NAG AD Library
g02ab_a1w_f (corrmat_nearest_bounded_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.
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1 Purpose

g02ab_a1w_f is the adjoint version of the primal routine g02abf.

2 Specification

Fortran Interface
Subroutine g02ab_a1w_f ( ad_handle, g, ldg, n, opt, alpha, w, 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) :: alpha, errtol
Type (nagad_a1w_w_rtype), Intent (Inout) :: g(ldg,n), w(*), x(ldx,n)
Type (nagad_a1w_w_rtype), Intent (Out) :: nrmgrd
Character (1), Intent (In) :: opt
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void g02ab_a1w_f_ ( void *&ad_handle, nagad_a1w_w_rtype g[], const Integer &ldg, const Integer &n, const char *opt, const nagad_a1w_w_rtype &alpha, nagad_a1w_w_rtype w[], 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, const Charlen length_opt)
The routine may be called by the names g02ab_a1w_f or nagf_correg_corrmat_nearest_bounded_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

g02ab_a1w_f is the adjoint version of the primal routine g02abf.
g02abf computes the nearest correlation matrix, in the Frobenius norm or weighted Frobenius norm, and optionally with bounds on the eigenvalues, to a given square, input matrix. For further information see Section 3 in the documentation for g02abf.

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, g02ab_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: opt – character Input
6: alphaType (nagad_a1w_w_rtype) Input
7: w(*) – Type (nagad_a1w_w_rtype) array Input/Output
8: errtolType (nagad_a1w_w_rtype) Input
9: maxits – Integer Input
10: maxit – Integer Input
11: x(ldx, n) – Type (nagad_a1w_w_rtype) array Output
12: ldx – Integer Input
13: iter – Integer Output
14: feval – Integer Output
15: nrmgrdType (nagad_a1w_w_rtype) Output
16: ifail – Integer Input/Output

6 Error Indicators and Warnings

g02ab_a1w_f preserves all error codes from g02abf and in addition can return:
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.
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

g02ab_a1w_f is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for g02abf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

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10.2 Tangent mode (t1w)

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10.3 Passive mode (p0w)

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