```// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
/*
This is an example illustrating the use of the RVM regression object
from the dlib C++ Library.

This example will train on data from 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 rvm regression
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.
typedef matrix<double,1,1> sample_type;

// Now sample some points from the sinc() function
sample_type m;
std::vector<sample_type> samples;
std::vector<double> labels;
for (double x = -10; x <= 4; x += 1)
{
m(0) = x;
samples.push_back(m);
labels.push_back(sinc(x));
}

// 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.

// Here we declare an instance of the rvm_regression_trainer object.  This is the
// object that we will later use to do the training.
rvm_regression_trainer<kernel_type> trainer;

// Here we set the kernel we want to use for training.   The radial_basis_kernel
// has a parameter called gamma that we need to determine.  As a rule of thumb, a good
// gamma to try is 1.0/(mean squared distance between your sample points).  So
// below we are using a similar value.   Note also that using an inappropriately large
// gamma will cause the RVM training algorithm to run extremely slowly.  What
// "large" means is relative to how spread out your data is.  So it is important
// to use a rule like this as a starting point for determining the gamma value
// if you want to use the RVM.  It is also probably a good idea to normalize your
// samples as shown in the rvm_ex.cpp example program.
const double gamma = 2.0/compute_mean_squared_distance(samples);
cout << "using gamma of " << gamma << endl;
trainer.set_kernel(kernel_type(gamma));

// One thing you can do to reduce the RVM training time is to make its
// stopping epsilon bigger.  However, this might make the outputs less
// reliable.  But sometimes it works out well.  0.001 is the default.
trainer.set_epsilon(0.001);

// now train a function based on our sample points
decision_function<kernel_type> test = trainer.train(samples, labels);

// now we output the value of the sinc function for a few test points as well as the
// value predicted by our regression.
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:
//using gamma of 0.05
//0.239389   0.240989
//0.998334   0.999538
//-0.189201   -0.188453
//-0.191785   -0.226516

// The first column is the true value of the sinc function and the second
// column is the output from the rvm estimate.

// Another thing that is worth knowing is that just about everything in dlib is serializable.
// So for example, you can save the test object to disk and recall it later like so:
ofstream fout("saved_function.dat",ios::binary);
serialize(test,fout);
fout.close();

// Now let's open that file back up and load the function object it contains.
ifstream fin("saved_function.dat",ios::binary);
deserialize(test, fin);

}

```