Forward–backward algorithm: Difference between revisions

Revision as of 16:13, 10 March 2009

Revision as of 16:21, 10 March 2009

Line 62:

<math>

\mathbf{b_{k+2:t}} = \begin{pmatrix} 1.0 &\\ 1.0\end{pmatrix}

</math>

Line 68:

<math>

\mathbf{f_{1:1}} = \alpha\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.5000 &\\ 0.5000 \end{pmatrix}=\alpha\begin{pmatrix}0.4500 &\\ 0.1000\end{pmatrix}=\begin{pmatrix}0.8182 &\\ 0.1818 \end{pmatrix}

</math>

<math>

\mathbf{f_{1:2}} = \alpha\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.8182 &\\ 0.1818 \end{pmatrix}=\alpha\begin{pmatrix}0.5645 &\\ 0.0745\end{pmatrix}=\begin{pmatrix}0.8834 &\\ 0.1165 \end{pmatrix}

</math>

<math>

\mathbf{f_{1:3}} = \alpha\begin{pmatrix}0.1 & 0.0 \\ 0.0 & 0.8 \end{pmatrix}\begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.8834 &\\ 0.1165 \end{pmatrix}=\alpha\begin{pmatrix}0.0653 &\\ 0.2772\end{pmatrix}=\begin{pmatrix}0.1906 &\\ 0.8093 \end{pmatrix}

</math>

<math>

\mathbf{f_{1:4}} = \alpha\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.1906 &\\ 0.8093 \end{pmatrix}=\alpha\begin{pmatrix}0.3386 &\\ 0.1247\end{pmatrix}=\begin{pmatrix}0.7308 &\\ 0.2691 \end{pmatrix}

</math>

<math>

\mathbf{f_{1:5}} = \alpha\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.7308 &\\ 0.2691 \end{pmatrix}=\alpha\begin{pmatrix}0.5331 &\\ 0.0815\end{pmatrix}=\begin{pmatrix}0.8673 &\\ 0.1326 \end{pmatrix}

</math>

Line 88 ⟶ 92:

<math>

\mathbf{b_{5:5}} = \begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix}1.0000 &\\ 1.0000 \end{pmatrix}=\begin{pmatrix}0.5984 &\\ 0.0543\end{pmatrix}=\begin{pmatrix}0.9168 &\\ 0.0831 \end{pmatrix}

</math>

<math>

\mathbf{b_{4:5}} = \begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix}0.9168 &\\ 0.0831 \end{pmatrix}=\begin{pmatrix}0.7308 &\\ 0.2691\end{pmatrix}=\begin{pmatrix}0.8593 &\\ 0.1407 \end{pmatrix}

</math>

<math>

\mathbf{b_{3:5}} = \begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.1 & 0.0 \\ 0.0 & 0.8 \end{pmatrix}\begin{pmatrix}0.8593 &\\ 0.1407 \end{pmatrix}=\begin{pmatrix}0.0178 &\\ 0.0845\end{pmatrix}=\begin{pmatrix}0.1739 &\\ 0.8260 \end{pmatrix}

</math>

<math>

\mathbf{b_{2:5}} = \begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix}0.1739 &\\ 0.8260 \end{pmatrix}=\begin{pmatrix}0.1405 &\\ 0.0189\end{pmatrix}=\begin{pmatrix}0.8814 &\\ 0.1185 \end{pmatrix}

</math>

<math>

\mathbf{b_{1:5}} = \begin{pmatrix} 0.7 & 0.3 \\ 0.3 & 0.7 \end{pmatrix}\begin{pmatrix}0.9 & 0.0 \\ 0.0 & 0.2 \end{pmatrix}\begin{pmatrix}0.8814 &\\ 0.1185 \end{pmatrix}=\begin{pmatrix}0.4600 &\\ 0.0462\end{pmatrix}=\begin{pmatrix}0.9087 &\\ 0.0912 \end{pmatrix}

</math>

Line 110 ⟶ 114:

<math>

\mathbf{sv_{5}} = \alpha\begin{pmatrix}1.0000 &\\ 1.0000 \end{pmatrix}\times \begin{pmatrix}0.8673 &\\ 0.1326 \end{pmatrix}=\alpha\begin{pmatrix}0.8673 &\\ 0.1326 \end{pmatrix}=\begin{pmatrix}0.8673 &\\ 0.1326 \end{pmatrix}

</math>

<math>

\mathbf{sv_{4}} = \alpha\begin{pmatrix}0.9168 &\\ 0.0831 \end{pmatrix}\times \begin{pmatrix}0.7308 &\\ 0.2691 \end{pmatrix}=\alpha\begin{pmatrix}0.6699 &\\ 0.0223\end{pmatrix}=\begin{pmatrix}0.9677 &\\ 0.322 \end{pmatrix}

</math>

<math>

\mathbf{sv_{3}} = \alpha\begin{pmatrix}0.8593 &\\ 0.1407 \end{pmatrix}\times \begin{pmatrix}0.1906 &\\ 0.8093 \end{pmatrix}=\alpha\begin{pmatrix}0.1637 &\\ 0.1138\end{pmatrix}=\begin{pmatrix}0.5899 &\\ 0.4101 \end{pmatrix}

</math>

<math>

\mathbf{sv_{2}} = \alpha\begin{pmatrix}0.1739 &\\ 0.8260 \end{pmatrix}\times \begin{pmatrix}0.8834 &\\ 0.1165 \end{pmatrix}=\alpha\begin{pmatrix}0.1536 &\\ 0.0962\end{pmatrix}=\begin{pmatrix}0.6148 &\\ 0.3852 \end{pmatrix}

</math>

<math>

\mathbf{sv_{1}} = \alpha\begin{pmatrix}0.8814 &\\ 0.1185 \end{pmatrix}\times \begin{pmatrix}0.8182 &\\ 0.1818 \end{pmatrix}=\alpha\begin{pmatrix}0.7211 &\\ 0.0215\end{pmatrix}=\begin{pmatrix}0.9710 &\\ 0.0289 \end{pmatrix}

</math>