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<html><head><title>dlib C++ Library - custom_trainer_ex.cpp</title></head><body bgcolor='white'><pre> |
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<font color='#009900'>// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt |
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</font><font color='#009900'>/* |
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This example program shows you how to create your own custom binary classification |
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trainer object and use it with the multiclass classification tools in the dlib C++ |
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library. This example assumes you have already become familiar with the concepts |
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introduced in the <a href="multiclass_classification_ex.cpp.html">multiclass_classification_ex.cpp</a> example program. |
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In this example we will create a very simple trainer object that takes a binary |
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classification problem and produces a decision rule which says a test point has the |
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same class as whichever centroid it is closest to. |
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The multiclass training dataset will consist of four classes. Each class will be a blob |
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of points in one of the quadrants of the cartesian plane. For fun, we will use |
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std::string labels and therefore the labels of these classes will be the following: |
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"upper_left", |
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"upper_right", |
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"lower_left", |
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"lower_right" |
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*/</font> |
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<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>dlib<font color='#5555FF'>/</font>svm_threaded.h<font color='#5555FF'>></font> |
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<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>iostream<font color='#5555FF'>></font> |
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<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>vector<font color='#5555FF'>></font> |
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<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>dlib<font color='#5555FF'>/</font>rand.h<font color='#5555FF'>></font> |
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<font color='#0000FF'>using</font> <font color='#0000FF'>namespace</font> std; |
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<font color='#0000FF'>using</font> <font color='#0000FF'>namespace</font> dlib; |
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<font color='#009900'>// Our data will be 2-dimensional data. So declare an appropriate type to contain these points. |
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</font><font color='#0000FF'>typedef</font> matrix<font color='#5555FF'><</font><font color='#0000FF'><u>double</u></font>,<font color='#979000'>2</font>,<font color='#979000'>1</font><font color='#5555FF'>></font> sample_type; |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>struct</font> <b><a name='custom_decision_function'></a>custom_decision_function</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This object is the representation of our binary decision rule. |
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!*/</font> |
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<font color='#009900'>// centers of the two classes |
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</font> sample_type positive_center, negative_center; |
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<font color='#0000FF'><u>double</u></font> <b><a name='operator'></a>operator</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> sample_type<font color='#5555FF'>&</font> x |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font> |
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<b>{</b> |
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<font color='#009900'>// if x is closer to the positive class then return +1 |
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</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#BB00BB'>length</font><font face='Lucida Console'>(</font>positive_center <font color='#5555FF'>-</font> x<font face='Lucida Console'>)</font> <font color='#5555FF'><</font> <font color='#BB00BB'>length</font><font face='Lucida Console'>(</font>negative_center <font color='#5555FF'>-</font> x<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font> |
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<font color='#0000FF'>return</font> <font color='#5555FF'>+</font><font color='#979000'>1</font>; |
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<font color='#0000FF'>else</font> |
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<font color='#0000FF'>return</font> <font color='#5555FF'>-</font><font color='#979000'>1</font>; |
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<b>}</b> |
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<b>}</b>; |
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<font color='#009900'>// Later on in this example we will save our decision functions to disk. This |
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</font><font color='#009900'>// pair of routines is needed for this functionality. |
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</font><font color='#0000FF'><u>void</u></font> <b><a name='serialize'></a>serialize</b> <font face='Lucida Console'>(</font><font color='#0000FF'>const</font> custom_decision_function<font color='#5555FF'>&</font> item, std::ostream<font color='#5555FF'>&</font> out<font face='Lucida Console'>)</font> |
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<b>{</b> |
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<font color='#009900'>// write the state of item to the output stream |
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</font> <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.positive_center, out<font face='Lucida Console'>)</font>; |
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<font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>item.negative_center, out<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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<font color='#0000FF'><u>void</u></font> <b><a name='deserialize'></a>deserialize</b> <font face='Lucida Console'>(</font>custom_decision_function<font color='#5555FF'>&</font> item, std::istream<font color='#5555FF'>&</font> in<font face='Lucida Console'>)</font> |
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<b>{</b> |
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<font color='#009900'>// read the data from the input stream and store it in item |
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</font> <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.positive_center, in<font face='Lucida Console'>)</font>; |
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<font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>item.negative_center, in<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'>class</font> <b><a name='simple_custom_trainer'></a>simple_custom_trainer</b> |
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<b>{</b> |
