    // 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 relevance vector machine
        utilities from the dlib C++ Library.

        This example creates a simple set of data to train on and then shows
        you how to use the cross validation and rvm training functions
        to find a good decision function that can classify examples in our
        data set.

        The data used in this example will be 2 dimensional data and will
        come from a distribution where points with a distance less than 10
        from the origin are labeled +1 and all other points are labeled
        as -1.

    */

    #include <iostream>
    #include <dlib/svm.h>

    using namespace std;
    using namespace dlib;

    int main()
    {
        // The rvm functions use column vectors to contain a lot of the data on which they
        // operate. So the first thing we do here is declare a convenient typedef.

        // This typedef declares a matrix with 2 rows and 1 column.  It will be the
        // object that contains each of our 2 dimensional samples.   (Note that if you wanted
        // more than 2 features in this vector you can simply change the 2 to something else.
        // Or if you don't know how many features you want until runtime then you can put a 0
        // here and use the matrix.set_size() member function)
        typedef matrix<double, 2, 1> sample_type;

        // This is a typedef for the type of kernel we are going to use in this example.
        // In this case I have selected the radial basis kernel that can operate on our
        // 2D sample_type objects
        typedef radial_basis_kernel<sample_type> kernel_type;

        // Now we make objects to contain our samples and their respective labels.
        std::vector<sample_type> samples;
        std::vector<double> labels;

        // Now let's put some data into our samples and labels objects.  We do this
        // by looping over a bunch of points and labeling them according to their
        // distance from the origin.
        for (int r = -20; r <= 20; ++r)
        {
            for (int c = -20; c <= 20; ++c)
            {
                sample_type samp;
                samp(0) = r;
                samp(1) = c;
                samples.push_back(samp);

                // if this point is less than 10 from the origin
                if (sqrt((double)r*r + c*c) <= 10)
                    labels.push_back(+1);
                else
                    labels.push_back(-1);

            }
        }

        // Here we normalize all the samples by subtracting their mean and dividing by their standard deviation.
        // This is generally a good idea since it often heads off numerical stability problems and also
        // prevents one large feature from smothering others.  Doing this doesn't matter much in this example
        // so I'm just doing this here so you can see an easy way to accomplish this with
        // the library.
        vector_normalizer<sample_type> normalizer;
        // let the normalizer learn the mean and standard deviation of the samples
        normalizer.train(samples);
        // now normalize each sample
        for (unsigned long i = 0; i < samples.size(); ++i)
            samples[i] = normalizer(samples[i]);

        // Now that we have some data we want to train on it.  However, there is a parameter to the
        // training.  This is the gamma parameter of the RBF kernel.  Our choice for this parameter will
        // influence how good the resulting decision function is.  To test how good a particular choice of
        // kernel parameters is we can use the cross_validate_trainer() function to perform n-fold cross
        // validation on our training data.  However, there is a problem with the way we have sampled
        // our distribution.  The problem is that there is a definite ordering to the samples.
        // That is, the first half of the samples look like they are from a different distribution
        // than the second half.  This would screw up the cross validation process but we can
        // fix it by randomizing the order of the samples with the following function call.
        randomize_samples(samples, labels);

        // here we make an instance of the rvm_trainer object that uses our kernel type.
        rvm_trainer<kernel_type> trainer;

        // One thing you can do to reduce the RVM training time is to make its
        // stopping epsilon bigger.  However, this might make the outputs less
        // reliable.  But sometimes it works out well.  0.001 is the default.
        trainer.set_epsilon(0.001);
        // You can also set an explicit limit on the number of iterations used by the numeric
        // solver.  The default is 2000.
        trainer.set_max_iterations(2000);

