is the AD Library version of the primal routine
Based (in the C++ interface) on overload resolution,
f07ca can be used for primal, tangent and adjoint
evaluation. It supports tangents and adjoints of first and second order.
The parameter ad_handle can be used to choose whether adjoints are computed using a symbolic adjoint or straightforward algorithmic differentiation.
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, dco::gt1s<dco::gt1s<double>::type>::type, dco::ga1s<dco::gt1s<double>::type>::type,
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.
You can set or access the adjoints of output argument b. The adjoints of all other output arguments are ignored.
f07ca increments the adjoints of input arguments b, d, du and dl according to the first order adjoint model.
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia https://www.netlib.org/lapack/lug
Du Toit J, Naumann U (2017) Adjoint Algorithmic Differentiation Tool Support for Typical Numerical Patterns in Computational Finance
In addition to the arguments present in the interface of the primal routine,
f07ca 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: must be set to , .
On exit: any errors are indicated as described in Section 6.
6Error Indicators and Warnings
f07ca uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07caf may be indicated with the same value returned by ifail. In addition, this routine may return:
An unexpected AD error has been triggered by this routine. Please
See Section 4.8.2 in the NAG AD Library Introduction for further information.
The routine was called using a mode that has not yet been implemented.
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.
8Parallelism and Performance
is not threaded in any implementation.
Since b is not a pure output and there is overwriting of variables, accessing adjoints later may result in wrong values, so a copy of the active input/output is used to obtain correct derivative values. See the example f07ca_a1_algo_dcoe.cpp for details.
The following examples are variants of the example for
modified to demonstrate calling the NAG AD Library.