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--- python_getting_started [2013/08/14 11:34]
asa
+++ python_getting_started [2016/08/09 10:25]
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-===== A bit of Python =====
-Python is available on any Linux/Unix machine including department machines and Macs.
-You can download and install python on your own computer by following
-instructions at [[http://www.python.org]]
-You can use the Python interpreter interactively by typing //python// at a terminal window.
-Ipython is a nicer front end to python that is invoked with
-  ipython
-To quit, type control-d
-To run python code in a file //code.py//, either type
-  run code.py
-in //ipython//, or type
-  python code.py
-at the unix command line.
-When in //ipython//, you may type python statements or expressions
-that are evaluated, or //ipython// commands.  See the
-[[http://showmedo.com/videotutorials/video?name=1000010&fromSeriesID=100|Video
-tutorial on using ipython]], in five parts by Jeff Rush, for help
-getting started with //ipython//.
-Documentation is immediately available for many things.  For example:
-<code>
-> ipython
-asa:~$ ipython
-Python 2.7.3 (v2.7.3:70274d53c1dd, Apr  9 2012, 20:52:43)
-Type "copyright", "credits" or "license" for more information.
-IPython 0.13.2 -- An enhanced Interactive Python.
-?         -> Introduction and overview of IPython's features.
-%quickref -> Quick reference.
-help      -> Python's own help system.
-object?   -> Details about 'object', use 'object??' for extra details.
-In [1]: list?
-Type:		type
-Base Class:	<type 'type'>
-String Form:	<type 'list'>
-Namespace:	Python builtin
-Docstring:
-    list() -> new list
-    list(sequence) -> new list initialized from sequence's items
-In [2]: help(list)
-Help on class list in module __builtin__:
-class list(object)
- |  list() -> new list
- |  list(sequence) -> new list initialized from sequence's items
- |
- |  Methods defined here:
-   .
-   .
-   .
- |  append(...)
- |      L.append(object) -- append object to end
- |
-   .
-   .
-   .
- |
- |  sort(...)
- |      L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*;
- |      cmp(x, y) -> -1, 0, 1
-</code>
-What is the value of $(100\cdot 2 - 12^2) / 7 \cdot 5 + 2\;\;\;$?
-<code python>
-  In [301]: (100*2 - 12**2) / 7*5 + 2
-  Out[301]: 42
-</code>
-In order to compute something like $\sin(\pi/2)$ we first need to //import// the //math// module:
-<code python>
-In [303]: import math
-In [304]: math.sin(math.pi/2)
-.0
-</code>
-How do I find out what other mathematical functions are available?
-  help("math")
-===== Plotting =====
-Let's get on to that all important step of visualizing data.  We will be using the [[http://matplotlib.org |matplotlib]] Python package for that.  Let's start by plotting the function $f(x) = x^2$.
-First, let's generate the numbers. Well, there are tons of ways to do so.  First, using a''for'' loop.
-<code python>
-In [3]: f = []
-In [4]: for i in range(10) :
-   ...:     f.append(i**2)
-   ...:
-In [5]: f
-Out[5]: [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
-</code>
-To plot the data, first import the ''pyplot'' module.
-<code python>
-In [6]: import matplotlib.pyplot as plt
-In [7]: plt.plot(range(10), f)
-Out[7]: [<matplotlib.lines.Line2D at 0x10549b590>]
-</code>
-In order to actually see the plot you need to do:
-<code python>
-In [8]: plt.show()
-</code>
-As an alternative, you can put matplotlib in interactive mode before plotting using the command ''plt.ion()''.
-Python has some nifty syntax for generating lists.  Watch this!  A [[http://www.secnetix.de/olli/Python/list_comprehensions.hawk|list comprehension]]!!
