d01tc is the AD Library version of the primal routine d01tcf. Based (in the C++ interface) on overload resolution, d01tc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine d01tc_AD_f (

ad_handle, itype, a, b, c, d, n, weight, abscis, ifail)

Integer, Intent (In)	::	itype, n
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	a, b, c, d
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:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w

C++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void d01tc (

void *&ad_handle, const Integer &itype, const ADTYPE &a, const ADTYPE &b, const ADTYPE &c, const ADTYPE &d, 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.

3 Description

d01tc is the AD Library version of the primal routine d01tcf.

d01tcf returns the weights (normal or adjusted) and abscissae for a Gaussian integration rule with a specified number of abscissae. Six different types of Gauss rule are allowed. For further information see Section 3 in the documentation for d01tcf.

4 References

Davis P J and Rabinowitz P (1975) Methods of Numerical Integration Academic Press

Golub G H and Welsch J H (1969) Calculation of Gauss quadrature rules Math. Comput. 23 221–230

Stroud A H and Secrest D (1966) Gaussian Quadrature Formulas Prentice–Hall

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01tc 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.

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: itype – Integer Input
3: a – ADTYPE Input
4: b – ADTYPE Input
5: c – ADTYPE Input
6: d – ADTYPE Input
7: n – Integer Input
8: weight(n) – ADTYPE array Output
9: abscis(n) – ADTYPE array Output
10: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01tc preserves all error codes from d01tcf and in addition can return:

$ifail = - 89$: 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

d01tc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01tcf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example returns the abscissae and (adjusted) weights for the seven-point Gauss–Laguerre formula.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	d01tc_a1w_fe.f90	None	d01tc_a1w_fe.r
C++	d01tc_a1w_hcppe.cpp	None	d01tc_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	d01tc_t1w_fe.f90	None	d01tc_t1w_fe.r
C++	d01tc_t1w_hcppe.cpp	None	d01tc_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	d01tc_p0w_fe.f90	None	d01tc_p0w_fe.r
C++	d01tc_p0w_hcppe.cpp	None	d01tc_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01tc: FL CL CPP AD

NAG AD Libraryd01tc (dim1_gauss_wgen)

▸▿ Contents

1 Purpose