1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Dense Output Stepper</title> 5<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint"> 8<link rel="up" href="../concepts.html" title="Concepts"> 9<link rel="prev" href="controlled_stepper.html" title="Controlled Stepper"> 10<link rel="next" href="state_algebra_operations.html" title="State Algebra Operations"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="boost_numeric_odeint.concepts.dense_output_stepper"></a><a class="link" href="dense_output_stepper.html" title="Dense Output Stepper">Dense 28 Output Stepper</a> 29</h3></div></div></div> 30<p> 31 This concept specifies the interface a dense output stepper has to fulfill 32 to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate 33 functions</a>. 34 </p> 35<h5> 36<a name="boost_numeric_odeint.concepts.dense_output_stepper.h0"></a> 37 <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.description"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.description">Description</a> 38 </h5> 39<p> 40 A dense output stepper following this Dense Output Stepper concept provides 41 the possibility to perform a single step of the solution <span class="emphasis"><em>x(t)</em></span> 42 of an ODE to obtain <span class="emphasis"><em>x(t+dt)</em></span>. The step-size <code class="computeroutput"><span class="identifier">dt</span></code> might be adjusted automatically due 43 to error control. Dense output steppers also can interpolate the solution 44 to calculate the state <span class="emphasis"><em>x(t')</em></span> at any point <span class="emphasis"><em>t 45 <= t' <= t+dt</em></span>. 46 </p> 47<h5> 48<a name="boost_numeric_odeint.concepts.dense_output_stepper.h1"></a> 49 <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.associated_types"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.associated_types">Associated 50 types</a> 51 </h5> 52<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 53<li class="listitem"> 54 <p><span class="bold"><strong>state_type</strong></span></p> 55<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p> 56<p>The 57 type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p> 58 </li> 59<li class="listitem"> 60 <p><span class="bold"><strong>deriv_type</strong></span></p> 61<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">deriv_type</span></code></p> 62<p>The 63 type characterizing the derivative of the ODE, hence <span class="emphasis"><em>d x/dt</em></span>.</p> 64 </li> 65<li class="listitem"> 66 <p><span class="bold"><strong>time_type</strong></span></p> 67<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p> 68<p>The 69 type characterizing the dependent variable of the ODE, hence the time 70 <span class="emphasis"><em>t</em></span>.</p> 71 </li> 72<li class="listitem"> 73 <p><span class="bold"><strong>value_type</strong></span></p> 74<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p> 75<p>The 76 numerical data type which is used within the stepper, something like 77 <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>, 78 <code class="computeroutput"><span class="identifier">complex</span><span class="special">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p> 79 </li> 80<li class="listitem"> 81 <p><span class="bold"><strong>stepper_category</strong></span></p> 82<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p> 83<p>A 84 tag type characterizing the category of the stepper. This type must be 85 convertible to <code class="computeroutput"><span class="identifier">dense_output_stepper_tag</span></code>.</p> 86 </li> 87</ul></div> 88<h5> 89<a name="boost_numeric_odeint.concepts.dense_output_stepper.h2"></a> 90 <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.notation"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.notation">Notation</a> 91 </h5> 92<div class="variablelist"> 93<p class="title"><b></b></p> 94<dl class="variablelist"> 95<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span></code></span></dt> 96<dd><p> 97 A type that is a model of Dense Output Stepper 98 </p></dd> 99<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt> 100<dd><p> 101 A type representing the state <span class="emphasis"><em>x</em></span> of the ODE 102 </p></dd> 103<dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt> 104<dd><p> 105 An object of type <code class="computeroutput"><span class="identifier">Stepper</span></code> 106 </p></dd> 107<dt><span class="term"><code class="computeroutput"><span class="identifier">x0</span></code>, <code class="computeroutput"><span class="identifier">x</span></code></span></dt> 108<dd><p> 109 Object of type <code class="computeroutput"><span class="identifier">State</span></code> 110 </p></dd> 111<dt><span class="term"><code class="computeroutput"><span class="identifier">t0</span></code>, <code class="computeroutput"><span class="identifier">dt0</span></code>, <code class="computeroutput"><span class="identifier">t</span></code></span></dt> 112<dd><p> 113 Objects of type <code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code> 114 </p></dd> 115<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt> 116<dd><p> 117 An object defining the ODE, should be a model of <a class="link" href="system.html" title="System">System</a>, 118 <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic 119 System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple 120 Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit 121 System</a>. 