numDerivs: Functions for creating Gradient and Hessian matrices by...
In propagate: Propagation of Uncertainty

Description Usage Arguments Details Value Note Author(s) Examples

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

1 2	numGrad(expr, envir = .GlobalEnv) numHess(expr, envir = .GlobalEnv)

`expr`	an expression, such as `expression(x/y)`.
`envir`	the `environment` to evaluate in.

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}

The numeric Gradient/Hessian matrices.

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], ... x[n] in the body of the function.

Andrej-Nikolai Spiess

## 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)