makeDerivs {propagate} | R Documentation |
Utility functions for creating Gradient- and Hessian-like matrices with symbolic derivatives and evaluating them in an environment
Description
These are three different utility functions that create matrices containing the symbolic partial derivatives of first (makeGrad
) and second (makeHess
) order and a function for evaluating these matrices in an environment. The evaluations of the symbolic derivatives are used within the propagate
function to calculate the propagated uncertainty, but these functions may also be useful for other applications.
Usage
makeGrad(expr, order = NULL)
makeHess(expr, order = NULL)
evalDerivs(deriv, envir)
Arguments
expr |
an expression, such as |
order |
order of creating partial derivatives, i.e. |
deriv |
a matrix returned from |
envir |
an environment to evaluate in. By default the workspace. |
Details
Given a function f(x_1, x_2, \ldots, x_n)
, the following matrices containing symbolic derivatives of f
are returned:
makeGrad:
\nabla(f) = \left[\frac{\partial f}{\partial x_1}, \ldots, \frac{\partial f}{\partial x_n}\right]
makeHess:
H(f) = \left[ \begin{array}{cccc} \frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_1\,\partial x_n} \\ \frac{\partial^2 f}{\partial x_2\,\partial x_1} & \frac{\partial^2 f}{\partial x_2^2} & \cdots & \frac{\partial^2 f}{\partial x_2\,\partial x_n} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial^2 f}{\partial x_n\,\partial x_1} & \frac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_n^2} \end{array} \right]
Value
The symbolic or evaluated Gradient/Hessian matrices.
Author(s)
Andrej-Nikolai Spiess
References
The Matrix Cookbook (Version November 2012).
Petersen KB & Pedersen MS.
http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/imm3274.pdf
Examples
EXPR <- expression(a^b + sin(c))
ENVIR <- list(a = 2, b = 3, c = 4)
## First-order partial derivatives: Gradient.
GRAD <- makeGrad(EXPR)
## This will evaluate the Gradient.
evalDerivs(GRAD, ENVIR)
## Second-order partial derivatives: Hessian.
HESS <- makeHess(EXPR)
## This will evaluate the Hessian.
evalDerivs(HESS, ENVIR)
## Change derivatives order.
GRAD <- makeGrad(EXPR, order = c(2,1,3))
evalDerivs(GRAD, ENVIR)