133 \item We shall plot a least squares fit curve for time-period(T) squared vs. length(L) plot of a Simple Pendulum. 

   133 \item We shall plot a least squares fit curve for time-period(T) squared vs. length(L) plot of a Simple Pendulum. 

   134 \item Given a file containing L and T values

   134 \item Given a file containing L and T values

   135 \end{itemize}

   135 \end{itemize}

   136 \end{frame}

   136 \end{frame}

   137 

   137 

   139 \frametitle{Least Squares Fit \ldots}

   139 \frametitle{Least Squares Fit \ldots}

   140 Machinery Required -

   140 Machinery Required -

   141 \begin{itemize}

   141 \begin{itemize}

   142 \item Reading files and parsing data

   142 \item Reading files and parsing data

   143 \item Plotting points, lines

   143 \item Plotting points, lines

   164 \end{lstlisting}

   164 \end{lstlisting}

   165 We now have two lists L and T

   165 We now have two lists L and T

   166 \end{frame}

   166 \end{frame}

   167 

   167 

   168 \begin{frame}[fragile]

   168 \begin{frame}[fragile]

   170 \begin{itemize}

   170 \begin{itemize}

   171 \item Each element of the list T must be squared

   171 \item Each element of the list T must be squared

   172 \item Iterating over each element of the list works

   172 \item Iterating over each element of the list works

   173 \item But very slow \ldots

   173 \item But very slow \ldots

   174 \item Instead, we use arrays

   174 \item Instead, we use arrays

   239 \begin{itemize}

   239 \begin{itemize}

   240 \item Use the poly1d function of pylab, to create a function for the line equation using the coefficients obtained

   240 \item Use the poly1d function of pylab, to create a function for the line equation using the coefficients obtained

   241 \begin{lstlisting}

   241 \begin{lstlisting}

   242 p=poly1d(coeffs)

   242 p=poly1d(coeffs)

   243 \end{lstlisting}

   243 \end{lstlisting}

   245 \begin{lstlisting}

   245 \begin{lstlisting}

   246 Tline = p(L)

   246 Tline = p(L)

   247 \end{lstlisting}

   247 \end{lstlisting}

   248 \item Now plot Tline vs. L, to get the Least squares fit line. 

   248 \item Now plot Tline vs. L, to get the Least squares fit line. 

   249 \begin{lstlisting}

   249 \begin{lstlisting}

   250 plot(L, Tline)

   250 plot(L, Tline)

   251 \end{lstlisting}

   251 \end{lstlisting}

   252 \end{frame}

   253 \end{frame}

   253 

   254 

   254 \end{document}

   255 \end{document}

   255 

   256 

   256 Least squares: Smooth curve fit. 

   257 Least squares: Smooth curve fit.