SimCop (version 0.7.3)

CrossSum: Calculations on cubes

Description

Implements several operations of objects of class ‘ADCube’.

Usage

CrossSum(u, w)
CrossMult(u, w)
CrossDivide(u, w)
CrossSquare(u)
CrossExp(u)
CrossLog(u)
CrossPow(u, r)
CrossSqrt(u)
CrossRaisePow(u, w)

Value

An object of class

‘ADCube’ is returned. See ‘Details’.

Arguments

u

an object of class ‘ADCube’.

w

an object of class ‘ADCube’.

r

a positive real number.

Author

Berwin A. Turlach

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