dsfa (version 2.0.2)

ind2joint: Independent to joint function

Description

Combines multiple derivs objects into a single derivs object.

Usage

ind2joint(f_list, tri_f_list, tri_h_list, deriv_order)

Value

Returns a derivs object.

Arguments

f_list

list of derivs objects of length \(M\), e.g. \(list(f_1(\cdot), f_2(\cdot),...,f_M(\cdot))\)

tri_f_list

list of length \(K\) trind_generator objects, the \(kth\) element corresponds to \(kth\) derivs object.

tri_h_list

list of length \(K\) trind_generator objects, the \(kth\) element corresponds to a derivs object with \(k \cdot (k+1)/2\) parameters.

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 \(h((x_{n1},x_{n2},...,x_{nK})) = (f_1(x_{n1}), f_2(x_{n2}), ... ,f_M(x_{nK}))\). In order to get the derivatives of \(h(\cdot)\) w.r.t all parameters \(x_{nk}\), the independent functions are combined. For more details see [trind()] and [trind_generator()].

See Also

Other derivs: chainrule(), derivs_transform(), differencerule(), 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)
ind2joint (list(A_derivs,B_derivs),
           list(trind_generator(1),trind_generator(1)),
           list(trind_generator(1),trind_generator(1+1)), 4)