genaDiff: Numeric Differentiation

In gena: Genetic Algorithm and Particle Swarm Optimization

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)

gena documentation built on Aug. 15, 2022, 9:08 a.m.