    // 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 Bayesian Network
        inference utilities found in the dlib C++ library.

        In this example all the nodes in the Bayesian network are
        boolean variables.  That is, they take on either the value
        0 or the value 1.

        The network contains 4 nodes and looks as follows:

            B     C
            \\   //
             \/ \/
               A
               ||
               \/
                D

        The probabilities of each node are summarized below.  (The probability
        of each node being 0 is not listed since it is just P(X=0) = 1-p(X=1) )

            p(B=1) = 0.01

            p(C=1) = 0.001

            p(A=1 | B=0, C=0) = 0.01
            p(A=1 | B=0, C=1) = 0.5
            p(A=1 | B=1, C=0) = 0.9
            p(A=1 | B=1, C=1) = 0.99

            p(D=1 | A=0) = 0.2
            p(D=1 | A=1) = 0.5

    */

    #include <dlib/bayes_utils.h>
    #include <dlib/graph_utils.h>
    #include <dlib/graph.h>
    #include <dlib/directed_graph.h>
    #include <iostream>

    using namespace dlib;
    using namespace std;

    // ----------------------------------------------------------------------------------------

    int main()
    {
        try
        {
            // There are many useful convenience functions in this namespace.  They all
            // perform simple access or modify operations on the nodes of a bayesian network.
            // You don't have to use them but they are convenient and they also will check for
            // various errors in your bayesian network when your application is built with
            // the DEBUG or ENABLE_ASSERTS preprocessor definitions defined.  So their use
            // is recommended.  In fact, most of the global functions used in this example
            // program are from this namespace.
            using namespace bayes_node_utils;

            // This statement declares a bayesian network called bn.  Note that a bayesian network
            // in the dlib world is just a directed_graph object that contains a special kind
            // of node called a bayes_node.
            directed_graph<bayes_node>::kernel_1a_c bn;

            // Use an enum to make some more readable names for our nodes.
            enum nodes
            {
                A = 0,
                B = 1,
                C = 2,
                D = 3
            };

            // The next few blocks of code setup our bayesian network.

            // The first thing we do is tell the bn object how many nodes it has
            // and also add the three edges.  Again, we are using the network
            // shown in ASCII art at the top of this file.
            bn.set_number_of_nodes(4);
            bn.add_edge(A, D);
            bn.add_edge(B, A);
            bn.add_edge(C, A);

            // Now we inform all the nodes in the network that they are binary
            // nodes.  That is, they only have two possible values.
            set_node_num_values(bn, A, 2);
            set_node_num_values(bn, B, 2);
            set_node_num_values(bn, C, 2);
            set_node_num_values(bn, D, 2);

            assignment parent_state;
            // Now we will enter all the conditional probability information for each node.
            // Each node's conditional probability is dependent on the state of its parents.
            // To specify this state we need to use the assignment object.  This assignment
            // object allows us to specify the state of each nodes parents.

            // Here we specify that p(B=1) = 0.01
            // parent_state is empty in this case since B is a root node.
            set_node_probability(bn, B, 1, parent_state, 0.01);
            // Here we specify that p(B=0) = 1-0.01
            set_node_probability(bn, B, 0, parent_state, 1-0.01);

            // Here we specify that p(C=1) = 0.001
            // parent_state is empty in this case since B is a root node.
            set_node_probability(bn, C, 1, parent_state, 0.001);
            // Here we specify that p(C=0) = 1-0.001
            set_node_probability(bn, C, 0, parent_state, 1-0.001);

            // This is our first node that has parents. So we set the parent_state
            // object to reflect that A has both B and C as parents.
            parent_state.add(B, 1);
            parent_state.add(C, 1);
            // Here we specify that p(A=1 | B=1, C=1) = 0.99
            set_node_probability(bn, A, 1, parent_state, 0.99);
            // Here we specify that p(A=0 | B=1, C=1) = 1-0.99
            set_node_probability(bn, A, 0, parent_state, 1-0.99);

