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1\hypertarget{classKalman}{
2\section{Kalman$<$ sq\_\-T $>$ Class Template Reference}
3\label{classKalman}\index{Kalman@{Kalman}}
4}
5\hyperlink{classKalman}{Kalman} filter with covariance matrices in square root form. 
6
7
8{\tt \#include $<$libKF.h$>$}
9
10Inheritance diagram for Kalman$<$ sq\_\-T $>$:\nopagebreak
11\begin{figure}[H]
12\begin{center}
13\leavevmode
14\includegraphics[width=400pt]{classKalman__inherit__graph}
15\end{center}
16\end{figure}
17Collaboration diagram for Kalman$<$ sq\_\-T $>$:\nopagebreak
18\begin{figure}[H]
19\begin{center}
20\leavevmode
21\includegraphics[width=79pt]{classKalman__coll__graph}
22\end{center}
23\end{figure}
24\subsection*{Public Member Functions}
25\begin{CompactItemize}
26\item 
27\hypertarget{classKalman_3d56b0a97b8c1e25fdd3b10eef3c2ad3}{
28\hyperlink{classKalman_3d56b0a97b8c1e25fdd3b10eef3c2ad3}{Kalman} (\hyperlink{classRV}{RV} rvx0, \hyperlink{classRV}{RV} rvy0, \hyperlink{classRV}{RV} rvu0)}
29\label{classKalman_3d56b0a97b8c1e25fdd3b10eef3c2ad3}
30
31\begin{CompactList}\small\item\em Default constructor. \item\end{CompactList}\item 
32\hypertarget{classKalman_ce38e31810aea4db45a83ad05eaba009}{
33\hyperlink{classKalman_ce38e31810aea4db45a83ad05eaba009}{Kalman} (const \hyperlink{classKalman}{Kalman}$<$ sq\_\-T $>$ \&K0)}
34\label{classKalman_ce38e31810aea4db45a83ad05eaba009}
35
36\begin{CompactList}\small\item\em Copy constructor. \item\end{CompactList}\item 
37\hypertarget{classKalman_239b28a0380946f5749b2f8d2807f93a}{
38void \hyperlink{classKalman_239b28a0380946f5749b2f8d2807f93a}{set\_\-parameters} (const mat \&A0, const mat \&B0, const mat \&C0, const mat \&D0, const sq\_\-T \&R0, const sq\_\-T \&Q0)}
39\label{classKalman_239b28a0380946f5749b2f8d2807f93a}
40
41\begin{CompactList}\small\item\em Set parameters with check of relevance. \item\end{CompactList}\item 
42\hypertarget{classKalman_80bcf29466d9a9dd2b8f74699807d0c0}{
43void \hyperlink{classKalman_80bcf29466d9a9dd2b8f74699807d0c0}{set\_\-est} (const vec \&mu0, const sq\_\-T \&P0)}
44\label{classKalman_80bcf29466d9a9dd2b8f74699807d0c0}
45
46\begin{CompactList}\small\item\em Set estimate values, used e.g. in initialization. \item\end{CompactList}\item 
47\hypertarget{classKalman_7750ffd73f261828a32c18aaeb65c75c}{
48void \hyperlink{classKalman_7750ffd73f261828a32c18aaeb65c75c}{bayes} (const vec \&dt)}
49\label{classKalman_7750ffd73f261828a32c18aaeb65c75c}
50
51\begin{CompactList}\small\item\em Here dt = \mbox{[}yt;ut\mbox{]} of appropriate dimensions. \item\end{CompactList}\item 
52\hypertarget{classKalman_67cccaf1c4dcdcd1df110e15ef326bfe}{
53const \hyperlink{classepdf}{epdf} \& \hyperlink{classKalman_67cccaf1c4dcdcd1df110e15ef326bfe}{\_\-epdf} () const }
54\label{classKalman_67cccaf1c4dcdcd1df110e15ef326bfe}
55
56\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
57\hypertarget{classKalman_11f82ef04e3dbc54bd1d3d89edb6aa07}{
58const \hyperlink{classenorm}{enorm}$<$ sq\_\-T $>$ $\ast$ \hyperlink{classKalman_11f82ef04e3dbc54bd1d3d89edb6aa07}{\_\-e} () const }
