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Neural Networks on C#

, 19 Nov 2006 GPL3
The articles describes a C# library for neural network computations, and their application for several problem solving.
neuro_demo.zip
neuro_demo
Back Propagation
Approximation
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Approximation.exe
Data Samples
sample1.csv
sample2.csv
TimeSeries
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Data Samples
exponent.csv
growing sinusoid.csv
parabola.csv
sigmoid.csv
sinusoid.csv
TimeSeries.exe
XORProblem
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
XORProblem.exe
Simple
Delta Rule Learning
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Classifier.exe
Data Samples
and.csv
cube.csv
or.csv
sample1.csv
sample2.csv
One-Layer Perceptron Classifier
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Classifier.exe
Data Samples
sample1.csv
sample2.csv
Perceptron Classifier
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Classifier.exe
Data Samples
and.csv
cube.csv
or.csv
SOM
2DOrganizing
2DOrganizing.exe
AForge.dll
AForge.Neuro.dll
Color
AForge.dll
AForge.Neuro.dll
Color.exe
TSP
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
TSP.exe
neuro_src.zip
neuro_src
Docs
AForge.Core.chm
AForge.Neuro.chm
Release
AForge.Controls.dll
AForge.dll
AForge.Neuro.dll
Samples
Neuro
Back Propagation
Approximation
App.ico
Data Samples
sample1.csv
sample2.csv
TimeSeries
App.ico
Data Samples
exponent.csv
growing sinusoid.csv
parabola.csv
sigmoid.csv
sinusoid.csv
XORProblem
App.ico
Simple
Delta Rule Learning
App.ico
Data Samples
and.csv
cube.csv
or.csv
sample1.csv
sample2.csv
One-Layer Perceptron Classifier
App.ico
Data Samples
sample1.csv
sample2.csv
Perceptron Classifier
App.ico
Data Samples
and.csv
cube.csv
or.csv
SOM
2DOrganizing
App.ico
Color
App.ico
TSP
App.ico
Sources
Controls
Core
Neuro
Activation Functions
Images
sigmoid.bmp
sigmoid_bipolar.bmp
threshold.bmp
Layers
Learning
Networks
Neurons
// AForge Framework
// One-Layer Perceptron Classifier
//
// Copyright � Andrew Kirillov, 2006
// andrew.kirillov@gmail.com
//

using System;
using System.Drawing;
using System.Collections;
using System.ComponentModel;
using System.Windows.Forms;
using System.Data;
using System.IO;
using System.Threading;

using AForge;
using AForge.Neuro;
using AForge.Neuro.Learning;
using AForge.Controls;

namespace Classifier
{
	/// <summary>
	/// Summary description for Form1.
	/// </summary>
	public class MainForm : System.Windows.Forms.Form
	{
		private System.Windows.Forms.GroupBox groupBox1;
		private AForge.Controls.Chart chart;
		private System.Windows.Forms.Button loadButton;
		private System.Windows.Forms.OpenFileDialog openFileDialog;
		private System.Windows.Forms.GroupBox groupBox2;
		private System.Windows.Forms.Label label1;
		private System.Windows.Forms.TextBox learningRateBox;
		private System.Windows.Forms.Label label2;
		private System.Windows.Forms.TextBox iterationsBox;
		private System.Windows.Forms.Button stopButton;
		private System.Windows.Forms.Button startButton;
		private System.Windows.Forms.CheckBox saveFilesCheck;
		private System.Windows.Forms.Label label3;
		private System.Windows.Forms.Label label4;
		private System.Windows.Forms.ListView weightsList;
		private System.Windows.Forms.ColumnHeader columnHeader1;
		private System.Windows.Forms.ColumnHeader columnHeader2;
		private System.Windows.Forms.ColumnHeader columnHeader3;
		private System.Windows.Forms.GroupBox groupBox3;
		private AForge.Controls.Chart errorChart;
		/// <summary>
		/// Required designer variable.
		/// </summary>
		private System.ComponentModel.Container components = null;

		private int			samples = 0;
		private double[,]	data = null;
		private int[]		classes = null;
		private int			classesCount = 0;
		private int[]		samplesPerClass = null;

		private double		learningRate = 0.1;
		private bool		saveStatisticsToFiles = false;

		private Thread	workerThread = null;
		private bool	needToStop = false;

