author | Prabhu Ramachandran <prabhu@aero.iitb.ac.in> |
Tue, 15 Jun 2010 02:50:08 -0400 | |
branch | scipy2010 |
changeset 400 | b9c7ef95d875 |
parent 78 | ec1346330649 |
permissions | -rw-r--r-- |
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1 |
\documentclass[12pt]{article} |
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\usepackage{amsmath} |
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\title{Python Workshop\\Problems and Exercises} |
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\author{Asokan Pichai\\Prabhu Ramachandran} |
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\begin{document} |
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\maketitle |
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\section{Matrices and Arrays \& 2D Plotting} |
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9 |
\subsection{Matrices and Arrays} |
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\subsubsection{Basic Numpy} |
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\begin{verbatim} |
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# Simple array math example |
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>>> import numpy as np |
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>>> a = np.array([1,2,3,4]) |
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>>> b = np.arange(2,6) |
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>>> b |
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array([2,3,4,5]) |
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>>> a*2 + b + 1 # Basic math! |
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array([5, 8, 11, 14]) |
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|
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# Pi and e are defined. |
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>>> x = np.linspace(0.0, 10.0, 1000) |
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>>> x *= 2*np.pi/10 # inplace. |
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# apply functions to array. |
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>>> y = np.sin(x) |
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>>> z = np.exp(y) |
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|
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>>> x = np.array([1., 2, 3, 4]) |
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>>> np.size(x) |
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4 |
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>>> x.dtype # What is a.dtype? |
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dtype('float64') |
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>>> x.shape |
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(4,) |
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>>> print np.rank(x), x.itemsize |
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1 8 |
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>>> x[0] = 10 |
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>>> print x[0], x[-1] |
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10.0 4.0 |
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|
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>>> a = np.array([[ 0, 1, 2, 3], |
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... [10,11,12,13]]) |
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>>> a.shape # (rows, columns) |
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(2, 4) |
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# Accessing and setting values |
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>>> a[1,3] |
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13 |
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>>> a[1,3] = -1 |
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>>> a[1] # The second row |
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array([10,11,12,-1]) |
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51 |
|
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>>> b=np.array([[0,2,4,2],[1,2,3,4]]) |
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>>> np.add(a,b,a) |
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>>> np.sum(x,axis=1) |
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>>> np.greater(a,4) |
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>>> np.sqrt(a) |
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58 |
\end{verbatim} |
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|
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60 |
\subsubsection{Array Creation} |
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\begin{verbatim} |
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>>> np.array([2,3,4]) |
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array([2, 3, 4]) |
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64 |
|
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>>> np.linspace(0, 2, 4) |
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array([0.,0.6666667,1.3333333,2.]) |
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67 |
|
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>>>np.ones([2,2]) |
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array([[ 1., 1.], |
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[ 1., 1.]]) |
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71 |
|
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>>>a = np.array([[1,2,3],[4,5,6]]) |
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>>>np.ones_like(a) |
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array([[1, 1, 1], |
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[1, 1, 1]]) |
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76 |
\end{verbatim} |
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\subsubsection{Slicing, Striding Arrays} |
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\begin{verbatim} |
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>>> a = np.array([[1,2,3], [4,5,6], |
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80 |
[7,8,9]]) |
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>>> a[0,1:3] |
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array([2, 3]) |
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>>> a[1:,1:] |
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array([[5, 6], |
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85 |
[8, 9]]) |
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>>> a[:,2] |
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array([3, 6, 9]) |
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>>> a[...,2] |
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array([3, 6, 9]) |
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90 |
|
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>>> a[0::2,0::2] |
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array([[1, 3], |
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93 |
[7, 9]]) |
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94 |
# Slices are references to the |
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95 |
# same memory! |
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96 |
\end{verbatim} |
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97 |
\subsubsection{Random Numbers} |
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\begin{verbatim} |
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>>> np.random.rand(3,2) |
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100 |