59\label{classKalman_11f82ef04e3dbc54bd1d3d89edb6aa07}
60
61\begin{CompactList}\small\item\em Returns a pointer to the \hyperlink{classepdf}{epdf} representing posterior density on parameters. Use with care! \item\end{CompactList}\item 
62\hypertarget{classKalman_980fcd41c6c548c5da7b8b67c8e6da79}{
63mat \& \hyperlink{classKalman_980fcd41c6c548c5da7b8b67c8e6da79}{\_\-\_\-K} ()}
64\label{classKalman_980fcd41c6c548c5da7b8b67c8e6da79}
65
66\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
67\hypertarget{classKalman_ac9540f3850b74d89a5fe4db6fc358ce}{
68vec \hyperlink{classKalman_ac9540f3850b74d89a5fe4db6fc358ce}{\_\-dP} ()}
69\label{classKalman_ac9540f3850b74d89a5fe4db6fc358ce}
70
71\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
72\hypertarget{classBM_0186270f75189677f390fe088a9947e9}{
73virtual void \hyperlink{classBM_0186270f75189677f390fe088a9947e9}{bayesB} (const mat \&Dt)}
74\label{classBM_0186270f75189677f390fe088a9947e9}
75
76\begin{CompactList}\small\item\em Batch Bayes rule (columns of Dt are observations). \item\end{CompactList}\item 
77virtual double \hyperlink{classBM_8a8ce6df431689964c41cc6c849cfd06}{logpred} (const vec \&dt) const
78\item 
79\hypertarget{classBM_cd0660f2a1a344b56ac39802708ff165}{
80vec \hyperlink{classBM_cd0660f2a1a344b56ac39802708ff165}{logpred\_\-m} (const mat \&dt) const }
81\label{classBM_cd0660f2a1a344b56ac39802708ff165}
82
83\begin{CompactList}\small\item\em Matrix version of logpred. \item\end{CompactList}\item 
84\hypertarget{classBM_5594d68ee9aa6fc8c1e79019da5c9d56}{
85virtual \hyperlink{classepdf}{epdf} $\ast$ \hyperlink{classBM_5594d68ee9aa6fc8c1e79019da5c9d56}{predictor} (const \hyperlink{classRV}{RV} \&\hyperlink{classBM_af00f0612fabe66241dd507188cdbf88}{rv}) const }
86\label{classBM_5594d68ee9aa6fc8c1e79019da5c9d56}
87
88\begin{CompactList}\small\item\em Constructs a predictive density (marginal density on data). \item\end{CompactList}\item 
89\hypertarget{classBM_126bd2595c48e311fc2a7ab72876092a}{
90const \hyperlink{classRV}{RV} \& \hyperlink{classBM_126bd2595c48e311fc2a7ab72876092a}{\_\-rv} () const }
91\label{classBM_126bd2595c48e311fc2a7ab72876092a}
92
93\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
94\hypertarget{classBM_87f4a547d2c29180be88175e5eab9c88}{
95double \hyperlink{classBM_87f4a547d2c29180be88175e5eab9c88}{\_\-ll} () const }
96\label{classBM_87f4a547d2c29180be88175e5eab9c88}
97
98\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
99\hypertarget{classBM_1ffa9f23669aabecc3760c06c6987522}{
100void \hyperlink{classBM_1ffa9f23669aabecc3760c06c6987522}{set\_\-evalll} (bool evl0)}
101\label{classBM_1ffa9f23669aabecc3760c06c6987522}
102
103\begin{CompactList}\small\item\em access function \item\end{CompactList}\item 
104virtual \hyperlink{classBM}{BM} $\ast$ \hyperlink{classBM_eb58c81d6a7b75b05fc6f276eed78887}{\_\-copy\_\-} (bool changerv=false)
105\end{CompactItemize}
106\subsection*{Protected Attributes}
107\begin{CompactItemize}
108\item 
109\hypertarget{classKalman_7501230c2fafa3655887d2da23b3184c}{
110\hyperlink{classRV}{RV} \hyperlink{classKalman_7501230c2fafa3655887d2da23b3184c}{rvy}}
