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67  <div class="navpath"><b>itpp</b>::<a class="el" href="classitpp_1_1Newton__Search.html">Newton_Search</a>
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70<div class="contents">
71<h1>itpp::Newton_Search Class Reference<br>
72<small>
73[<a class="el" href="group__optimization.html">Numerical Optimization Module</a>]</small>
74</h1><!-- doxytag: class="itpp::Newton_Search" -->Newton Search. 
75<a href="#_details">More...</a>
76<p>
77<code>#include &lt;<a class="el" href="newton__search_8h-source.html">newton_search.h</a>&gt;</code>
78<p>
79
80<p>
81<a href="classitpp_1_1Newton__Search-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
82<tr><td></td></tr>
83<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f2558289b4da03e0b56224fb51e4b0f1"></a><!-- doxytag: member="itpp::Newton_Search::Newton_Search" ref="f2558289b4da03e0b56224fb51e4b0f1" args="()" -->
85&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#f2558289b4da03e0b56224fb51e4b0f1">Newton_Search</a> ()</td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="698fd6b5b775b94774550a337824fabd"></a><!-- doxytag: member="itpp::Newton_Search::~Newton_Search" ref="698fd6b5b775b94774550a337824fabd" args="()" -->
89&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#698fd6b5b775b94774550a337824fabd">~Newton_Search</a> ()</td></tr>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Destructor. <br></td></tr>
92<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ac5225964563fc602de7be9ab613eda8"></a><!-- doxytag: member="itpp::Newton_Search::set_function" ref="ac5225964563fc602de7be9ab613eda8" args="(double(*function)(const vec &amp;))" -->
93void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#ac5225964563fc602de7be9ab613eda8">set_function</a> (double(*function)(const vec &amp;))</td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set function pointer. <br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8f419c7b3b2519fb4bf75cec80083855"></a><!-- doxytag: member="itpp::Newton_Search::set_gradient" ref="8f419c7b3b2519fb4bf75cec80083855" args="(vec(*gradient)(const vec &amp;))" -->
97void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#8f419c7b3b2519fb4bf75cec80083855">set_gradient</a> (vec(*gradient)(const vec &amp;))</td></tr>
98
99<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set gradient function pointer. <br></td></tr>
100<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b237075fd274ed916bdeb062f9fdc035"></a><!-- doxytag: member="itpp::Newton_Search::set_functions" ref="b237075fd274ed916bdeb062f9fdc035" args="(double(*function)(const vec &amp;), vec(*gradient)(const vec &amp;))" -->
101void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#b237075fd274ed916bdeb062f9fdc035">set_functions</a> (double(*function)(const vec &amp;), vec(*gradient)(const vec &amp;))</td></tr>
102
103<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set both function and gradient function pointers. <br></td></tr>
104<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cc2e96363cadcc4b0710f3501a7896d7"></a><!-- doxytag: member="itpp::Newton_Search::set_start_point" ref="cc2e96363cadcc4b0710f3501a7896d7" args="(const vec &amp;x, const mat &amp;D)" -->
105void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#cc2e96363cadcc4b0710f3501a7896d7">set_start_point</a> (const vec &amp;x, const mat &amp;D)</td></tr>
106
107<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set start point <code>x</code> for search and approx inverse Hessian at <code>x</code>. <br></td></tr>
108<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="02eb78847956e69fff2017510e37e11a"></a><!-- doxytag: member="itpp::Newton_Search::set_start_point" ref="02eb78847956e69fff2017510e37e11a" args="(const vec &amp;x)" -->
109void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#02eb78847956e69fff2017510e37e11a">set_start_point</a> (const vec &amp;x)</td></tr>
110
111<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set start point <code>x</code> for search. <br></td></tr>
112<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1bab0c5a4ec62f2c722f54a35c907fa2"></a><!-- doxytag: member="itpp::Newton_Search::get_solution" ref="1bab0c5a4ec62f2c722f54a35c907fa2" args="()" -->
113vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#1bab0c5a4ec62f2c722f54a35c907fa2">get_solution</a> ()</td></tr>
114