		// color for data series
		private static Color[]	dataSereisColors = new Color[10] {
																	 Color.Red,		Color.Blue,
																	 Color.Green,	Color.DarkOrange,
																	 Color.Violet,	Color.Brown,
																	 Color.Black,	Color.Pink,
																	 Color.Olive,	Color.Navy };

		// Constructor
		public MainForm( )
		{
			//
			// Required for Windows Form Designer support
			//
			InitializeComponent();

			// update some controls
			saveFilesCheck.Checked = saveStatisticsToFiles;
			UpdateSettings( );

			// initialize charts
			errorChart.AddDataSeries( "error", Color.Red, Chart.SeriesType.ConnectedDots, 3 );
		}

		/// <summary>
		/// Clean up any resources being used.
		/// </summary>
		protected override void Dispose( bool disposing )
		{
			if( disposing )
			{
				if (components != null) 
				{
					components.Dispose();
				}
			}
			base.Dispose( disposing );
		}

		#region Windows Form Designer generated code
		/// <summary>
		/// Required method for Designer support - do not modify
		/// the contents of this method with the code editor.
		/// </summary>
		private void InitializeComponent()
		{
			this.groupBox1 = new System.Windows.Forms.GroupBox();
			this.loadButton = new System.Windows.Forms.Button();
			this.chart = new AForge.Controls.Chart();
			this.openFileDialog = new System.Windows.Forms.OpenFileDialog();
			this.groupBox2 = new System.Windows.Forms.GroupBox();
			this.weightsList = new System.Windows.Forms.ListView();
			this.columnHeader1 = new System.Windows.Forms.ColumnHeader();
			this.columnHeader2 = new System.Windows.Forms.ColumnHeader();
			this.columnHeader3 = new System.Windows.Forms.ColumnHeader();
			this.label4 = new System.Windows.Forms.Label();
			this.label3 = new System.Windows.Forms.Label();
			this.saveFilesCheck = new System.Windows.Forms.CheckBox();
			this.stopButton = new System.Windows.Forms.Button();
			this.startButton = new System.Windows.Forms.Button();
			this.iterationsBox = new System.Windows.Forms.TextBox();
			this.label2 = new System.Windows.Forms.Label();
			this.learningRateBox = new System.Windows.Forms.TextBox();
			this.label1 = new System.Windows.Forms.Label();
			this.groupBox3 = new System.Windows.Forms.GroupBox();
			this.errorChart = new AForge.Controls.Chart();
			this.groupBox1.SuspendLayout();
			this.groupBox2.SuspendLayout();
			this.groupBox3.SuspendLayout();
			this.SuspendLayout();
			// 
			// groupBox1
			// 
			this.groupBox1.Controls.AddRange(new System.Windows.Forms.Control[] {
																					this.loadButton,
																					this.chart});
			this.groupBox1.Location = new System.Drawing.Point(10, 10);
			this.groupBox1.Name = "groupBox1";
			this.groupBox1.Size = new System.Drawing.Size(220, 255);
			this.groupBox1.TabIndex = 0;
			this.groupBox1.TabStop = false;
			this.groupBox1.Text = "Data";
			// 
			// loadButton
			// 
			this.loadButton.Location = new System.Drawing.Point(10, 225);
			this.loadButton.Name = "loadButton";
			this.loadButton.TabIndex = 1;
			this.loadButton.Text = "&Load";
			this.loadButton.Click += new System.EventHandler(this.loadButton_Click);
			// 
			// chart
			// 
			this.chart.Location = new System.Drawing.Point(10, 20);
			this.chart.Name = "chart";
			this.chart.Size = new System.Drawing.Size(200, 200);
			this.chart.TabIndex = 0;
			// 
			// openFileDialog
			// 
			this.openFileDialog.Filter = "CSV (Comma delimited) (*.csv)|*.csv";
			this.openFileDialog.Title = "Select data file";
			// 
			// groupBox2
			// 
			this.groupBox2.Controls.AddRange(new System.Windows.Forms.Control[] {
																					this.weightsList,
																					this.label4,
																					this.label3,
																					this.saveFilesCheck,
																					this.stopButton,
																					this.startButton,
																					this.iterationsBox,
																					this.label2,
																					this.learningRateBox,
																					this.label1});
			this.groupBox2.Location = new System.Drawing.Point(240, 10);
			this.groupBox2.Name = "groupBox2";
			this.groupBox2.Size = new System.Drawing.Size(240, 410);
			this.groupBox2.TabIndex = 1;
			this.groupBox2.TabStop = false;
			this.groupBox2.Text = "Training";
			// 
			// weightsList
			// 
			this.weightsList.Columns.AddRange(new System.Windows.Forms.ColumnHeader[] {
																						  this.columnHeader1,
																						  this.columnHeader2,
																						  this.columnHeader3});
			this.weightsList.FullRowSelect = true;
			this.weightsList.GridLines = true;
