g02da (linregm_fit) : NAG AD Library Routine Document, Mark 28

g02da is the AD Library version of the primal routine g02daf. Based (in the C++ interface) on overload resolution, g02da can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine g02da_AD_f (

mean, weight, n, x, ldx, m, isx, ip, y, wt, rss, idf, b, se, cov, res, h, q, ldq, svd, irank, p, tol, wk, ifail)

Integer, Intent (In)	::	n, ldx, m, isx(m), ip, ldq
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	idf, irank
ADTYPE, Intent (In)	::	x(ldx,m), y(n), wt(*), tol
ADTYPE, Intent (Inout)	::	q(ldq,ip+1)
ADTYPE, Intent (Out)	::	rss, b(ip), se(ip), cov(ip(ip+1)/2), res(n), h(n), p(2ip+ipip), wk(max(2,5(ip-1)+ip*ip))
Logical, Intent (Out)	::	svd
Character (1), Intent (In)	::	mean, weight
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

C++ Interface

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

void g02da (

handle_t &ad_handle, const char *mean, const char *weight, const Integer &n, const ADTYPE x[], const Integer &ldx, const Integer &m, const Integer isx[], const Integer &ip, const ADTYPE y[], const ADTYPE wt[], ADTYPE &rss, Integer &idf, ADTYPE b[], ADTYPE se[], ADTYPE cov[], ADTYPE res[], ADTYPE h[], ADTYPE q[], const Integer &ldq, logical &svd, Integer &irank, ADTYPE p[], const ADTYPE &tol, ADTYPE wk[], 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

3 Description

g02daf performs a general multiple linear regression when the independent variables may be linearly dependent. Parameter estimates, standard errors, residuals and influence statistics are computed. g02daf may be used to perform a weighted regression. For further information see Section 3 in the documentation for g02daf.

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

g02da preserves all error codes from g02daf 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

Data from an experiment with four treatments and three observations per treatment are read in. The treatments are represented by dummy (

0 - 1

) variables. An unweighted model is fitted with a mean included in the model. g02bu is then called to calculate the total sums of squares and the coefficient of determination (