day1/session5.tex
author Puneeth Chaganti <punchagan@fossee.in>
Wed, 28 Oct 2009 12:35:01 +0530
changeset 221 9ed9539446bc
parent 202 2b902f2d25e5
child 222 ffa8f417d761
permissions -rw-r--r--
Updated day1 session5 and session6.
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     2
%Tutorial slides on Python.
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     3
%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     4
% Author: FOSSEE 
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     5
% Copyright (c) 2009, FOSSEE, IIT Bombay
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     7
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     8
\documentclass[14pt,compress]{beamer}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
     9
%\documentclass[draft]{beamer}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    10
%\documentclass[compress,handout]{beamer}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    11
%\usepackage{pgfpages} 
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    12
%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    13
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    14
% Modified from: generic-ornate-15min-45min.de.tex
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    15
\mode<presentation>
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    16
{
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    17
  \usetheme{Warsaw}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    18
  \useoutertheme{split}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    19
  \setbeamercovered{transparent}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    20
}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    21
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    22
\usepackage[english]{babel}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    23
\usepackage[latin1]{inputenc}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    24
%\usepackage{times}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    25
\usepackage[T1]{fontenc}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    26
\usepackage{amsmath}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    27
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    28
% Taken from Fernando's slides.
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    29
\usepackage{ae,aecompl}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    30
\usepackage{mathpazo,courier,euler}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    31
\usepackage[scaled=.95]{helvet}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    32
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    33
\definecolor{darkgreen}{rgb}{0,0.5,0}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    34
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    35
\usepackage{listings}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    36
\lstset{language=Python,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    37
    basicstyle=\ttfamily\bfseries,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    38
    commentstyle=\color{red}\itshape,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    39
  stringstyle=\color{darkgreen},
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    40
  showstringspaces=false,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    41
  keywordstyle=\color{blue}\bfseries}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    42
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    43
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    44
% Macros
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    45
\setbeamercolor{emphbar}{bg=blue!20, fg=black}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    46
\newcommand{\emphbar}[1]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    47
{\begin{beamercolorbox}[rounded=true]{emphbar} 
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    48
      {#1}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    49
 \end{beamercolorbox}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    50
}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    51
\newcounter{time}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    52
\setcounter{time}{0}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    53
\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    54
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    55
\newcommand{\typ}[1]{\lstinline{#1}}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    56
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    57
\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    58
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    59
%%% This is from Fernando's setup.
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    60
% \usepackage{color}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    61
% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    62
% % Use and configure listings package for nicely formatted code
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    63
% \usepackage{listings}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    64
% \lstset{
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    65
%    language=Python,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    66
%    basicstyle=\small\ttfamily,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    67
%    commentstyle=\ttfamily\color{blue},
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    68
%    stringstyle=\ttfamily\color{orange},
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    69
%    showstringspaces=false,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    70
%    breaklines=true,
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    71
%    postbreak = \space\dots
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    72
% }
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    73
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    74
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    75
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    76
% Title page
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    77
\title[Basic Python]{Interpolation, Differentiation and Integration}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    78
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    79
\author[FOSSEE] {FOSSEE}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    80
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    81
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    82
\date[] {31, October 2009\\Day 1, Session 4}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    83
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    84
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    85
%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    86
%\logo{\pgfuseimage{iitmlogo}}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    87
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    88
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    89
%% Delete this, if you do not want the table of contents to pop up at
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    90
%% the beginning of each subsection:
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    91
\AtBeginSubsection[]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    92
{
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    93
  \begin{frame}<beamer>
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    94
    \frametitle{Outline}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    95
    \tableofcontents[currentsection,currentsubsection]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    96
  \end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    97
}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    98
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
    99
%%\AtBeginSection[]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   100
%%{
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   101
  %%\begin{frame}<beamer>
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   102
%%    \frametitle{Outline}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   103
  %%  \tableofcontents[currentsection,currentsubsection]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   104
  %%\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   105
%%}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   106
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   107
% If you wish to uncover everything in a step-wise fashion, uncomment
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   108
% the following command: 
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   109
%\beamerdefaultoverlayspecification{<+->}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   110
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   111
%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   112
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   113
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   114
% DOCUMENT STARTS
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   115
\begin{document}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   116
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   117
\begin{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   118
  \titlepage
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   119
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   120
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   121
\begin{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   122
  \frametitle{Outline}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   123
  \tableofcontents
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   124
%  \pausesections
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   125
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   126
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   127
\section{Interpolation}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   128
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   129
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   130
\frametitle{Interpolation}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   131
\begin{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   132
\item Let us begin with interpolation
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   133
\item Let's use the L and T arrays and interpolate this data to obtain data at new points
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   134
\end{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   135
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   136
In []: L = []
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   137
In []: T = []
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   138
In []: for line in open('pendulum.txt'):
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   139
           l, t = line.split()
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   140
           L.append(float(l))
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   141
           T.append(float(t))
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   142
In []: L = array(L)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   143
In []: T = array(T)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   144
In []: Tsq = T*T
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   145
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   146
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   147
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   148