array([[ 0.96276665, 0.77174861], |
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101 |
[ 0.35138557, 0.61462271], |
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102 |
[ 0.16789255, 0.43848811]]) |
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103 |
>>> np.random.randint(1,100) |
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104 |
42 |
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105 |
\end{verbatim} |
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106 |
|
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107 |
\subsubsection{Problem Set} |
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108 |
\begin{verbatim} |
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109 |
>>> from scipy import misc |
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110 |
>>> A=misc.imread(name) |
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111 |
>>> misc.imshow(A) |
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112 |
\end{verbatim} |
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113 |
\begin{enumerate} |
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114 |
\item Convert an RGB image to Grayscale. $ Y = 0.5R + 0.25G + 0.25B $. |
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115 |
\item Scale the image to 50\%. |
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116 |
\item Introduce some random noise. |
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117 |
\item Smooth the image using a mean filter. |
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118 |
\\\small{Each element in the array is replaced by mean of all the neighbouring elements} |
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119 |
\\\small{How fast does your code run?} |
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120 |
\end{enumerate} |
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121 |
|
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122 |
\subsection{2D Plotting} |
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123 |
\subsubsection{Basic 2D Plotting} |
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124 |
\begin{verbatim} |
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125 |
$ ipython -pylab |
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126 |
>>> x = linspace(0, 2*pi, 1000) |
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127 |
>>> plot(x, sin(x)) |
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128 |
>>> plot(x, sin(x), 'ro') |
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129 |
>>> xlabel(r'$\chi$', color='g') |
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130 |
# LaTeX markup! |
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131 |
>>> ylabel(r'sin($\chi$)', color='r') |
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132 |
>>> title('Simple figure', fontsize=20) |
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133 |
>>> savefig('/tmp/test.eps') |
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134 |
\end{verbatim} |
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135 |
\subsubsection{Tweaking plots} |
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136 |
\begin{verbatim} |
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137 |
# Set properties of objects: |
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138 |
>>> l, = plot(x, sin(x)) |
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139 |
# Why "l,"? |
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140 |
>>> setp(l, linewidth=2.0, color='r') |
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141 |
>>> l.set_linewidth(2.0) |
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142 |
>>> draw() # Redraw. |
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143 |
>>> setp(l) # Print properties. |
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144 |
>>> clf() # Clear figure. |
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145 |
>>> close() # Close figure. |
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146 |
\end{verbatim} |
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147 |
|
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148 |
\subsubsection{Working with text} |
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149 |
\begin{verbatim} |
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150 |
>>> w = arange(-2,2,.1) |
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|
151 |
>>> plot(w,exp(-(w*w))*cos) |
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152 |
>>> ylabel('$f(\omega)$') |
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153 |
>>> xlabel('$\omega$') |
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154 |
>>> title(r"$f(\omega)=e^{-\omega^2} |
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155 |
cos({\omega^2})$") |
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156 |
>>> annotate('maxima',xy=(0, 1), |
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157 |
xytext=(1, 0.8), |
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|
158 |
arrowprops=dict( |
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|
159 |
facecolor='black', |
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|
160 |
shrink=0.05)) |
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161 |
\end{verbatim} |
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162 |
|
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163 |
\subsubsection{Legends} |
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164 |
\begin{verbatim} |
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165 |
>>> x = linspace(0, 2*np.pi, 1000) |
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|
166 |
>>> plot(x, cos(5*x), 'r--', |
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|
167 |
label='cosine') |
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|
168 |
>>> plot(x, sin(5*x), 'g--', |
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|
169 |
label='sine') |
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|
170 |
>>> legend() |
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|
171 |
# Or use: |
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|
172 |
>>> legend(['cosine', 'sine']) |
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173 |
\end{verbatim} |
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|
174 |
|
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175 |
\subsubsection{Multiple figures} |
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176 |
\begin{verbatim} |
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177 |
>>> figure(1) |
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178 |
>>> plot(x, sin(x)) |
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179 |
>>> figure(2) |
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|
180 |
>>> plot(x, tanh(x)) |
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181 |
>>> figure(1) |
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|
182 |
>>> title('Easy as 1,2,3') |
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|
183 |
|
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184 |
\end{verbatim} |
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185 |
|
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186 |
\subsubsection{Problem Set} |
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187 |
\begin{enumerate} |
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188 |
\item Write a function that plots any regular n-gon given n. |
