d01ua
is the AD Library version of the primal routine
d01uaf.
Based (in the C++ interface) on overload resolution,
d01ua can be used for primal, tangent and adjoint
evaluation. It supports tangents and adjoints of first order.
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types: double, dco::ga1s<double>::type, dco::gt1s<double>::type
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.
3Description
d01ua
is the AD Library version of the primal routine
d01uaf.
d01uaf computes an estimate of the definite integral of a function of known analytical form, using a Gaussian quadrature formula with a specified number of abscissae. Formulae are provided for a finite interval (Gauss–Legendre), a semi-infinite interval (Gauss–Laguerre, rational Gauss), and an infinite interval (Gauss–Hermite).
For further information see Section 3 in the documentation for d01uaf.
4References
Davis P J and Rabinowitz P (1975) Methods of Numerical Integration Academic Press
Fröberg C E (1970) Introduction to Numerical Analysis Addison–Wesley
Ralston A (1965) A First Course in Numerical Analysis pp. 87–90 McGraw–Hill
Stroud A H and Secrest D (1966) Gaussian Quadrature Formulas Prentice–Hall
5Arguments
In addition to the arguments present in the interface of the primal routine,
d01ua includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine.
A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
f
needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer.
If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.