meta
|
||||
function and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">end</span></code> to
|
||||
obtain the iterators of your range:
|
||||
</p>
|
||||
<p>
|
||||
table which steppers support boost::range and with which algebra
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">></span>
|
||||
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span>
|
||||
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="identifier">Deriv</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span>
|
||||
|
||||
<span class="comment">// fill dxdt</span>
|
||||
<span class="special">}</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
If your range is a random access-range you can also apply the bracket operator
|
||||
to the iterator to access the elements in the range:
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">></span>
|
||||
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span>
|
||||
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="identifier">Deriv</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span>
|
||||
|
||||
<span class="identifier">dxdt</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f1</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span>
|
||||
<span class="identifier">dxdt</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f2</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span>
|
||||
<span class="special">}</span>
|
||||
<span class="special">};</span>
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
The following two tables show which steppers and which algebras are compatible
|
||||
with <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>.
|
||||
</p>
|
||||
<div class="table">
|
||||
<a name="boost_sandbox_numeric_odeint.odeint_in_detail.using_boost__range.steppers_supporting_boost_range"></a><p class="title"><b>Table 1.10. Steppers supporting Boost.Range</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Steppers supporting Boost.Range">
|
||||
<colgroup><col></colgroup>
|
||||
<thead><tr><th>
|
||||
<p>
|
||||
Stepper
|
||||
</p>
|
||||
</th></tr></thead>
|
||||
<tbody>
|
||||
<tr><td>
|
||||
<p>
|
||||
adams_bashforth_moulton
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
bulirsch_stoer_dense_out
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
bulirsch_stoer
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
controlled_runge_kutta
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
dense_output_runge_kutta
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
euler
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
explicit_error_generic_rk
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
explicit_generic_rk
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
rosenbrock4_controller
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
rosenbrock4_dense_output
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
rosenbrock4
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta4_classic
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta4
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta_cash_karp54_classic
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta_cash_karp54
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta_dopri5
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
runge_kutta_fehlberg78
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
symplectic_euler
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
symplectic_rkn_sb3a_mclachlan
|
||||
</p>
|
||||
</td></tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<br class="table-break"><div class="table">
|
||||
<a name="boost_sandbox_numeric_odeint.odeint_in_detail.using_boost__range.algebra_supporting_boost_range"></a><p class="title"><b>Table 1.11. Algebra supporting Boost.Range</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Algebra supporting Boost.Range">
|
||||
<colgroup><col></colgroup>
|
||||
<thead><tr><th>
|
||||
<p>
|
||||
algebra
|
||||
</p>
|
||||
</th></tr></thead>
|
||||
<tbody>
|
||||
<tr><td>
|
||||
<p>
|
||||
range_algebra
|
||||
</p>
|
||||
</td></tr>
|
||||
<tr><td>
|
||||
<p>
|
||||
thrust_algebra
|
||||
</p>
|
||||
</td></tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<br class="table-break">
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
|
||||
@ -21,7 +21,7 @@
|
||||
classes</a>
|
||||
</h3></div></div></div>
|
||||
<div class="table">
|
||||
<a name="boost_sandbox_numeric_odeint.old_reference.stepper_classes.stepper_algorithms"></a><p class="title"><b>Table 1.10. Stepper Algorithms</b></p>
|
||||
<a name="boost_sandbox_numeric_odeint.old_reference.stepper_classes.stepper_algorithms"></a><p class="title"><b>Table 1.12. Stepper Algorithms</b></p>
|
||||
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
|
||||
<colgroup>
|
||||
<col>
|
||||
|
||||
@ -125,7 +125,7 @@
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: April 02, 2012 at 16:04:40 GMT</small></p></td>
|
||||
<td align="left"><p><small>Last revised: April 03, 2012 at 11:27:53 GMT</small></p></td>
|
||||
<td align="right"><div class="copyright-footer"></div></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
|
||||
@ -1,11 +1,44 @@
|
||||
[section Using boost::range]
|
||||
|
||||
Most steppers in odeint also accept the state give as a range. A range is sequence of values modelled by a range concept, see __boost_range for an overview over existing concepts and examples of ranges.
|
||||
Most steppers in odeint also accept the state give as a range. A range is sequence of values modelled by a range concept. See __boost_range for an overview over existing concepts and examples of ranges. This means that the `state_type` of the stepper must not necessarily used to call the `do_step` method.
|
||||
|
||||
state type mus not necessary be used in the steppers
|
||||
One use case for __boost_range in odeint has been shown in __tut_chaotic_system where the state consists of two parts: one for the original state and one for the perturbations. The ranges are used to initialize (solve) only the system part where the perturbation part is not touched, that is a range consisting only of the system part is used. After that the complete state including also the perturbations is solved.
|
||||
|
||||
example
|
||||
Another use case is a system consisting of coupled units where you want to initialize each unit separately with the ODE of the uncoupled unit. An example is a chain of coupled van-der-Pol-oscillators which are initialized uniformily from the uncoupled van-der-Pol-oscillator. Then you can use __boost_range to solve only one individual oscillator in the chain.
