NewCube: Cross-derivatives via automatic differentiation

In SimCop: Simulate from Arbitrary Copulae

Cross-derivatives via automatic differentiation

Description

Basic building blocks for evaluating functionals f:R^d \to R and all their cross-derivatives at a given point x \in R^d.

Usage

NewCube(x, j, dim = 2)

Arguments

x	(scalar) value at which the function is evaluated.
j	optional input. See ‘Details’.
dim	dimension d of the input vector, defaults to two.

Details

If the optional argument j is specfied, then the function f(x)=x_j and all its cross-derivatives (all of which but one will be zero, the derivative with respect to the jth component being 1) are evaluated with x_j being set to the value of x.

If the optional argument j is not used, then the function f(x) =c and all its cross-derivatives (all of which will be zero) are evaluated with c beting set to the value of x.

From these primitive function evaluations, more complicated functions can be constructed using the operations documented in CrossSum.

Value

NewCube returns an object of class ‘ADCube’ according to its inputs. See ‘Details’.

Author(s)

Berwin A. Turlach [e-mail]

References

Griewank, A., Lehmann, L., Leovey, H. and Zilberman, M. (2014). Automatic evaluations of cross-derivatives, Mathematics of Computation 83(285): 251-274.

See Also

CrossSum

SimCop documentation built on April 13, 2025, 5:09 p.m.