			this.weightsList.HeaderStyle = System.Windows.Forms.ColumnHeaderStyle.Nonclickable;
			this.weightsList.Location = new System.Drawing.Point(10, 130);
			this.weightsList.Name = "weightsList";
			this.weightsList.Size = new System.Drawing.Size(220, 270);
			this.weightsList.TabIndex = 14;
			this.weightsList.View = System.Windows.Forms.View.Details;
			// 
			// columnHeader1
			// 
			this.columnHeader1.Text = "Neuron";
			// 
			// columnHeader2
			// 
			this.columnHeader2.Text = "Weigh";
			// 
			// columnHeader3
			// 
			this.columnHeader3.Text = "Value";
			this.columnHeader3.Width = 65;
			// 
			// label4
			// 
			this.label4.Location = new System.Drawing.Point(10, 110);
			this.label4.Name = "label4";
			this.label4.Size = new System.Drawing.Size(55, 16);
			this.label4.TabIndex = 13;
			this.label4.Text = "Weights:";
			// 
			// label3
			// 
			this.label3.BorderStyle = System.Windows.Forms.BorderStyle.FixedSingle;
			this.label3.Location = new System.Drawing.Point(10, 100);
			this.label3.Name = "label3";
			this.label3.Size = new System.Drawing.Size(220, 2);
			this.label3.TabIndex = 12;
			// 
			// saveFilesCheck
			// 
			this.saveFilesCheck.Location = new System.Drawing.Point(10, 80);
			this.saveFilesCheck.Name = "saveFilesCheck";
			this.saveFilesCheck.Size = new System.Drawing.Size(150, 16);
			this.saveFilesCheck.TabIndex = 11;
			this.saveFilesCheck.Text = "Save weights and errors to files";
			// 
			// stopButton
			// 
			this.stopButton.Enabled = false;
			this.stopButton.Location = new System.Drawing.Point(155, 49);
			this.stopButton.Name = "stopButton";
			this.stopButton.TabIndex = 10;
			this.stopButton.Text = "S&top";
			this.stopButton.Click += new System.EventHandler(this.stopButton_Click);
			// 
			// startButton
			// 
			this.startButton.Enabled = false;
			this.startButton.Location = new System.Drawing.Point(155, 19);
			this.startButton.Name = "startButton";
			this.startButton.TabIndex = 9;
			this.startButton.Text = "&Start";
			this.startButton.Click += new System.EventHandler(this.startButton_Click);
			// 
			// iterationsBox
			// 
			this.iterationsBox.Location = new System.Drawing.Point(90, 50);
			this.iterationsBox.Name = "iterationsBox";
			this.iterationsBox.ReadOnly = true;
			this.iterationsBox.Size = new System.Drawing.Size(50, 20);
			this.iterationsBox.TabIndex = 3;
			this.iterationsBox.Text = "";
			// 
			// label2
			// 
			this.label2.Location = new System.Drawing.Point(10, 52);
			this.label2.Name = "label2";
			this.label2.Size = new System.Drawing.Size(55, 13);
			this.label2.TabIndex = 2;
			this.label2.Text = "Iterations:";
			// 
			// learningRateBox
			// 
			this.learningRateBox.Location = new System.Drawing.Point(90, 20);
			this.learningRateBox.Name = "learningRateBox";
			this.learningRateBox.Size = new System.Drawing.Size(50, 20);
			this.learningRateBox.TabIndex = 1;
			this.learningRateBox.Text = "";
			// 
			// label1
			// 
			this.label1.Location = new System.Drawing.Point(10, 22);
			this.label1.Name = "label1";
			this.label1.Size = new System.Drawing.Size(80, 17);
			this.label1.TabIndex = 0;
			this.label1.Text = "Learning rate:";
			// 
			// groupBox3
			// 
			this.groupBox3.Controls.AddRange(new System.Windows.Forms.Control[] {
																					this.errorChart});
			this.groupBox3.Location = new System.Drawing.Point(10, 270);
			this.groupBox3.Name = "groupBox3";
			this.groupBox3.Size = new System.Drawing.Size(220, 150);
			this.groupBox3.TabIndex = 2;
			this.groupBox3.TabStop = false;
			this.groupBox3.Text = "Error\'s dynamics";
			// 
			// errorChart
			// 
			this.errorChart.Location = new System.Drawing.Point(10, 20);
			this.errorChart.Name = "errorChart";
			this.errorChart.Size = new System.Drawing.Size(200, 120);
			this.errorChart.TabIndex = 0;
			this.errorChart.Text = "chart1";
			// 
			// MainForm
			// 
			this.AutoScaleBaseSize = new System.Drawing.Size(5, 13);
			this.ClientSize = new System.Drawing.Size(489, 430);
			this.Controls.AddRange(new System.Windows.Forms.Control[] {
																		  this.groupBox3,
																		  this.groupBox2,
																		  this.groupBox1});
			this.FormBorderStyle = System.Windows.Forms.FormBorderStyle.FixedDialog;
			this.MaximizeBox = false;
			this.Name = "MainForm";
			this.Text = "One-Layer Perceptron Classifier";
			this.Closing += new System.ComponentModel.CancelEventHandler(this.MainForm_Closing);
			this.Load += new System.EventHandler(this.MainForm_Load);
			this.groupBox1.ResumeLayout(false);
			this.groupBox2.ResumeLayout(false);
			this.groupBox3.ResumeLayout(false);
			this.ResumeLayout(false);

