Basic building blocks for evaluating functionals \(f:R^d \to R\) and all their cross-derivatives at a given point \(x \in R^d\).
NewCube(x, j, dim = 2)NewCube returns an object of class
‘ADCube’ according to its inputs. See ‘Details’.
(scalar) value at which the function is evaluated.
optional input. See ‘Details’.
dimension \(d\) of the input vector, defaults to two.
Berwin A. Turlach berwin.turlach@gmail.com
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 \(j\)th 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.
Griewank, A., Lehmann, L., Leovey, H. and Zilberman, M. (2014). Automatic evaluations of cross-derivatives, Mathematics of Computation 83(285): 251-274.
CrossSum