# grad: Numerical Gradient In pracma: Practical Numerical Math Functions

## Usage

 1 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.

## Details

(\frac{\partial f}{\partial x_1}, …, \frac{\partial f}{\partial x_n})

numerically using the “central difference formula”.

## Value

Vector of the same length as x0.

## References

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

fderiv

## Examples

  1 2 3 4 5 6 7 8 9 10 11 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 

### Example output

[1] 15 14  4
[1] 1
[1] 0 0


pracma documentation built on Dec. 11, 2021, 9:57 a.m.