111\label{classKalman_7501230c2fafa3655887d2da23b3184c}
112
113\begin{CompactList}\small\item\em Indetifier of output rv. \item\end{CompactList}\item 
114\hypertarget{classKalman_44a16ffd5ac1e6e39bae34fea9e1e498}{
115\hyperlink{classRV}{RV} \hyperlink{classKalman_44a16ffd5ac1e6e39bae34fea9e1e498}{rvu}}
116\label{classKalman_44a16ffd5ac1e6e39bae34fea9e1e498}
117
118\begin{CompactList}\small\item\em Indetifier of exogeneous rv. \item\end{CompactList}\item 
119\hypertarget{classKalman_39c8c403b46fa3b8c7da77cb2e3729eb}{
120int \hyperlink{classKalman_39c8c403b46fa3b8c7da77cb2e3729eb}{dimx}}
121\label{classKalman_39c8c403b46fa3b8c7da77cb2e3729eb}
122
123\begin{CompactList}\small\item\em cache of rv.count() \item\end{CompactList}\item 
124\hypertarget{classKalman_ba17b956df1e38b31fbbc299c8213b6a}{
125int \hyperlink{classKalman_ba17b956df1e38b31fbbc299c8213b6a}{dimy}}
126\label{classKalman_ba17b956df1e38b31fbbc299c8213b6a}
127
128\begin{CompactList}\small\item\em cache of rvy.count() \item\end{CompactList}\item 
129\hypertarget{classKalman_b0153795a1444b6968a86409c778d9ce}{
130int \hyperlink{classKalman_b0153795a1444b6968a86409c778d9ce}{dimu}}
131\label{classKalman_b0153795a1444b6968a86409c778d9ce}
132
133\begin{CompactList}\small\item\em cache of rvu.count() \item\end{CompactList}\item 
134\hypertarget{classKalman_5e02efe86ee91e9c74b93b425fe060b9}{
135mat \hyperlink{classKalman_5e02efe86ee91e9c74b93b425fe060b9}{A}}
136\label{classKalman_5e02efe86ee91e9c74b93b425fe060b9}
137
138\begin{CompactList}\small\item\em Matrix A. \item\end{CompactList}\item 
139\hypertarget{classKalman_dc87704284a6c0bca13bf51f4345a50a}{
140mat \hyperlink{classKalman_dc87704284a6c0bca13bf51f4345a50a}{B}}
141\label{classKalman_dc87704284a6c0bca13bf51f4345a50a}
142
143\begin{CompactList}\small\item\em Matrix B. \item\end{CompactList}\item 
144\hypertarget{classKalman_86a805cd6515872d1132ad0d6eb5dc13}{
145mat \hyperlink{classKalman_86a805cd6515872d1132ad0d6eb5dc13}{C}}
146\label{classKalman_86a805cd6515872d1132ad0d6eb5dc13}
147
148\begin{CompactList}\small\item\em Matrix C. \item\end{CompactList}\item 
149\hypertarget{classKalman_d69f774ba3335c970c1c5b1d182f4dd1}{
150mat \hyperlink{classKalman_d69f774ba3335c970c1c5b1d182f4dd1}{D}}
151\label{classKalman_d69f774ba3335c970c1c5b1d182f4dd1}
152
153\begin{CompactList}\small\item\em Matrix D. \item\end{CompactList}\item 
154\hypertarget{classKalman_9b69015c800eb93f3ee49da23a6f55d9}{
155sq\_\-T \hyperlink{classKalman_9b69015c800eb93f3ee49da23a6f55d9}{Q}}
156\label{classKalman_9b69015c800eb93f3ee49da23a6f55d9}
157
158\begin{CompactList}\small\item\em Matrix Q in square-root form. \item\end{CompactList}\item 
159\hypertarget{classKalman_11d171dc0e0ab111c56a70f98b97b3ec}{
160sq\_\-T \hyperlink{classKalman_11d171dc0e0ab111c56a70f98b97b3ec}{R}}
161\label{classKalman_11d171dc0e0ab111c56a70f98b97b3ec}
162
163\begin{CompactList}\small\item\em Matrix R in square-root form. \item\end{CompactList}\item 
164\hypertarget{classKalman_5568c74bac67ae6d3b1061dba60c9424}{
165\hyperlink{classenorm}{enorm}$<$ sq\_\-T $>$ \hyperlink{classKalman_5568c74bac67ae6d3b1061dba60c9424}{est}}
