Compute numerical derivatives — numerical

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

Usage

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

# }