dsfa (version 2.0.2)

quotientrule: Quotientrule

Description

Quotientrule for derivs objects.

Usage

quotientrule(f_list, tri, deriv_order)

Value

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

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 \(h((x_{n1},x_{n2},...,x_{nK})) = f_1(\cdot) / f_2(\cdot) ... / f_M(x_{n1},x_{n2},...,x_{nK}))\). In order to get the derivatives of \(h(\cdot)\) w.r.t all parameters \(x_{nk}\), the quotientrule is applied. For more details see [trind()] and [trind_generator()].The values of the derivs objects must be positive. Numerically not precise, but included for reasons of completeness.

See Also

Other derivs: chainrule(), derivs_transform(), differencerule(), ind2joint(), list2derivs(), productrule(), 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=2)
B_derivs<-derivs_transform(A, type="inv", par=0,  trind_generator(1), deriv_order=2)
quotientrule (list(A_derivs, B_derivs), trind_generator(1), deriv_order=2) #A/(1/A)=A^2