g02aa: FL CL CPP AD

NAG AD Library
g02aa_a1w_f (corrmat_nearest_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

G02 (Correg) Chapter Contents

G02 (Correg) Chapter Introduction (FL)

g02aa: 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

g02aa_a1w_f is the adjoint version of the primal routine g02aaf.

2 Specification

Fortran Interface

Subroutine g02aa_a1w_f (

ad_handle, g, ldg, n, errtol, maxits, maxit, x, ldx, iter, feval, nrmgrd, ifail)

Integer, Intent (In)	::	ldg, n, maxits, maxit, ldx
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	iter, feval
Type (nagad_a1w_w_rtype), Intent (In)	::	errtol
Type (nagad_a1w_w_rtype), Intent (Inout)	::	g(ldg,n), x(ldx,n)
Type (nagad_a1w_w_rtype), Intent (Out)	::	nrmgrd
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void g02aa_a1w_f_ (

void *&ad_handle, nagad_a1w_w_rtype g[], const Integer &ldg, const Integer &n, const nagad_a1w_w_rtype &errtol, const Integer &maxits, const Integer &maxit, nagad_a1w_w_rtype x[], const Integer &ldx, Integer &iter, Integer &feval, nagad_a1w_w_rtype &nrmgrd, Integer &ifail)

The routine may be called by the names g02aa_a1w_f or nagf_correg_corrmat_nearest_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

g02aa_a1w_f is the adjoint version of the primal routine g02aaf.

g02aaf computes the nearest correlation matrix, in the Frobenius norm, to a given square, input matrix. For further information see Section 3 in the documentation for g02aaf.

4 References

Borsdorf R and Higham N J (2010) A preconditioned (Newton) algorithm for the nearest correlation matrix IMA Journal of Numerical Analysis 30(1) 94–107

Qi H and Sun D (2006) A quadratically convergent Newton method for computing the nearest correlation matrix SIAM J. Matrix AnalAppl 29(2) 360–385

5 Arguments

In addition to the arguments present in the interface of the primal routine, g02aa_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: g(ldg, n) – Type (nagad_a1w_w_rtype) array Input/Output
3: ldg – Integer Input
4: n – Integer Input
5: errtol – Type (nagad_a1w_w_rtype) Input
6: maxits – Integer Input
7: maxit – Integer Input
8: x(ldx, n) – Type (nagad_a1w_w_rtype) array Output
9: ldx – Integer Input
10: iter – Integer Output
11: feval – Integer Output
12: nrmgrd – Type (nagad_a1w_w_rtype) Output
13: ifail – Integer Input/Output

6 Error Indicators and Warnings

g02aa_a1w_f preserves all error codes from g02aaf 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

g02aa_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g02aaf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	g02aa_a1w_fe.f90	g02aa_a1w_fe.d	g02aa_a1w_fe.r
C++	g02aa_a1w_hcppe.cpp	g02aa_a1w_hcppe.d	g02aa_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	g02aa_t1w_fe.f90	g02aa_t1w_fe.d	g02aa_t1w_fe.r
C++	g02aa_t1w_hcppe.cpp	g02aa_t1w_hcppe.d	g02aa_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	g02aa_p0w_fe.f90	g02aa_p0w_fe.d	g02aa_p0w_fe.r
C++	g02aa_p0w_hcppe.cpp	g02aa_p0w_hcppe.d	g02aa_p0w_hcppe.r