| deriv {stats} | R Documentation |
Compute derivatives of simple expressions, symbolically.
D (expr, name)
deriv(expr, namevec, function.arg, tag = ".expr", hessian = FALSE)
deriv3(expr, namevec, function.arg, tag = ".expr", hessian = TRUE)
expr |
expression or call to
be differentiated. |
name,namevec |
character vector, giving the variable names (only
one for D()) with respect to which derivatives will be
computed. |
function.arg |
If specified, a character vector of arguments for
a function return, or a function (with empty body) or TRUE,
the latter indicating that a function with argument names
namevec should be used. |
tag |
character; the prefix to be used for the locally created variables in result. |
hessian |
a logical value indicating whether the second derivatives should be calculated and incorporated in the return value. |
D is modelled after its S namesake 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”. If function.arg is a function,
its arguments can have default values, see the fx example below.
Currently, deriv.formula just calls deriv.default after
extracting the expression to the right of ~.
deriv3 and its methods are equivalent to deriv and its
methods except that hessian defaults to TRUE for
deriv3.
D returns a call and therefore can easily be iterated
for higher derivatives.
deriv and deriv3 normally return an
expression object whose evaluation returns the function
values with a "gradient" attribute containing the gradient
matrix. If hessian is TRUE the evaluation also returns
a "hessian" attribute containing the Hessian array.
If function.arg is specified, deriv and deriv3
return a function with those arguments rather than an expression.
Griewank, A. and Corliss, G. F. (1991) Automatic Differentiation of Algorithms: Theory, Implementation, and Application. SIAM proceedings, Philadelphia.
Bates, D. M. and Chambers, J. M. (1992) Nonlinear models. Chapter 10 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
nlm and optim for numeric minimization
which could make use of derivatives,
## formula argument :
dx2x <- deriv(~ x^2, "x") ; dx2x
## Not run:
expression({
.value <- x^2
.grad <- array(0, c(length(.value), 1), list(NULL, c("x")))
.grad[, "x"] <- 2 * x
attr(.value, "gradient") <- .grad
.value
})
## End(Not run)
mode(dx2x)
x <- -1:2
eval(dx2x)
## Something 'tougher':
trig.exp <- expression(sin(cos(x + y^2)))
( D.sc <- D(trig.exp, "x") )
all.equal(D(trig.exp[[1]], "x"), D.sc)
( dxy <- deriv(trig.exp, c("x", "y")) )
y <- 1
eval(dxy)
eval(D.sc)
## function returned:
deriv((y ~ sin(cos(x) * y)), c("x","y"), func = TRUE)
## function with defaulted arguments:
(fx <- deriv(y ~ b0 + b1 * 2^(-x/th), c("b0", "b1", "th"),
function(b0, b1, th, x = 1:7){} ) )
fx(2,3,4)
## Higher derivatives
deriv3(y ~ b0 + b1 * 2^(-x/th), c("b0", "b1", "th"),
c("b0", "b1", "th", "x") )
## Higher derivatives:
DD <- function(expr,name, order = 1) {
if(order < 1) stop("'order' must be >= 1")
if(order == 1) D(expr,name)
else DD(D(expr, name), name, order - 1)
}
DD(expression(sin(x^2)), "x", 3)
## showing the limits of the internal "simplify()" :
## Not run:
-sin(x^2) * (2 * x) * 2 + ((cos(x^2) * (2 * x) * (2 * x) + sin(x^2) *
2) * (2 * x) + sin(x^2) * (2 * x) * 2)
## End(Not run)