NMath User's Guide

TOC | Previous | Next | Index

34.2 Integrating Functions of Two Variables (.NET, C#, CSharp, VB, Visual Basic, F#)

The Integrate() method on TwoVariableIntegrator integrates a given two-variable function over a given region. For example, to compute the double integral:

 

 

 

First write the function:

Code Example – C# integration

private double F( DoubleVector v )

{

  return 1.0 / ( 1.0 - ( v[0] * v[0] * v[1] * v[1] ) );

}

Code Example – VB integration

Function F(V As DoubleVector) As Double

  Return 1.0 / (1.0 - (V(0) * V(0) * V(1) * V(1)))

End Function

Then encapsulate the function as a MultiVariableFunction:

Code Example – C# integration

var function = new MultiVariableFunction(

  new Func<DoubleVector, double>( F ) );

Code Example – VB integration

Dim MultiFunction As New MultiVariableFunction(

  New Func(Of DoubleVector, Double)(F))

Finally, compute the integral:

Code Example – C# integration

var integrator = new TwoVariableIntegrator();

double xLower = 0;

double xUpper = 1;

double yLower = 0;

double yUpper = 1;

double integral = integrator.Integrate( function, xLower, xUpper, 

  yLower, yUpper );

Code Example – VB integration

Dim Integrator As New TwoVariableIntegrator()

Dim XLower As Double = 0

Dim XUpper As Double = 1

Dim YLower As Double = 0

Dim YUpper As Double = 1

Dim Integral As Double = integrator.Integrate(MultiFunction, 

  XLower, XUpper, YLower, YUpper)

The code above explicitly sets the x and y bounds. You can also set the y lower bound, y upper bound, or both, as a function of x. For example, to compute this double integral:

 

 

 

First define the function:

Code Example – C# integration

private double F( DoubleVector v )

{

  return ( 9.0 * v[0] * v[0] ) - ( 3.0 * v[1] );

}

Code Example – VB integration

Function F(V As DoubleVector) As Double

  Return (9.0 * V(0) * V(0)) - (3.0 * V(1))

End Function

Then encapsulate the function as a MultiVariableFunction:

Code Example – C# integration

var function = new MultiVariableFunction(

  new Func<DoubleVector, double>( F ) );

Code Example – VB integration

Dim function As New MultiVariableFunction(

  New Func(Of DoubleVector, Double)(F))

Then define the y bounding functions and encapsulate them as OneVariableFunction objects:

Code Example – C# integration

private double YUpperF( double x )

{

  return Math.Sqrt( 9.0 - ( x * x ) );

}





private double YLowerF( double x )




{




  return -YUpperF( x );




}








var yLowerFunction = new OneVariableFunction(




  new NMathFunctions.DoubleUnaryFunction( YLowerF ) );




var yUpperFunction = new OneVariableFunction(




  new NMathFunctions.DoubleUnaryFunction( YUpperF ) );




Code Example – VB integration


Function YUpperF(X As Double) As Double




  Return Math.Sqrt(9.0 - (X * X))




End Function








Function YLowerF(X As Double) As Double




  Return -YUpperF(X)




End Function








Dim YLowerFunction As New OneVariableFunction(




  New Func(Of Double, Double)(AddressOf YLowerF))




Dim YUpperFunction As New OneVariableFunction(




  New Func(Of Double, Double)(AddressOf YUpperF))




Finally, compute the integral:


Code Example – C# integration


var integrator = new TwoVariableIntegrator();




double xLower = -3;




double xUpper = 3;




double integral = integrator.Integrate( function, xLower, xUpper,




  yLowerFunction, yUpperFunction );




Code Example – VB integration


Dim Integrator As New TwoVariableIntegrator()




Dim XLower As Double = -3




Dim Xupper As Double = 3




Dim Integral As Double = integrator.Integrate(MultiFunction,




  XLower, XUpper, YLowerFunction, YUpperFunction)








Top

		


		
	

		

	


	



Top