    // 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.
        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   0.239362
        // 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;
    }