122 </p></dd> 123</dl> 124</div> 125<h5> 126<a name="boost_numeric_odeint.concepts.dense_output_stepper.h3"></a> 127 <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.valid_expressions"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.valid_expressions">Valid 128 Expressions</a> 129 </h5> 130<div class="informaltable"><table class="table"> 131<colgroup> 132<col> 133<col> 134<col> 135<col> 136</colgroup> 137<thead><tr> 138<th> 139 <p> 140 Name 141 </p> 142 </th> 143<th> 144 <p> 145 Expression 146 </p> 147 </th> 148<th> 149 <p> 150 Type 151 </p> 152 </th> 153<th> 154 <p> 155 Semantics 156 </p> 157 </th> 158</tr></thead> 159<tbody> 160<tr> 161<td> 162 <p> 163 Initialize integration 164 </p> 165 </td> 166<td> 167 <p> 168 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">initialize</span><span class="special">(</span> 169 <span class="identifier">x0</span> <span class="special">,</span> 170 <span class="identifier">t0</span> <span class="special">,</span> 171 <span class="identifier">dt0</span> <span class="special">)</span></code> 172 </p> 173 </td> 174<td> 175 <p> 176 void 177 </p> 178 </td> 179<td> 180 <p> 181 Initializes the stepper with initial values <code class="computeroutput"><span class="identifier">x0</span></code>, 182 <code class="computeroutput"><span class="identifier">t0</span></code> and <code class="computeroutput"><span class="identifier">dt0</span></code>. 183 </p> 184 </td> 185</tr> 186<tr> 187<td> 188 <p> 189 Do step 190 </p> 191 </td> 192<td> 193 <p> 194 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> 195 <span class="identifier">sys</span> <span class="special">)</span></code> 196 </p> 197 </td> 198<td> 199 <p> 200 <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> 201 <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">,</span> 202 <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code> 203 </p> 204 </td> 205<td> 206 <p> 207 Performs one step using the ODE defined by <code class="computeroutput"><span class="identifier">sys</span></code>. 208 The step-size might be changed internally due to error control. 209 This function returns a pair containing <code class="computeroutput"><span class="identifier">t</span></code> 210 and <code class="computeroutput"><span class="identifier">t</span><span class="special">+</span><span class="identifier">dt</span></code> representing the interval 211 for which interpolation can be performed. 212 </p> 213 </td> 214</tr> 215<tr> 216<td> 217 <p> 218 Do interpolation 219 </p> 220 </td> 221<td> 222 <p> 223 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">calc_state</span><span class="special">(</span> 224 <span class="identifier">t_inter</span> <span class="special">,</span> 225 <span class="identifier">x</span> <span class="special">)</span></code> 226 </p> 227 </td> 228<td> 229 <p> 230 <code class="computeroutput"><span class="keyword">void</span></code> 231 </p> 232 </td> 233<td> 234 <p> 235 Performs the interpolation to calculate /x(t<sub>inter</sub>/) where /t <= 236 t<sub>inter</sub> <= t+dt/. 237 </p> 238 </td> 239</tr> 240<tr> 241<td> 242 <p> 243 Get current time 244 </p> 245 </td> 246<td> 247 <p> 248 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code> 249 </p> 250 </td> 251<td> 252 <p> 253 <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span><span class="special">&</span></code> 254 </p> 255 </td> 256<td> 257 <p> 258 Returns the current time <span class="emphasis"><em>t+dt</em></span> of the stepper, 259 that is the end time of the last step and the starting time for 260 the next call of <code class="computeroutput"><span class="identifier">do_step</span></code> 261 </p> 262 </td> 263</tr> 264<tr> 265<td> 266 <p> 267 Get current state 268 </p> 269 </td> 270<td> 271 <p> 272 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_state</span><span class="special">()</span></code> 273 </p> 274 </td> 275<td> 276 <p> 277 <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span><span class="special">&</span></code> 278 </p> 279 </td> 280<td> 281 <p> 282 Returns the current state of the stepper, that is <span class="emphasis"><em>x(t+dt)</em></span>, 283 the state at the time returned by <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code> 284 </p> 285 </td> 286</tr> 287<tr> 288<td> 289 <p> 290 Get current time step 291 </p> 292 </td> 293<td> 294 <p> 295 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time_step</span><span class="special">()</span></code> 296 </p> 297 </td> 298<td> 299 <p> 300 <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span><span class="special">&</span></code> 301 </p> 302 </td> 303<td> 304 <p> 305 Returns the current step size of the stepper, that is <span class="emphasis"><em>dt</em></span> 306 </p> 307 </td> 308</tr> 309</tbody> 310</table></div> 311<h5> 312<a name="boost_numeric_odeint.concepts.dense_output_stepper.h4"></a> 313 <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.models"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.models">Models</a> 314 </h5> 315<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 316<li class="listitem"> 317 <code class="computeroutput"><span class="identifier">dense_output_controlled_explicit_fsal</span><span class="special"><</span> <span class="identifier">controlled_error_stepper_fsal</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span> 318 <span class="special">></span></code> 319 </li> 320<li class="listitem"> 321 <code class="computeroutput"><span class="identifier">bulirsch_stoer_dense_out</span></code> 322 </li> 323<li class="listitem"> 324 <code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</span></code> 325 </li> 326</ul></div> 327</div> 328<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 329<td align="left"></td> 330<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 331 Distributed under the Boost Software License, Version 1.0. (See accompanying 332 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>) 333 </p> 334</div></td> 335</tr></table> 336<hr> 337<div class="spirit-nav"> 338<a accesskey="p" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 339</div> 340</body> 341</html> 342
