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 cs-470:gnuplothelp [2015/01/06 14:48]ryancha created cs-470:gnuplothelp [2015/01/06 14:49] (current)ryancha 2015/01/06 14:49 ryancha 2015/01/06 14:48 ryancha created 2015/01/06 14:49 ryancha 2015/01/06 14:48 ryancha created Line 63: Line 63: == Multivariate Normal == == Multivariate Normal == - For the Kalman lab, you will need to show multivariate normals. ​ The following sample file shows how this should be done.  Feel free to play around with the palette and isosamples settings. ​ The complete file can be seen at [http://​aml.cs.byu.edu/​~kseppi/​cs470sp07files/​kalman.gpi kalman.gpi] and the image is available at [http://​aml.cs.byu.edu/​~kseppi/​cs470sp07files/​kalman.png kalman.png]. Note that the code given below uses sigma-x, sigma-y and rho (where rho (<​math>​\rho​) is the [[correlation]] between ​<​math>​X ​and <​math>​Y​) to represent the covariance matrix which we called ​<​math>​\Sigma ​in class. Remember that <​math>​\Sigma ​is symmetric so we really only need three values to represent it. Thus any 2-d <​math>​\Sigma ​can be represented by sigma-x, sigma-y and <​math>​\rho ​as shown here: + For the Kalman lab, you will need to show multivariate normals. ​ The following sample file shows how this should be done.  Feel free to play around with the palette and isosamples settings. ​ The complete file can be seen at [http://​aml.cs.byu.edu/​~kseppi/​cs470sp07files/​kalman.gpi kalman.gpi] and the image is available at [http://​aml.cs.byu.edu/​~kseppi/​cs470sp07files/​kalman.png kalman.png]. Note that the code given below uses sigma-x, sigma-y and rho (where rho ($\rho$) is the [[correlation]] between ​$X$ and $Y$) to represent the covariance matrix which we called ​$\Sigma$ in class. Remember that $\Sigma$ is symmetric so we really only need three values to represent it. Thus any 2-d $\Sigma$ can be represented by sigma-x, sigma-y and $\rho$ as shown here: - :<​math>​ + :$\Sigma = \Sigma = \begin{bmatrix} \begin{bmatrix} Line 71: Line 71: \rho \sigma_x \sigma_y ​ & \sigma_y^2 \rho \sigma_x \sigma_y ​ & \sigma_y^2 \end{bmatrix}. \end{bmatrix}. - ​ +$ and as explained on  [http://​en.wikipedia.org/​wiki/​Multivariate_normal_distribution wikipedia] and as explained on  [http://​en.wikipedia.org/​wiki/​Multivariate_normal_distribution wikipedia]