CrossSum function

Calculations on cubes

Implements several operations of objects of class ADCube .

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.

Returns

An object of class ADCube is returned. See Details .

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.

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

NewCube

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com