Namespaces

Types in MathNet.Numerics

Type ContourIntegrate

Namespace MathNet.Numerics

Numerical Contour Integration of a complex-valued function over a real variable,.

Static Functions

Public Static Functions

Complex DoubleExponential(Func<double, Complex> f, double intervalBegin, double intervalEnd, double targetAbsoluteError)

Approximation of the definite integral of an analytic smooth complex function by double-exponential quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.
Parameters
Func<double, Complex> f

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

double intervalBegin

Where the interval starts.

double intervalEnd

Where the interval stops.

double targetAbsoluteError

The expected relative accuracy of the approximation.

Return
Complex

Approximation of the finite integral in the given interval.

Complex GaussKronrod(Func<double, Complex> f, double intervalBegin, double intervalEnd, double targetRelativeError, int maximumDepth, int order)

Approximation of the definite integral of an analytic smooth function by Gauss-Kronrod quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.
Parameters
Func<double, Complex> f

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

double intervalBegin

Where the interval starts.

double intervalEnd

Where the interval stops.

double targetRelativeError

The expected relative accuracy of the approximation.

int maximumDepth

The maximum number of interval splittings permitted before stopping

int order

The number of Gauss-Kronrod points. Pre-computed for 15, 21, 31, 41, 51 and 61 points

Return
Complex

Approximation of the finite integral in the given interval.

Complex GaussKronrod(Func<double, Complex> f, double intervalBegin, double intervalEnd, Double& error, Double& L1Norm, double targetRelativeError, int maximumDepth, int order)

Complex GaussLegendre(Func<double, Complex> f, double intervalBegin, double intervalEnd, int order)

Approximation of the definite integral of an analytic smooth complex function by double-exponential quadrature. When either or both limits are infinite, the integrand is assumed rapidly decayed to zero as x -> infinity.
Parameters
Func<double, Complex> f

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

double intervalBegin

Where the interval starts.

double intervalEnd

Where the interval stops.

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.