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189 |
\item Consider the logistic map, $f(x) = kx(1-x)$, plot it for |
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190 |
$k=2.5, 3.5$ and $4$ in the same plot. |
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191 |
|
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192 |
\item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = |
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193 |
kx(1-x)$. Plot the successive iterates of this process. |
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194 |
\item Plot this using a cobweb plot as follows: |
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195 |
\begin{enumerate} |
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196 |
\item Start at $(x_0, 0)$ |
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197 |
\item Draw line to $(x_i, f(x_i))$; |
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198 |
\item Set $x_{i+1} = f(x_i)$ |
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199 |
\item Draw line to $(x_i, x_i)$ |
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200 |
\item Repeat from 2 for as long as you want |
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201 |
\end{enumerate} |
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202 |
\end{enumerate} |
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203 |
|
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204 |
\section{Advanced Numpy} |
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205 |
|
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206 |
\subsection{Broadcasting} |
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\begin{verbatim} |
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208 |
>>> a = np.arange(4) |
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209 |
>>> b = np.arange(5) |
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>>> a+b #Does this work? |
72
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>>> a+3 |
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212 |
>>> c=np.array([3]) |
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>>> a+c #Works! |
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214 |
>>> b+c #But how? |
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215 |
>>> a.shape, b.shape, c.shape |
72
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216 |
|
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217 |
>>> a = np.arange(4) |
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218 |
>>> a+3 |
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219 |
array([3, 4, 5, 6]) |
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220 |
|
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221 |
>>> x = np.ones((3, 5)) |
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222 |
>>> y = np.ones(8) |
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223 |
>>> (x[..., None] + y).shape |
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224 |
(3, 5, 8) |
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225 |
|
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226 |
\end{verbatim} |
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227 |
|
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228 |
\subsection{Copies \& Views} |
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229 |
\begin{verbatim} |
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230 |
>>> a = np.array([[1,2,3],[4,5,6]]) |
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231 |
>>> b = a |
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232 |
>>> b is a |
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233 |
>>> b[0,0]=0; print a |
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234 |
>>> c = a.view() |
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235 |
>>> c is a |
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236 |
>>> c.base is a |
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237 |
>>> c.flags.owndata |
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|
238 |
>>> d = a.copy() |
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239 |
>>> d.base is a |
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|
240 |
>>> d.flags.owndata |
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241 |
|
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|
242 |
>>> a = np.arange(1,9) |
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|
243 |
>>> a.shape=3,3 |
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244 |
>>> b = a[0,1:3] |
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|
245 |
>>> c = a[0::2,0::2] |
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|
246 |
>>> a.flags.owndata |
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247 |
>>> b.flags.owndata |
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248 |
>>> b.base |
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249 |
>>> c.base is a |
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250 |
|
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251 |
>>> b = a[np.array([0,1,2])] |
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|
252 |
array([[1, 2, 3], |
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253 |
[4, 5, 6], |
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|
254 |
[7, 8, 9]]) |
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|
255 |
>>> b.flags.owndata |
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|
256 |
>>> abool=np.greater(a,2) |
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|
257 |
>>> c = a[abool] |
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|
258 |
>>> c.flags.owndata |
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|
259 |
|
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|
260 |
\end{verbatim} |
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|
261 |
|
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|
262 |
\section{Scipy} |
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|
263 |
\subsection{Linear Algebra} |
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|
264 |
\begin{verbatim} |
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|
265 |
>>> import scipy as sp |
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|
266 |
>>> from scipy import linalg |
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267 |
>>> A=sp.mat(np.arange(1,10)) |
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|
268 |
>>> A.shape=3,3 |
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|
269 |
>>> linalg.inv(A) |
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|
270 |
>>> linalg.det(A) |
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|
271 |
>>> linalg.norm(A) |
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|
272 |
>>> linalg.expm(A) #logm |
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|
273 |
>>> linalg.sinm(A) #cosm, tanm, ... |
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|
274 |
|
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|
275 |
>>> A = sp.mat(np.arange(1,10)) |
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|
276 |
>>> A.shape=3,3 |
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|
277 |
>>> linalg.lu(A) |
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|
278 |
>>> linalg.eig(A) |
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|
279 |
>>> linalg.eigvals(A) |
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|
280 |
\end{verbatim} |