115<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Get solution, function value and gradient at solution point. <br></td></tr>
116<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9acde957c070ce24446987d090ec4e9d"></a><!-- doxytag: member="itpp::Newton_Search::search" ref="9acde957c070ce24446987d090ec4e9d" args="()" -->
117bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#9acde957c070ce24446987d090ec4e9d">search</a> ()</td></tr>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Do the line search. <br></td></tr>
120<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bd9426e757961f4521e43c7f7e140234"></a><!-- doxytag: member="itpp::Newton_Search::search" ref="bd9426e757961f4521e43c7f7e140234" args="(vec &amp;xn)" -->
121bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#bd9426e757961f4521e43c7f7e140234">search</a> (vec &amp;xn)</td></tr>
122
123<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Do the line search and return solution. <br></td></tr>
124<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="342ec7ca94c9c4130ac4e9a1ce77868f"></a><!-- doxytag: member="itpp::Newton_Search::search" ref="342ec7ca94c9c4130ac4e9a1ce77868f" args="(const vec &amp;x0, vec &amp;xn)" -->
125bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#342ec7ca94c9c4130ac4e9a1ce77868f">search</a> (const vec &amp;x0, vec &amp;xn)</td></tr>
126
127<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set starting point, do the Newton search, and return the solution. <br></td></tr>
128<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3732a9d0458c01cf1fad6c4e1eb07dd0"></a><!-- doxytag: member="itpp::Newton_Search::set_stop_values" ref="3732a9d0458c01cf1fad6c4e1eb07dd0" args="(double epsilon_1, double epsilon_2)" -->
129void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#3732a9d0458c01cf1fad6c4e1eb07dd0">set_stop_values</a> (double epsilon_1, double epsilon_2)</td></tr>
130
131<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set stop criterion values. <br></td></tr>
132<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3e3ec46a1ef6e157c6621dbe0292ab1e"></a><!-- doxytag: member="itpp::Newton_Search::get_epsilon_1" ref="3e3ec46a1ef6e157c6621dbe0292ab1e" args="()" -->
133double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#3e3ec46a1ef6e157c6621dbe0292ab1e">get_epsilon_1</a> ()</td></tr>
134
135<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return stop value rho. <br></td></tr>
136<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f5ce0562ea68754325e8a0b5dc257b91"></a><!-- doxytag: member="itpp::Newton_Search::get_epsilon_2" ref="f5ce0562ea68754325e8a0b5dc257b91" args="()" -->
137double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#f5ce0562ea68754325e8a0b5dc257b91">get_epsilon_2</a> ()</td></tr>
138
139<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return stop value beta. <br></td></tr>
140<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bed2b41f7515870ea5a60b456d925994"></a><!-- doxytag: member="itpp::Newton_Search::set_max_evaluations" ref="bed2b41f7515870ea5a60b456d925994" args="(int value)" -->
141void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#bed2b41f7515870ea5a60b456d925994">set_max_evaluations</a> (int value)</td></tr>
142
143<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set max number of function evaluations. <br></td></tr>
144<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e154713ed00af54e524b393e0dce10a3"></a><!-- doxytag: member="itpp::Newton_Search::get_max_evaluations" ref="e154713ed00af54e524b393e0dce10a3" args="()" -->
145int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#e154713ed00af54e524b393e0dce10a3">get_max_evaluations</a> ()</td></tr>
146
147<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return max number of function evaluations. <br></td></tr>
148<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9f74486ed06013efdf91912889e4041b"></a><!-- doxytag: member="itpp::Newton_Search::set_initial_stepsize" ref="9f74486ed06013efdf91912889e4041b" args="(double value)" -->
149void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#9f74486ed06013efdf91912889e4041b">set_initial_stepsize</a> (double value)</td></tr>
150
151<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set max stepsize. <br></td></tr>
152<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="953f157baee161ac6363f9aedccb539b"></a><!-- doxytag: member="itpp::Newton_Search::get_initial_stepsize" ref="953f157baee161ac6363f9aedccb539b" args="()" -->
