public void Test__NormalizeDataForInOut()
{
/*
-1 -1 1;
-1 1 -1;
1 -1 -1;
1 1 1
*/
Input i = new Input(4,3);
i[0, 0] = -1;
i[0, 1] = -1;
i[0, 2] = 1;
i[1, 0] = -1;
i[1, 1] = 1;
i[1, 2] = -1;
i[2, 0] = 1;
i[2, 1] = -1;
i[2, 2] = -1;
i[3, 0] = 1;
i[3, 1] = 1;
i[3, 2] = 1;
var input = i.CopyColumns(i.Cols - 2).ToInput();
Assert.AreEqual(2, input.Cols);
Assert.AreEqual(4, input.Rows);
input.Normalize();
/*
-1 -1
-1 1
1 -1
1 1
*/
Assert.AreEqual(-1, input[0, 0]); Assert.AreEqual(-1, input[0, 1]);
Assert.AreEqual(-1, input[1, 0]); Assert.AreEqual(1, input[1, 1]);
Assert.AreEqual(1, input[2, 0]); Assert.AreEqual(-1, input[2, 1]);
Assert.AreEqual(1, input[3, 0]); Assert.AreEqual(1, input[3, 1]);
var output = i.LastColumn.ToOutput();
Assert.AreEqual(1, output.Cols);
Assert.AreEqual(4, output.Rows);
output.Normalize();
Assert.AreEqual(1, output[0, 0]);
Assert.AreEqual(0, output[1, 0]);
Assert.AreEqual(0, output[2, 0]);
Assert.AreEqual(1, output[3, 0]);
/*
1
0
0
1
*/
}
/// <summary>
/// Convert MatrixMB to Input
/// </summary>
/// <param name="mat">MatrixMB</param>
/// <returns>Input</returns>
public static Input ToInput(this MatrixMB mat)
{
Input input = new Input(mat.Rows, mat.Cols);
for (int col = 0; col < mat.Cols; col++)
{
for (int row = 0; row < mat.Rows; row++)
{
input.Data[row][col] = mat.Data[row][col];
}
}
return input;
}
public void Test___Error___Calculation___Test()
{
/*
*
*
Kod testowy matlaba
*
function obliczanie_bledu()
inp = [-1 -1;-1 1; 1 -1];
dout = [1;0;0];
topo = [3 1 2 4 1 2 3];
w = [1 1 1 1 1 1 1];
act = [2 0];
gain = [1 1];
param = [3 2 1 7 2];
iw = [1 4 8];
format long;
error = calculate_error(inp,dout,topo,w,act,gain,param,iw);
fprintf('Obliczanie błędu uczenia sieci\nBłąd wynosi: %.20f\n', error);
%Otrzymany wynik
%Obliczanie błędu uczenia sieci
%Błąd wynosi: 13.83283022280404000000
end
*
*
*/
Input input = new Input(3, 2);//inp = [-1 -1;-1 1; 1 -1];
input[0, 0] = -1;
input[0, 1] = -1;
input[1, 0] = -1;
input[1, 1] = 1;
input[2, 0] = 1;
input[2, 1] = -1;
Output output = new Output(3, 1);//dout = [1;0;0];
output[0, 0] = 1;
output[1, 0] = 0;
output[2, 0] = 0;
NetworkInfo info = new NetworkInfo();//param = [3 2 1 7 2];
info.ni = 2;
info.nn = 2;
info.no = 1;
info.np = 3;
info.nw = 7;
VectorHorizontal vh = new VectorHorizontal(3);
vh[0, 0] = 2;
vh[0, 1] = 1;
vh[0, 2] = 1;
Topography topo = Topography.Generate(TopographyType.BMLP, vh);//topo = [3 1 2 4 1 2 3];
//w C# indeksy są od zera a nie od 1 więc wszystko o 1 w dół przestawione jest
Assert.AreEqual(2, topo[0]);
Assert.AreEqual(0, topo[1]);
Assert.AreEqual(1, topo[2]);
Assert.AreEqual(3, topo[3]);
Assert.AreEqual(0, topo[4]);
Assert.AreEqual(1, topo[5]);
Assert.AreEqual(2, topo[6]);
Weights weights = new Weights(info.nw);//w = [1 1 1 1 1 1 1];
weights.FillWithNumber(1);//załatwione
Activation act = new Activation(2);//act = [2 0];
act[0] = 2;
act[1] = 0;
Gain gain = new Gain(2);//gain = [1 1];
gain[0] = 1;
gain[1] = 1;
Index iw = Index.Find(ref topo);//iw = [1 4 8];
//ta sama sytuacja, indeksy od 0 startują
Assert.AreEqual(0, iw[0]);
Assert.AreEqual(3, iw[1]);
Assert.AreEqual(7, iw[2]);
NetworkError ne = new NetworkError();
var error = ne.CalculateError(ref info, ref input, ref output, ref topo, weights, ref act, ref gain, ref iw);