        // Now we loop over some different gamma values to see how good they are.  Note
        // that this is a very simple way to try out a few possible parameter choices.  You
        // should look at the model_selection_ex.cpp program for examples of more sophisticated
        // strategies for determining good parameter choices.
        cout << "doing cross validation" << endl;
        for (double gamma = 0.000001; gamma <= 1; gamma *= 5)
        {
            // tell the trainer the parameters we want to use
            trainer.set_kernel(kernel_type(gamma));

            cout << "gamma: " << gamma;
            // Print out the cross validation accuracy for 3-fold cross validation using the current gamma.
            // cross_validate_trainer() returns a row vector.  The first element of the vector is the fraction
            // of +1 training examples correctly classified and the second number is the fraction of -1 training
            // examples correctly classified.
            cout << "     cross validation accuracy: " << cross_validate_trainer(trainer, samples, labels, 3);
        }

        // From looking at the output of the above loop it turns out that a good value for
        // gamma for this problem is 0.08.  So that is what we will use.

        // Now we train on the full set of data and obtain the resulting decision function.  We use the
        // value of 0.08 for gamma.  The decision function will return values >= 0 for samples it predicts
        // are in the +1 class and numbers < 0 for samples it predicts to be in the -1 class.
        trainer.set_kernel(kernel_type(0.08));
        typedef decision_function<kernel_type> dec_funct_type;
        typedef normalized_function<dec_funct_type> funct_type;

        // Here we are making an instance of the normalized_function object.  This object provides a convenient
        // way to store the vector normalization information along with the decision function we are
        // going to learn.
        funct_type learned_function;
        learned_function.normalizer = normalizer;  // save normalization information
        learned_function.function = trainer.train(samples, labels); // perform the actual RVM training and save the results

        // Print out the number of relevance vectors in the resulting decision function.
        cout << "\nnumber of relevance vectors in our learned_function is "
             << learned_function.function.basis_vectors.size() << endl;

        // Now let's try this decision_function on some samples we haven't seen before
        sample_type sample;

        sample(0) = 3.123;
        sample(1) = 2;
        cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;

        sample(0) = 3.123;
        sample(1) = 9.3545;
        cout << "This is a +1 class example, the classifier output is " << learned_function(sample) << endl;

        sample(0) = 13.123;
        sample(1) = 9.3545;
        cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;

        sample(0) = 13.123;
        sample(1) = 0;
        cout << "This is a -1 class example, the classifier output is " << learned_function(sample) << endl;

        // We can also train a decision function that reports a well conditioned probability
        // instead of just a number > 0 for the +1 class and < 0 for the -1 class.  An example
        // of doing that follows:
        typedef probabilistic_decision_function<kernel_type> probabilistic_funct_type;
        typedef normalized_function<probabilistic_funct_type> pfunct_type;

        pfunct_type learned_pfunct;
        learned_pfunct.normalizer = normalizer;
        learned_pfunct.function = train_probabilistic_decision_function(trainer, samples, labels, 3);
        // Now we have a function that returns the probability that a given sample is of the +1 class.

        // print out the number of relevance vectors in the resulting decision function.
        // (it should be the same as in the one above)
        cout << "\nnumber of relevance vectors in our learned_pfunct is "
             << learned_pfunct.function.decision_funct.basis_vectors.size() << endl;

        sample(0) = 3.123;
        sample(1) = 2;
        cout << "This +1 class example should have high probability.  Its probability is: "
             << learned_pfunct(sample) << endl;

        sample(0) = 3.123;
        sample(1) = 9.3545;
        cout << "This +1 class example should have high probability.  Its probability is: "
             << learned_pfunct(sample) << endl;

        sample(0) = 13.123;
        sample(1) = 9.3545;
        cout << "This -1 class example should have low probability.  Its probability is: "
             << learned_pfunct(sample) << endl;

        sample(0) = 13.123;
        sample(1) = 0;
        cout << "This -1 class example should have low probability.  Its probability is: "
             << learned_pfunct(sample) << endl;

        // Another thing that is worth knowing is that just about everything in dlib is serializable.
        // So for example, you can save the learned_pfunct object to disk and recall it later like so:
        serialize("saved_function.dat") << learned_pfunct;

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

    }