# NAG AD Libraryd01tc (dim1_gauss_wgen)

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## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine d01tc_AD_f ( 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:
C++ Interface
#include <dco.hpp>
namespace nag {
 void d01tc ( handle_t &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.

## 3Description

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.

## 4References

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

## 5Arguments

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.
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: itype – Integer Input
3: Input
4: Input
5: Input
6: Input
7: n – Integer Input
8: weight(n) – ADTYPE array Output
9: abscis(n) – ADTYPE array Output
10: ifail – Integer Input/Output

## 6Error Indicators and Warnings

d01tc preserves all error codes from d01tcf 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

d01tc is not threaded in any implementation.

None.

## 10Example

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.

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

### 10.2Tangent 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

### 10.3Passive 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