maxLik (version 0.5-6)

numericGradient: Functions to Calculate Numeric Derivatives

Description

Calculate (central) numeric gradient and Hessian. numericGradient accepts vector-valued functions.

Usage

numericGradient(f, t0, eps=1e-06, ...)
numericHessian(f, grad=NULL, t0, eps=1e-06, ...)
numericNHessian(f, t0, eps=1e-6, ...)

Arguments

f

function to be differentiated. The first argument must be the parameter vector with respect to which it is differentiated.

grad

function, gradient of f

t0

vector, the value of parameters

eps

numeric, the step for numeric differentiation

...

furter arguments for f

Value

• Matrix. For numericGradient, the number of rows is equal to the length of the function value vector, and the number of columns is equal to the length of the parameter vector.

  For the numericHessian, both numer of rows and columns is equal to the length of the parameter vector.

Warning

Be careful when using numerical differentiation in optimisation routines. Although quite precise in simple cases, they may work very poorly in more complicated cases.

Details

numericGradient numerically differentiates a (vector valued) function with respect to it's (vector valued) argument. If the functions value is a NVal * 1 vector and the argument is Npar * 1 vector, the resulting gradient is a NVal * NPar matrix.

numericHessian checks whether a gradient function is present and calculates a gradient of the gradient (if present), or full numeric Hessian (numericNHessian) if grad is NULL.

See Also

compareDerivatives, deriv

Examples

# A simple example with Gaussian bell
f0 <- function(t0) exp(-t0[1]^2 - t0[2]^2)
numericGradient(f0, c(1,2))
numericHessian(f0, t0=c(1,2))

# An example with the analytic gradient
gradf0 <- function(t0) -2*t0*f0(t0)
numericHessian(f0, gradf0, t0=c(1,2))
# The results should be similar as in the previous case

# The central numeric derivatives have usually quite a high precision
compareDerivatives(f0, gradf0, t0=1:2)
# The differenc is around 1e-10