%% \begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   149
%% \frametitle{Interpolation \ldots}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   150
%% \begin{small}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   151
%%   \typ{In []: from scipy.interpolate import interp1d}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   152
%% \end{small}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   153
%% \begin{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   154
%% \item The \typ{interp1d} function returns a function
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   155
%% \begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   156
%%   In []: f = interp1d(L, T)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   157
%% \end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   158
%% \item Functions can be assigned to variables 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   159
%% \item This function interpolates between known data values to obtain unknown
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   160
%% \end{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   161
%% \end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   162
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   163
%% \begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   164
%% \frametitle{Interpolation \ldots}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   165
%% \begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   166
%% In []: Ln = arange(0.1,0.99,0.005)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   167
%% # Interpolating! 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   168
%% # The new values in range of old data
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   169
%% In []: plot(L, T, 'o', Ln, f(Ln), '-')
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   170
%% In []: f = interp1d(L, T, kind='cubic')
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   171
%% # When kind not specified, it's linear
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   172
%% # Others are ...
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   173
%% # 'nearest', 'zero', 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   174
%% # 'slinear', 'quadratic'
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   175
%% \end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   176
%% \end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   177
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   178
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   179
\frametitle{Spline Interpolation}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   180
\begin{small}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   181
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   182
In []: from scipy.interpolate import splrep
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   183
In []: from scipy.interpolate import splev
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   184
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   185
\end{small}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   186
\begin{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   187
\item Involves two steps
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   188
  \begin{enumerate}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   189
  \item Find out the spline curve, coefficients
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   190
  \item Evaluate the spline at new points
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   191
  \end{enumerate}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   192
\end{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   193
\end{frame}
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   194
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   195
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   196
\frametitle{\typ{splrep}}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   197
To find the B-spline representation
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   198
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   199
In []: tck = splrep(L, T)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   200
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   201
Returns a tuple containing 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   202
\begin{enumerate}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   203
\item the vector of knots, 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   204
\item the B-spline coefficients 
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   205
\item the degree of the spline (default=3)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   206
\end{enumerate}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   207
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   208
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   209
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   210
\frametitle{\typ{splev}}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   211
To Evaluate a B-spline and it's derivatives
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   212
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   213
In []: Lnew = arange(0.1,1,0.005)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   214
In []: Tnew = splev(Lnew, tck)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   215
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   216
#To obtain derivatives of the spline
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   217
#use der=1, 2,.. for 1st, 2nd,.. order
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   218
In []: Tnew = splev(Lnew, tck, der=1)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   219
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   220
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   222
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   223
\frametitle{}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   224
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   225
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   226
\section{Differentiation}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   227
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   228
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   229
\frametitle{Numerical Differentiation}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   230
\begin{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   231
\item Given function $f(x)$ or data points $y=f(x)$
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   232
\item We wish to calculate $f^{'}(x)$ at points $x$
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   233
\item Taylor series - finite difference approximations
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   234
\end{itemize}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   235
\begin{center}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   236
\begin{tabular}{l l}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   237
$f(x+h)=f(x)+h.f^{'}(x)$ &Forward \\
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   238
$f(x-h)=f(x)-h.f^{'}(x)$ &Backward
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   239
\end{tabular}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   240
\end{center}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   241
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   242
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   243
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   244
\frametitle{Forward Difference}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   245
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   246
In []: x = linspace(0, 2*pi, 100)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   247
In []: y = sin(x)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   248
In []: deltax = x[1] - x[0]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   249
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   250
Obtain the finite forward difference of y
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   251
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   252
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   253
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   254
\frametitle{Forward Difference \ldots}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   255
\begin{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   256
In []: fD = (y[1:] - y[:-1]) / deltax
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   257
In []: plot(x, y, x[:-1], fD)
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   258
\end{lstlisting}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   259
\begin{center}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   260
  \includegraphics[height=2in, interpolate=true]{data/fwdDiff}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   261
\end{center}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   262
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   263
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   264
\begin{frame}[fragile]
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   265
\frametitle{}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   266
\end{frame}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   267
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   268
\section{Quadrature}
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   269
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   270
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   271
\frametitle{Quadrature}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   272
\begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   273
\item We wish to find area under a curve
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   274
\item Area under $(sin(x) + x^2)$ in $(0,1)$
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   275
\item scipy has functions to do that
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   276
\end{itemize}
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   277
\begin{small}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   278
  \typ{In []: from scipy.integrate import quad}
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   279
\end{small}
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   280
\begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   281
\item Inputs - function to integrate, limits
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   282
\end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   283
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   284
In []: x = 0
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   285
In []: quad(sin(x)+x**2, 0, 1)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   286
\end{lstlisting}
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   287
\begin{small}
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   288
\alert{\typ{error:}}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   289
\typ{First argument must be a callable function.}
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   290
\end{small}
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   291
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   292
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   293
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   294
\frametitle{Functions - Definition}
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   295
We have been using them all along. Now let's see how to define them.