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|
281 |
|
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|
282 |
\subsection{Solving Linear Equations} |
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|
283 |
|
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|
284 |
\begin{align*} |
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|
285 |
3x + 2y - z & = 1 \\ |
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|
286 |
2x - 2y + 4z & = -2 \\ |
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|
287 |
-x + \frac{1}{2}y -z & = 0 |
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|
288 |
\end{align*} |
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|
289 |
To Solve this, |
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|
290 |
\begin{verbatim} |
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|
291 |
>>> A = sp.mat([[3,2,-1],[2,-2,4] |
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|
292 |
,[-1,1/2,-1]]) |
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|
293 |
>>> B = sp.mat([[1],[-2],[0]]) |
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|
294 |
>>> linalg.solve(A,B) |
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|
295 |
\end{verbatim} |
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|
296 |
|
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|
297 |
\subsection{Integrate} |
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|
298 |
\subsubsection{Quadrature} |
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|
299 |
Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$ |
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|
300 |
\begin{verbatim} |
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|
301 |
>>> def f(x): |
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|
302 |
return np.sin(x)+x**2 |
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|
303 |
>>> integrate.quad(f, 0, 1) |
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|
304 |
\end{verbatim} |
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|
305 |
|
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|
306 |
\subsubsection{ODE Integration} |
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|
307 |
Numerically solve ODEs\\ |
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|
308 |
\begin{align*} |
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|
309 |
\frac{dx}{dt} &=-e^{-t}x^2\\ |
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|
310 |
x(0) &=2 |
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|
311 |
\end{align*} |
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parents:
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|
312 |
\begin{verbatim} |
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|
313 |
>>> def dx_dt(x,t): |
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parents:
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|
314 |
... return -np.exp(-t)*x**2 |
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parents:
diff
changeset
|
315 |
>>> x=integrate.odeint(dx_dt, 2, t) |
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parents:
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|
316 |
>>> plt.plot(x,t) |
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parents:
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changeset
|
317 |
\end{verbatim} |
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parents:
diff
changeset
|
318 |
|
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parents:
diff
changeset
|
319 |
\subsection{Interpolation} |
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parents:
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|
320 |
\subsubsection{1D Interpolation} |
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parents:
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|
321 |
\begin{verbatim} |
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parents:
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|
322 |
>>> from scipy import interpolate |
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parents:
diff
changeset
|
323 |
>>> interpolate.interp1d? |
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parents:
diff
changeset
|
324 |
>>> x = np.arange(0,2*np.pi,np.pi/4) |
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parents:
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|
325 |
>>> y = np.sin(x) |
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parents:
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changeset
|
326 |
>>> fl = interpolate.interp1d( |
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parents:
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|
327 |
x,y,kind='linear') |
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parents:
diff
changeset
|
328 |
>>> fc = interpolate.interp1d( |
1c1d6aaa2be3
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parents:
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|
329 |
x,y,kind='cubic') |
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parents:
diff
changeset
|
330 |
>>> fl(np.pi/3) |
1c1d6aaa2be3
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parents:
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changeset
|
331 |
>>> fc(np.pi/3) |
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parents:
diff
changeset
|
332 |
\end{verbatim} |
1c1d6aaa2be3
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parents:
diff
changeset
|
333 |
|
1c1d6aaa2be3
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parents:
diff
changeset
|
334 |
\subsubsection{Splines} |
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parents:
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changeset
|
335 |
Plot the Cubic Spline of $sin(x)$ |
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parents:
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changeset
|
336 |
\begin{verbatim} |
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parents:
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|
337 |
>>> x = np.arange(0,2*np.pi,np.pi/4) |
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parents:
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changeset
|
338 |
>>> y = np.sin(x) |
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
339 |
>>> tck = interpolate.splrep(x,y) |
1c1d6aaa2be3
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parents:
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changeset
|
340 |
>>> X = np.arange(0,2*np.pi,np.pi/50) |
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parents:
diff
changeset
|
341 |
>>> Y = interpolate.splev(X,tck,der=0) |
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parents:
diff
changeset
|
342 |
>>> plt.plot(x,y,'o',x,y,X,Y) |
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
343 |
>>> plt.show() |
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parents:
diff
changeset
|
344 |
\end{verbatim} |
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parents:
diff
changeset
|
345 |
|
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parents:
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changeset
|
346 |
\subsection{Signal \& Image Processing} |
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parents:
diff
changeset
|
347 |
Applying a simple median filter |
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parents:
diff
changeset
|
348 |
\begin{verbatim} |
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parents:
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changeset
