```// 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 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.  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.  (Note that if you don't know the
// dimensionality of your vectors at compile time you can change the first number to
// a 0 and then set the size at runtime)
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.

// 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   0.239362
// 0.998334   0.998333
// -0.189201   -0.189201
// -0.191785   -0.197267

// The first column is the true value of the sinc function and the second
// column is the output from the krls 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:
serialize("saved_krls_object.dat") << test;

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

// If you don't want to save the whole krls object (it might be a bit large)
// you can save just the decision function it has learned so far.  You can get
// the decision function out of it by calling test.get_decision_function() and
// then you can serialize that object instead.  E.g.
decision_function<kernel_type> funct = test.get_decision_function();
serialize("saved_krls_function.dat") << funct;
}

```