private static DiscreteDistribution Bivariate(BivariateContinuousDistribution distribution, DistributionsOperation operation)
{
if (operation == DistributionsOperation.PowerInv)
{
distribution = distribution.Rotate();
}
int samples = distribution.Samples;
double[] range = CommonRandomMath.GetRange(distribution.SupportMinLeft, distribution.SupportMaxLeft, distribution.SupportMinRight, distribution.SupportMaxRight, operation);
double[] rightAxis = CommonRandomMath.GenerateXAxis(distribution.SupportMinRight, distribution.SupportMaxRight, samples, out double rightStep);
double[] xAxis = CommonRandomMath.GenerateXAxis(range[0], range[1], samples, out double step);
double[] result = new double[samples];
switch (operation)
{
case DistributionsOperation.Add:
{
Parallel.For(0, xAxis.Length, i =>
{
double x = xAxis[i];
double sum = 0;
// Trap rule is useless because both normal and t-distributions are smoooth.
for (int j = 1; j < samples; j++)
{
double m = rightAxis[j];
sum += distribution.ProbabilityDensityFunction(x - m, m);
}
result[i] = sum * rightStep;
});
break;
}
case DistributionsOperation.Sub:
{
Parallel.For(0, xAxis.Length, i =>
{
double x = xAxis[i];
double sum = 0;
for (int j = 1; j < samples; j++)
{
double m = rightAxis[j];
sum += distribution.ProbabilityDensityFunction(x + m, m);
}
result[i] = sum * rightStep;
});
break;
}
case DistributionsOperation.Muliply:
{
Parallel.For(0, xAxis.Length, i =>
{
double x = xAxis[i];
double sum = 0;
for (int j = 1; j < samples; j++)
{
double m = rightAxis[j];
if (m != 0)
{
sum += distribution.ProbabilityDensityFunction(x / m, m) / Math.Abs(m);
}
}
result[i] = sum * rightStep;
});
break;
}
case DistributionsOperation.Divide:
{
Parallel.For(0, xAxis.Length, i =>
{
double x = xAxis[i];
double sum = 0;
for (int j = 1; j < samples; j++)
{
double m = rightAxis[j];
if (m != 0)
{
sum += distribution.ProbabilityDensityFunction(x * m, m) * Math.Abs(m);
}
}
result[i] = sum * rightStep;
});
break;
}
case DistributionsOperation.PowerInv:
{
Parallel.For(0, xAxis.Length, i =>
{
double m = 0;
double sum = 0;
double x = xAxis[i];
double d = 0;
double k = 0;
for (int j = 1; j < samples; j++)
{
m = rightAxis[j];
d = Math.Log(x, m);
k = Math.Abs(Math.Log(m) * x);
sum += distribution.ProbabilityDensityFunction(d, m) / k;
}
result[i] = sum * rightStep;
});
break;
}
case DistributionsOperation.Log:
{
Parallel.For(0, xAxis.Length, i =>
{
double m = 0;
double sum = 0;
double x = xAxis[i];
double d = 0;
double k = 0;
for (int j = 1; j < samples; j++)
{
m = rightAxis[j];
d = Math.Pow(m, x);
k = Math.Abs(Math.Log(m) * d);
sum += distribution.ProbabilityDensityFunction(d, m) * k;
}
result[i] = sum * rightStep;
});
break;
}
default:
{
throw new DistributionsInvalidOperationException();
}
}
return(new DiscreteDistribution(xAxis, result));
}
private static DiscreteDistribution TwoDiscreteDistributions(DiscreteDistribution dpdfLeft, DiscreteDistribution dpdfRight, DistributionsOperation action)
{
var exchange = Swap(dpdfLeft, dpdfRight, action, out DistributionsOperation newAction);
action = newAction;
dpdfLeft = exchange[0];
dpdfRight = exchange[1];
int lengthLeft = dpdfLeft.InnerSamples;
int lengthRight = dpdfRight.InnerSamples;
double stepRight = dpdfRight.Step;
double stepLeft = dpdfLeft.Step;
double leftMinX = dpdfLeft.MinX;
double leftMaxX = dpdfLeft.MaxX;
double[] leftX = dpdfLeft.XCoordinatesInternal;
double[] leftY = dpdfLeft.YCoordinatesInternal;
double[] rightX = dpdfRight.XCoordinatesInternal;
