chainrule {dsfa}

R Documentation

Chainrule

Description

Calculates the partial derivatives of the function h(x_1,x_2,...,x_{K})=f(g(x_1,x_2,...,x_{K})) up to order four. Here K is the number of inputs for function g(\cdot). The function f(\cdot) can only have a single input. Alternatively chainrule can calculate the partial derivatives of h(x_1,x_2,...,x_{K})=f(g_1(x_1),g_2(x_2),...,g_K(x_{K})) up to order four. Here each g_k(\cdot) can only take a single input x_k. If x_i \neq x_j for i,j \in \{1,...,K \} then the input argument g can be a list with elements g_k(x_k). The function checks the number of inputs of f(\cdot) by counting the number of partial derivatives and then decides automatically how to proceed.

Usage

chainrule(f = NULL, g = NULL, deriv = 2, tri = NULL)

Arguments

f	vector of f(\cdot) evaluated at g(\cdot) with derivatives as attributes.
g	matrix of g(\cdot) with derivatives as attributes. Alternatively written as g(\cdot)=g_1(x_1),g_2(x_2),...,g_K(x_{K})). In this case, g can be a vector or a list of length k
deriv	derivative of order deriv. Available are 0,2 and 4.
tri	optional, index arrays for upper triangular for g, generated by trind.generator().

Details

Mostly internal function, which is helpful in calculating the partial derivatives of the loglikelihood.

Value

A list with partial derivatives. The index of the list corresponds to a matrix with all partial derivatives of that order.

Examples

x<-1 #For K=1, x_1 value is set to 1.

g<-1/x #g(x_1) = 1/x
attr(g,"gradient")<-matrix(-1/x^2,ncol=1)
attr(g,"hessian")<-matrix(2/x^3,ncol=1)
attr(g,"l3")<-matrix(-6/x^4,ncol=1)
attr(g,"l4")<-matrix(24/x^5,ncol=1)


zeta_g<-zeta(g, deriv=4) #f(g(x)) = zeta(g(x))

chainrule(f=zeta_g, g=g, deriv=4)

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