   Non-Adaptive Gauss-Kronrod integration method. Inheritance Hierarchy
SystemObject

Namespace:  Accord.Math.Integration
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0 Syntax
```public class NonAdaptiveGaussKronrod : IUnivariateIntegration,

The NonAdaptiveGaussKronrod type exposes the following members. Constructors
NameDescription NonAdaptiveGaussKronrod
Creates a new NonAdaptiveGaussKronrod integration algorithm. NonAdaptiveGaussKronrod(FuncDouble, Double)
Creates a new NonAdaptiveGaussKronrod integration algorithm. NonAdaptiveGaussKronrod(FuncDouble, Double, Double, Double)
Creates a new NonAdaptiveGaussKronrod integration algorithm.
Top Properties
NameDescription 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 function to be differentiated. FunctionEvaluations
Gets the number of function evaluations performed in the last call to the Compute method. Range
Gets or sets the input range under which the integral must be computed. Status
Get the exit code returned in the last call to the Compute method. ToleranceAbsolute
Desired absolute accuracy. If set to zero, this parameter will be ignored and only other requisites will be taken into account. Default is zero. ToleranceRelative
Desired relative accuracy. If set to zero, this parameter will be ignored and only other requisites will be taken into account. Default is 1e-3.
Top Methods
NameDescription Clone
Creates a new object that is a copy of the current instance. Compute
Computes the area of the function under the selected Range. The computed value will be available at this object's Area. 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)
Computes the area under the integral for the given function, in the given integration interval, using Gauss-Kronrod method.  Integrate(FuncDouble, Double, Double, Double, Double)
Computes the area under the integral for the given function, in the given integration interval, using the Non-Adaptive Gauss Kronrod algorithm. MemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.) ToString
Returns a string that represents the current object.
(Inherited from Object.)
Top Extension Methods
NameDescription 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.) ToTOverloaded.
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.)
Top Remarks

The algorithm implemented by this class has been based on the original FORTRAN implementation from QUADPACK. The function implemented the Non-adaptive Gauss- Kronrod integration is qng(f,a,b,epsabs,epsrel,result,abserr,neval,ier). The original source code is in the public domain, but this version is under the LGPL. The original authors, as long as the original routine description, are listed below:

Robert Piessens, Elise de Doncker; Applied Mathematics and Programming Division, K.U.Leuven, Leuvenappl. This routine calculates an approximation result to a given definite integral i = integral of f over (a,b), hopefully satisfying following claim for accuracy abs(i-result).le.max(epsabs,epsrel*abs(i)).

References: Examples

Let's say we would like to compute the definite integral of the function f(x) = cos(x) in the interval -1 to +1 using a variety of integration methods, including the TrapezoidalRule, RombergMethod and NonAdaptiveGaussKronrod. Those methods can compute definite integrals where the integration interval is finite:

```// Declare the function we want to integrate
Func<double, double> f = (x) => Math.Cos(x);

// We would like to know its integral from -1 to +1
double a = -1, b = +1;

// Integrate!
double trapez  = TrapezoidalRule.Integrate(f, a, b, steps: 1000); // 1.6829414
double romberg = RombergMethod.Integrate(f, a, b);                // 1.6829419
double nagk    = NonAdaptiveGaussKronrod.Integrate(f, a, b);      // 1.6829419```

Moreover, it is also possible to calculate the value of improper integrals (it is, integrals with infinite bounds) using InfiniteAdaptiveGaussKronrod, as shown below. Let's say we would like to compute the area under the Gaussian curve from -infinite to +infinite. While this function has infinite bounds, this function is known to integrate to 1.

```// Declare the Normal distribution's density function (which is the Gaussian's bell curve)
Func<double, double> g = (x) => (1 / Math.Sqrt(2 * Math.PI)) * Math.Exp(-(x * x) / 2);

// Integrate!
double iagk = InfiniteAdaptiveGaussKronrod.Integrate(g,
Double.NegativeInfinity, Double.PositiveInfinity);   // Result should be 0.99999...``` See Also