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<font color='#009900'>/*! |
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WHAT THIS OBJECT REPRESENTS |
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This is our example custom binary classifier trainer object. It simply |
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computes the means of the +1 and -1 classes, puts them into our |
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custom_decision_function, and returns the results. |
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Below we define the train() function. I have also included the |
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requires/ensures definition for a generic binary classifier's train() |
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!*/</font> |
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<font color='#0000FF'>public</font>: |
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custom_decision_function <b><a name='train'></a>train</b> <font face='Lucida Console'>(</font> |
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<font color='#0000FF'>const</font> std::vector<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> samples, |
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<font color='#0000FF'>const</font> std::vector<font color='#5555FF'><</font><font color='#0000FF'><u>double</u></font><font color='#5555FF'>></font><font color='#5555FF'>&</font> labels |
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<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font> |
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<font color='#009900'>/*! |
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requires |
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- is_binary_classification_problem(samples, labels) == true |
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(e.g. labels consists of only +1 and -1 values, samples.size() == labels.size()) |
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ensures |
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- returns a decision function F with the following properties: |
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- if (new_x is a sample predicted have +1 label) then |
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- F(new_x) >= 0 |
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- else |
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- F(new_x) < 0 |
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!*/</font> |
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<b>{</b> |
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sample_type positive_center, negative_center; |
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<font color='#009900'>// compute sums of each class |
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</font> positive_center <font color='#5555FF'>=</font> <font color='#979000'>0</font>; |
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negative_center <font color='#5555FF'>=</font> <font color='#979000'>0</font>; |
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<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> samples.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font> |
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<b>{</b> |
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<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>labels[i] <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#5555FF'>+</font><font color='#979000'>1</font><font face='Lucida Console'>)</font> |
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positive_center <font color='#5555FF'>+</font><font color='#5555FF'>=</font> samples[i]; |
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<font color='#0000FF'>else</font> <font color='#009900'>// this is a -1 sample |
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</font> negative_center <font color='#5555FF'>+</font><font color='#5555FF'>=</font> samples[i]; |
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<b>}</b> |
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<font color='#009900'>// divide by number of +1 samples |
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</font> positive_center <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#BB00BB'>sum</font><font face='Lucida Console'>(</font><font color='#BB00BB'>mat</font><font face='Lucida Console'>(</font>labels<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#5555FF'>+</font><font color='#979000'>1</font><font face='Lucida Console'>)</font>; |
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<font color='#009900'>// divide by number of -1 samples |
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</font> negative_center <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#BB00BB'>sum</font><font face='Lucida Console'>(</font><font color='#BB00BB'>mat</font><font face='Lucida Console'>(</font>labels<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#5555FF'>-</font><font color='#979000'>1</font><font face='Lucida Console'>)</font>; |
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custom_decision_function df; |
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df.positive_center <font color='#5555FF'>=</font> positive_center; |
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df.negative_center <font color='#5555FF'>=</font> negative_center; |
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<font color='#0000FF'>return</font> df; |
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<b>}</b> |
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<b>}</b>; |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'><u>void</u></font> <b><a name='generate_data'></a>generate_data</b> <font face='Lucida Console'>(</font> |
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std::vector<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> samples, |
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std::vector<font color='#5555FF'><</font>string<font color='#5555FF'>></font><font color='#5555FF'>&</font> labels |
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<font face='Lucida Console'>)</font>; |
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<font color='#009900'>/*! |
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ensures |
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- make some four class data as described above. |
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- each class will have 50 samples in it |
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!*/</font> |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'><u>int</u></font> <b><a name='main'></a>main</b><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> |
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<b>{</b> |
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std::vector<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font> samples; |
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std::vector<font color='#5555FF'><</font>string<font color='#5555FF'>></font> labels; |
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<font color='#009900'>// First, get our labeled set of training data |
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</font> <font color='#BB00BB'>generate_data</font><font face='Lucida Console'>(</font>samples, labels<font face='Lucida Console'>)</font>; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>samples.size(): </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> samples.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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<font color='#009900'>// Define the trainer we will use. The second template argument specifies the type |
