f07fj
is the AD Library version of the primal routine
f07fjf (dpotri).
Based (in the C++ interface) on overload resolution,
f07fj 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
f07fj
is the AD Library version of the primal routine
f07fjf (dpotri).
f07fjf (dpotri) computes the inverse of a real symmetric positive definite matrix $A$, where $A$ has been factorized by f07fdf.
For further information see Section 3 in the documentation for f07fjf (dpotri).
4References
Du Croz J J and Higham N J (1992) Stability of methods for matrix inversion IMA J. Numer. Anal.12 1–19
5Arguments
In addition to the arguments present in the interface of the primal routine,
f07fj 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 $0$, $-1\text{\hspace{0.25em}or\hspace{0.25em}}1$.
On exit: any errors are indicated as described in Section 6.
6Error Indicators and Warnings
f07fj uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f07fjf may be indicated with the same value returned by ifail. In addition, this routine may return:
${\mathbf{ifail}}=-89$
An unexpected AD error has been triggered by this routine. Please
contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.
7Accuracy
Not applicable.
8Parallelism and Performance
f07fj
is not threaded in any implementation.
9Further Comments
None.
10Example
The following examples are variants of the example for
f07fjf (dpotri),
modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example computes the inverse of the matrix $A$, where