double errorFromMatLab = 13.83283022280404000000;
Console.WriteLine("Testowanie obliczania błędu");
Console.WriteLine("Użyte dane:");
Console.WriteLine("\nDane wejściowe:");
Console.WriteLine(input.MatrixToString());
Console.WriteLine("\nDane wyjściowe:");
Console.WriteLine(output.MatrixToString());
Console.WriteLine("\nWagi;");
Console.WriteLine(weights.MatrixToString());
Console.WriteLine("\nTopologia:");
Console.WriteLine(topo.MatrixToString());
Console.WriteLine("\nIndeksy topologii:");
Console.WriteLine(iw.MatrixToString());
Console.WriteLine("\nFunkcje aktywacji:");
Console.WriteLine(act.MatrixToString());
Console.WriteLine("\nWzmocnienia (gains):");
Console.WriteLine(gain.MatrixToString());
Console.WriteLine("\nParametry (param):");
Console.WriteLine(info.ToString());
Assert.AreEqual(errorFromMatLab, error);
Console.WriteLine(string.Format("{0} - wynik NBN C#",error));
Console.WriteLine(string.Format("{0} - wynik NBN w MatLabie",errorFromMatLab));
}
/// <summary>
/// Initialize NBN with data from specified file
/// </summary>
/// <param name="filename">String - filename</param>
/// <returns>bool - success flag</returns>
private bool loadInputData(String filename)
{
try
{
if (!File.Exists(filename))
{
throw new NeuralNetworkError(String.Format(Properties.Settings.Default.NBN1, filename));
}
try
{
var data = MatrixMB.Load(filename);
if (MatLabCompareDataFolder.Length > 0)
{
//data from matlab are normalized
string name = Path.GetFileNameWithoutExtension(Directory.GetFiles(MatLabCompareDataFolder, "*.dat")[0]);
inputLearn = MatrixMB.Load(string.Format("{0}\\uczenie_wejscie_{1}.txt", MatLabCompareDataFolder, name)).ToInput();
inputTest = MatrixMB.Load(string.Format("{0}\\testowanie_wejscie_{1}.txt", MatLabCompareDataFolder, name)).ToInput();
outputLearn = MatrixMB.Load(string.Format("{0}\\uczenie_wyjscie_{1}.txt", MatLabCompareDataFolder, name)).ToOutput();
outputTest = MatrixMB.Load(string.Format("{0}\\testowanie_wyjscie_{1}.txt", MatLabCompareDataFolder, name)).ToOutput();
}
else
{
input = data.CopyColumnsWithoutLast().ToInput();
input.Normalize();
output = data.LastColumn.ToOutput();
output.Normalize();
if (IsClassification)
{
int Tnp = data.Rows;
inputLearn = input.CopyRows(Tnp - 1).ToInput();
inputTest = input.CopyRows(Tnp - 1).ToInput();
outputLearn = output.CopyRows(Tnp - 1).ToOutput();
outputTest = output.CopyRows(Tnp - 1).ToOutput();
}
else
{
int[] ind = data.Rows.RandomPermutation();
int Tnp = Math.Round(data.Rows * 0.7).ToInt();
inputTest = input.CopyRows(Tnp, input.Rows - 1).ToInput();
inputLearn = input.CopyRows(Tnp - 1).ToInput();
outputTest = output.CopyRows(Tnp, input.Rows - 1).ToOutput();
outputLearn = output.CopyRows(Tnp - 1).ToOutput();
}
}
try
{
if (IsResearchMode)//export for matlab - out of use
{
string name = Path.GetFileNameWithoutExtension(filename);
DateTime d = DateTime.Now;
string dir = String.Format("{0}\\Executed research\\{1}\\{2}_{3}_{4}_{5}_{6}_{7}",
Path.GetDirectoryName(filename), name,
d.Year, d.Month, d.Day, d.Hour, d.Minute, d.Second);
if (!Directory.Exists(dir)) Directory.CreateDirectory(dir);
extractionFolder = dir;
_reasearch_folder = dir;
string learn_input = String.Format("{0}\\{1}_learn_input.dat", dir, name);
