genaDiff {gena}

Numeric Differentiation

Description

Numeric estimation of the gradient and Hessian.

Usage

gena.grad(
  fn,
  par,
  eps = sqrt(.Machine$double.eps) * abs(par),
  method = "central-difference",
  fn.args = NULL
)

gena.hessian(
  fn = NULL,
  gr = NULL,
  par,
  eps = sqrt(.Machine$double.eps) * abs(par),
  fn.args = NULL,
  gr.args = NULL
)

Arguments

fn

function for which gradient or Hessian should be calculated.

par

point (parameters' value) at which fn should be differentiated.

eps

numeric vector representing increment of the par. So eps[i] represents increment of par[i]. If eps is a constant then all increments are the same.

method

numeric differentiation method: "central-difference" or "forward-difference".

fn.args

list containing arguments of fn except par.

gr

gradient function of fn.

gr.args

list containing arguments of gr except par.

Details

It is possible to substantially improve numeric Hessian accuracy by using analytical gradient gr. If both fn and gr are provided then only gr will be used. If only fn is provided for gena.hessian then eps will be transformed to sqrt(eps) for numeric stability purposes.

Value

Function gena.grad returns a vector that is a gradient of fn at point par calculated via method numeric differentiation approach using increment eps.

Function gena.hessian returns a matrix that is a Hessian of fn at point par.

Examples

# Consider the following function
fn <- function(par, a = 1, b = 2)
{
  val <- par[1] * par[2] - a * par[1] ^ 2 - b * par[2] ^ 2
}

# Calculate the gradient at point (2, 5) respect to 'par' 
# when 'a = 1' and 'b = 1'
par <- c(2, 5)
fn.args = list(a = 1, b = 1)
gena.grad(fn = fn, par = par, fn.args = fn.args)

# Calculate Hessian at the same point
gena.hessian(fn = fn, par = par, fn.args = fn.args)

# Repeat calculation of the Hessian using analytical gradient
gr <- function(par, a = 1, b = 2)
{
  val <- c(par[2] - 2 * a * par[1],
           par[1] - 2 * b * par[2])
}
gena.hessian(gr = gr, par = par, gr.args = fn.args)