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</font> <font color='#009900'>// of label used, which is string in this case. |
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</font> <font color='#0000FF'>typedef</font> one_vs_one_trainer<font color='#5555FF'><</font>any_trainer<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font>, string<font color='#5555FF'>></font> ovo_trainer; |
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ovo_trainer trainer; |
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<font color='#009900'>// Now tell the one_vs_one_trainer that, by default, it should use the simple_custom_trainer |
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</font> <font color='#009900'>// to solve the individual binary classification subproblems. |
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</font> trainer.<font color='#BB00BB'>set_trainer</font><font face='Lucida Console'>(</font><font color='#BB00BB'>simple_custom_trainer</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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<font color='#009900'>// Next, to make things a little more interesting, we will setup the one_vs_one_trainer |
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</font> <font color='#009900'>// to use kernel ridge regression to solve the upper_left vs lower_right binary classification |
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</font> <font color='#009900'>// subproblem. |
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</font> <font color='#0000FF'>typedef</font> radial_basis_kernel<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font> rbf_kernel; |
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krr_trainer<font color='#5555FF'><</font>rbf_kernel<font color='#5555FF'>></font> rbf_trainer; |
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rbf_trainer.<font color='#BB00BB'>set_kernel</font><font face='Lucida Console'>(</font><font color='#BB00BB'>rbf_kernel</font><font face='Lucida Console'>(</font><font color='#979000'>0.1</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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trainer.<font color='#BB00BB'>set_trainer</font><font face='Lucida Console'>(</font>rbf_trainer, "<font color='#CC0000'>upper_left</font>", "<font color='#CC0000'>lower_right</font>"<font face='Lucida Console'>)</font>; |
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<font color='#009900'>// Now let's do 5-fold cross-validation using the one_vs_one_trainer we just setup. |
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</font> <font color='#009900'>// As an aside, always shuffle the order of the samples before doing cross validation. |
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</font> <font color='#009900'>// For a discussion of why this is a good idea see the <a href="svm_ex.cpp.html">svm_ex.cpp</a> example. |
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</font> <font color='#BB00BB'>randomize_samples</font><font face='Lucida Console'>(</font>samples, labels<font face='Lucida Console'>)</font>; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>cross validation: \n</font>" <font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>cross_validate_multiclass_trainer</font><font face='Lucida Console'>(</font>trainer, samples, labels, <font color='#979000'>5</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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<font color='#009900'>// This dataset is very easy and everything is correctly classified. Therefore, the output of |
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</font> <font color='#009900'>// cross validation is the following confusion matrix. |
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</font> <font color='#009900'>/* |
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50 0 0 0 |
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0 50 0 0 |
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0 0 50 0 |
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0 0 0 50 |
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*/</font> |
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<font color='#009900'>// We can also obtain the decision rule as always. |
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</font> one_vs_one_decision_function<font color='#5555FF'><</font>ovo_trainer<font color='#5555FF'>></font> df <font color='#5555FF'>=</font> trainer.<font color='#BB00BB'>train</font><font face='Lucida Console'>(</font>samples, labels<font face='Lucida Console'>)</font>; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>predicted label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>df</font><font face='Lucida Console'>(</font>samples[<font color='#979000'>0</font>]<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>, true label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> labels[<font color='#979000'>0</font>] <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>predicted label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>df</font><font face='Lucida Console'>(</font>samples[<font color='#979000'>90</font>]<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>, true label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> labels[<font color='#979000'>90</font>] <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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<font color='#009900'>// The output is: |
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</font> <font color='#009900'>/* |
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predicted label: upper_right, true label: upper_right |
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predicted label: lower_left, true label: lower_left |
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*/</font> |
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<font color='#009900'>// Finally, let's save our multiclass decision rule to disk. Remember that we have |
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</font> <font color='#009900'>// to specify the types of binary decision function used inside the one_vs_one_decision_function. |
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</font> one_vs_one_decision_function<font color='#5555FF'><</font>ovo_trainer, |
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custom_decision_function, <font color='#009900'>// This is the output of the simple_custom_trainer |
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</font> decision_function<font color='#5555FF'><</font>radial_basis_kernel<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font> <font color='#5555FF'>></font> <font color='#009900'>// This is the output of the rbf_trainer |
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</font> <font color='#5555FF'>></font> df2, df3; |
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df2 <font color='#5555FF'>=</font> df; |
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<font color='#009900'>// save to a file called df.dat |
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</font> <font color='#BB00BB'>serialize</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>df.dat</font>"<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> df2; |
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<font color='#009900'>// load the function back in from disk and store it in df3. |
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</font> <font color='#BB00BB'>deserialize</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>df.dat</font>"<font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>></font> df3; |