string test_input = String.Format("{0}\\{1}_test_input.dat", dir, name);
string learn_output = String.Format("{0}\\{1}_learn_output.dat", dir, name);
string test_output = String.Format("{0}\\{1}_test_output.dat", dir, name);
string initialWweights = String.Format("{0}\\{1}_initial_weights.dat", dir, name);
inputTest.Store(test_input);
inputLearn.Store(learn_input);
outputTest.Store(test_output);
outputLearn.Store(learn_output);
}
}
catch (Exception)
{ }
}
catch (Exception iex)
{
throw new NeuralNetworkError(String.Format(Properties.Settings.Default.NBN2, filename), iex);
}
return true;
}
catch (Exception ex)
{
updateErrorNBN(ex);
return false;
}
}
/// <summary>
/// Checks data
/// </summary>
/// <param name="inp">Input - input patterns</param>
/// <param name="dout">Output</param>
/// <param name="topo">Topology</param>
/// <param name="iw">Index</param>
/// <returns>NetworkInfo</returns>
private NetworkInfo checkInputs(ref Input inp, ref Output dout, ref Topography topo, out Index iw)
{
if (topo.Length == 0) throw new NeuralNetworkError(Properties.Settings.Default.FE4);
if (!topo.IsCorrect) throw new NeuralNetworkError(Properties.Settings.Default.FE3);
if (inp.Rows != dout.Rows) throw new NeuralNetworkError(Properties.Settings.Default.FE2);
NetworkInfo info = new NetworkInfo();
iw = Index.Find(ref topo);
info.np = inp.Rows;
info.ni = inp.Cols;
info.no = dout.Cols;
info.nw = topo.Length;
info.nn = iw.Length - 1;
return info;
}
/// <summary>
/// Train neural netowrk
/// </summary>
/// <param name="setting">NeuralNetworkSettings</param>
/// <param name="info">NetworkInfo</param>
/// <param name="inp">Input</param>
/// <param name="dout">Output</param>
/// <param name="topo">Topography</param>
/// <param name="initialWeights">Weights</param>
/// <param name="act">Activation</param>
/// <param name="gain">Gain</param>
/// <param name="iw">Index</param>
public TrainResult Train(ref NeuralNetworkSettings setting, ref NetworkInfo info, ref Input inp, ref Output dout,
ref Topography topo, Weights initialWeights, ref Activation act, ref Gain gain, ref Index iw)
{
TrainResult result = new TrainResult();
result.weights = new Weights(initialWeights.Length);
result.iterations = 0;
result.sse = 0;
try
{
if (OnDebug != null)
{
debug(setting.ToString());
debug(act.ToString());
debug(gain.ToString());
}
result.weights = initialWeights.Backup();
error.CalculateError(ref info, ref inp, ref dout, ref topo, result.weights, ref act, ref gain, ref iw);
if (OnDebug != null)
{
debug("\r\nFirst error value: " + error.Error.ToString() + "\r\n");
}
SSE.Clear();
RMSE.Clear();
SSE[0] = result.sse = error.Error;
hessians.Clear();
var hessian = new Hessian(ref info);
Input ii = inp.Copy().ToInput();
Output oo = dout.Copy().ToOutput();
for (result.iterations = 1; result.iterations < setting.MaxIterations; result.iterations++)
{
hessian.Compute(ref info, ref inp, ref dout, ref topo, result.weights, ref act, ref gain, ref iw);
if (OnDebug != null) debug(hessian.ToString());
hessians.Add(hessian.HessianMat);
Weights ww_backup = result.weights.Backup();
for (int jw = 0; jw < 30; jw++)
{
var diff = (hessian.HessianMat + (I * setting.MU)).SolveEquatation(hessian.GradientMat).Transposed;
