R: Symbolic and Algorithmic Derivatives of Simple Expressions

Symbolic and Algorithmic Derivatives of Simple Expressions

Usage

D(expr, namevec)
deriv(expr, namevec, function.arg = NULL, tag = ".expr")

Arguments

`expr`	expression which should be derivated
`namevec`	character vector, giving the variable names with respect to which derivatives will be computed.
`function.arg`	... ?? ...
`tag`	... ?? ...

Description

D is modelled after its S pendant for taking simple symbolic derivatives.

deriv is a generic function with a default and a formula method. It returns a call for computing the expr and its (partial) derivatives, simultaneously. It uses so-called ``algorithmic derivatives''.

Currently, deriv.formula just calls deriv.default after extracting the expression to the right of ~.

Value

D returns an expression and therefore can easily be iterated for higher derivatives.

deriv returns a call object which becomes an expression when evaluated once. Evaluation of the latter expression returns the function values with a ".gradient" attribute containing the gradient matrix.

Note

This help page should be fixed up by one of R&R or someone else who fluently speaks the language in `$RHOME/src/main/deriv.c'.

It's author, MM, has only got a vague idea and thinks that a help page is better than none.

References

A. Griewank, G. F. Corliss (1991). Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM proceedings, Philadelphia.

Examples

## formula argument :
dx2x <- deriv(~ x^2, "x") ; dx2x
##- expression({
##-         .value <- x^2
##-         .grad <- array(0, c(length(.value), 1), list(NULL, c("x")))
##-         .grad[, "x"] <- 2 * x
##-         attr(.value, "gradient") <- .grad
##-         .value
##- })
mode(dx2x)
x <- -1:2
eval(dx2x)

## Something `tougher':
trig.exp <- expression(sin(cos(x + y^2)))
( D.sc <- D(trig.exp, c("x", "y")) )

( dxy <- deriv(trig.exp, c("x", "y")) )
y <- 1
eval(dxy)
eval(D.sc)

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