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60<div class="contents">
61<h1>Numerical Integration<br>
62<small>
63[<a class="el" href="group__math.html">Auxiliary math functions</a>]</small>
64</h1>Numerical integration routines. 
65<a href="#_details">More...</a>
66<p>
67<table border="0" cellpadding="0" cellspacing="0">
68<tr><td></td></tr>
69<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__integration.html#g680b7d0ff7b4fe8bad1a5524a54b2f33">itpp::quad</a> (double(*f)(double), double a, double b, double tol)</td></tr>
71
72<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="group__integration.html#gccd3a6ad5542f171411339b37b4a0fae">itpp::quadl</a> (double(*f)(double), double a, double b, double tol)</td></tr>
73
74</table>
75<hr><a name="_details"></a><h2>Detailed Description</h2>
76Numerical integration routines. <hr><h2>Function Documentation</h2>
77<a class="anchor" name="g680b7d0ff7b4fe8bad1a5524a54b2f33"></a><!-- doxytag: member="itpp::quad" ref="g680b7d0ff7b4fe8bad1a5524a54b2f33" args="(double(*f)(double), double a, double b, double tol)" -->
78<div class="memitem">
79<div class="memproto">
80      <table class="memname">
81        <tr>
82          <td class="memname">double itpp::quad           </td>
83          <td>(</td>
84          <td class="paramtype">double(*)(double)&nbsp;</td>
85          <td class="paramname"> <em>f</em>, </td>
86        </tr>
87        <tr>
88          <td class="paramkey"></td>
89          <td></td>
90          <td class="paramtype">double&nbsp;</td>
91          <td class="paramname"> <em>a</em>, </td>
92        </tr>
93        <tr>
94          <td class="paramkey"></td>
95          <td></td>
96          <td class="paramtype">double&nbsp;</td>
97          <td class="paramname"> <em>b</em>, </td>
98        </tr>
99        <tr>
100          <td class="paramkey"></td>
101          <td></td>
102          <td class="paramtype">double&nbsp;</td>
103          <td class="paramname"> <em>tol</em> = <code>std::numeric_limits&lt;&nbsp;double&nbsp;&gt;::epsilon()</code></td><td>&nbsp;</td>
104        </tr>
105        <tr>
106          <td></td>
107          <td>)</td>
108          <td></td><td></td><td></td>
109        </tr>
110      </table>
111</div>
112<div class="memdoc">
113
114<p>
1151-dimensional numerical Simpson quadrature integration<p>
116Calculate the 1-dimensional integral <p class="formulaDsp">
117<img class="formulaDsp" alt="\[ \int_a^b f(x) dx \]" src="form_183.png">
118<p>
119<p>
120Uses an adaptive Simpson quadrature method. See [Gander] for more details. The integrand is specified as a function <div class="fragment"><pre class="fragment"> <span class="keywordtype">double</span>
121  f(<span class="keywordtype">double</span>)
122</pre></div>.<p>
123Example: <div class="fragment"><pre class="fragment"><span class="preprocessor">  #include "<a class="code" href="itbase_8h.html" title="Include file for the IT++ base module.">itpp/itbase.h</a>"</span>
124
125  <span class="keywordtype">double</span> f(<span class="keyword">const</span> <span class="keywordtype">double</span> x)
126  {
127    <span class="keywordflow">return</span> x*<a class="code" href="group__logexpfunc.html#g60e39caa21db1b5f9f6006cf7508fbcb" title="The natural logarithm of the elements.">log</a>(x);
128  }
129
130  <span class="keywordtype">int</span> main()
131  {
132    <span class="keywordtype">double</span> res = <a class="code" href="group__integration.html#g680b7d0ff7b4fe8bad1a5524a54b2f33">quad</a>( f, 1.5, 3.5);
133    cout &lt;&lt; <span class="stringliteral">"res = "</span> &lt;&lt; res &lt;&lt; endl;
134
