pracma (version 1.7.0)

grad: Numerical Gradient

Description

Numerical function gradient.

Usage

grad(f, x0, heps = .Machine$double.eps^(1/3), ...)

Arguments

f

function of several variables.

x0

point where the gradient is to build.

heps

step size.

...

more variables to be passed to function f.

Value

• Vector of the same length as x0.

Details

Computes the gradient $$(\frac{\partial f}{\partial x_1}, \ldots, \frac{\partial f}{\partial x_n})$$ numerically using the ``central difference formula''.

References

Mathews, J. H., and K. D. Fink (1999). Numerical Methods Using Matlab. Third Edition, Prentice Hall.

See Also

fderiv

Examples

f <- function(u) {
    x <- u[1]; y <- u[2]; z <- u[3]
    return(x^3 + y^2 + z^2 +12*x*y + 2*z)
 }
x0 <- c(1,1,1)
grad(f, x0)     # 15 14  4        # direction of steepest descent

sum(grad(f, x0) * c(1, -1, 0))    # 1 , directional derivative

f <- function(x) x[1]^2 + x[2]^2
grad(f, c(0,0))                   # 0 0 , i.e. a local optimum