numericDeriv
Evaluate derivatives numerically

### Description

Evaluates an expression and the gradient of the expression numerically.

### Usage

    numericDeriv(expr, theta, rho = parent.frame(), dir = 1)

### Arguments

expr | an expression to be differentiated. The value of the expression should be a numeric vector.
theta | a vector of variable names. The derivative of expr with respect to each element of each variable is approximated. These variables must be accessible in the environment rho, and they must be numeric, not integer or complex.
rho | the environment in which the expression is evaluated. All variables in expr must be accessible in this environment. The value and derivatives of expr are evaluated at the values of the variables in this environment.
dir | a numeric vector of directions. Typically -1 or 1: the length of theta (if shorter, it is repeated to the length of theta). These are used to determine the change in the dependent variable when computing finite difference approximations to the derivatives. This is useful when you need to estimate the derivative at the edge of the domain of a function.

### Details

numericDeriv uses the one-sided secant method to compute a finite difference approximation to the derivative. The dependent variable is perturbed by a factor of 1.0 + dir * sqrt(.Machine$double.eps), unless the variable is 0, in which case dir * sqrt(.Machine$double.eps) is added to it.
Value
returns the value of the expression with the attribute of "gradient". The columns of "gradient" are the derivatives of the value corresponding to the elements of the variables named in theta.
See Also
eval, deriv, nls.
Examples

    x <- c(1,2,3,4)
    y <- c(4, 15, 32, 54)
    p0 <- 3
    p1 <- 2
    numericDeriv(quote( p0 * x^p1 ), c("p0", "p1"))
    numericDeriv(quote( sum((y - p0 * x^p1) ^ 2)), c("p0", "p1"))
    numericDeriv(quote(det(m)), "m", list2env(list(m=matrix(c(1,2,3,5),2,2))))

Package stats version 6.1.5-18
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