    // 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 epsilon-insensitive support vector
        regression object from the dlib C++ Library.

        In this example we will draw some points from the sinc() function and do a
        non-linear regression on them.
    */

    #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 svr_trainer
    // 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.
        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;

        std::vector<sample_type> samples;
        std::vector<double> targets;

        // The first thing we do is pick a few training points from the sinc() function.
        sample_type m;
        for (double x = -10; x <= 4; x += 1)
        {
            m(0) = x;

            samples.push_back(m);
            targets.push_back(sinc(x));
        }

        // Now setup a SVR trainer object.  It has three parameters, the kernel and
        // two parameters specific to SVR.
        svr_trainer<kernel_type> trainer;
        trainer.set_kernel(kernel_type(0.1));

        // This parameter is the usual regularization parameter.  It determines the trade-off
        // between trying to reduce the training error or allowing more errors but hopefully
        // improving the generalization of the resulting function.  Larger values encourage exact
        // fitting while smaller values of C may encourage better generalization.
        trainer.set_c(10);

        // Epsilon-insensitive regression means we do regression but stop trying to fit a data
        // point once it is "close enough" to its target value.  This parameter is the value that
        // controls what we mean by "close enough".  In this case, I'm saying I'm happy if the
        // resulting regression function gets within 0.001 of the target value.
        trainer.set_epsilon_insensitivity(0.001);

        // Now do the training and save the results
        decision_function<kernel_type> df = trainer.train(samples, targets);

        // now we output the value of the sinc function for a few test points as well as the
        // value predicted by SVR.
        m(0) = 2.5; cout << sinc(m(0)) << "   " << df(m) << endl;
        m(0) = 0.1; cout << sinc(m(0)) << "   " << df(m) << endl;
        m(0) = -4;  cout << sinc(m(0)) << "   " << df(m) << endl;
        m(0) = 5.0; cout << sinc(m(0)) << "   " << df(m) << endl;

        // The output is as follows:
        //  0.239389   0.23905
        //  0.998334   0.997331
        // -0.189201   -0.187636
        // -0.191785   -0.218924

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

        // We can also do 5-fold cross-validation and find the mean squared error and R-squared
        // values.  Note that we need to randomly shuffle the samples first.  See the svm_ex.cpp
        // for a discussion of why this is important.
        randomize_samples(samples, targets);
        cout << "MSE and R-Squared: "<< cross_validate_regression_trainer(trainer, samples, targets, 5) << endl;
        // The output is:
        // MSE and R-Squared: 1.65984e-05    0.999901
    }