quotientrule {dsfa}

R Documentation

Quotientrule

Description

Quotientrule for derivs objects.

Usage

quotientrule(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) / 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.

Value

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

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

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