c05au_a1w_f (contfn_brent_interval_a1w) : NAG AD Library Routine Document, Mark 27

NAG AD Library
c05au_a1w_f (contfn_brent_interval_a1w)

Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

2 Specification

Fortran Interface

Subroutine c05au_a1w_f (

ad_handle, x, h, eps, eta, f, a, b, iuser, ruser, ifail)

Integer, Intent (Inout)	::	iuser(*), ifail
External	::	f
Type (nagad_a1w_w_rtype), Intent (In)	::	h, eps, eta
Type (nagad_a1w_w_rtype), Intent (Inout)	::	x, ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	a, b
Type (c_ptr), Intent (In)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void c05au_a1w_f_ (

void *&ad_handle, nagad_a1w_w_rtype &x, const nagad_a1w_w_rtype &h, const nagad_a1w_w_rtype &eps, const nagad_a1w_w_rtype &eta,
void (NAG_CALL f)(void *&ad_handle, nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[]),
nagad_a1w_w_rtype &a, nagad_a1w_w_rtype &b, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names c05au_a1w_f or nagf_roots_contfn_brent_interval_a1w.

3 Description

c05au_a1w_f is the adjoint version of the primal routine c05auf.

c05auf locates a simple zero of a continuous function from a given starting value. It uses a binary search to locate an interval containing a zero of the function, then Brent's method, which is a combination of nonlinear interpolation, linear extrapolation and bisection, to locate the zero precisely. For further information see Section 3 in the documentation for c05auf.

5 Arguments

In addition to the arguments present in the interface of the primal routine, c05au_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

On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.

2: x – Type (nagad_a1w_w_rtype) Input/Output

3: h – Type (nagad_a1w_w_rtype) Input

4: eps – Type (nagad_a1w_w_rtype) Input

5: eta – Type (nagad_a1w_w_rtype) Input

6: f – Subroutine External Procedure

Note that f is a subroutine in this interface, returning the function value via the additional output parameter retval.

The specification of f is:

Fortran Interface

Subroutine f (

ad_handle, x, retval, iuser, ruser)

Integer, Intent (Inout)	::	iuser(*)
Type (nagad_a1w_w_rtype), Intent (In)	::	x
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	retval
Type (c_ptr), Intent (In)	::	ad_handle

C++ Interface

#include <nagad.h>

void f (

void *&ad_handle, nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[])

1: ad_handle – Type (c_ptr) Input: On entry: a handle to the AD configuration data object.
2: x – Type (nagad_a1w_w_rtype) Input
3: retval – Type (nagad_a1w_w_rtype) Output: On exit: the value of $f$ at the specified point.
4: iuser – Integer array User Workspace
5: ruser – Type (nagad_a1w_w_rtype) array User Workspace

7: a – Type (nagad_a1w_w_rtype) Output

8: b – Type (nagad_a1w_w_rtype) Output

9: iuser(

*

) – Integer array User Workspace

10: ruser(

*

) – Type (nagad_a1w_w_rtype) array User Workspace

11: ifail – Integer Input/Output

6 Error Indicators and Warnings

c05au_a1w_f preserves all error codes from c05auf and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.5.2 in the NAG AD Library Introduction for further information.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 4.5.1 in the NAG AD Library Introduction for further information.

9 Further Comments

Please note that the algorithmic adjoint of Brent's method may be ill-conditioned. This means that derivatives of the zero returned in x, with respect to function parameters stored in ruser, may have limited accuracy when computed in algorithmic mode. The routine c05ay_a1w_f (which requires an initial interval containing the zero) can be used in symbolic mode and will compute accurate derivatives.

Language	Source File	Data	Results
Fortran	c05au_a1w_fe.f90	None	c05au_a1w_fe.r
C++	c05au_a1w_hcppe.cpp	None	c05au_a1w_hcppe.r

NAG AD Library
c05au_a1w_f (contfn_brent_interval_a1w)

▸▿ 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

NAG AD Libraryc05au_a1w_f (contfn_brent_interval_a1w)

▸▿ 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

NAG AD Library
c05au_a1w_f (contfn_brent_interval_a1w)