FeynmanKac.GetSplineCoefficientsPrime Method

FeynmanKacGetSplineCoefficientsPrime Method

Returns the first derivatives of the Hermite quintic spline coefficients that represent an approximate solution of the Feynman-Kac PDE.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

Copy

public double[,] GetSplineCoefficientsPrime()

Public Function GetSplineCoefficientsPrime As Double(,)

public:
array<double,2>^ GetSplineCoefficientsPrime()

member GetSplineCoefficientsPrime : unit -> float[,]

Return Value

Type: Double
A double matrix of dimension (tGrid.Length+1) by (3*xGrid.Length) containing the first derivatives (in time) of the coefficients of the Hermite quintic spline representation of the approximate solution for the Feynman-Kac PDE at time points 0, tGrid[0],...,tGrid[tGrid.Length-1]. The approximate solution itself is given by

$f_t(x,\bar{t}) = \sum_{j=0}^{3*\text{nxGrid}-1}y_{ij}' \beta_j(x) \quad \mbox{for} \; \bar{t} = \text{tGrid}[i-1], i=1,\ldots,\text{ntGrid},$

and

$f_t(x,\bar{t})=\sum_{j=0}^{3*\text{nxGrid}-1}y_{0j}^\prime\beta_j(x) \quad \mbox{for} \; \bar{t} = 0 \, .$

The (ntGrid+1) by (3*nxGrid) matrix

$(y_{ij}')_{i=0,\ldots,\text{ntGrid}}^{j=0,\ldots,3*\text{nxGrid}-1}$

is stored row-wise in the returned array.

Remarks

The ComputeCoefficients method must be invoked first before invoking this method. Otherwise, the method throws an InvalidOperationException exception.

Reference

FeynmanKac Class

Imsl.Math Namespace