```// 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 kernel ridge 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 kernel ridge 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 krr_trainer object.  This is the
// object that we will later use to do the training.
krr_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 computed from at most 2000 randomly selected
// samples.
const double gamma = 3.0/compute_mean_squared_distance(randomly_subsample(samples, 2000));
cout << "using gamma of " << gamma << endl;
trainer.set_kernel(kernel_type(gamma));

// 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 0.075
//    0.239389   0.239389
//    0.998334   0.998362
//    -0.189201   -0.189254
//    -0.191785   -0.186618

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

// Note that the krr_trainer has the ability to tell us the leave-one-out predictions
// for each sample.
std::vector<double> loo_values;
trainer.train(samples, labels, loo_values);
cout << "mean squared LOO error: " << mean_squared_error(labels,loo_values) << endl;
cout << "R^2 LOO value:          " << r_squared(labels,loo_values) << endl;
// Which outputs the following:
// mean squared LOO error: 8.29575e-07
// R^2 LOO value:          0.999995

// 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:
serialize("saved_function.dat") << test;

// Now let's open that file back up and load the function object it contains.
deserialize("saved_function.dat") >> test;

}

```