		}
		#endregion

		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		[STAThread]
		static void Main( ) 
		{
			Application.Run( new MainForm( ) );
		}

		// On main form closing
		private void MainForm_Closing(object sender, System.ComponentModel.CancelEventArgs e)
		{
			// check if worker thread is running
			if ( ( workerThread != null ) && ( workerThread.IsAlive ) )
			{
				needToStop = true;
				workerThread.Join( );
			}
		}

		// Load input data
		private void loadButton_Click(object sender, System.EventArgs e)
		{
			// data file format:
			// X1, X2, class

			// load maximum 10 classes !

			// show file selection dialog
			if ( openFileDialog.ShowDialog( ) == DialogResult.OK )
			{
				StreamReader reader = null;

				// temp buffers (for 200 samples only)
				double[,]	tempData = new double[200, 2];
				int[]		tempClasses = new int[200];

				// min and max X values
				double minX = double.MaxValue;
				double maxX = double.MinValue;

				// samples count
				samples = 0;
				// classes count
				classesCount = 0;
				samplesPerClass = new int[10];

				try
				{
					string	str = null;

					// open selected file
					reader = File.OpenText( openFileDialog.FileName );

					// read the data
					while ( ( samples < 200 ) && ( ( str = reader.ReadLine( ) ) != null ) )
					{
						// split the string
						string[] strs = str.Split( ';' );
						if ( strs.Length == 1 )
							strs = str.Split( ',' );

						// check tokens count
						if ( strs.Length != 3 )
							throw new ApplicationException( "Invalid file format" );

						// parse tokens
						tempData[samples, 0] = double.Parse( strs[0] );
						tempData[samples, 1] = double.Parse( strs[1] );
						tempClasses[samples] = int.Parse( strs[2] );

						// skip classes over 10, except only first 10 classes
						if ( tempClasses[samples] >= 10 )
							continue;

						// count the amount of different classes
						if ( tempClasses[samples] >= classesCount )
							classesCount = tempClasses[samples] + 1;
						// count samples per class
						samplesPerClass[tempClasses[samples]]++;

