chainrule {dsfa}

R Documentation

Chainrule

Description

Chainrule for derivs objects.

Usage

chainrule(f_list, tri, deriv_order)

Arguments

f_list	list of derivs objects of length M, e.g. list(f_1(\cdot), f_2(\cdot),...,f_M(\cdot))
tri	list; created by the function [trind_generator()].
deriv_order	integer; maximum order of derivative. Available are 0,2 and 4.

Details

Let f_m be a function defined in [trind()], where m \in {1,...,M}. Define h((x_{n1},x_{n2},...,x_{nK})) = f_1(\cdot) \circ f_2(\cdot) ... \circ f_M(x_{n1},x_{n2},...,x_{nK})). In order to get the derivatives of h(\cdot) w.r.t all parameters x_{nk}, the chainrule is applied. For more details see [trind()] and [trind_generator()].

Value

Returns an object of class derivs for the function h(\cdot).

See Also

Other derivs: derivs_transform(), differencerule(), ind2joint(), list2derivs(), productrule(), quotientrule(), sumrule(), trind_generator(), trind()

Examples

A<-matrix(c(1:9)/10, ncol=1)
A_derivs<-list2derivs(list(A, A^0, A^2, A^3, A^4), deriv_order=4)
B_derivs<-transform(A, type="exp", par=0, deriv_order=4)
C_derivs<-transform(B_derivs, type="log", par=0, deriv_order=4)
chainrule(list(C_derivs, B_derivs), trind_generator(1), deriv_order=4) #equal to A_derivs

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