[99] | 1 | \section{ARX Class Reference} |
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| 2 | \label{classARX}\index{ARX@{ARX}} |
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| 3 | Linear Autoregressive model with Gaussian noise. |
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| 4 | |
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| 5 | |
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| 6 | {\tt \#include $<$arx.h$>$} |
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| 7 | |
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| 8 | Inheritance diagram for ARX:\nopagebreak |
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| 9 | \begin{figure}[H] |
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| 10 | \begin{center} |
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| 11 | \leavevmode |
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| 12 | \includegraphics[width=40pt]{classARX__inherit__graph} |
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| 13 | \end{center} |
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| 14 | \end{figure} |
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| 15 | Collaboration diagram for ARX:\nopagebreak |
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| 16 | \begin{figure}[H] |
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| 17 | \begin{center} |
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| 18 | \leavevmode |
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| 19 | \includegraphics[width=90pt]{classARX__coll__graph} |
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| 20 | \end{center} |
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| 21 | \end{figure} |
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| 22 | \subsection*{Public Member Functions} |
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| 23 | \begin{CompactItemize} |
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| 24 | \item |
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| 25 | {\bf ARX} ({\bf RV} \&{\bf rv}, mat \&V0, double \&nu0, double frg0=1.0)\label{classARX_5fc6c18e73dcc0f1135eef33f42db8be} |
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| 26 | |
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| 27 | \begin{CompactList}\small\item\em Full constructor. \item\end{CompactList}\item |
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[140] | 28 | void \textbf{set\_\-parameters} (mat \&V0, double \&nu0)\label{classARX_3ccef8dc9dbed00ec74dddc949845d39} |
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| 29 | |
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| 30 | \item |
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| 31 | void \textbf{get\_\-parameters} (mat \&V0, double \&nu0)\label{classARX_29f55b43b8b6f5c4a55f6176aa85c494} |
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| 32 | |
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| 33 | \item |
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[99] | 34 | void {\bf bayes} (const vec \&dt)\label{classARX_ba82c956ca893826811aefe1e4af465d} |
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| 35 | |
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| 36 | \begin{CompactList}\small\item\em Here $dt = [y_t psi_t] $. \item\end{CompactList}\item |
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| 37 | {\bf epdf} \& {\bf \_\-epdf} ()\label{classARX_9d8eff7a9df81786191a4c55b27e5b8a} |
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| 38 | |
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| 39 | \begin{CompactList}\small\item\em Returns a pointer to the \doxyref{epdf}{p.}{classepdf} representing posterior density on parameters. Use with care! \item\end{CompactList}\item |
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| 40 | ivec {\bf structure\_\-est} ({\bf egiw} Eg0) |
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| 41 | \begin{CompactList}\small\item\em Brute force structure estimation. \item\end{CompactList}\item |
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[140] | 42 | double {\bf \_\-tll} ()\label{classARX_b8827048ceec8999849e2ed15400cae7} |
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| 43 | |
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| 44 | \begin{CompactList}\small\item\em access function \item\end{CompactList}\item |
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[99] | 45 | void {\bf bayes} (mat Dt)\label{classBM_87b07867fd4c133aa89a18543f68d9f9} |
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| 46 | |
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| 47 | \begin{CompactList}\small\item\em Batch Bayes rule (columns of Dt are observations). \item\end{CompactList}\item |
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| 48 | const {\bf RV} \& {\bf \_\-rv} () const \label{classBM_126bd2595c48e311fc2a7ab72876092a} |
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| 49 | |
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| 50 | \begin{CompactList}\small\item\em access function \item\end{CompactList}\item |
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| 51 | double {\bf \_\-ll} () const \label{classBM_87f4a547d2c29180be88175e5eab9c88} |
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| 52 | |
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| 53 | \begin{CompactList}\small\item\em access function \item\end{CompactList}\end{CompactItemize} |
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| 54 | \subsection*{Protected Attributes} |
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| 55 | \begin{CompactItemize} |
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| 56 | \item |
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| 57 | {\bf egiw} {\bf est}\label{classARX_691d023662beffa1dda611b416c0e27e} |
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| 58 | |
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| 59 | \begin{CompactList}\small\item\em Posterior estimate of $\theta,r$ in the form of Normal-inverse Wishart density. \item\end{CompactList}\item |