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<font color='#009900'>// Test df3 to see that this worked. |
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</font> cout <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>predicted label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>df3</font><font face='Lucida Console'>(</font>samples[<font color='#979000'>0</font>]<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>, true label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> labels[<font color='#979000'>0</font>] <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>predicted label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>df3</font><font face='Lucida Console'>(</font>samples[<font color='#979000'>90</font>]<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>, true label: </font>"<font color='#5555FF'><</font><font color='#5555FF'><</font> labels[<font color='#979000'>90</font>] <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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<font color='#009900'>// Test df3 on the samples and labels and print the confusion matrix. |
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</font> cout <font color='#5555FF'><</font><font color='#5555FF'><</font> "<font color='#CC0000'>test deserialized function: \n</font>" <font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#BB00BB'>test_multiclass_decision_function</font><font face='Lucida Console'>(</font>df3, samples, labels<font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> endl; |
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<b>}</b> |
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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<font color='#0000FF'><u>void</u></font> <b><a name='generate_data'></a>generate_data</b> <font face='Lucida Console'>(</font> |
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std::vector<font color='#5555FF'><</font>sample_type<font color='#5555FF'>></font><font color='#5555FF'>&</font> samples, |
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std::vector<font color='#5555FF'><</font>string<font color='#5555FF'>></font><font color='#5555FF'>&</font> labels |
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<font face='Lucida Console'>)</font> |
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<b>{</b> |
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<font color='#0000FF'>const</font> <font color='#0000FF'><u>long</u></font> num <font color='#5555FF'>=</font> <font color='#979000'>50</font>; |
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sample_type m; |
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dlib::rand rnd; |
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<font color='#009900'>// add some points in the upper right quadrant |
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</font> m <font color='#5555FF'>=</font> <font color='#979000'>10</font>, <font color='#979000'>10</font>; |
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<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> num; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font> |
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<b>{</b> |
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samples.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>m <font color='#5555FF'>+</font> <font color='#BB00BB'>randm</font><font face='Lucida Console'>(</font><font color='#979000'>2</font>,<font color='#979000'>1</font>,rnd<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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labels.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>upper_right</font>"<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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<font color='#009900'>// add some points in the upper left quadrant |
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</font> m <font color='#5555FF'>=</font> <font color='#5555FF'>-</font><font color='#979000'>10</font>, <font color='#979000'>10</font>; |
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<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> num; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font> |
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<b>{</b> |
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samples.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>m <font color='#5555FF'>+</font> <font color='#BB00BB'>randm</font><font face='Lucida Console'>(</font><font color='#979000'>2</font>,<font color='#979000'>1</font>,rnd<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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labels.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>upper_left</font>"<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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|
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<font color='#009900'>// add some points in the lower right quadrant |
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</font> m <font color='#5555FF'>=</font> <font color='#979000'>10</font>, <font color='#5555FF'>-</font><font color='#979000'>10</font>; |
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<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> num; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font> |
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<b>{</b> |
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samples.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>m <font color='#5555FF'>+</font> <font color='#BB00BB'>randm</font><font face='Lucida Console'>(</font><font color='#979000'>2</font>,<font color='#979000'>1</font>,rnd<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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labels.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>lower_right</font>"<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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|
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<font color='#009900'>// add some points in the lower left quadrant |
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</font> m <font color='#5555FF'>=</font> <font color='#5555FF'>-</font><font color='#979000'>10</font>, <font color='#5555FF'>-</font><font color='#979000'>10</font>; |
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<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> num; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font> |
|
<b>{</b> |
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samples.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>m <font color='#5555FF'>+</font> <font color='#BB00BB'>randm</font><font face='Lucida Console'>(</font><font color='#979000'>2</font>,<font color='#979000'>1</font>,rnd<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>; |
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labels.<font color='#BB00BB'>push_back</font><font face='Lucida Console'>(</font>"<font color='#CC0000'>lower_left</font>"<font face='Lucida Console'>)</font>; |
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<b>}</b> |
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|
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<b>}</b> |
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|
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<font color='#009900'>// ---------------------------------------------------------------------------------------- |
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</font> |
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</pre></body></html> |