            // Here we use the [] notation because B and C have already
            // been added into parent state.
            parent_state[B] = 1;
            parent_state[C] = 0;
            // Here we specify that p(A=1 | B=1, C=0) = 0.9
            set_node_probability(bn, A, 1, parent_state, 0.9);
            set_node_probability(bn, A, 0, parent_state, 1-0.9);

            parent_state[B] = 0;
            parent_state[C] = 1;
            // Here we specify that p(A=1 | B=0, C=1) = 0.5
            set_node_probability(bn, A, 1, parent_state, 0.5);
            set_node_probability(bn, A, 0, parent_state, 1-0.5);

            parent_state[B] = 0;
            parent_state[C] = 0;
            // Here we specify that p(A=1 | B=0, C=0) = 0.01
            set_node_probability(bn, A, 1, parent_state, 0.01);
            set_node_probability(bn, A, 0, parent_state, 1-0.01);

            // Here we set probabilities for node D.
            // First we clear out parent state so that it doesn't have any of
            // the assignments for the B and C nodes used above.
            parent_state.clear();
            parent_state.add(A,1);
            // Here we specify that p(D=1 | A=1) = 0.5
            set_node_probability(bn, D, 1, parent_state, 0.5);
            set_node_probability(bn, D, 0, parent_state, 1-0.5);

            parent_state[A] = 0;
            // Here we specify that p(D=1 | A=0) = 0.2
            set_node_probability(bn, D, 1, parent_state, 0.2);
            set_node_probability(bn, D, 0, parent_state, 1-0.2);

            // We have now finished setting up our bayesian network.  So let's compute some
            // probability values.  The first thing we will do is compute the prior probability
            // of each node in the network.  To do this we will use the join tree algorithm which
            // is an algorithm for performing exact inference in a bayesian network.

            // First we need to create an undirected graph which contains set objects at each node and
            // edge.  This long declaration does the trick.
            typedef dlib::set<unsigned long>::compare_1b_c set_type;
            typedef graph<set_type, set_type>::kernel_1a_c join_tree_type;
            join_tree_type join_tree;

            // Now we need to populate the join_tree with data from our bayesian network.  The next
            // function calls do this.  Explaining exactly what they do is outside the scope of this
            // example.  Just think of them as filling join_tree with information that is useful
            // later on for dealing with our bayesian network.
            create_moral_graph(bn, join_tree);
            create_join_tree(join_tree, join_tree);

            // Now that we have a proper join_tree we can use it to obtain a solution to our
            // bayesian network.  Doing this is as simple as declaring an instance of
            // the bayesian_network_join_tree object as follows:
            bayesian_network_join_tree solution(bn, join_tree);

            // now print out the probabilities for each node
            cout << "Using the join tree algorithm:\n";
            cout << "p(A=1) = " << solution.probability(A)(1) << endl;
            cout << "p(A=0) = " << solution.probability(A)(0) << endl;
            cout << "p(B=1) = " << solution.probability(B)(1) << endl;
            cout << "p(B=0) = " << solution.probability(B)(0) << endl;
            cout << "p(C=1) = " << solution.probability(C)(1) << endl;
            cout << "p(C=0) = " << solution.probability(C)(0) << endl;
            cout << "p(D=1) = " << solution.probability(D)(1) << endl;
            cout << "p(D=0) = " << solution.probability(D)(0) << endl;
            cout << "\n\n\n";

            // Now to make things more interesting let's say that we have discovered that the C
            // node really has a value of 1.  That is to say, we now have evidence that
            // C is 1.  We can represent this in the network using the following two function
            // calls.
            set_node_value(bn, C, 1);
            set_node_as_evidence(bn, C);

            // Now we want to compute the probabilities of all the nodes in the network again
            // given that we now know that C is 1.  We can do this as follows:
            bayesian_network_join_tree solution_with_evidence(bn, join_tree);