						// search for min value
						if ( tempData[samples, 0] < minX )
							minX = tempData[samples, 0];
						// search for max value
						if ( tempData[samples, 0] > maxX )
							maxX = tempData[samples, 0];

						samples++;
					}

					// allocate and set data
					data = new double[samples, 2];
					Array.Copy( tempData, 0, data, 0, samples * 2 );
					classes = new int[samples];
					Array.Copy( tempClasses, 0, classes, 0, samples );

					// clear current result
					weightsList.Items.Clear( );
					errorChart.UpdateDataSeries( "error", null );
				}
				catch ( Exception )
				{
					MessageBox.Show( "Failed reading the file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error );
					return;
				}
				finally
				{
					// close file
					if ( reader != null )
						reader.Close( );
				}

				// update chart
				chart.RangeX = new DoubleRange( minX, maxX );
				ShowTrainingData( );

				// enable start button
				startButton.Enabled = true;
			}
		}

		// Update settings controls
		private void UpdateSettings( )
		{
			learningRateBox.Text = learningRate.ToString( );
		}

		// Show training data on chart
		private void ShowTrainingData( )
		{
			double[][,]	dataSeries = new double[classesCount][,];
			int[]		indexes = new int[classesCount];

			// allocate data arrays
			for ( int i = 0; i < classesCount; i++ )
			{
				dataSeries[i] = new double[samplesPerClass[i], 2];
			}

			// fill data arrays
			for ( int i = 0; i < samples; i++ )
			{
				// get sample's class
				int dataClass = classes[i];
				// copy data into appropriate array
				dataSeries[dataClass][indexes[dataClass], 0] = data[i, 0];
				dataSeries[dataClass][indexes[dataClass], 1] = data[i, 1];
				indexes[dataClass]++;
			}

			// remove all previous data series from chart control
			chart.RemoveAllDataSeries( );

			// add new data series
			for ( int i = 0; i < classesCount; i++ )
			{
				string className = string.Format( "class" + i );

				// add data series
				chart.AddDataSeries( className, dataSereisColors[i], Chart.SeriesType.Dots, 5 );
				chart.UpdateDataSeries( className, dataSeries[i] );
				// add classifier
				chart.AddDataSeries( string.Format( "classifier" + i ), Color.Gray, Chart.SeriesType.Line, 1, false );
			}
		}

		// Enable/disale controls
		private void EnableControls( bool enable )
		{
			learningRateBox.Enabled	= enable;
			loadButton.Enabled		= enable;
			startButton.Enabled		= enable;
			saveFilesCheck.Enabled	= enable;
			stopButton.Enabled		= !enable;
		}

		// On "Start" button click
		private void startButton_Click(object sender, System.EventArgs e)
		{
			// get learning rate
			try
			{
				learningRate = Math.Max( 0.00001, Math.Min( 1, double.Parse( learningRateBox.Text ) ) );
			}
			catch
			{
				learningRate = 0.1;
			}
			saveStatisticsToFiles = saveFilesCheck.Checked;

			// update settings controls
			UpdateSettings( );

			// disable all settings controls
			EnableControls( false );

			// run worker thread
			needToStop = false;
			workerThread = new Thread( new ThreadStart( SearchSolution ) );
			workerThread.Start( );
		}

		// On "Stop" button click
		private void stopButton_Click(object sender, System.EventArgs e)
		{
			// stop worker thread
			needToStop = true;
			workerThread.Join( );
			workerThread = null;
		}

		// Worker thread
		void SearchSolution( )
		{
			// prepare learning data
			double[][] input = new double[samples][];
			double[][] output = new double[samples][];

			for ( int i = 0; i < samples; i++ )
			{
				input[i] = new double[2];
				output[i] = new double[classesCount];

				// set input
				input[i][0] = data[i, 0];
				input[i][1] = data[i, 1];
				// set output
				output[i][classes[i]] = 1;
			}

			// create perceptron
			ActivationNetwork	network = new ActivationNetwork( new ThresholdFunction( ), 2, classesCount );
			ActivationLayer		layer = network[0];
			// create teacher
			PerceptronLearning teacher = new PerceptronLearning( network );
			// set learning rate
			teacher.LearningRate = learningRate;

