adam greenberg edited Future changes.tex  about 10 years ago

Commit id: da961954d24777293e5aa1ba6f05542455d31e3e

deletions | additions      

       

\section{Future changes}  The addition of SRIF to \textbf{shape} has improved fitting performance, but additional changes must still be made to allow \textbf{shape} to function with real-world data.  \subsection{Penalty functions}  The SPF routine can currently fit models to data while taking into account a suite of "penalty functions", to ensure that the models that are generated are physical. In a way, these penalty functions serve to make the fits operate in a more global context -- there may be a local minimum in $\chi^2$-space which the fitting algorithm would want to tend towards, but that minimum can be ruled out \textit{a priori} thanks to physical limitations. These penalty functions include limits on ellipsoid axis ratios, constraints to surface concavities, limits on the model center of mass distance from the image center of mass, as well as others. These penalties are not currently implemented in the SRIF algorithm, but can be added in the future. Specifically, by redefining the residual vector as   \[ R'' = \left( \begin{array}{c} \vec{z} - \vec{m} \\ \vec{R_p} \end{array} \right)\]   Where   \[ R_p = \left( \begin{array}{c}   p_1\times w_1 \\   \vdots \\   p_N\times w_N \end{array} \right)\]   for $\{p_i\}$ , $\{w_i\}$ are the set of penalty functions and penalty weights, respectively, and  \[A'' = -\frac{\partial \vec{R''}}{\partial \vec{x}}\]  \subsection{Global vs local variable partitioning} The data that are fitted with \textbf{shape} are typically split into sets, with each set corresponding to a different observing run (for the same object). Correspondingly, the models that are fit to these data have both global and local variables, meaning there are parameters that are tied matrix to the set, and parameters that are tied to the object itself. For example, how far off the object's center of mass is from the predicted center of mass is date-specific. Intelligent grouping of local and global parameters can potentially lead to a drastic computation time decrease.