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1Purpose

f08ae is the AD Library version of the primal routine f08aef (dgeqrf). Based (in the C++ interface) on overload resolution, f08ae can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2Specification

Fortran Interface
 Subroutine f08ae_AD_f ( ad_handle, m, n, a, lda, tau, work, lwork, ifail)
 Integer, Intent (In) :: m, n, lda, lwork Integer, Intent (Inout) :: ifail ADTYPE, Intent (Inout) :: a(lda,*), tau(*) ADTYPE, Intent (Out) :: work(max(1,lwork)) Type (c_ptr), Intent (Inout) :: ad_handle
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:
#include <dco.hpp>
namespace nag {
 void f08ae ( void *&ad_handle, const Integer &m, const Integer &n, ADTYPE a[], const Integer &lda, ADTYPE tau[], ADTYPE work[], const Integer &lwork, Integer &ifail)
}
}
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

3Description

f08ae is the AD Library version of the primal routine f08aef (dgeqrf).
f08aef (dgeqrf) computes the $QR$ factorization of a real $m×n$ matrix. For further information see Section 3 in the documentation for f08aef (dgeqrf).

4References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5Arguments

In addition to the arguments present in the interface of the primal routine, f08ae 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 handle to the AD configuration data object, as created by x10aa.
2: m – Integer Input
3: n – Integer Input
4: a(lda, $*$) – ADTYPE array Input/Output
5: lda – Integer Input
6: tau($*$) – ADTYPE array Output
7: work($\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{lwork}}\right)$) – ADTYPE array Workspace
8: lwork – Integer Input
9: ifail – Integer Input/Output
On entry: must be set to $0$, .
On exit: any errors are indicated as described in Section 6.

6Error Indicators and Warnings

f08ae uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f08aef may be indicated with the same value returned by ifail. In addition, this routine may return:
${\mathbf{ifail}}=-89$
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.
${\mathbf{ifail}}=-443$
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.

Not applicable.

8Parallelism and Performance

f08ae is not threaded in any implementation.

None.

10Example

The following examples are variants of the example for f08aef (dgeqrf), modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example solves the linear least squares problems
 $minimize⁡‖Axi-bi‖2 , i=1,2$
where ${b}_{1}$ and ${b}_{2}$ are the columns of the matrix $B$,
 $A = ( -0.57 -1.28 -0.39 0.25 -1.93 1.08 -0.31 -2.14 2.30 0.24 0.40 -0.35 -1.93 0.64 -0.66 0.08 0.15 0.30 0.15 -2.13 -0.02 1.03 -1.43 0.50 ) and B= ( -3.15 2.19 -0.11 -3.64 1.99 0.57 -2.70 8.23 0.26 -6.35 4.50 -1.48 ) .$

Language Source File Data Results
Fortran f08ae_a1w_fe.f90 f08ae_a1w_fe.d f08ae_a1w_fe.r
C++ f08ae_a1w_hcppe.cpp f08ae_a1w_hcppe.d f08ae_a1w_hcppe.r

10.2Tangent modes

Language Source File Data Results
Fortran f08ae_t1w_fe.f90 f08ae_t1w_fe.d f08ae_t1w_fe.r
C++ f08ae_t1w_hcppe.cpp f08ae_t1w_hcppe.d f08ae_t1w_hcppe.r

10.3Passive mode

Language Source File Data Results
Fortran f08ae_p0w_fe.f90 f08ae_p0w_fe.d f08ae_p0w_fe.r
C++ f08ae_p0w_hcppe.cpp f08ae_p0w_hcppe.d f08ae_p0w_hcppe.r