e02de is the AD Library version of the primal routine e02def. Based (in the C++ interface) on overload resolution, e02de can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e02de_AD_f (

m, px, py, x, y, lamda, mu, c, ff, wrk, iwrk, ifail)

Integer, Intent (In)	::	m, px, py
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	iwrk(py-4)
ADTYPE, Intent (In)	::	x(m), y(m), lamda(px), mu(py), c((px-4)*(py-4))
ADTYPE, Intent (Out)	::	ff(m), wrk(py-4)
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++ Interface

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

void e02de (

handle_t &ad_handle, const Integer &m, const Integer &px, const Integer &py, const ADTYPE x[], const ADTYPE y[], const ADTYPE lamda[], const ADTYPE mu[], const ADTYPE c[], ADTYPE ff[], ADTYPE wrk[], Integer iwrk[], 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

e02de is the AD Library version of the primal routine e02def.

e02def calculates values of a bicubic spline from its B-spline representation. For further information see Section 3 in the documentation for e02def.

4 References

Anthony G T, Cox M G and Hayes J G (1982) DASL – Data Approximation Subroutine Library National Physical Laboratory

Cox M G (1978) The numerical evaluation of a spline from its B-spline representation J. Inst. Math. Appl. 21 135–143

5 Arguments

In addition to the arguments present in the interface of the primal routine, e02de 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 – nag::ad::handle_t Input/Output: 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: m – Integer Input
3: px – Integer Input
4: py – Integer Input
5: x(m) – ADTYPE array Input
6: y(m) – ADTYPE array Input
7: lamda(px) – ADTYPE array Input
8: mu(py) – ADTYPE array Input
9: c( $(px - 4) \times (py - 4)$ ) – ADTYPE array Input
10: ff(m) – ADTYPE array Output
11: wrk( $py - 4$ ) – ADTYPE array Workspace
12: iwrk( $py - 4$ ) – Integer array Workspace
13: ifail – Integer Input/Output

6 Error Indicators and Warnings

e02de preserves all error codes from e02def and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.

$ifail = - 199$: 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.

$ifail = - 444$: 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 Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e02de is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e02def, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This program reads in knot sets

lamda (1), \dots, lamda (px)

and

mu (1), \dots, mu (py)

, and a set of bicubic spline coefficients

c_{i j}

. Following these are a value for

m

and the coordinates

(x_{r}, y_{r})

, for

r = 1, 2, \dots, m

, at which the spline is to be evaluated.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e02de_a1w_fe.f90	e02de_a1w_fe.d	e02de_a1w_fe.r
C++	e02de_a1w_hcppe.cpp	e02de_a1w_hcppe.d	e02de_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e02de_t1w_fe.f90	e02de_t1w_fe.d	e02de_t1w_fe.r
C++	e02de_t1w_hcppe.cpp	e02de_t1w_hcppe.d	e02de_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e02de_p0w_fe.f90	e02de_p0w_fe.d	e02de_p0w_fe.r
C++	e02de_p0w_hcppe.cpp	e02de_p0w_hcppe.d	e02de_p0w_hcppe.r

NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E02 (Fit) Chapter Contents

E02 (Fit) Chapter Introduction (FL)

e02de: FL CL CPP AD

NAG AD Librarye02de (dim2_spline_evalv)

▸▿ Contents

1 Purpose