166\label{classKalman_5568c74bac67ae6d3b1061dba60c9424}
167
168\begin{CompactList}\small\item\em posterior density on \$x\_\-t\$ \item\end{CompactList}\item 
169\hypertarget{classKalman_e580ab06483952bd03f2e651763e184f}{
170\hyperlink{classenorm}{enorm}$<$ sq\_\-T $>$ \hyperlink{classKalman_e580ab06483952bd03f2e651763e184f}{fy}}
171\label{classKalman_e580ab06483952bd03f2e651763e184f}
172
173\begin{CompactList}\small\item\em preditive density on \$y\_\-t\$ \item\end{CompactList}\item 
174\hypertarget{classKalman_d422f51467c7a06174af2476d2826132}{
175mat \hyperlink{classKalman_d422f51467c7a06174af2476d2826132}{\_\-K}}
176\label{classKalman_d422f51467c7a06174af2476d2826132}
177
178\begin{CompactList}\small\item\em placeholder for \hyperlink{classKalman}{Kalman} gain \item\end{CompactList}\item 
179\hypertarget{classKalman_764bbc95238eda11fc81c5ebd0b1dcfd}{
180vec \& \hyperlink{classKalman_764bbc95238eda11fc81c5ebd0b1dcfd}{\_\-yp}}
181\label{classKalman_764bbc95238eda11fc81c5ebd0b1dcfd}
182
183\begin{CompactList}\small\item\em cache of fy.mu \item\end{CompactList}\item 
184\hypertarget{classKalman_45c9f928d2d62e0c884900fb3380f904}{
185sq\_\-T \& \hyperlink{classKalman_45c9f928d2d62e0c884900fb3380f904}{\_\-Ry}}
186\label{classKalman_45c9f928d2d62e0c884900fb3380f904}
187
188\begin{CompactList}\small\item\em cache of fy.R \item\end{CompactList}\item 
189\hypertarget{classKalman_fe803a81d2d847b0b1db3c6b29c18061}{
190vec \& \hyperlink{classKalman_fe803a81d2d847b0b1db3c6b29c18061}{\_\-mu}}
191\label{classKalman_fe803a81d2d847b0b1db3c6b29c18061}
192
193\begin{CompactList}\small\item\em cache of est.mu \item\end{CompactList}\item 
194\hypertarget{classKalman_9fb808cc94a4c2652e1fb93be9bb7dcf}{
195sq\_\-T \& \hyperlink{classKalman_9fb808cc94a4c2652e1fb93be9bb7dcf}{\_\-P}}
196\label{classKalman_9fb808cc94a4c2652e1fb93be9bb7dcf}
197
198\begin{CompactList}\small\item\em cache of est.R \item\end{CompactList}\item 
199\hypertarget{classBM_af00f0612fabe66241dd507188cdbf88}{
200\hyperlink{classRV}{RV} \hyperlink{classBM_af00f0612fabe66241dd507188cdbf88}{rv}}
201\label{classBM_af00f0612fabe66241dd507188cdbf88}
202
203\begin{CompactList}\small\item\em Random variable of the posterior. \item\end{CompactList}\item 
204\hypertarget{classBM_5623fef6572a08c2b53b8c87b82dc979}{
205double \hyperlink{classBM_5623fef6572a08c2b53b8c87b82dc979}{ll}}
206\label{classBM_5623fef6572a08c2b53b8c87b82dc979}
207
208\begin{CompactList}\small\item\em Logarithm of marginalized data likelihood. \item\end{CompactList}\item 
209\hypertarget{classBM_bf6fb59b30141074f8ee1e2f43d03129}{
210bool \hyperlink{classBM_bf6fb59b30141074f8ee1e2f43d03129}{evalll}}
211\label{classBM_bf6fb59b30141074f8ee1e2f43d03129}
212
213\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 computational time. \item\end{CompactList}\end{CompactItemize}
214
215
216\subsection{Detailed Description}
217\subsubsection*{template$<$class sq\_\-T$>$ class Kalman$<$ sq\_\-T $>$}
218
219\hyperlink{classKalman}{Kalman} filter with covariance matrices in square root form.
