    // 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.
        typedef radial_basis_kernel<sample_type> kernel_type;

        // 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;

    }