            // now print out the probabilities for each node
            cout << "Using the join tree algorithm:\n";
            cout << "p(A=1 | C=1) = " << solution_with_evidence.probability(A)(1) << endl;
            cout << "p(A=0 | C=1) = " << solution_with_evidence.probability(A)(0) << endl;
            cout << "p(B=1 | C=1) = " << solution_with_evidence.probability(B)(1) << endl;
            cout << "p(B=0 | C=1) = " << solution_with_evidence.probability(B)(0) << endl;
            cout << "p(C=1 | C=1) = " << solution_with_evidence.probability(C)(1) << endl;
            cout << "p(C=0 | C=1) = " << solution_with_evidence.probability(C)(0) << endl;
            cout << "p(D=1 | C=1) = " << solution_with_evidence.probability(D)(1) << endl;
            cout << "p(D=0 | C=1) = " << solution_with_evidence.probability(D)(0) << endl;
            cout << "\n\n\n";

            // Note that when we made our solution_with_evidence object we reused our join_tree object.
            // This saves us the time it takes to calculate the join_tree object from scratch.  But
            // it is important to note that we can only reuse the join_tree object if we haven't changed
            // the structure of our bayesian network.  That is, if we have added or removed nodes or
            // edges from our bayesian network then we must recompute our join_tree.  But in this example
            // all we did was change the value of a bayes_node object (we made node C be evidence)
            // so we are ok.

            // Next this example will show you how to use the bayesian_network_gibbs_sampler object
            // to perform approximate inference in a bayesian network.  This is an algorithm
            // that doesn't give you an exact solution but it may be necessary to use in some
            // instances.  For example, the join tree algorithm used above, while fast in many
            // instances, has exponential runtime in some cases.  Moreover, inference in bayesian
            // networks is NP-Hard for general networks so sometimes the best you can do is
            // find an approximation.
            // However, it should be noted that the gibbs sampler does not compute the correct
            // probabilities if the network contains a deterministic node.  That is, if any
            // of the conditional probability tables in the bayesian network have a probability
            // of 1.0 for something the gibbs sampler should not be used.

            // This Gibbs sampler algorithm works by randomly sampling possibles values of the
            // network.  So to use it we should set the network to some initial state.

            set_node_value(bn, A, 0);
            set_node_value(bn, B, 0);
            set_node_value(bn, D, 0);

            // We will leave the C node with a value of 1 and keep it as an evidence node.

            // First create an instance of the gibbs sampler object
            bayesian_network_gibbs_sampler sampler;

            // To use this algorithm all we do is go into a loop for a certain number of times
            // and each time through we sample the bayesian network.  Then we count how
            // many times a node has a certain state.  Then the probability of that node
            // having that state is just its count/total times through the loop.

            // The following code illustrates the general procedure.
            unsigned long A_count = 0;
            unsigned long B_count = 0;
            unsigned long C_count = 0;
            unsigned long D_count = 0;

            // The more times you let the loop run the more accurate the result will be.  Here we loop
            // 2000 times.
            const long rounds = 2000;
            for (long i = 0; i < rounds; ++i)
            {
                sampler.sample_graph(bn);

                if (node_value(bn, A) == 1)
                    ++A_count;
                if (node_value(bn, B) == 1)
                    ++B_count;
                if (node_value(bn, C) == 1)
                    ++C_count;
                if (node_value(bn, D) == 1)
                    ++D_count;
            }

            cout << "Using the approximate Gibbs Sampler algorithm:\n";
            cout << "p(A=1 | C=1) = " << (double)A_count/(double)rounds << endl;
            cout << "p(B=1 | C=1) = " << (double)B_count/(double)rounds << endl;
            cout << "p(C=1 | C=1) = " << (double)C_count/(double)rounds << endl;
            cout << "p(D=1 | C=1) = " << (double)D_count/(double)rounds << endl;
        }
        catch (std::exception& e)
        {
            cout << "exception thrown: " << endl;
            cout << e.what() << endl;
            cout << "hit enter to terminate" << endl;
            cin.get();
        }
    }