NAG Library Manual, Mark 27.1
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 Library
d01tc_a1w_f (dim1_gauss_wgen_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
D01 (Quad) Chapter Contents
D01 (Quad) Chapter Introduction (FL)
d01tc:  FL   CL   CPP   AD 

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© The Numerical Algorithms Group Ltd. 2020
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1 Purpose

d01tc_a1w_f is the adjoint version of the primal routine d01tcf.

2 Specification

Fortran Interface
Subroutine d01tc_a1w_f ( ad_handle, itype, a, b, c, d, n, weight, abscis, ifail)
Integer, Intent (In) :: itype, n
Integer, Intent (Inout) :: ifail
Type (nagad_a1w_w_rtype), Intent (In) :: a, b, c, d
Type (nagad_a1w_w_rtype), Intent (Out) :: weight(n), abscis(n)
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void d01tc_a1w_f_ ( void *&ad_handle, const Integer &itype, const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b, const nagad_a1w_w_rtype &c, const nagad_a1w_w_rtype &d, const Integer &n, nagad_a1w_w_rtype weight[], nagad_a1w_w_rtype abscis[], Integer &ifail)
The routine may be called by the names d01tc_a1w_f or nagf_quad_dim1_gauss_wgen_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01tc_a1w_f is the adjoint 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_a1w_f 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 – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: itype – Integer Input
3: a – Type (nagad_a1w_w_rtype) Input
4: b – Type (nagad_a1w_w_rtype) Input
5: c – Type (nagad_a1w_w_rtype) Input
6: d – Type (nagad_a1w_w_rtype) Input
7: n – Integer Input
8: weight(n) – Type (nagad_a1w_w_rtype) array Output
9: abscis(n) – Type (nagad_a1w_w_rtype) array Output
10: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01tc_a1w_f 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=-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_a1w_f 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.

10.1 Adjoint mode (a1w)

LanguageSource FileDataResults
Fortrand01tc_a1w_fe.f90Noned01tc_a1w_fe.r
C++d01tc_a1w_hcppe.cppNoned01tc_a1w_hcppe.r

10.2 Tangent mode (t1w)

LanguageSource FileDataResults
Fortrand01tc_t1w_fe.f90Noned01tc_t1w_fe.r
C++d01tc_t1w_hcppe.cppNoned01tc_t1w_hcppe.r

10.3 Passive mode (p0w)

LanguageSource FileDataResults
Fortrand01tc_p0w_fe.f90Noned01tc_p0w_fe.r
C++d01tc_p0w_hcppe.cppNoned01tc_p0w_hcppe.r
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
D01 (Quad) Chapter Contents
D01 (Quad) Chapter Introduction (FL)
d01tc:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2020