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| 60 | {\bf ldmat} \& {\bf V}\label{classARX_2291297861dd74ca0175a01f910a0ef7} |
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| 61 | |
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| 62 | \begin{CompactList}\small\item\em cached value of est.V \item\end{CompactList}\item |
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| 63 | double \& {\bf nu}\label{classARX_a4182c281098b2d86b62518a7493d9be} |
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| 64 | |
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| 65 | \begin{CompactList}\small\item\em cached value of est.nu \item\end{CompactList}\item |
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| 66 | double {\bf frg}\label{classARX_e467144efb0a5acbc10dba4eff8638fe} |
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| 67 | |
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| 68 | \begin{CompactList}\small\item\em forgetting factor \item\end{CompactList}\item |
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| 69 | double {\bf last\_\-lognc}\label{classARX_6d0cd0f0734aa77cdc5e48f1cf6737ec} |
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| 70 | |
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[106] | 71 | \begin{CompactList}\small\item\em cached value of lognc() in the previous step (used in evaluation of {\tt ll} ) \item\end{CompactList}\item |
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[140] | 72 | double {\bf tll}\label{classARX_64ea7c8ff48bf2548bac3e985e24da19} |
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| 73 | |
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| 74 | \begin{CompactList}\small\item\em total likelihood \item\end{CompactList}\item |
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[99] | 75 | {\bf RV} {\bf rv}\label{classBM_af00f0612fabe66241dd507188cdbf88} |
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| 76 | |
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| 77 | \begin{CompactList}\small\item\em Random variable of the posterior. \item\end{CompactList}\item |
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| 78 | double {\bf ll}\label{classBM_5623fef6572a08c2b53b8c87b82dc979} |
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| 79 | |
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| 80 | \begin{CompactList}\small\item\em Logarithm of marginalized data likelihood. \item\end{CompactList}\item |
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| 81 | bool {\bf evalll}\label{classBM_bf6fb59b30141074f8ee1e2f43d03129} |
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| 82 | |
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| 83 | \begin{CompactList}\small\item\em If true, the filter will compute likelihood of the data record and store it in {\tt ll} . Set to false if you want to save time. \item\end{CompactList}\end{CompactItemize} |
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| 84 | |
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| 85 | |
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| 86 | \subsection{Detailed Description} |
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| 87 | Linear Autoregressive model with Gaussian noise. |
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| 88 | |
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| 89 | Regression of the following kind: \[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \] where unknown parameters {\tt rv} are $[\theta r]$, regression vector $\psi=\psi(y_{1:t},u_{1:t})$ is a known function of past outputs and exogeneous variables $u_t$. Distrubances $e_t$ are supposed to be normally distributed: \[ e_t \sim \mathcal{N}(0,1). \] |
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| 90 | |
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| 91 | Extension for time-variant parameters $\theta_t,r_t$ may be achived using exponential forgetting (Kulhavy and Zarrop, 1993). In such a case, the forgetting factor {\tt frg} $\in <0,1>$ should be given in the constructor. Time-invariant parameters are estimated for {\tt frg} = 1. |
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| 92 | |
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| 93 | \subsection{Member Function Documentation} |
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| 94 | \index{ARX@{ARX}!structure\_\-est@{structure\_\-est}} |
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| 95 | \index{structure\_\-est@{structure\_\-est}!ARX@{ARX}} |
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[140] | 96 | \subsubsection[structure\_\-est]{\setlength{\rightskip}{0pt plus 5cm}ivec ARX::structure\_\-est ({\bf egiw} {\em Eg0})}\label{classARX_130bb7336aac681ce14b027b8f1409fa} |
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[99] | 97 | |
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| 98 | |
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| 99 | Brute force structure estimation. |
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| 100 | |
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| 101 | \begin{Desc} |
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| 102 | \item[Returns:]indeces of accepted regressors. \end{Desc} |
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| 103 | |
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| 104 | |
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| 105 | References RV::count(), est, egiw::lognc(), and BM::rv. |
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| 106 | |
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| 107 | The documentation for this class was generated from the following files:\begin{CompactItemize} |
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| 108 | \item |
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| 109 | work/mixpp/bdm/estim/{\bf arx.h}\item |
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| 110 | work/mixpp/bdm/estim/arx.cpp\end{CompactItemize} |
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