propagate (version 1.0-4)

numDerivs: 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

expr

an expression, such as expression(x/y).

envir

the environment to evaluate in.

Value

The numeric Gradient/Hessian matrices.

Details

Calculates first- and second-order numerical approximation using Richardson's central difference formula: $$f'_i(x) \approx \frac{f(x_1, \ldots, x_i + d, \ldots, x_n) - f(x_1, \ldots, x_i - d, \ldots, x_n)}{2d}$$ $$f''_i(x) \approx \frac{f(x_1, \ldots, x_i + d, \ldots, x_n) - 2f(x_1, \ldots, x_n) + f(x_1, \ldots, x_i - d, \ldots, x_n)}{d^2}$$

Examples

# NOT RUN {
## 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)
# }