e01da: FL CL CPP AD

NAG AD Library
e01da_a1w_f (dim2_spline_grid_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.

Keyword Search:

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E01 (Interp) Chapter Contents

E01 (Interp) Chapter Introduction (FL)

e01da: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

1 Purpose

e01da_a1w_f is the adjoint version of the primal routine e01daf.

2 Specification

Fortran Interface

Subroutine e01da_a1w_f (

ad_handle, 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
Type (nagad_a1w_w_rtype), Intent (In)	::	x(mx), y(my), f(mx*my)
Type (nagad_a1w_w_rtype), Intent (Out)	::	lamda(mx+4), mu(my+4), c(mxmy), wrk((mx+6)(my+6))
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void e01da_a1w_f_ (

void *&ad_handle, const Integer &mx, const Integer &my, const nagad_a1w_w_rtype x[], const nagad_a1w_w_rtype y[], const nagad_a1w_w_rtype f[], Integer &px, Integer &py, nagad_a1w_w_rtype lamda[], nagad_a1w_w_rtype mu[], nagad_a1w_w_rtype c[], nagad_a1w_w_rtype wrk[], Integer &ifail)

The routine may be called by the names e01da_a1w_f or nagf_interp_dim2_spline_grid_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

e01da_a1w_f is the adjoint 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_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: mx – Integer Input
3: my – Integer Input
4: x(mx) – Type (nagad_a1w_w_rtype) array Input
5: y(my) – Type (nagad_a1w_w_rtype) array Input
6: f( $mx \times my$ ) – Type (nagad_a1w_w_rtype) array Input
7: px – Integer Output
8: py – Integer Output
9: lamda( $mx + 4$ ) – Type (nagad_a1w_w_rtype) array Output
10: mu( $my + 4$ ) – Type (nagad_a1w_w_rtype) array Output
11: c( $mx \times my$ ) – Type (nagad_a1w_w_rtype) array Output
12: wrk( $(mx + 6) \times (my + 6)$ ) – Type (nagad_a1w_w_rtype) array Workspace
13: ifail – Integer Input/Output

6 Error Indicators and Warnings

e01da_a1w_f 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 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

e01da_a1w_f 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.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	e01da_a1w_fe.f90	e01da_a1w_fe.d	e01da_a1w_fe.r
C++	e01da_a1w_hcppe.cpp	e01da_a1w_hcppe.d	e01da_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	e01da_t1w_fe.f90	e01da_t1w_fe.d	e01da_t1w_fe.r
C++	e01da_t1w_hcppe.cpp	e01da_t1w_hcppe.d	e01da_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	e01da_p0w_fe.f90	e01da_p0w_fe.d	e01da_p0w_fe.r
C++	e01da_p0w_hcppe.cpp	e01da_p0w_hcppe.d	e01da_p0w_hcppe.r