```// 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 multilayer perceptron
from the dlib C++ Library.

This example creates a simple set of data to train on and shows
you how to train a mlp object on that data.

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 0.

*/

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

using namespace std;
using namespace dlib;

int main()
{
// The mlp takes column vectors as input and gives column vectors as output.  The dlib::matrix
// object is used to represent the column vectors. So the first thing we do here is declare
// a convenient typedef for the matrix object we will be using.

// 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)
typedef matrix<double, 2, 1> sample_type;

// make an instance of a sample matrix so we can use it below
sample_type sample;

// Create a multi-layer perceptron network.   This network has 2 nodes on the input layer
// (which means it takes column vectors of length 2 as input) and 5 nodes in the first
// hidden layer.  Note that the other 4 variables in the mlp's constructor are left at
// their default values.
mlp::kernel_1a_c net(2,5);

// Now let's put some data into our sample and train on it.  We do this
// by looping over 41*41 points and labeling them according to their
// distance from the origin.
for (int i = 0; i < 1000; ++i)
{
for (int r = -20; r <= 20; ++r)
{
for (int c = -20; c <= 20; ++c)
{
sample(0) = r;
sample(1) = c;

// if this point is less than 10 from the origin
if (sqrt((double)r*r + c*c) <= 10)
net.train(sample,1);
else
net.train(sample,0);
}
}
}

// Now we have trained our mlp.  Let's see how well it did.
// Note that if you run this program multiple times you will get different results. This
// is because the mlp network is randomly initialized.

// each of these statements prints out the output of the network given a particular sample.

sample(0) = 3.123;
sample(1) = 4;
cout << "This sample should be close to 1 and it is classified as a " << net(sample) << endl;

sample(0) = 13.123;
sample(1) = 9.3545;
cout << "This sample should be close to 0 and it is classified as a " << net(sample) << endl;

sample(0) = 13.123;
sample(1) = 0;
cout << "This sample should be close to 0 and it is classified as a " << net(sample) << endl;
}

```