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).

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



[Package dsfa version 2.0.2 Index]