c05au: FL CL CPP AD

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. 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

C05 (Roots) Chapter Contents

C05 (Roots) Chapter Introduction (FL)

c05au: 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

c05au_a1w_f is the adjoint version of the primal routine c05auf.

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 (Inout)	::	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, const 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. The corresponding t1w and p0w variants of this routine are also available.

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.

4 References

Brent R P (1973) Algorithms for Minimization Without Derivatives Prentice–Hall

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/Output

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 (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void f (

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

1: ad_handle – Type (c_ptr) Input/Output: 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 4.8.2 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

c05au_a1w_f is not threaded in any implementation.

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.