## Types in MathNet.Numerics.Integration

Type GaussLegendreRule

Namespace MathNet.Numerics.Integration

Approximates a definite integral using an Nth order Gauss-Legendre rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

### Public Constructors

#### GaussLegendreRule(double intervalBegin, double intervalEnd, int order)

Initializes a new instance of the GaussLegendreRule class.
##### Parameters
###### `double` intervalBegin

Where the interval starts, inclusive and finite.

###### `double` intervalEnd

Where the interval stops, inclusive and finite.

###### `int` order

Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

### Public Static Functions

#### ComplexContourIntegrate(Func<double, Complex> f, double invervalBegin, double invervalEnd, int order)

Approximates a definite integral using an Nth order Gauss-Legendre rule.
##### Parameters
###### `Func<double, Complex>` f

The analytic smooth complex function to integrate, defined on the real domain.

###### `double` invervalBegin

Where the interval starts, exclusive and finite.

###### `double` invervalEnd

Where the interval ends, exclusive and finite.

###### `int` order

Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

##### Return
###### `Complex`

Approximation of the finite integral in the given interval.

#### doubleIntegrate(Func<double, double> f, double invervalBegin, double invervalEnd, int order)

Approximates a definite integral using an Nth order Gauss-Legendre rule.
##### Parameters
###### `Func<double, double>` f

The analytic smooth function to integrate.

###### `double` invervalBegin

Where the interval starts, exclusive and finite.

###### `double` invervalEnd

Where the interval ends, exclusive and finite.

###### `int` order

Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

##### Return
###### `double`

Approximation of the finite integral in the given interval.

#### doubleIntegrate(Func<double, double, double> f, double invervalBeginA, double invervalEndA, double invervalBeginB, double invervalEndB, int order)

Approximates a 2-dimensional definite integral using an Nth order Gauss-Legendre rule over the rectangle [a,b] x [c,d].
##### Parameters
###### `Func<double, double, double>` f

The 2-dimensional analytic smooth function to integrate.

###### `double` invervalBeginA

Where the interval starts for the first (inside) integral, exclusive and finite.

###### `double` invervalEndA

Where the interval ends for the first (inside) integral, exclusive and finite.

###### `double` invervalBeginB

Where the interval starts for the second (outside) integral, exclusive and finite.

###### `double` invervalEndB

Where the interval ends for the second (outside) integral, exclusive and finite.

###### `int` order

Defines an Nth order Gauss-Legendre rule. The order also defines the number of abscissas and weights for the rule. Precomputed Gauss-Legendre abscissas/weights for orders 2-20, 32, 64, 96, 100, 128, 256, 512, 1024 are used, otherwise they're calculated on the fly.

##### Return
###### `double`

Approximation of the finite integral in the given interval.

### Public Methods

#### doubleGetAbscissa(int index)

Gettter for the ith abscissa.
##### Parameters
###### `int` index

Index of the ith abscissa.

##### Return
###### `double`

The ith abscissa.

#### doubleGetWeight(int index)

Getter for the ith weight.
##### Parameters
###### `int` index

Index of the ith weight.

The ith weight.

### Public Properties

#### Double[]Abscissas get;

Getter that returns a clone of the array containing the abscissas.

#### doubleIntervalBegin get;

Getter for the InvervalBegin.

#### doubleIntervalEnd get;

Getter for the InvervalEnd.

#### intOrder get;

Getter for the order.

#### Double[]Weights get;

Getter that returns a clone of the array containing the weights.