if (OnDebug != null)
{
debug("\r\nOdejmuję");
debug(diff.MatrixToString());
}
result.weights = ww_backup - diff.ToWeights();
result.weights.Name = "Weights nr " + jw.ToString();
if (OnDebug != null)
{
bool areSame = result.weights.IsEqual(ww_backup);
debug("\r\nWeights are same as previously backed up");
debug(result.weights.ToString());
}
SSE[result.iterations] = result.sse = error.CalculateError(ref info, ref inp, ref dout, ref topo, result.weights, ref act, ref gain, ref iw);
if (OnDebug != null) debug("\r\nSSE[" + result.iterations.ToString() + "] = " + error.Error.ToString());
if (SSE.CurrentSSE() <= SSE.PreviousSSE(result.iterations))
{
if (setting.MU > setting.MUL)
{
setting.MU /= setting.Scale;
}
break;
}
if (setting.MU < setting.MUH)
{
setting.MU *= setting.Scale;
}
}
double rmse = Math.Sqrt((SSE.CurrentSSE()) / inp.Rows);
RMSE[result.iterations] = rmse;
updateChart(result.iterations, rmse);
if ((double)SSE[result.iterations] < setting.MaxError)
{
break;
}
if (OnDebug != null) debug("Błąd: " + rmse.ToString());
if (
(SSE.PreviousSSE(result.iterations) - ((double)SSE[result.iterations]))
/
SSE.PreviousSSE(result.iterations)
<
NetworkError.DesiredError//0.000000000000001
)
{
break;
}
}
}
catch (Exception ex)
{
throw new NeuralNetworkError("Błąd uczenia sieci. " + ex.Message, ex);
}
return result;
}
public void Hessian___Gradient___Calculation___Test()
{
int accuracy = 15;
/*
function obliczanie_hesjan_gradient()
clear();
inp = [-1 -1;-1 1; 1 -1];
dout = [1;0;0];
topo = [3 1 2 4 1 2 3];
ww = [1 1 1 1 1 1 1];
act = [2 0];
gain = [1 1];
param = [3 2 1 7 2];
iw = [1 4 8];
format long;
[gradient,hessian] = Hessian(inp,dout,topo,ww,act,gain,param,iw);
fprintf('Otrzymany gradient:\n');
disp(gradient);
fprintf('\nOtrzymany hesjan:\n');
disp(hessian);
% To jest otrzymywane
% Otrzymany gradient:
% -0.839948683228052
% 2.319597374905329
% 2.319597374905329
% -2.000000000000000
% 5.523188311911530
% 5.523188311911531
% 6.889667569278484
%
%
% Otrzymany hesjan:
% Columns 1 through 6
%
% 1.058270685684809 -0.705513790456539 -0.705513790456539 2.519846049684157 -1.679897366456105 -1.679897366456105
% -0.705513790456539 1.058270685684809 0.352756895228269 -1.679897366456105 2.519846049684157 0.839948683228052
% -0.705513790456539 0.352756895228269 1.058270685684809 -1.679897366456105 0.839948683228052 2.519846049684157
% 2.519846049684157 -1.679897366456105 -1.679897366456105 6.000000000000000 -4.000000000000000 -4.000000000000000
% -1.679897366456105 2.519846049684157 0.839948683228052 -4.000000000000000 6.000000000000000 2.000000000000000
% -1.679897366456105 0.839948683228052 2.519846049684157 -4.000000000000000 2.000000000000000 6.000000000000000
% -0.639700008449225 1.279400016898449 1.279400016898449 -1.523188311911530 3.046376623823059 3.046376623823059
%
% Column 7
%
% -0.639700008449225
% 1.279400016898449
% 1.279400016898449
% -1.523188311911530
% 3.046376623823059
% 3.046376623823059
% 3.480153950315843
end
*/
Input input = new Input(3, 2);//inp = [-1 -1;-1 1; 1 -1];
input[0, 0] = -1;
input[0, 1] = -1;
input[1, 0] = -1;
input[1, 1] = 1;
input[2, 0] = 1;
input[2, 1] = -1;
Output output = new Output(3, 1);//dout = [1;0;0];
output[0, 0] = 1;
