NAG AD Library
g02da_a1w_f (linregm_fit_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

g02da_a1w_f is the adjoint version of the primal routine g02daf.

2 Specification

Fortran Interface
Subroutine g02da_a1w_f ( ad_handle, 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
Type (nagad_a1w_w_rtype), Intent (In) :: x(ldx,m), y(n), wt(*), tol
Type (nagad_a1w_w_rtype), Intent (Inout) :: q(ldq,ip+1)
Type (nagad_a1w_w_rtype), 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
C++ Header Interface
#include <nagad.h>
void g02da_a1w_f_ ( void *&ad_handle, const char *mean, const char *weight, const Integer &n, const nagad_a1w_w_rtype x[], const Integer &ldx, const Integer &m, const Integer isx[], const Integer &ip, const nagad_a1w_w_rtype y[], const nagad_a1w_w_rtype wt[], nagad_a1w_w_rtype &rss, Integer &idf, nagad_a1w_w_rtype b[], nagad_a1w_w_rtype se[], nagad_a1w_w_rtype cov[], nagad_a1w_w_rtype res[], nagad_a1w_w_rtype h[], nagad_a1w_w_rtype q[], const Integer &ldq, logical &svd, Integer &irank, nagad_a1w_w_rtype p[], const nagad_a1w_w_rtype &tol, nagad_a1w_w_rtype wk[], Integer &ifail, const Charlen length_mean, const Charlen length_weight)
The routine may be called by the names g02da_a1w_f or nagf_correg_linregm_fit_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

g02da_a1w_f is the adjoint 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_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: mean – character Input
3: weight – character Input
4: n – Integer Input
5: x(ldx, m) – Type (nagad_a1w_w_rtype) array Input
6: ldx – Integer Input
7: m – Integer Input
8: isx(m) – Integer array Input
9: ip – Integer Input
10: y(n) – Type (nagad_a1w_w_rtype) array Input
11: wt(*) – Type (nagad_a1w_w_rtype) array Input
12: rssType (nagad_a1w_w_rtype) Output
13: idf – Integer Output
14: b(ip) – Type (nagad_a1w_w_rtype) array Output
15: se(ip) – Type (nagad_a1w_w_rtype) array Output
16: cov(ip×(ip+1)/2) – Type (nagad_a1w_w_rtype) array Output
17: res(n) – Type (nagad_a1w_w_rtype) array Output
18: h(n) – Type (nagad_a1w_w_rtype) array Output
19: q(ldq, ip+1) – Type (nagad_a1w_w_rtype) array Output
20: ldq – Integer Input
21: svd – logical Output
22: irank – Integer Output
23: p(2×ip+ip×ip) – Type (nagad_a1w_w_rtype) array Output
24: tolType (nagad_a1w_w_rtype) Input
25: wk(max(2,5×(ip-1)+ip×ip)) – Type (nagad_a1w_w_rtype) array Output
26: ifail – Integer Input/Output

6 Error Indicators and Warnings

g02da_a1w_f 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 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

g02da_a1w_f 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.

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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