153double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#953f157baee161ac6363f9aedccb539b">get_initial_stepsize</a> ()</td></tr>
154
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return max number of iterations. <br></td></tr>
156<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e508c4bfde1556e6a183c4ee61a2c5d4"></a><!-- doxytag: member="itpp::Newton_Search::set_method" ref="e508c4bfde1556e6a183c4ee61a2c5d4" args="(const Newton_Search_Method &amp;method)" -->
157void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#e508c4bfde1556e6a183c4ee61a2c5d4">set_method</a> (const <a class="el" href="group__optimization.html#g08746316b0b24694973fcb008de0f0e1">Newton_Search_Method</a> &amp;method)</td></tr>
158
159<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set Line search method. <br></td></tr>
160<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d7721f4ee34e9ea9d74736282c7d0dd3"></a><!-- doxytag: member="itpp::Newton_Search::get_function_value" ref="d7721f4ee34e9ea9d74736282c7d0dd3" args="()" -->
161double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#d7721f4ee34e9ea9d74736282c7d0dd3">get_function_value</a> ()</td></tr>
162
163<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get function value at solution point <br></td></tr>
164<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4262b2ebee6b2268d843c45e8cd920e5"></a><!-- doxytag: member="itpp::Newton_Search::get_stop_1" ref="4262b2ebee6b2268d843c45e8cd920e5" args="()" -->
165double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#4262b2ebee6b2268d843c45e8cd920e5">get_stop_1</a> ()</td></tr>
166
167<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get value of stop criterion 1 at solution point <br></td></tr>
168<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="581044cdd13ab388366c6d3ec058b206"></a><!-- doxytag: member="itpp::Newton_Search::get_stop_2" ref="581044cdd13ab388366c6d3ec058b206" args="()" -->
169double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#581044cdd13ab388366c6d3ec058b206">get_stop_2</a> ()</td></tr>
170
171<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get value of stop criterion 2 at solution point <br></td></tr>
172<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d7b4a84ea4fadfadab8cde97cc8bd7c0"></a><!-- doxytag: member="itpp::Newton_Search::get_no_iterations" ref="d7b4a84ea4fadfadab8cde97cc8bd7c0" args="()" -->
173int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#d7b4a84ea4fadfadab8cde97cc8bd7c0">get_no_iterations</a> ()</td></tr>
174
175<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get number of iterations used to reach solution <br></td></tr>
176<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f0016598b0356150f72c250d29541f17"></a><!-- doxytag: member="itpp::Newton_Search::get_no_function_evaluations" ref="f0016598b0356150f72c250d29541f17" args="()" -->
177int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#f0016598b0356150f72c250d29541f17">get_no_function_evaluations</a> ()</td></tr>
178
179<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get number of function evaluations used to reach solution <br></td></tr>
180<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d1d1d137bab656d6e5ef827d640bcd7f"></a><!-- doxytag: member="itpp::Newton_Search::enable_trace" ref="d1d1d137bab656d6e5ef827d640bcd7f" args="()" -->
181void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#d1d1d137bab656d6e5ef827d640bcd7f">enable_trace</a> ()</td></tr>
182
183<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">enable trace mode <br></td></tr>
184<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af99928a904021ea7708f4093bb862df"></a><!-- doxytag: member="itpp::Newton_Search::disable_trace" ref="af99928a904021ea7708f4093bb862df" args="()" -->
185void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#af99928a904021ea7708f4093bb862df">disable_trace</a> ()</td></tr>
186
187<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">disable trace <br></td></tr>
188<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classitpp_1_1Newton__Search.html#6c13a367616b02e22d152cd26cade4a3">get_trace</a> (<a class="el" href="classitpp_1_1Array.html">Array</a>&lt; vec &gt; &amp;xvalues, vec &amp;Fvalues, vec &amp;ngvalues, vec &amp;dvalues)</td></tr>
189
190</table>
191<hr><a name="_details"></a><h2>Detailed Description</h2>
192Newton Search.
