Class FractionalAdamsFunctions

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The free functions of QuantLib's fractionaladams.hpp.

public static class FractionalAdamsFunctions

Inheritance

object

FractionalAdamsFunctions

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Methods

RiemannLiouvilleIntegral<T>(ReadOnlySpan<T>, double, double)

The product-trapezoidal Riemann-Liouville fractional integral I^α y(t_N) = (1/Γ(α)) ∫₀^{t_N} (t_N − s)^{α−1} y(s) ds, α ≥ 0, from the values of y on a uniform grid, by integrating y's piecewise linear interpolant against the kernel: at α = 1 the trapezoidal rule, and the identity as α falls to 0.

public static T RiemannLiouvilleIntegral<T>(ReadOnlySpan<T> y, double alpha, double dt) where T : INumberBase<T>

Parameters

y ReadOnlySpan<T>

The values on the grid, at least two.

alpha double

The integration order, not negative.

dt double

The grid's spacing.

Returns

T

The integral.

Type Parameters

T

The values' type: double, or Complex.

Remarks

It builds the weights at every call; integrations on one (α, N) grid can share a RiemannLiouvilleWeights.

Exceptions

ArgumentException

alpha is negative, there are fewer than two values, or dt isn't positive.