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   296
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   297
In []: def f(x):
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   298
           return sin(x)+x**2
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   299
In []: quad(f, 0, 1)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   300
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   301
\begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   302
\item \typ{def}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   303
\item arguments
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   304
\item \typ{return}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   305
\end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   306
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   307
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   308
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   309
\frametitle{Functions - Calling them}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   310
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   311
In [15]: f()
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   312
---------------------------------------
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   313
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   314
\alert{\typ{TypeError:}}\typ{f() takes exactly 1 argument}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   315
\typ{(0 given)}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   316
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   317
In []: f(0)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   318
Out[]: 0.0
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   319
In []: f(1)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   320
Out[]: 1.8414709848078965
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   321
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   322
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   323
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   324
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   325
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   326
\frametitle{Functions - Default Arguments}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   327
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   328
In []: def f(x=1):
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   329
           return sin(x)+x**2
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   330
In []: f(10)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   331
Out[]: 99.455978889110625
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   332
In []: f(1)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   333
Out[]: 1.8414709848078965
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   334
In []: f()
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   335
Out[]: 1.8414709848078965
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   336
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   337
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   338
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   339
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   340
\frametitle{Functions - Keyword Arguments}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   341
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   342
In []: def f(x=1, y=pi):
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   343
           return sin(y)+x**2
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   344
In []: f()
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   345
Out[]: 1.0000000000000002
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   346
In []: f(2)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   347
Out[]: 4.0
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   348
In []: f(y=2)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   349
Out[]: 1.9092974268256817
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   350
In []: f(y=pi/2,x=0)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   351
Out[]: 1.0
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   352
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   353
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   354
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   355
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   356
  \frametitle{More on functions}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   357
  \begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   358
  \item Scope of variables in the function is local
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   359
  \item Mutable items are \alert{passed by reference}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   360
  \item First line after definition may be a documentation string
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   361
    (\alert{recommended!})
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   362
  \item Function definition and execution defines a name bound to the
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   363
    function
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   364
  \item You \emph{can} assign a variable to a function!
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   365
  \end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   366
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   367
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   368
\begin{frame}[fragile]
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   369
\frametitle{Quadrature \ldots}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   370
\begin{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   371
In []: quad(f, 0, 1)
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   372
\end{lstlisting}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   373
Returns the integral and an estimate of the absolute error in the result.
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   374
\begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   375
\item Use \typ{dblquad} for Double integrals
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   376
\item Use \typ{tplquad} for Triple integrals
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   377
\end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   378
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   379
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   380
\begin{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   381
  \frametitle{Things we have learned}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   382
  \begin{itemize}
221
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   383
  \item Interpolation
9ed9539446bc Updated day1 session5 and session6.
Puneeth Chaganti <punchagan@fossee.in>
parents: 202
diff changeset
   384
  \item Differentiation
202
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   385
  \item Functions
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   386
    \begin{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   387
    \item Definition
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   388
    \item Calling
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   389
    \item Default Arguments
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   390
    \item Keyword Arguments
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   391
    \end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   392
  \item Quadrature
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   393
  \end{itemize}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   394
\end{frame}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   395
\end{document}
2b902f2d25e5 Started session5.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff changeset
   396