# CrossSum: Calculations on cubes In SimCop: Simulate from Arbitrary Copulae

## Description

Implements several operations of objects of `class` ‘ADCube’.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```CrossSum(u, w) CrossMult(u, w) CrossDivide(u, w) CrossSquare(u) CrossExp(u) CrossLog(u) CrossPow(u, r) CrossSqrt(u) CrossRaisePow(u, w) ```

## Arguments

 `u` an object of `class` ‘ADCube’. `w` an object of `class` ‘ADCube’. `r` a positive real number.

## Details

Assume `u` and `w` contain the evaluations of functions f() and g(), together with evaluations of all their cross-derivatives, at points x and y, respectively.

`CrossSum` returns the evaluation of f()+g(), together with all evaluated cross-derivates.

`CrossMult` returns the evaluation of f()g(), together with all evaluated cross-derivates.

`CrossDivide` returns the evaluation of f()/g(), together with all evaluated cross-derivates.

`CrossSquare` returns the evaluation of (f())^2, together with all evaluated cross-derivates.

`CrossExp` returns the evaluation of exp(f()), together with all evaluated cross-derivates.

`CrossLog` returns the evaluation of log(f()), together with all evaluated cross-derivates.

`CrossPow` returns the evaluation of (f())^r, together with all evaluated cross-derivates.

`CrossSqrt` returns the evaluation of sqrt(f()), together with all evaluated cross-derivates.

`CrossRaisePow` returns the evaluation of f()^{g()}, together with all evaluated cross-derivates.

## Value

An object of `class` ‘ADCube’ is returned. See ‘Details’.

## Author(s)

Berwin A. Turlach <berwin.turlach@gmail.com>

## References

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

`NewCube`