|
349 |
>>> from scipy import signal, ndimage |
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
350 |
>>> from scipy import lena |
1c1d6aaa2be3
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
351 |
>>> A=lena().astype('float32') |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
352 |
>>> B=signal.medfilt2d(A) |
1c1d6aaa2be3
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
353 |
>>> imshow(B) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
354 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
355 |
Zooming an array - uses spline interpolation |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
356 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
357 |
>>> b=ndimage.zoom(A,0.5) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
358 |
>>> imshow(b) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
359 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
360 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
361 |
\section{3D Data Visualization} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
362 |
\subsection{Using mlab} |
1c1d6aaa2be3
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Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
363 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
364 |
>>> from enthought.mayavi import mlab |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
365 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
366 |
>>> mlab.test_<TAB> |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
367 |
>>> mlab.test_contour3d() |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
368 |
>>> mlab.test_contour3d?? |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
369 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
370 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
371 |
\subsubsection{Plotting Functions} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
372 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
373 |
>>> from numpy import * |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
374 |
>>> t = linspace(0, 2*pi, 50) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
375 |
>>> u = cos(t)*pi |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
376 |
>>> x, y, z = sin(u), cos(u), sin(t) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
377 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
378 |
>>> x = mgrid[-3:3:100j,-3:3:100j] |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
379 |
>>> z = sin(x*x + y*y) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
380 |
>>> mlab.surf(x, y, z) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
381 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
382 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
383 |
\subsubsection{Large 2D Data} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
384 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
385 |
>>> mlab.mesh(x, y, z) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
386 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
387 |
>>> phi, theta = numpy.mgrid[0:pi:20j, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
388 |
... 0:2*pi:20j] |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
389 |
>>> x = sin(phi)*cos(theta) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
390 |
>>> y = sin(phi)*sin(theta) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
391 |
>>> z = cos(phi) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
392 |
>>> mlab.mesh(x, y, z, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
393 |
... representation= |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
394 |
... 'wireframe') |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
395 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
396 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
397 |
\subsubsection{Large 3D Data} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
398 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
399 |
>>> x, y, z = ogrid[-5:5:64j, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
400 |
... -5:5:64j, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
401 |
... -5:5:64j] |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
402 |
>>> mlab.contour3d(x*x*0.5 + y*y + |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
403 |
z*z*2) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
404 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
405 |
>>> mlab.test_quiver3d() |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
406 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
407 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
408 |
\subsection{Motivational Problem} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
409 |
Atmospheric data of temperature over the surface of the earth. Let temperature ($T$) vary linearly with height ($z$)\\ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
410 |
$T = 288.15 - 6.5z$ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
411 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
412 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
413 |
lat = linspace(-89, 89, 37) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
414 |
lon = linspace(0, 360, 37) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
415 |
z = linspace(0, 100, 11) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
416 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
417 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
418 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
419 |
x, y, z = mgrid[0:360:37j,-89:89:37j, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
420 |
0:100:11j] |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
421 |
t = 288.15 - 6.5*z |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
422 |
mlab.contour3d(x, y, z, t) |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
423 |
mlab.outline() |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
424 |
mlab.colorbar() |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
425 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
426 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
427 |
\subsection{Lorenz equation} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
428 |
\begin{eqnarray*} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
429 |
\frac{d x}{dt} &=& s (y-x)\\ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
430 |
\frac{d y}{d t} &=& rx -y -xz\\ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
431 |
\frac{d z}{d t} &=& xy - bz\\ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
432 |
\end{eqnarray*} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
433 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
434 |
Let $s=10,$ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
435 |
$r=28,$ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
436 |
$b=8./3.$ |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
437 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
438 |
\begin{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
439 |
x, y, z = mgrid[-50:50:20j,-50:50:20j, |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
440 |
-10:60:20j] |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
441 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
442 |
\end{verbatim} |
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
443 |
|
1c1d6aaa2be3
Added first cut of Day2 handout; Minor edits to sessions 2 and 3.
Puneeth Chaganti <punchagan@fossee.in>
parents:
diff
changeset
|
444 |
\end{document} |