Functions for creating Gradient and Hessian matrices by numerical differentiation (Richardson's method) of the partial derivatives

Description

These two functions create Gradient and Hessian matrices by Richardson's central finite difference method of the partial derivatives for any expression.

Usage

numGrad(expr, envir = .GlobalEnv)
numHess(expr, envir = .GlobalEnv)

Arguments

Details

Calculates first- and second-order numerical approximation using Richardson's central difference formula:

f'_i(x) approx frac{f(x_1, …, x_i + d, …, x_n) - f(x_1, …, x_i - d, …, x_n)}{2d}

f''_i(x) approx frac{f(x_1, …, x_i + d, …, x_n) - 2f(x_1, …, x_n) + f(x_1, …, x_i - d, …, x_n)}{d^2}

Value

The numeric Gradient/Hessian matrices.

Note

The two functions are modified versions of the genD function in the 'numDeriv' package, but a bit more easy to handle because they use expressions and the function's x value must not be defined as splitted scalar values x[1], x[2], ... in the body of the function.

Author(s)

Andrej-Nikolai Spiess

Examples

## Check for equality of symbolic  
## and numerical derivatives.
EXPR <- expression(2^x + sin(2 * y) - cos(z))
x <- 5
y <- 10
z <- 20

symGRAD <- evalDerivs(makeGrad(EXPR))
numGRAD <- numGrad(EXPR)
all.equal(symGRAD, numGRAD)

symHESS <- evalDerivs(makeHess(EXPR))
numHESS <- numHess(EXPR)
all.equal(symHESS, numHESS)

Results