    // 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 support 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 svm 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 svm 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 are two
        // parameters to the training.  These are the nu and gamma parameters.  Our choice for
        // these parameters will influence how good the resulting decision function is.  To
        // test how good a particular choice of these 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
        // above.  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);

        // The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1
        // labels in the training data.  This function finds that value.
        const double max_nu = maximum_nu(labels);

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

        // Now we loop over some different nu and 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 = 0.00001; gamma <= 1; gamma *= 5)
        {
            for (double nu = 0.00001; nu < max_nu; nu *= 5)
            {
                // tell the trainer the parameters we want to use
                trainer.set_kernel(kernel_type(gamma));
                trainer.set_nu(nu);

                cout << "gamma: " << gamma << "    nu: " << nu;
                // Print out the cross validation accuracy for 3-fold cross validation using
                // the current gamma and nu.  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 nu
        // and gamma for this problem is 0.15625 for both.  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 0.15625 for nu and 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(0.15625));
        trainer.set_nu(0.15625);
        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 SVM training and save the results

        // print out the number of support vectors in the resulting decision function
        cout << "\nnumber of support 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 support vectors in the resulting decision function.
        // (it should be the same as in the one above)
        cout << "\nnumber of support 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;

        // Note that there is also an example program that comes with dlib called the
        // file_to_code_ex.cpp example.  It is a simple program that takes a file and outputs a
        // piece of C++ code that is able to fully reproduce the file's contents in the form of
        // a std::string object.  So you can use that along with the std::istringstream to save
        // learned decision functions inside your actual C++ code files if you want.

        // Lastly, note that the decision functions we trained above involved well over 200
        // basis vectors.  Support vector machines in general tend to find decision functions
        // that involve a lot of basis vectors.  This is significant because the more basis
        // vectors in a decision function, the longer it takes to classify new examples.  So
        // dlib provides the ability to find an approximation to the normal output of a trainer
        // using fewer basis vectors.

        // Here we determine the cross validation accuracy when we approximate the output using
        // only 10 basis vectors.  To do this we use the reduced2() function.  It takes a
        // trainer object and the number of basis vectors to use and returns a new trainer
        // object that applies the necessary post processing during the creation of decision
        // function objects.
        cout << "\ncross validation accuracy with only 10 support vectors: "
             << cross_validate_trainer(reduced2(trainer,10), samples, labels, 3);

        // Let's print out the original cross validation score too for comparison.
        cout << "cross validation accuracy with all the original support vectors: "
             << cross_validate_trainer(trainer, samples, labels, 3);

        // When you run this program you should see that, for this problem, you can reduce the
        // number of basis vectors down to 10 without hurting the cross validation accuracy.

        // To get the reduced decision function out we would just do this:
        learned_function.function = reduced2(trainer,10).train(samples, labels);
        // And similarly for the probabilistic_decision_function:
        learned_pfunct.function = train_probabilistic_decision_function(reduced2(trainer,10), samples, labels, 3);
    }