output[1, 0] = 0;
output[2, 0] = 0;
NetworkInfo info = new NetworkInfo();//param = [3 2 1 7 2];
info.ni = 2;
info.nn = 2;
info.no = 1;
info.np = 3;
info.nw = 7;
VectorHorizontal vh = new VectorHorizontal(3);
vh[0, 0] = 2;
vh[0, 1] = 1;
vh[0, 2] = 1;
Topography topo = Topography.Generate(TopographyType.BMLP, vh);//topo = [3 1 2 4 1 2 3];
//w C# indeksy są od zera a nie od 1 więc wszystko o 1 w dół przestawione jest
Assert.AreEqual(2, topo[0]);
Assert.AreEqual(0, topo[1]);
Assert.AreEqual(1, topo[2]);
Assert.AreEqual(3, topo[3]);
Assert.AreEqual(0, topo[4]);
Assert.AreEqual(1, topo[5]);
Assert.AreEqual(2, topo[6]);
Weights weights = new Weights(info.nw);//w = [1 1 1 1 1 1 1];
weights.FillWithNumber(1);//załatwione
Activation act = new Activation(2);//act = [2 0];
act[0] = 2;
act[1] = 0;
Gain gain = new Gain(2);//gain = [1 1];
gain[0] = 1;
gain[1] = 1;
Index iw = Index.Find(ref topo);//iw = [1 4 8];
//ta sama sytuacja, indeksy od 0 startują
Assert.AreEqual(0, iw[0]);
Assert.AreEqual(3, iw[1]);
Assert.AreEqual(7, iw[2]);
Console.WriteLine("Testowanie obliczania gradientu i macierzy hesjana");
Console.WriteLine("Użyte dane:");
Console.WriteLine("\nDane wejściowe:");
Console.WriteLine(input.MatrixToString());
Console.WriteLine("\nDane wyjściowe:");
Console.WriteLine(output.MatrixToString());
Console.WriteLine("\nWagi;");
Console.WriteLine(weights.MatrixToString());
Console.WriteLine("\nTopologia:");
Console.WriteLine(topo.MatrixToString());
Console.WriteLine("\nIndeksy topologii:");
Console.WriteLine(iw.MatrixToString());
Console.WriteLine("\nFunkcje aktywacji:");
Console.WriteLine(act.MatrixToString());
Console.WriteLine("\nWzmocnienia (gains):");
Console.WriteLine(gain.MatrixToString());
Console.WriteLine("\nParametry (param):");
Console.WriteLine(info.ToString());
Hessian hess = new Hessian(ref info);
hess.Compute(ref info, ref input, ref output, ref topo, weights, ref act, ref gain, ref iw);
var g = hess.GradientMat;
var h = hess.HessianMat;
Console.WriteLine("\nSprawdzanie gradientu z dokładnością do 15 miejsc po przecinku");
var matG = new double[] { -0.839948683228052, 2.319597374905329, 2.319597374905329, -2.000000000000000, 5.523188311911530, 5.523188311911531, 6.889667569278484 };
/*
% Otrzymany gradient:
% -0.839948683228052
% 2.319597374905329
% 2.319597374905329
% -2.000000000000000
% 5.523188311911530
% 5.523188311911531
% 6.889667569278484
*/
for (int i = 0; i < matG.Length; i++)
{
Console.WriteLine(string.Format("NBN C#: {0}\tMatLab NBN: {1}\t{2}", Math.Round(g[i, 0], accuracy), matG[i], Math.Round(g[i, 0], accuracy) == matG[i] ? "OK" : "źle"));
}
Assert.AreEqual(-0.839948683228052, Math.Round(g[0, 0], accuracy));
Assert.AreEqual(2.319597374905329, Math.Round(g[1, 0], accuracy));
Assert.AreEqual(2.319597374905329, Math.Round(g[2, 0], accuracy));
Assert.AreEqual(-2.000000000000000, Math.Round(g[3, 0], accuracy));
Assert.AreEqual(5.523188311911530, Math.Round(g[4, 0], accuracy));
Assert.AreEqual(5.523188311911531, Math.Round(g[5, 0], accuracy));
Assert.AreEqual(6.889667569278484, Math.Round(g[6, 0], accuracy));
Console.WriteLine("\nSprawdzanie macierzy hesjana\nPorównania z dokładnością do 15 miejsc po przecinku");
MatrixMB matH = new MatrixMB(7, 7);
