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72 % } |
72 % } |
73 |
73 |
74 |
74 |
75 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
75 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
76 % Title page |
76 % Title page |
77 \title[Matrices \& Equations]{Python for Science and Engg: Matrices, Least Square Fit, \& Solution of equations} |
77 \title[Matrices \& Curve Fitting]{Python for Science and Engg: Matrices \& Least Square Fit} |
78 |
78 |
79 \author[FOSSEE] {FOSSEE} |
79 \author[FOSSEE] {FOSSEE} |
80 |
80 |
81 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
81 \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} |
82 \date[] {31 October, 2009\\Day 1, Session 4} |
82 \date[] {31 October, 2009\\Day 1, Session 4} |
275 \item Resize image to half by dropping alternate pixels |
275 \item Resize image to half by dropping alternate pixels |
276 \end{itemize} |
276 \end{itemize} |
277 \end{frame} |
277 \end{frame} |
278 |
278 |
279 \begin{frame}[fragile] |
279 \begin{frame}[fragile] |
280 \frametitle{Slicing \& Striding Exercises \ldots} |
280 \frametitle{Solutions} |
281 \begin{small} |
281 \begin{small} |
282 \begin{lstlisting} |
282 \begin{lstlisting} |
283 In []: imshow(A[:256,:256]) |
283 In []: imshow(A[:256,:256]) |
284 Out[]: <matplotlib.image.AxesImage object at 0xb6f658c> |
284 Out[]: <matplotlib.image.AxesImage object at 0xb6f658c> |
285 |
285 |
460 |
460 |
461 \begin{frame}[fragile] |
461 \begin{frame}[fragile] |
462 \frametitle{\typ{lstsq}} |
462 \frametitle{\typ{lstsq}} |
463 \begin{itemize} |
463 \begin{itemize} |
464 \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$ |
464 \item We need to fit a line through points for the equation $T^2 = m \cdot L+c$ |
465 \item The equation can be re-written as $T^2 = A \cdot p$ |
465 \item In matrix form, the equation can be represented as $T^2 = A \cdot p$, where A is |
466 \item where A is |
|
467 $\begin{bmatrix} |
466 $\begin{bmatrix} |
468 L_1 & 1 \\ |
467 L_1 & 1 \\ |
469 L_2 & 1 \\ |
468 L_2 & 1 \\ |
470 \vdots & \vdots\\ |
469 \vdots & \vdots\\ |
471 L_N & 1 \\ |
470 L_N & 1 \\ |
534 \begin{lstlisting} |
533 \begin{lstlisting} |
535 In []: plot(L, Tline) |
534 In []: plot(L, Tline) |
536 \end{lstlisting} |
535 \end{lstlisting} |
537 \end{frame} |
536 \end{frame} |
538 |
537 |
|
538 \begin{frame}[fragile] |
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539 \frametitle{Least Squares Fit} |
|
540 \vspace{-0.15in} |
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541 \begin{figure} |
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542 \includegraphics[width=4in]{data/least-sq-fit} |
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543 \end{figure} |
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544 \end{frame} |
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545 |
539 \section{Summary} |
546 \section{Summary} |
540 \begin{frame} |
547 \begin{frame} |
541 \frametitle{What did we learn??} |
548 \frametitle{What did we learn?} |
542 \begin{itemize} |
549 \begin{itemize} |
543 \item Matrices |
550 \item Matrices |
544 \begin{itemize} |
551 \begin{itemize} |
545 \item Accessing elements |
552 \item Accessing elements |
|
553 \item Slicing and Striding |
546 \item Transpose |
554 \item Transpose |
547 \item Addition |
555 \item Addition |
548 \item Multiplication |
556 \item Multiplication |
549 \item Inverse of a matrix |
557 \item Inverse of a matrix |
550 \item Determinant |
558 \item Determinant |