NAG AD Library
g02da (linregm_fit)

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1 Purpose

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(2*ip+ip*ip), 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:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

g02da is the AD Library version of the primal routine g02daf.
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

Cook R D and Weisberg S (1982) Residuals and Influence in Regression Chapman and Hall
Draper N R and Smith H (1985) Applied Regression Analysis (2nd Edition) Wiley
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
Hammarling S (1985) The singular value decomposition in multivariate statistics SIGNUM Newsl. 20(3) 2–25
McCullagh P and Nelder J A (1983) Generalized Linear Models Chapman and Hall
Searle S R (1971) Linear Models Wiley

5 Arguments

In addition to the arguments present in the interface of the primal routine, g02da 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_handlenag::ad::handle_t Input/Output
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: mean – character Input
3: weight – character Input
4: n – Integer Input
5: x(ldx, m) – ADTYPE array Input
6: ldx – Integer Input
7: m – Integer Input
8: isx(m) – Integer array Input
9: ip – Integer Input
10: y(n) – ADTYPE array Input
11: wt(*) – ADTYPE array Input
12: rssADTYPE Output
13: idf – Integer Output
14: b(ip) – ADTYPE array Output
15: se(ip) – ADTYPE array Output
16: cov(ip×(ip+1)/2) – ADTYPE array Output
17: res(n) – ADTYPE array Output
18: h(n) – ADTYPE array Output
19: q(ldq, ip+1) – ADTYPE array Output
20: ldq – Integer Input
21: svd – logical Output
22: irank – Integer Output
23: p(2×ip+ip×ip) – ADTYPE array Output
24: tolADTYPE Input
25: wk(max(2,5×(ip-1)+ip×ip)) – ADTYPE array Output
26: ifail – Integer Input/Output

6 Error Indicators and Warnings

g02da preserves all error codes from g02daf and in addition can return:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g02da is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for g02daf, modified to demonstrate calling the NAG AD Library.
Description of the primal 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 (R2), adjusted R2 and Akaike's information criteria (AIC) are calculated.

10.1 Adjoint modes

Language Source File Data Results
Fortran g02da_a1w_fe.f90 g02da_a1w_fe.d g02da_a1w_fe.r
C++ g02da_a1w_hcppe.cpp g02da_a1w_hcppe.d g02da_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran g02da_t1w_fe.f90 g02da_t1w_fe.d g02da_t1w_fe.r
C++ g02da_t1w_hcppe.cpp g02da_t1w_hcppe.d g02da_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran g02da_p0w_fe.f90 g02da_p0w_fe.d g02da_p0w_fe.r
C++ g02da_p0w_hcppe.cpp g02da_p0w_hcppe.d g02da_p0w_hcppe.r