| deriv {stats} | R Documentation |
Compute derivatives of simple expressions, symbolically.
D (expr, name)
deriv(expr, ...)
deriv3(expr, ...)
## Default S3 method:
deriv(expr, namevec, function.arg = NULL, tag = ".expr",
hessian = FALSE, ...)
## S3 method for class 'formula'
deriv(expr, namevec, function.arg = NULL, tag = ".expr",
hessian = FALSE, ...)
## Default S3 method:
deriv3(expr, namevec, function.arg = NULL, tag = ".expr",
hessian = TRUE, ...)
## S3 method for class 'formula'
deriv3(expr, namevec, function.arg = NULL, tag = ".expr",
hessian = TRUE, ...)
expr |
A |
name,namevec |
character vector, giving the variable names (only
one for |
function.arg |
If specified and non- |
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. |
... |
arguments to be passed to or from methods. |
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.
The internal code knows about the arithmetic operators +,
-, *, / and ^, and the single-variable
functions exp, log, sin, cos, tan,
sinh, cosh, sqrt, pnorm, dnorm,
asin, acos, atan, gamma, lgamma,
digamma and trigamma, as well as psigamma for one
or two arguments (but derivative only with respect to the first).
(Note that only the standard normal distribution is considered.)
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 not NULL, 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)