Types in MathNet.Numerics.Integration

Type NewtonCotesTrapeziumRule

Namespace MathNet.Numerics.Integration

Approximation algorithm for definite integrals by the Trapezium rule of the Newton-Cotes family.

Public Static Functions

ComplexContourIntegrateAdaptive(Func<double, Complex> f, double intervalBegin, double intervalEnd, double targetError)

Adaptive approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, Complex>` f

The analytic smooth complex function to integrate, define don real domain.

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`double` targetError

The expected accuracy of the approximation.

Return
`Complex`

Approximation of the finite integral in the given interval.

ComplexContourIntegrateAdaptiveTransformedOdd(Func<double, Complex> f, double intervalBegin, double intervalEnd, IEnumerable<Double[]> levelAbscissas, IEnumerable<Double[]> levelWeights, double levelOneStep, double targetRelativeError)

Adaptive approximation of the definite integral by the trapezium rule.
Parameters
`Func<double, Complex>` f

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

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`IEnumerable<Double[]>` levelAbscissas

Abscissa vector per level provider.

`IEnumerable<Double[]>` levelWeights

Weight vector per level provider.

First Level Step

`double` targetRelativeError

The expected relative accuracy of the approximation.

Return
`Complex`

Approximation of the finite integral in the given interval.

ComplexContourIntegrateComposite(Func<double, Complex> f, double intervalBegin, double intervalEnd, int numberOfPartitions)

Composite N-point approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, Complex>` f

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

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`int` numberOfPartitions

Number of composite subdivision partitions.

Return
`Complex`

Approximation of the finite integral in the given interval.

ComplexContourIntegrateTwoPoint(Func<double, Complex> f, double intervalBegin, double intervalEnd)

Direct 2-point approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, Complex>` f

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

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

Return
`Complex`

Approximation of the finite integral in the given interval.

doubleIntegrateAdaptive(Func<double, double> f, double intervalBegin, double intervalEnd, double targetError)

Adaptive approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, double>` f

The analytic smooth function to integrate.

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`double` targetError

The expected accuracy of the approximation.

Return
`double`

Approximation of the finite integral in the given interval.

doubleIntegrateAdaptiveTransformedOdd(Func<double, double> f, double intervalBegin, double intervalEnd, IEnumerable<Double[]> levelAbscissas, IEnumerable<Double[]> levelWeights, double levelOneStep, double targetRelativeError)

Adaptive approximation of the definite integral by the trapezium rule.
Parameters
`Func<double, double>` f

The analytic smooth function to integrate.

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`IEnumerable<Double[]>` levelAbscissas

Abscissa vector per level provider.

`IEnumerable<Double[]>` levelWeights

Weight vector per level provider.

First Level Step

`double` targetRelativeError

The expected relative accuracy of the approximation.

Return
`double`

Approximation of the finite integral in the given interval.

doubleIntegrateComposite(Func<double, double> f, double intervalBegin, double intervalEnd, int numberOfPartitions)

Composite N-point approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, double>` f

The analytic smooth function to integrate.

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

`int` numberOfPartitions

Number of composite subdivision partitions.

Return
`double`

Approximation of the finite integral in the given interval.

doubleIntegrateTwoPoint(Func<double, double> f, double intervalBegin, double intervalEnd)

Direct 2-point approximation of the definite integral in the provided interval by the trapezium rule.
Parameters
`Func<double, double>` f

The analytic smooth function to integrate.

`double` intervalBegin

Where the interval starts, inclusive and finite.

`double` intervalEnd

Where the interval stops, inclusive and finite.

Return
`double`

Approximation of the finite integral in the given interval.