193<p>
194Newton or Quasi-Newton optimization method that try to minimize the objective function <img class="formulaInl" alt="$f(\mathbf{x})$" src="form_323.png"> given an initial guess <img class="formulaInl" alt="$\mathbf{x}$" src="form_324.png">.<p>
195The search is stopped when either criterion 1: <p class="formulaDsp">
196<img class="formulaDsp" alt="\[ \left\| \mathbf{f}'(\mathbf{x})\right\|_{\infty} \leq \varepsilon_1 \]" src="form_325.png">
197<p>
198 or criterion 2: <p class="formulaDsp">
199<img class="formulaDsp" alt="\[ \left\| d\mathbf{x}\right\|_{2} \leq \varepsilon_2 (\varepsilon_2 + \| \mathbf{x} \|_{2} ) \]" src="form_326.png">
200<p>
201 is fulfilled. Another possibility is that the search is stopped when the number of function evaluations exceeds a threshold (100 per default).<p>
202The default update rule for the inverse of the Hessian matrix is the BFGS algorithm with <img class="formulaInl" alt="$\varepsilon_1 = 10^{-4}$" src="form_327.png"> an <img class="formulaInl" alt="$\varepsilon_2 = 10^{-8}$" src="form_328.png">. <hr><h2>Member Function Documentation</h2>
203<a class="anchor" name="6c13a367616b02e22d152cd26cade4a3"></a><!-- doxytag: member="itpp::Newton_Search::get_trace" ref="6c13a367616b02e22d152cd26cade4a3" args="(Array&lt; vec &gt; &amp;xvalues, vec &amp;Fvalues, vec &amp;ngvalues, vec &amp;dvalues)" -->
204<div class="memitem">
205<div class="memproto">
206      <table class="memname">
207        <tr>
208          <td class="memname">void itpp::Newton_Search::get_trace           </td>
209          <td>(</td>
210          <td class="paramtype"><a class="el" href="classitpp_1_1Array.html">Array</a>&lt; vec &gt; &amp;&nbsp;</td>
211          <td class="paramname"> <em>xvalues</em>, </td>
212        </tr>
213        <tr>
214          <td class="paramkey"></td>
215          <td></td>
216          <td class="paramtype">vec &amp;&nbsp;</td>
217          <td class="paramname"> <em>Fvalues</em>, </td>
218        </tr>
219        <tr>
220          <td class="paramkey"></td>
221          <td></td>
222          <td class="paramtype">vec &amp;&nbsp;</td>
223          <td class="paramname"> <em>ngvalues</em>, </td>
224        </tr>
225        <tr>
226          <td class="paramkey"></td>
227          <td></td>
228          <td class="paramtype">vec &amp;&nbsp;</td>
229          <td class="paramname"> <em>dvalues</em></td><td>&nbsp;</td>
230        </tr>
231        <tr>
232          <td></td>
233          <td>)</td>
234          <td></td><td></td><td></td>
235        </tr>
236      </table>
237</div>
238<div class="memdoc">
239
240<p>
241get trace outputs <code>xvalues</code> are the solutions of every iteration <code>Fvalues</code> are the function values <code>ngvalues</code> are the norm(gradient,inf) values <code>dvalues</code> are the delta values
242<p>References <a class="el" href="itassert_8h-source.html#l00173">it_warning</a>.</p>
243
244</div>
245</div><p>
246<hr>The documentation for this class was generated from the following files:<ul>
247<li><a class="el" href="newton__search_8h-source.html">newton_search.h</a><li><a class="el" href="newton__search_8cpp.html">newton_search.cpp</a></ul>
248</div>
249<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jun 2 10:02:19 2009 for mixpp by&nbsp;
250<a href="http://www.doxygen.org/index.html">
251<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.8 </small></address>
252</body>
253</html>
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