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MonteCarloIntegration Class |
Inheritance HierarchyAccord.Math.IntegrationMonteCarloIntegration
Namespace: Accord.Math.Integration
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntaxpublic class MonteCarloIntegration : INumericalIntegration, ICloneable, IMultidimensionalIntegration
The MonteCarloIntegration type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | MonteCarloIntegration(Int32) |
Constructs a new Monte Carlo integration method.
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| MonteCarloIntegration(Int32, FuncDouble, Double) |
Constructs a new Monte Carlo integration method.
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Properties| Name | Description | |
|---|---|---|
 | Area |
Gets the numerically computed result of the
definite integral for the specified function.
|
| Error |
Gets the integration error for the
computed Area value.
|
| Function |
Gets or sets the multidimensional function
whose integral should be computed.
|
| Iterations |
Gets or sets the number of random samples
(iterations) generated by the algorithm.
|
| NumberOfParameters |
Gets the number of parameters expected by
the Function to be integrated.
|
| Random |
Gets or sets the random generator algorithm to be used within
this Monte Carlo method.
|
| Range |
Gets or sets the range of each input variable
under which the integral must be computed.
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Methods| Name | Description | |
|---|---|---|
| Clone |
Creates a new object that is a copy of the current instance.
|
| Compute | |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
 | Integrate(FuncDouble, Double, Double, Double) | |
| Integrate(FuncDouble, Double, Double, Double, Int32) |
Computes the area under the integral for the given function, in the
given integration interval, using a Monte Carlo integration algorithm.
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| Integrate(FuncDouble, Double, Double, Double, Int32) | |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| Reset |
Manually resets the previously computed area and error
estimates, so the integral can be computed from scratch
without reusing previous computations.
|
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
Extension Methods| Name | Description | |
|---|---|---|
 | HasMethod |
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) |
| IsEqual |
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.) |
| To(Type) | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |
| ToT | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |
RemarksIn mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly choose points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integrals. There are different methods to perform a Monte Carlo integration, such as uniform sampling, stratified sampling and importance sampling.
References:
ExamplesA common Monte-Carlo integration example is to compute the value of Pi. This is the same example given in Wikipedia's page for Monte-Carlo Integration, available at https://en.wikipedia.org/wiki/Monte_Carlo_integration#Example
// Define a function H that tells whether two points // are inside a unit circle (a circle of radius one): // Func<double, double, double> H = (x, y) => (x * x + y * y <= 1) ? 1 : 0; // We will check how many points in the square (-1,-1), (-1,+1), // (+1, -1), (+1, +1) fall into the circle defined by function H. // double[] from = { -1, -1 }; double[] to = { +1, +1 }; int samples = 100000; // Integrate it! double area = MonteCarloIntegration.Integrate(x => H(x[0], x[1]), from, to, samples); // Output should be approximately 3.14.
See Also