double[] rightY = dpdfRight.YCoordinatesInternal;
double[] yCoordinates = new double[lengthRight];
double[] range = CommonRandomMath.GetRange(dpdfLeft.InnerMinX, dpdfLeft.InnerMaxX, dpdfRight.InnerMinX, dpdfRight.InnerMaxX, action);
double[] xCoordinates = CommonRandomMath.GenerateXAxis(range[0], range[1], lengthRight, out double stepX0);
switch (action)
{
case DistributionsOperation.Add:
{
List <int> operations = new List <int>();
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double x = xCoordinates[i];
double sum = 0;
double y = 0;
double r = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
r = y * GetYByX(x - m, leftY, leftMinX, leftMaxX, stepLeft, lengthLeft);
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
yCoordinates[i] = sum * stepRight;
});
break;
}
case DistributionsOperation.Sub:
{
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double x = xCoordinates[i];
double sum = 0;
double r = 0;
double y = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
r = y * GetYByX(x + m, leftY, leftMinX, leftMaxX, stepLeft, lengthLeft);
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
yCoordinates[i] = sum * stepRight;
});
break;
}
case DistributionsOperation.Muliply:
{
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double sum = 0;
double x = xCoordinates[i];
double k = 0;
double r = 0;
double y = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
k = Math.Abs(m);
if (k != 0)
{
r = y * GetYByX(x / m, leftY, leftMinX, leftMaxX, stepLeft, lengthLeft) / k;
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
}
yCoordinates[i] = sum * stepRight;
});
// in case when both of distributions cross Oy it is inf in zero
if (dpdfLeft.MinX <= 0 && dpdfLeft.MaxX >= 0 && dpdfRight.MinX <= 0 && dpdfRight.MaxX >= 0)
{
for (int i = 0; i < lengthRight - 1; i++)
{
if (xCoordinates[i] <= 0 && xCoordinates[i + 1] > 0)
{
yCoordinates[i] = double.PositiveInfinity;
break;
}
}
}
break;
}
case DistributionsOperation.Divide:
{
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double sum = 0;
double x = xCoordinates[i];
double k = 0;
double r = 0;
double y = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
k = Math.Abs(m);
if (k != 0)
{
r = y * GetYByX(x * m, leftY, leftMinX, leftMaxX, stepLeft, lengthLeft) * k;
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
}
yCoordinates[i] = sum * stepRight;
});
break;
}
case DistributionsOperation.PowerInv:
{
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double sum = 0;
double x = xCoordinates[i];
double k = 0;
double r = 0;
double y = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
k = Math.Abs(Math.Log(m) * x);
if (k != 0)
{
r = y * GetYByX(Math.Log(x, m), leftY, leftMinX, leftMaxX, stepLeft, lengthLeft) / k;
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
}
yCoordinates[i] = sum * stepRight;
});
break;
}
case DistributionsOperation.Log:
{
Parallel.For(0, lengthRight, i =>
{
double m = 0;
double sum = 0;
double x = xCoordinates[i];
double d = 0;
double k = 0;
double r = 0;
double y = 0;
for (int j = 0; j < lengthRight; j++)
{
m = rightX[j];
y = rightY[j];
d = Math.Pow(m, x);
k = Math.Abs(Math.Log(m) * d);
if (k != 0)
{
r = y * GetYByX(d, leftY, leftMinX, leftMaxX, stepLeft, lengthLeft) * k;
if (j == 0 || j == lengthRight - 1)
{
r /= 2;
}
sum += r;
}
}
yCoordinates[i] = sum * stepRight;
});
break;
}
default:
{
throw new NotImplementedException();
}
}
var result = new DiscreteDistribution(xCoordinates, yCoordinates);
return(result);
}