			// iterations
			int iteration = 1;

			// statistic files
			StreamWriter errorsFile = null;
			StreamWriter weightsFile = null;

			try
			{
				// check if we need to save statistics to files
				if ( saveStatisticsToFiles )
				{
					// open files
					errorsFile	= File.CreateText( "errors.csv" );
					weightsFile	= File.CreateText( "weights.csv" );
				}

				// erros list
				ArrayList errorsList = new ArrayList( );

				// loop
				while ( !needToStop )
				{
					// save current weights
					if ( weightsFile != null )
					{
						for ( int i = 0; i < classesCount; i++ )
						{
							weightsFile.Write( "neuron" + i + ";" );
							weightsFile.Write( layer[i][0] + ";" );
							weightsFile.Write( layer[i][1] + ";" );
							weightsFile.WriteLine( layer[i].Threshold );
						}
					}

					// run epoch of learning procedure
					double error = teacher.RunEpoch( input, output );
					errorsList.Add( error );

					// save current error
					if ( errorsFile != null )
					{
						errorsFile.WriteLine( error );
					}				

					// show current iteration
					iterationsBox.Text = iteration.ToString( );

					// stop if no error
					if ( error == 0 )
						break;

					// show classifiers
					for ( int j = 0; j < classesCount; j++ )
					{
						double k = - layer[j][0] / layer[j][1];
						double b = - layer[j].Threshold / layer[j][1];

						double[,] classifier = new double[2, 2] {
							{ chart.RangeX.Min, chart.RangeX.Min * k + b },
							{ chart.RangeX.Max, chart.RangeX.Max * k + b }
																};

						// update chart
						chart.UpdateDataSeries( string.Format( "classifier" + j ), classifier );
					}

					iteration++;
				}

				// show perceptron's weights
				weightsList.Items.Clear( );
				for ( int i = 0; i < classesCount; i++ )
				{
					string neuronName = string.Format( "Neuron {0}", i + 1 );

					// weight 0
					ListViewItem item = weightsList.Items.Add( neuronName );
					item.SubItems.Add( "Weight 1" );
					item.SubItems.Add( layer[i][0].ToString( "F6" ) );
					// weight 1
					item = weightsList.Items.Add( neuronName );
					item.SubItems.Add( "Weight 2" );
					item.SubItems.Add( layer[i][1].ToString( "F6" ) );
					// threshold
					item = weightsList.Items.Add( neuronName );
					item.SubItems.Add( "Threshold" );
					item.SubItems.Add( layer[i].Threshold.ToString( "F6" ) );
				}

				// show error's dynamics
				double[,] errors = new double[errorsList.Count, 2];

				for ( int i = 0, n = errorsList.Count; i < n; i++ )
				{
					errors[i, 0] = i;
					errors[i, 1] = (double) errorsList[i];
				}

				errorChart.RangeX = new DoubleRange( 0, errorsList.Count - 1 );
				errorChart.UpdateDataSeries( "error", errors );
			}
			catch ( IOException )
			{
				MessageBox.Show( "Failed writing file", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error );
			}
			finally
			{
				// close files
				if ( errorsFile != null )
					errorsFile.Close( );
				if ( weightsFile != null )
					weightsFile.Close( );
			}

			// enable settings controls
			EnableControls( true );
		}

		private void MainForm_Load(object sender, System.EventArgs e)
		{
		
		}
	}
}

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About the Author

Andrew Kirillov
Software Developer (Senior) Cisco Systems
United Kingdom United Kingdom
Started software development at about 15 years old and it seems like now it lasts most part of my life. Fortunately did not spend too much time with Z80 and BK0010 and switched to 8086 and further. Similar with programming languages – luckily managed to get away from BASIC and Pascal to things like Assembler, C, C++ and then C#. Apart from daily programming for food, do it also for hobby, where mostly enjoy areas like Computer Vision, Robotics and AI. This led to some open source stuff like AForge.NET.

Going out of computers I am just a man loving his family, enjoying traveling, a bit of books, a bit of movies and a mixture of everything else. Always wanted to learn playing guitar, but it seems like 6 strings are much harder than few dozens of keyboard’s keys. Will keep progressing ...

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