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)
An object of class
‘ADCube’ is returned. See ‘Details’.
Berwin A. Turlach <berwin.turlach@gmail.com>
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.
Griewank, A., Lehmann, L., Leovey, H. and Zilberman, M. (2014). Automatic evaluations of cross-derivatives, Mathematics of Computation 83(285): 251-274.
NewCube