135    <span class="keywordflow">return</span> 0;
136  }
137</pre></div><p>
138References:<p>
139[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at <a href="http://www.inf.ethz.ch/personal/gander.">http://www.inf.ethz.ch/personal/gander.</a> 
140<p>References <a class="el" href="matfunc_8h-source.html#l00077">itpp::sum()</a>.</p>
141
142</div>
143</div><p>
144<a class="anchor" name="gccd3a6ad5542f171411339b37b4a0fae"></a><!-- doxytag: member="itpp::quadl" ref="gccd3a6ad5542f171411339b37b4a0fae" args="(double(*f)(double), double a, double b, double tol)" -->
145<div class="memitem">
146<div class="memproto">
147      <table class="memname">
148        <tr>
149          <td class="memname">double itpp::quadl           </td>
150          <td>(</td>
151          <td class="paramtype">double(*)(double)&nbsp;</td>
152          <td class="paramname"> <em>f</em>, </td>
153        </tr>
154        <tr>
155          <td class="paramkey"></td>
156          <td></td>
157          <td class="paramtype">double&nbsp;</td>
158          <td class="paramname"> <em>a</em>, </td>
159        </tr>
160        <tr>
161          <td class="paramkey"></td>
162          <td></td>
163          <td class="paramtype">double&nbsp;</td>
164          <td class="paramname"> <em>b</em>, </td>
165        </tr>
166        <tr>
167          <td class="paramkey"></td>
168          <td></td>
169          <td class="paramtype">double&nbsp;</td>
170          <td class="paramname"> <em>tol</em> = <code>std::numeric_limits&lt;&nbsp;double&nbsp;&gt;::epsilon()</code></td><td>&nbsp;</td>
171        </tr>
172        <tr>
173          <td></td>
174          <td>)</td>
175          <td></td><td></td><td></td>
176        </tr>
177      </table>
178</div>
179<div class="memdoc">
180
181<p>
1821-dimensional numerical adaptive Lobatto quadrature integration<p>
183Calculate the 1-dimensional integral <p class="formulaDsp">
184<img class="formulaDsp" alt="\[ \int_a^b f(x) dx \]" src="form_183.png">
185<p>
186<p>
187Uses an adaptive Lobatto quadrature method. See [Gander] for more details. The integrand is specified as a function <div class="fragment"><pre class="fragment"> <span class="keywordtype">double</span>
188  f(<span class="keywordtype">double</span>)
189</pre></div>.<p>
190Example: <div class="fragment"><pre class="fragment"><span class="preprocessor">  #include "<a class="code" href="itbase_8h.html" title="Include file for the IT++ base module.">itpp/itbase.h</a>"</span>
191
192  <span class="keywordtype">double</span> f(<span class="keyword">const</span> <span class="keywordtype">double</span> x)
193  {
194    <span class="keywordflow">return</span> x*<a class="code" href="group__logexpfunc.html#g60e39caa21db1b5f9f6006cf7508fbcb" title="The natural logarithm of the elements.">log</a>(x);
195  }
196
197  <span class="keywordtype">int</span> main()
198  {
199    <span class="keywordtype">double</span> res = <a class="code" href="group__integration.html#gccd3a6ad5542f171411339b37b4a0fae">quadl</a>( f, 1.5, 3.5);
200    cout &lt;&lt; <span class="stringliteral">"res = "</span> &lt;&lt; res &lt;&lt; endl;
201
202    <span class="keywordflow">return</span> 0;
203  }
204</pre></div><p>
205References:<p>
206[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at <a href="http://">http://</a> www.inf.ethz.ch/personal/gander.
207<p>References <a class="el" href="fix__functions_8cpp-source.html#l00076">itpp::abs()</a>, <a class="el" href="elem__math_8h-source.html#l00089">itpp::sign()</a>, and <a class="el" href="elem__math_8h-source.html#l00126">itpp::sqrt()</a>.</p>
208
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