added the krls example

--HG--
extra : convert_revision : svn%3Afdd8eb12-d10e-0410-9acb-85c331704f74/trunk%402254

examples/CMakeLists.txt

@@ -33,6 +33,7 @@ add_example(dir_nav_ex)
 add_example(file_to_code_ex)
 add_example(gui_api_ex)
 add_example(image_ex)
+add_example(krls_ex)
 add_example(logger_ex)
 add_example(logger_ex_2)
 add_example(matrix_ex)

examples/krls_ex.cpp

+/*
+    This is an example illustrating the use of the krls object 
+    from the dlib C++ Library.
+
+    The krls object allows you to perform online regression.  This
+    example will train an instance of it on the sinc function.
+
+*/
+
+#include <iostream>
+#include <vector>
+
+#include "dlib/svm.h"
+
+using namespace std;
+using namespace dlib;
+
+// Here is the sinc function we will be trying to learn with the krls
+// object.
+double sinc(double x)
+{
+    if (x == 0)
+        return 1;
+    return sin(x)/x;
+}
+
+int main()
+{
+    // Here we declare that our samples will be 1 dimensional column vectors.  The reason for
+    // using a matrix here is that in general you can use N dimensional vectors as inputs to the
+    // krls object.  But here we only have 1 dimension to make the example simple.
+    typedef matrix<double,1,1> sample_type;
+
+    // Now we are making a typedef for the kind of kernel we want to use.  I picked the
+    // radial basis kernel because it only has one parameter and generally gives good
+    // results without much fiddling.
+    typedef radial_basis_kernel<sample_type> kernel_type;
+
+    // Here we declare an instance of the krls object.  The first argument to the constructor
+    // is the kernel we wish to use.  The second is a parameter that determines the numerical 
+    // accuracy with which the object will perform part of the regression algorithm.  Generally
+    // smaller values give better results but cause the algorithm to run slower.  You just have
+    // to play with it to decide what balance of speed and accuracy is right for your problem.
+    // Here we have set it to 0.001.
+    krls<kernel_type> test(kernel_type(0.1),0.001);
+
+    // now we train our object on a few samples of the sinc function.
+    sample_type m;
+    for (double x = -10; x <= 4; x += 1)
+    {
+        m(0) = x;
+        test.train(m, sinc(x));
+    }
+
+    // now we output the value of the sinc function for a few test points as well as the 
+    // value predicted by krls object.
+    m(0) = 2.5; cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = 0.1; cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = -4;  cout << sinc(m(0)) << "   " << test(m) << endl;
+    m(0) = 5.0; cout << sinc(m(0)) << "   " << test(m) << endl;
+
+    // The output is as follows:
+    // 0.239389   0.238808
+    // 0.998334   0.997779
+    // -0.189201   -0.189754
+    // -0.191785   -0.1979
+
+    // The first column is the true value of the sinc function and the second
+    // column is the output from the krls estimate.  
+
+}
+
+