//col 1
matH[0, 0] = 1.058270685684809;
matH[1, 0] = -0.705513790456539;
matH[2, 0] = -0.705513790456539;
matH[3, 0] = 2.519846049684157;
matH[4, 0] = -1.679897366456105;
matH[5, 0] = -1.679897366456105;
matH[6, 0] = -0.639700008449225;
//col 2
matH[0, 1] = -0.705513790456539;
matH[1, 1] = 1.058270685684809;
matH[2, 1] = 0.352756895228269;
matH[3, 1] = -1.679897366456105;
matH[4, 1] = 2.519846049684157;
matH[5, 1] = 0.839948683228052;
matH[6, 1] = 1.279400016898449;
//col 3
matH[0, 2] = -0.705513790456539;
matH[1, 2] = 0.352756895228269;
matH[2, 2] = 1.058270685684809;
matH[3, 2] = -1.679897366456105;
matH[4, 2] = 0.839948683228052;
matH[5, 2] = 2.519846049684157;
matH[6, 2] = 1.279400016898449;
//col 4
matH[0, 3] = 2.519846049684157;
matH[1, 3] = -1.679897366456105;
matH[2, 3] = -1.679897366456105;
matH[3, 3] = 6.000000000000000;
matH[4, 3] = -4.000000000000000;
matH[5, 3] = -4.000000000000000;
matH[6, 3] = -1.523188311911530;
//col 5
matH[0, 4] = -1.679897366456105;
matH[1, 4] = 2.519846049684157;
matH[2, 4] = 0.839948683228052;
matH[3, 4] = -4.000000000000000;
matH[4, 4] = 6.000000000000000;
matH[5, 4] = 2.000000000000000;
matH[6, 4] = 3.046376623823059;
//col 6
matH[0, 5] = -1.679897366456105;
matH[1, 5] = 0.839948683228052;
matH[2, 5] = 2.519846049684157;
matH[3, 5] = -4.000000000000000;
matH[4, 5] = 2.000000000000000;
matH[5, 5] = 6.000000000000000;
matH[6, 5] = 3.046376623823059;
//col 7
matH[0, 6] = -0.639700008449225;
matH[1, 6] = 1.279400016898449;
matH[2, 6] = 1.279400016898449;
matH[3, 6] = -1.523188311911530;
matH[4, 6] = 3.046376623823059;
matH[5, 6] = 3.046376623823059;
matH[6, 6] = 3.480153950315843;
for (int k = 0; k < h.Cols; k++)
{
Console.WriteLine(string.Format("Kolumna {0}", k + 1));
for (int w = 0; w < h.Rows; w++)
{
decimal dh = Math.Round((decimal)h[w, k], accuracy);
decimal dmh = Math.Round((decimal)matH[w, k], accuracy);
Console.WriteLine(string.Format("NBN C#: {0}\tMatLab NBN: {1}\t{2}", dh, dmh, dh == dmh ? "OK" : "źle"));
}
Console.WriteLine("");
}
for (int k = 0; k < h.Cols; k++)
{
for (int w = 0; w < h.Rows; w++)
{
decimal dh = Math.Round((decimal)h[w, k], accuracy);
decimal dmh = Math.Round((decimal)matH[w, k], accuracy);
Assert.AreEqual(dmh, dh);
}
}
/*
% Otrzymany hesjan:
% Columns 1 through 6
%
% 1.058270685684809 -0.705513790456539 -0.705513790456539 2.519846049684157 -1.679897366456105 -1.679897366456105
% -0.705513790456539 1.058270685684809 0.352756895228269 -1.679897366456105 2.519846049684157 0.839948683228052
% -0.705513790456539 0.352756895228269 1.058270685684809 -1.679897366456105 0.839948683228052 2.519846049684157
% 2.519846049684157 -1.679897366456105 -1.679897366456105 6.000000000000000 -4.000000000000000 -4.000000000000000
% -1.679897366456105 2.519846049684157 0.839948683228052 -4.000000000000000 6.000000000000000 2.000000000000000
% -1.679897366456105 0.839948683228052 2.519846049684157 -4.000000000000000 2.000000000000000 6.000000000000000
% -0.639700008449225 1.279400016898449 1.279400016898449 -1.523188311911530 3.046376623823059 3.046376623823059
%
% Column 7
%
% -0.639700008449225
% 1.279400016898449
% 1.279400016898449
% -1.523188311911530
% 3.046376623823059
% 3.046376623823059
% 3.480153950315843
*/
}