public Form1()
{
InitializeComponent();
//Main objective function
Func <DV, D> fOBJ = delegate(DV abx)
{
// y = a*ln(x) + b
D a = abx[0];
D b = abx[1];
D x = abx[2];
//Calculate result
D r = a * AD.Log(x) + b;
//D r = a * x*x+ b;
return(r);
};
//Original Dataset Variables
const double aOrig = 3.0;
const double bOrig = 8.0;
double[] xOrig = new double[100];
double[] yOrig = new double[100];
#region Calculate Original data
//Calculate original dataset
for (int x = 0; x < 100; x++)
{
xOrig[x] = x + 1;
DV param = new DV(new D[] { aOrig, bOrig, xOrig[x] });
yOrig[x] = fOBJ(param);
}
//Create series
Series origSeries = new Series("Original")
{
ChartType = SeriesChartType.Line,
Color = Color.Black,
BorderDashStyle = ChartDashStyle.Solid,
BorderWidth = 2,
ChartArea = chartResults.ChartAreas[0].Name,
LegendText = "Original a=" + aOrig.ToString("F3") + " b=" + bOrig.ToString("F3")
};
for (int i = 0; i < xOrig.Length; i++)
{
origSeries.Points.AddXY(xOrig[i], yOrig[i]);
}
#endregion
#region Calculate random error version
double[] yNoisy = new double[100];
Random rand = new Random();
//Noisy version
for (int i = 0; i < xOrig.Length; i++)
{
double percentModifyA = 0.98 + (1.02 - 0.98) * rand.NextDouble();
double percentModifyB = 0.98 + (1.02 - 0.98) * rand.NextDouble();
double percentModifyY = 1.0; // 0.98 + (1.02 - 0.98) * rand.NextDouble();
DV param = new DV(new D[] { aOrig *percentModifyA, bOrig *percentModifyB, xOrig[i] });
yNoisy[i] = fOBJ(param) * percentModifyY;
}
//Create series
Series noisySeries = new Series("Noisy")
{
ChartType = SeriesChartType.Point,
Color = Color.DarkGray,
MarkerStyle = MarkerStyle.Star4,
MarkerSize = 7,
BorderWidth = 0,
ChartArea = chartResults.ChartAreas[0].Name
};
for (int i = 0; i < xOrig.Length; i++)
{
noisySeries.Points.AddXY(xOrig[i], yNoisy[i]);
}
#endregion
#region Calculate a and b using error function and gradient descent
//Error equation
Func <DV, D> fMSE = delegate(DV ab)
{
//Get parameters
D a = ab[0];
D b = ab[1];
//Compute squared error for each point
D errorSum = 0;
for (int i = 0; i < xOrig.Length; i++)
{
//Compute object function value
DV param = new DV(new D[] { a, b, xOrig[i] });
D yCalc = fOBJ(param);
//Check for error
if (double.IsNaN(yCalc))
{
continue;
}
//Compute error between noisy version and calculated version
D err = AD.Pow(yNoisy[i] - yCalc, 2);
errorSum += err;
}
//Compute least square
D mse = AD.Pow(errorSum, 0.5);
//return results
return(mse);
};
//Calculate optimization for a and b
DV startPoint = new DV(new D[] { 10, 5 });
int calcsF;
int calcsGradient;
DV result = GradientDescent.FirstOrder_OneDimensionalMethod(fMSE, startPoint, 0.01, out calcsF, out calcsGradient);//, out calcsHessian);
double aFit = result[0];
double bFit = result[1];
DV paramMseFit = new DV(new D[] { aFit, bFit });
double mseFit = fMSE(paramMseFit);
//Create series
Series fitSeries = new Series("Fit")
{
ChartType = SeriesChartType.Point,
Color = Color.Red,
MarkerSize = 3,
MarkerStyle = MarkerStyle.Circle,
ChartArea = chartResults.ChartAreas[0].Name,
LegendText = "Fit a=" + aFit.ToString("F3") + " b=" + bFit.ToString("F3") + " MSE=" + mseFit.ToString("F3")
};
for (int i = 0; i < xOrig.Length; i++)
{
DV param = new DV(new D[] { aFit, bFit, xOrig[i] });
fitSeries.Points.AddXY(xOrig[i], fOBJ(param));
}
#endregion
//Add series to chart
chartResults.Series.Clear();
chartResults.Series.Add(origSeries);
chartResults.Series.Add(noisySeries);
chartResults.Series.Add(fitSeries);
}
