NAG AD Libraryd01tb (dim1_gauss_wres)

Settings help

1Purpose

d01tb is the AD Library version of the primal routine d01tbf. Based (in the C++ interface) on overload resolution, d01tb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2Specification

Fortran Interface
 Subroutine d01tb_AD_f ( key, a, b, n, weight, abscis, ifail)
 Integer, Intent (In) :: key, n Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: a, b ADTYPE, Intent (Out) :: weight(n), abscis(n) 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:
C++ Interface
#include <dco.hpp>
namespace nag {
 void d01tb ( handle_t &ad_handle, const Integer &key, const ADTYPE &a, const ADTYPE &b, const Integer &n, ADTYPE weight[], ADTYPE abscis[], 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
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3Description

d01tb is the AD Library version of the primal routine d01tbf.
d01tbf returns the weights and abscissae appropriate to a Gaussian quadrature formula with a specified number of abscissae. The formulae provided are for Gauss–Legendre, rational Gauss, Gauss–Laguerre and Gauss–Hermite. For further information see Section 3 in the documentation for d01tbf.

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, d01tb 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.
2: key – Integer Input
3: Input
4: Input
5: n – Integer Input
6: weight(n) – ADTYPE array Output
7: abscis(n) – ADTYPE array Output
8: ifail – Integer Input/Output

6Error Indicators and Warnings

d01tb preserves all error codes from d01tbf and in addition can return:
${\mathbf{ifail}}=-89$
See Error Handling in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-444$
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 Error Handling in the NAG AD Library Introduction for further information.

Not applicable.

8Parallelism and Performance

d01tb is not threaded in any implementation.

None.

10Example

The following examples are variants of the example for d01tbf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example returns the abscissae and (adjusted) weights for the six-point Gauss–Laguerre formula.

Language Source File Data Results
Fortran d01tb_a1w_fe.f90 None d01tb_a1w_fe.r
C++ d01tb_a1w_hcppe.cpp None d01tb_a1w_hcppe.r

10.2Tangent modes

Language Source File Data Results
Fortran d01tb_t1w_fe.f90 None d01tb_t1w_fe.r
C++ d01tb_t1w_hcppe.cpp None d01tb_t1w_hcppe.r

10.3Passive mode

Language Source File Data Results
Fortran d01tb_p0w_fe.f90 None d01tb_p0w_fe.r
C++ d01tb_p0w_hcppe.cpp None d01tb_p0w_hcppe.r