NewCube function

Cross-derivatives via automatic differentiation

Basic building blocks for evaluating functionals $f:R^d -> R$ and all their cross-derivatives at a given point $x in R^d$.

NewCube(x, j, dim = 2)

Arguments

• x: (scalar) value at which the function is evaluated.
• j: optional input. See Details .
• dim: dimension $d$ of the input vector, defaults to two.

Returns

NewCube returns an object of class ADCube according to its inputs. See Details .

Details

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.

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

CrossSum

Author(s)

Berwin A. Turlach berwin.turlach@gmail.com