Compute numerical derivatives

Compute numerical derivatives using forward/backward difference, central difference, or Richardson extrapolation.

numerical_deriv(
  par,
  f,
  ...,
  delta = 1e-05,
  gradient = TRUE,
  type = "Richardson"
)

Arguments

par

a vector of parameters to find partial derivative at

f

the objective function being evaluated

...

additional arguments to be passed to f

delta

the term used to perturb the f function. Default is 1e-5

gradient

logical; compute the gradient terms? If FALSE then the Hessian is computed instead

type

type of difference to compute. Can be either 'forward' for the forward difference, 'central' for the central difference, or 'Richardson' for the Richardson extrapolation (default). Backward difference is achieved by supplying a negative delta value with 'forward'. When type = 'Richardson', the default value of delta is increased to delta * 1000 for the Hessian and delta * 10 for the gradient to provide a reasonable perturbation starting location (each delta is halved at each iteration).

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples

# \donttest{
f <- function(x) 3*x[1]^3 - 4*x[2]^2
par <- c(3,8)

# grad = 9 * x^2 , -8 * y
(actual <- c(9 * par[1]^2, -8 * par[2]))
#> [1]  81 -64
numerical_deriv(par, f, type = 'forward')
#> [1]  81.00027 -64.00004
numerical_deriv(par, f, type = 'central')
#> [1]  81 -64
numerical_deriv(par, f, type = 'Richardson') # default
#> [1]  81 -64

# Hessian = h11 -> 18 * x, h22 -> -8, h12 -> h21 -> 0
(actual <- matrix(c(18 * par[1], 0, 0, -8), 2, 2))
#>      [,1] [,2]
#> [1,]   54    0
#> [2,]    0   -8
numerical_deriv(par, f, type = 'forward', gradient = FALSE)
#>          [,1]      [,2]
#> [1,] 54.00011  0.000000
#> [2,]  0.00000 -7.999574
numerical_deriv(par, f, type = 'central', gradient = FALSE)
#>          [,1]      [,2]
#> [1,] 54.00004  0.000000
#> [2,]  0.00000 -7.999645
numerical_deriv(par, f, type = 'Richardson', gradient = FALSE) # default
#>      [,1] [,2]
#> [1,]   54    0
#> [2,]    0   -8

# }