    // 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.  In particular, we show how to use the
        C parametrization of the SVM in this example.

        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.  You can use your own custom
        // kernels with these tools as well, see custom_trainer_ex.cpp for an
        // example.
        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 it.
        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 C 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 are 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);

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

        // Now we loop over some different C 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 C = 1; C < 100000; C *= 5)
            {
                // tell the trainer the parameters we want to use
                trainer.set_kernel(kernel_type(gamma));
                trainer.set_c(C);

                cout << "gamma: " << gamma << "    C: " << C;
                // Print out the cross validation accuracy for 3-fold cross validation using
                // the current gamma and C.  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 good
        // values for C and gamma for this problem are 5 and 0.15625 respectively.
        // So that is what we will use.

        // Now we train on the full set of data and obtain the resulting decision
        // function.  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_c(5);
        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);
    }