e01da is the AD Library version of the primal routine e01daf. Based (in the C++ interface) on overload resolution, e01da can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e01da_AD_f (

mx, my, x, y, f, px, py, lamda, mu, c, wrk, ifail)

Integer, Intent (In)	::	mx, my
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	px, py
ADTYPE, Intent (In)	::	x(mx), y(my), f(mx*my)
ADTYPE, Intent (Out)	::	lamda(mx+4), mu(my+4), c(mxmy), wrk((mx+6)(my+6))
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 e01da (

handle_t &ad_handle, const Integer &mx, const Integer &my, const ADTYPE x[], const ADTYPE y[], const ADTYPE f[], Integer &px, Integer &py, ADTYPE lamda[], ADTYPE mu[], ADTYPE c[], ADTYPE wrk[], 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

e01da is the AD Library version of the primal routine e01daf.

e01daf computes a bicubic spline interpolating surface through a set of data values, given on a rectangular grid in the

x

y

plane. For further information see Section 3 in the documentation for e01daf.

4 References

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

Cox M G (1975) An algorithm for spline interpolation J. Inst. Math. Appl. 15 95–108

de Boor C (1972) On calculating with B-splines J. Approx. Theory 6 50–62

Hayes J G and Halliday J (1974) The least squares fitting of cubic spline surfaces to general data sets J. Inst. Math. Appl. 14 89–103

5 Arguments

In addition to the arguments present in the interface of the primal routine, e01da 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: mx – Integer Input
3: my – Integer Input
4: x(mx) – ADTYPE array Input
5: y(my) – ADTYPE array Input
6: f( $mx \times my$ ) – ADTYPE array Input
7: px – Integer Output
8: py – Integer Output
9: lamda( $mx + 4$ ) – ADTYPE array Output
10: mu( $my + 4$ ) – ADTYPE array Output
11: c( $mx \times my$ ) – ADTYPE array Output
12: wrk( $(mx + 6) \times (my + 6)$ ) – ADTYPE array Workspace
13: ifail – Integer Input/Output

6 Error Indicators and Warnings

e01da preserves all error codes from e01daf 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

e01da is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e01daf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads in values of

m_{x}

x_{q}

, for

q = 1, 2, \dots, m_{x}

m_{y}

and

y_{r}

, for

r = 1, 2, \dots, m_{y}

, followed by values of the ordinates

f_{q, r}

defined at the grid points

(x_{q}, y_{r})

It then calls e01da to compute a bicubic spline interpolant of the data values, and prints the values of the knots and B-spline coefficients. Finally it evaluates the spline at a small sample of points on a rectangular grid.