Changeset 271 for doc/latex/arx.tex

Timestamp:

02/16/09 10:03:13 (16 years ago)

Author:

smidl

Message:

Next major revision

Files:

• doc/latex/arx.tex (modified) (1 diff)

doc/latex/arx.tex

@@ -1 @@
-Here, we use the {\tt ARX} class to estimate parameters and structure. ARX model is defined as follows: \[ y_t = \theta' \psi_t + \rho e_t \] where $y_t$ is the system output, $[\theta,\rho]$ is vector of unknown parameters, $\psi_t$ is an vector of data-dependent regressors, and noise $e_t$ is assumed to be Normal distributed $\mathcal{N}(0,1)$.
+\hypertarget{arx_ui}{}\subsection{Running experiment $\backslash$c estimator with ARX data fields}\label{arx_ui}
+The experiment estimator::cpp can be run either on command line, or as a mex file in Matlab.\hypertarget{arx_ui_cmd}{}\section{Command-line usage}\label{arx_ui_cmd}
+In order to use it for estimation of an ARX model, we can define the following \hyperlink{ui}{User Infos and their use} structure: 
 
-Special cases include:...\hypertarget{arx_math}{}\section{Mathematical background:}\label{arx_math}
-This particular model belongs to the exponential family, hence it has conjugate distribution of the Gauss-inverse-Wishart form (class egiw). See, \mbox{[}reference\mbox{]} for details.
+\begin{DocInclude}\begin{verbatim}//Data generating system
+system = {
+        type = "ArxDS";
+        y = {type="rv"; names=["y", "u"];};
+        u = {type="rv"; names=[]; };
+        rgr = {type="rv";
+                names = ["y","y","y","u"];
+                times = [-1, -2, -3, -1];
+        };
+        //AR parameters
+        theta = [0.8, -0.3, 0.4, 1.0,
+                 0.0, 0.0, 0.0, 0.0];
+        // offset
+        offset = [0.0, 0.0];
+        //variance
+        r = [0.1, 0.0,
+             0.0, 1.0];
+        // log also theta
+        opt="L_theta";
+};
 
-For this model, structure estimation is a form of model selection procedure. Specifically, we compare hypotheses that the data were generated by the full model with hypotheses that some regressors in vector $\psi$ are redundant. The number of possible hypotheses is then the number of all possible combinations of all regressors.\hypertarget{arx_soft}{}\section{Software implementation:}\label{arx_soft}
-Estimation with this class of model is perfromed by class ARX which is derived from class BMEF (estimation of exponential family). The posterior density ( ARX::\_\-epdf() ) is class egiw, which represents Gauss-inverse-Wishart density.
+//store results
+logger = {
+        type= "dirfilelog";
+        dirname = "exp/arx_ui";
+        maxlen = 1000; //
+};
 
-Structure estimation is implemented in method ARX::structure\_\-est() which uses brute force tree search approach.\hypertarget{arx_exa}{}\section{Examples of Use:}\label{arx_exa}
-There are many ways how to use the object.\begin{itemize}
-\item Pure C++, as it is used in unit testing of the class arx, \hyperlink{arx__test_8cpp}{arx\_\-test.cpp}\item C++ application with UI configuration file, arx\_\-test\_\-ui\item Matlab interface, arx\_\-matlab \end{itemize}
+//estimation
+estimator = {
+        type = "ARXest";
+        y = {type="rv"; names=["y"]; };
+        rgr = {type="rv";
+                names = ["y","y","y","u"];
+                times = [-1, -2, -3, -1];
+        };
+
+        //optional fields
+        dV0 = [1e-3, 1e-5, 1e-5, 1e-5, 1e-5]; //default: 1e-3 for y, 1e-5 for rgr
+        nu0 = 8.;      //default: rgrlen + 2
+        frg = 1.0;    // forgetting, default frg=1.0
+};
+
+//experiment description
+experiment:{
+        ndat = 9000;
+};
+\end{verbatim}
+\end{DocInclude}
+ \hypertarget{arx_ui}{}\subsection{Running experiment $\backslash$c estimator with ARX data fields}\label{arx_ui}
+The experiment estimator::cpp can be run either on command line, or as a mex file in Matlab.\hypertarget{arx_ui_cmd}{}\section{Command-line usage}\label{arx_ui_cmd}
+In order to use it for estimation of an ARX model, we can define the following \hyperlink{ui}{User Infos and their use} structure: 
+
+\begin{DocInclude}\begin{verbatim}//Data generating system
+system = {
+        type = "ArxDS";
+        y = {type="rv"; names=["y", "u"];};
+        u = {type="rv"; names=[]; };
+        rgr = {type="rv";
+                names = ["y","y","y","u"];
+                times = [-1, -2, -3, -1];
+        };
+        //AR parameters
+        theta = [0.8, -0.3, 0.4, 1.0,
+                 0.0, 0.0, 0.0, 0.0];
+        // offset
+        offset = [0.0, 0.0];
+        //variance
+        r = [0.1, 0.0,
+             0.0, 1.0];
+        // log also theta
+        opt="L_theta";
+};
+
+//store results
+logger = {
+        type= "dirfilelog";
+        dirname = "exp/arx_ui";
+        maxlen = 1000; //
+};
+
+//estimation
+estimator = {
+        type = "ARXest";
+        y = {type="rv"; names=["y"]; };
+        rgr = {type="rv";
+                names = ["y","y","y","u"];
+                times = [-1, -2, -3, -1];
+        };
+
+        //optional fields
+        dV0 = [1e-3, 1e-5, 1e-5, 1e-5, 1e-5]; //default: 1e-3 for y, 1e-5 for rgr
+        nu0 = 8.;      //default: rgrlen + 2
+        frg = 1.0;    // forgetting, default frg=1.0
+};
+
+//experiment description
+experiment:{
+        ndat = 9000;
+};
+\end{verbatim}
+\end{DocInclude}
+