220
221Parameter evolution model:\[ x_t = A x_{t-1} + B u_t + Q^{1/2} e_t \] Observation model: \[ y_t = C x_{t-1} + C u_t + Q^{1/2} w_t. \] Where \$e\_\-t\$ and \$w\_\-t\$ are independent vectors Normal(0,1)-distributed disturbances.
222
223\subsection{Member Function Documentation}
224\hypertarget{classBM_8a8ce6df431689964c41cc6c849cfd06}{
225\index{Kalman@{Kalman}!logpred@{logpred}}
226\index{logpred@{logpred}!Kalman@{Kalman}}
227\subsubsection[logpred]{\setlength{\rightskip}{0pt plus 5cm}virtual double BM::logpred (const vec \& {\em dt}) const\hspace{0.3cm}{\tt  \mbox{[}inline, virtual, inherited\mbox{]}}}}
228\label{classBM_8a8ce6df431689964c41cc6c849cfd06}
229
230
231Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.
232
233Reimplemented in \hyperlink{classARX_e7f9e7823aec9bf7ddc3b42d9b3304c4}{ARX}, \hyperlink{classMixEF_424ca64f36d4e41de7a7e7ae921d35ea}{MixEF}, and \hyperlink{classmultiBM_13e26a61757278981fd8cac9a7ef91eb}{multiBM}.
234
235Referenced by BM::logpred\_\-m().\hypertarget{classBM_eb58c81d6a7b75b05fc6f276eed78887}{
236\index{Kalman@{Kalman}!\_\-copy\_\-@{\_\-copy\_\-}}
237\index{\_\-copy\_\-@{\_\-copy\_\-}!Kalman@{Kalman}}
238\subsubsection[\_\-copy\_\-]{\setlength{\rightskip}{0pt plus 5cm}virtual {\bf BM}$\ast$ BM::\_\-copy\_\- (bool {\em changerv} = {\tt false})\hspace{0.3cm}{\tt  \mbox{[}inline, virtual, inherited\mbox{]}}}}
239\label{classBM_eb58c81d6a7b75b05fc6f276eed78887}
240
241
242Copy function required in vectors, Arrays of \hyperlink{classBM}{BM} etc. Have to be DELETED manually! Prototype: BM$\ast$ \hyperlink{classBM_eb58c81d6a7b75b05fc6f276eed78887}{\_\-copy\_\-()}\{\hyperlink{classBM}{BM} Tmp$\ast$=new Tmp(this$\ast$); return Tmp; \} 
243
244Reimplemented in \hyperlink{classARX_5de61fbd4f97fa3216760b1f733f5af0}{ARX}, and \hyperlink{classBMEF_97f5312efe4a5bedb86d2daec59d8651}{BMEF}.
245
246The documentation for this class was generated from the following file:\begin{CompactItemize}
247\item 
248work/git/mixpp/bdm/estim/\hyperlink{libKF_8h}{libKF.h}\end{CompactItemize}
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