NAG AD Library
e02bb (dim1_spline_eval)

e02bb is the AD Library version of the primal routine e02bbf. Based (in the C++ interface) on overload resolution, e02bb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e02bb_AD_f (

ad_handle, ncap7, lamda, c, x, s, ifail)

Integer, Intent (In)	::	ncap7
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	lamda(ncap7), c(ncap7), x
ADTYPE, Intent (Out)	::	s
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++ Header Interface

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

void e02bb (

void *&ad_handle, const Integer &ncap7, const ADTYPE lamda[], const ADTYPE c[], const ADTYPE &x, ADTYPE &s, 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

e02bb is the AD Library version of the primal routine e02bbf.

e02bbf evaluates a cubic spline from its B-spline representation. For further information see Section 3 in the documentation for e02bbf.

4 References

Cox M G (1972) The numerical evaluation of B-splines J. Inst. Math. Appl. 10 134–149

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

Cox M G and Hayes J G (1973) Curve fitting: a guide and suite of algorithms for the non-specialist user NPL Report NAC26 National Physical Laboratory

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

5 Arguments

In addition to the arguments present in the interface of the primal routine, e02bb 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 – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: ncap7 – Integer Input
3: lamda(ncap7) – ADTYPE array Input
4: c(ncap7) – ADTYPE array Input
5: x – ADTYPE Input
6: s – ADTYPE Output
7: ifail – Integer Input/Output

6 Error Indicators and Warnings

e02bb preserves all error codes from e02bbf 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e02bb is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e02bbf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

Evaluate at nine equally-spaced points in the interval

1.0 \leq x \leq 9.0

the cubic spline with (augmented) knots

1.0

1.0

1.0

1.0

3.0

6.0

8.0

9.0

9.0

9.0

9.0

and normalized cubic B-spline coefficients

1.0

2.0

4.0

7.0

6.0

4.0

3.0

The example program is written in a general form that will enable a cubic spline with

\bar{n}

intervals, in its normalized cubic B-spline form, to be evaluated at

m

equally-spaced points in the interval

lamda (4) \leq x \leq lamda (\bar{n} + 4)

. The program is self-starting in that any number of datasets may be supplied.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e02bb_a1w_fe.f90	None	e02bb_a1w_fe.r
C++	e02bb_a1w_hcppe.cpp	None	e02bb_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e02bb_t1w_fe.f90	None	e02bb_t1w_fe.r
C++	e02bb_t1w_hcppe.cpp	None	e02bb_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e02bb_p0w_fe.f90	None	e02bb_p0w_fe.r
C++	e02bb_p0w_hcppe.cpp	None	e02bb_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E02 (Fit) Chapter Contents

E02 (Fit) Chapter Introduction (FL)

e02bb: FL CL CPP AD

NAG AD Librarye02bb (dim1_spline_eval)

▸▿ Contents

1 Purpose