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)

[Package *stats* version 2.2.1 Index]