g02ab (corrmat_nearest_bounded) : NAG AD Library Routine Document, Mark 28

g02ab is the AD Library version of the primal routine g02abf. Based (in the C++ interface) on overload resolution, g02ab can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

2 Specification

Fortran Interface

Subroutine g02ab_AD_f (

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
ADTYPE, Intent (In)	::	alpha, errtol
ADTYPE, Intent (Inout)	::	g(ldg,n), w(*), x(ldx,n)
ADTYPE, Intent (Out)	::	nrmgrd
Character (1), Intent (In)	::	opt
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
when ADTYPE is	Type(nagad_a1t1w_w_rtype)	then AD is a1t1w
when ADTYPE is	Type(nagad_t2w_w_rtype)	then AD is t2w

C++ Interface

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

void g02ab (

handle_t &ad_handle, ADTYPE g[], const Integer &ldg, const Integer &n, const char *opt, const ADTYPE &alpha, ADTYPE w[], const ADTYPE &errtol, const Integer &maxits, const Integer &maxit, ADTYPE x[], const Integer &ldx, Integer &iter, Integer &feval, ADTYPE &nrmgrd, 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,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::type,

3 Description

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

5 Arguments

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.

6 Error Indicators and Warnings

g02ab preserves all error codes from g02abf and in addition can return:

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

$ifail = - 199$: The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.

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

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

This example finds the nearest correlation matrix to:

G = (\begin{matrix} 2 & −1 & 0 & 0 \\ −1 & 2 & −1 & 0 \\ 0 & −1 & 2 & −1 \\ 0 & 0 & −1 & 2 \end{matrix})

weighted by

W^{\frac{1}{2}} = diag (100, 20, 20, 20)

with minimum eigenvalue

0.02

Language	Source File	Data	Results
Fortran	g02ab_a1t1w_fe.f90	g02ab_a1t1w_fe.d	g02ab_a1t1w_fe.r
Fortran	g02ab_a1w_fe.f90	g02ab_a1w_fe.d	g02ab_a1w_fe.r
C++	g02ab_a1_algo_dcoe.cpp	None	g02ab_a1_algo_dcoe.r
C++	g02ab_a1t1_algo_dcoe.cpp	None	g02ab_a1t1_algo_dcoe.r

Language

Source File

Data

Results

Fortran

Fortran

C++

g02ab_a1_algo_dcoe.cpp

None

g02ab_a1_algo_dcoe.r

C++

g02ab_a1t1_algo_dcoe.cpp

None

g02ab_a1t1_algo_dcoe.r

Language	Source File	Data	Results
Fortran	g02ab_t1w_fe.f90	g02ab_t1w_fe.d	g02ab_t1w_fe.r
Fortran	g02ab_t2w_fe.f90	g02ab_t2w_fe.d	g02ab_t2w_fe.r
C++	g02ab_t1_dcoe.cpp	None	g02ab_t1_dcoe.r
C++	g02ab_t2_dcoe.cpp	None	g02ab_t2_dcoe.r

Language

Source File

Data

Results

Fortran

Fortran