|
||||
|
||||
table which steppers support boost::range and with which algebra
|
||||
An example was given in __tut_chaotic_system tutorial. Using Boost.Range usually means that your system function needs to adapt to the iterators of Boost.Range. That is, your function is called with a range and you need to get the iterators from that range. This can easily be done. You have to implement your system as a class or a struct and you have to templatize the `operator()`. Then you can use the `range_iterator`-meta function and `boost::begin` and `boost::end` to obtain the iterators of your range:
|
||||
|
||||
``
|
||||
class sys
|
||||
{
|
||||
template< class State , class Deriv >
|
||||
void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
|
||||
{
|
||||
typename boost::range_iterator< const State >::type x = boost::begin( x_ );
|
||||
typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
|
||||
|
||||
// fill dxdt
|
||||
}
|
||||
};
|
||||
``
|
||||
|
||||
If your range is a random access-range you can also apply the bracket operator to the iterator to access the elements in the range:
|
||||
``
|
||||
class sys
|
||||
{
|
||||
template< class State , class Deriv >
|
||||
void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
|
||||
{
|
||||
typename boost::range_iterator< const State >::type x = boost::begin( x_ );
|
||||
typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
|
||||
|
||||
dxdt[0] = f1( x[0] , x[1] );
|
||||
dxdt[1] = f2( x[0] , x[1] );
|
||||
}
|
||||
};
|
||||
``
|
||||
|
||||
The following two tables show which steppers and which algebras are compatible with __boost_range.
|
||||
[include range_table.qbk]
|
||||
|
||||
[endsect]
|
||||
|
||||
@ -66,6 +66,8 @@
|
||||
[link boost_sandbox_numeric_odeint.odeint_in_detail.integrate_functions integrate functions]]
|
||||
[def __tut_solar_system
|
||||
[link boost_sandbox_numeric_odeint.tutorial.solar_system Solar System]]
|
||||
[def __tut_chaotic_system
|
||||
[link boost_sandbox_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents Chaotic system]]
|
||||
[def __using_steppers
|
||||
[link boost_sandbox_numeric_odeint.odeint_in_detail.steppers.using_steppers Using steppers]]
|
||||
[def __generation_functions
|
||||
|
||||
57
libs/numeric/odeint/doc/range_table.qbk
Normal file
57
libs/numeric/odeint/doc/range_table.qbk
Normal file
@ -0,0 +1,57 @@
|
||||
[/
|
||||
Steppers supporting __boost_range:
|
||||
|
||||
* adams_bashforth_moulton
|
||||
* bulirsch_stoer_dense_out
|
||||
* bulirsch_stoer
|
||||
* controlled_runge_kutta
|
||||
* dense_output_runge_kutta
|
||||
* euler
|
||||
* explicit_error_generic_rk
|
||||
* explicit_generic_rk
|
||||
* rosenbrock4_controller
|
||||
* rosenbrock4_dense_output
|
||||
* rosenbrock4
|
||||
* runge_kutta4_classic
|
||||
* runge_kutta4
|
||||
* runge_kutta_cash_karp54_classic
|
||||
* runge_kutta_cash_karp54
|
||||
* runge_kutta_dopri5
|
||||
* runge_kutta_fehlberg78
|
||||
* symplectic_euler
|
||||
* symplectic_rkn_sb3a_mclachlan
|
||||
|
||||
Algebras supporting __boost_range
|
||||
|
||||
* range_algebra
|
||||
* thrust_algebra
|
||||
/]
|
||||
|
||||
[table Steppers supporting Boost.Range
|
||||
[[Stepper]]
|
||||
[[adams_bashforth_moulton]]
|
||||
[[bulirsch_stoer_dense_out]]
|
||||
[[bulirsch_stoer]]
|
||||
[[controlled_runge_kutta]]
|
||||
[[dense_output_runge_kutta]]
|
||||
[[euler]]
|
||||
[[explicit_error_generic_rk]]
|
||||
[[explicit_generic_rk]]
|
||||
[[rosenbrock4_controller]]
|
||||
[[rosenbrock4_dense_output]]
|
||||
[[rosenbrock4]]
|
||||
[[runge_kutta4_classic]]
|
||||
[[runge_kutta4]]
|
||||
[[runge_kutta_cash_karp54_classic]]
|
||||
[[runge_kutta_cash_karp54]]
|
||||
[[runge_kutta_dopri5]]
|
||||
[[runge_kutta_fehlberg78]]
|
||||
[[symplectic_euler]]
|
||||
[[symplectic_rkn_sb3a_mclachlan]]
|
||||
]
|
||||
|
||||
[table Algebra supporting Boost.Range
|
||||
[[algebra]]
|
||||
[[range_algebra]]
|
||||
[[thrust_algebra]]
|
||||
]
|
||||
Loading…
x
Reference in New Issue
Block a user