-<code python>
-In [9]: f = [i**2 for i in range(10)]
-In [10]: f
-Out[10]: [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
-</code>
-There's an alternative way of doing this using ''numpy'':
-<code python>
-In [11]: import numpy as np
-In [12]: f = np.arange(10)**2
-In [13]: f
-Out[13]: array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])
-</code>
-Note that plotting functions to accept either lists or ''numpy'' arrays, so a fast way of doing our plot is
-<code python>
-In [14]: plt.plot(np.arange(10), np.arange(10)**2)
-</code>
-For a smoother plot:
-<code python>
-In [14]: x = np.arange(10, 0.1)
-In [15]: plt.plot(x, x**2, 'ob')
-Out[15]: [<matplotlib.lines.Line2D at 0x1054162d0>]
-</code>
-/* {{ Notes:plot2.png?400  }}*/
-We can add a second plot to the same axes by calling //plot// again:
-<code python>
-In [16]: plt.plot(x, x, 'dr')
-Out[16]: [<matplotlib.lines.Line2D object at 0x3608990>]
-</code>
-/*{{ Notes:plot3.png?400  }}*/
-===== Matrices in Python =====
-Can I work with vectors and matrices in python?
-Of course!  No data analysis tool is worth the bytes it burns if it
-doesn't. The ''numpy'' package provides the required magic.
-Let's create an array that represents the following matrix:
-\[\left ( \begin{array}{cc}
-& 2\\
-& 4\\
-& 6
-	\end{array} \right ) \]
-by doing
-<code>
-In [17]: import numpy as np
-In [18]: m = np.array([[1,2], [3,4], [5,6]])
-In [19]: m
-Out[19]:
-array([[1, 2],
-       [3, 4],
-       [5, 6]])
-</code>
-Let's construct the matrices
-\[a = \left ( \begin{array}{cc}
-& 2 & 2\\
-& 2 & 2\\
-& 2 & 2
-	\end{array} \right ) \]
-and
-\[b = \left ( \begin{array}{cc}
-& 2 & 3\\
-& 5 & 6\\
-& 8 & 9
-	\end{array} \right ) \]
-<code python>
-In [16]: a = np.ones((3,3)) * 2
-In [17]: a
-Out[17]:
-array([[ 2.,  2.,  2.],
-       [ 2.,  2.,  2.],
-       [ 2.,  2.,  2.]])
-In [18]: b = np.resize(np.arange(9)+1,(3,3))
-In [19]: b
-Out[19]:
-array([[1, 2, 3],
-       [4, 5, 6],
-       [7, 8, 9]])
-</code>
-What is the value of $a * b$?
-<code python>
-In [20]: a * b
-Out[21]:
-array([[ 2,  4,  6],
-       [ 8, 10, 12],
-       [14, 16, 18]])
-</code>
-The ''*'' operator does a component-wise multiplication.  Use the
-''numpy'' function ''dot'' to do matrix multiplication.
-<code python>
-In [22]: np.dot(a,b)
-Out[22]:
-array([[24, 30, 36],
-       [24, 30, 36],
-       [24, 30, 36]])
-</code>
-An array is transposed by
-<code python>
-In [23]: b.transpose()
-Out[23]:
-array([[1, 4, 7],
-       [2, 5, 8],
-       [3, 6, 9]])
-In [24]: b.T
-Out[24]:
-array([[1, 4, 7],
-       [2, 5, 8],
-       [3, 6, 9]])
-</code>
-Elements and sub-matrices are easily extracted:
-<code>
-In [25]: b
-Out[25]:
-array([[1, 2, 3],
-       [4, 5, 6],
-       [7, 8, 9]])
-In [26]: b[0,0]
-Out[26]: 1
-In [27]: b[0,1]
-Out[27]: 2
-In [28]: b[0:2, 1:3]
-Out[28]:
-array([[2, 3],
-       [5, 6]])
-</code>
-Let's multiply the first row of a $a$ by the second column of $b$.
-<code>
-In [29]: np.dot(a[0], b[:,1])
-Out[29]: 30.0
-In [30]: np.dot(a[0],b.T[1])
-Out[30]: 30.0
-</code>
-How do I find the inverse of a matrix?
-<code python>
-In [2]: z = np.array([[2,1,1],[1,2,2],[2,3,4]])
-In [3]: z
-Out[3]:
-array([[2, 1, 1],
-       [1, 2, 2],
-       [2, 3, 4]])
-In [4]: np.linalg.inv(z)
-Out[4]:
-array([[ 0.66666667, -0.33333333,  0.        ],
-       [ 0.        ,  2.        , -1.        ],
-       [-0.33333333, -1.33333333,  1.        ]])
-In [5]: np.dot(z, np.linalg.inv(z))
-Out[5]:
-array([[ 1.,  0.,  0.],
-       [ 0.,  1.,  0.],
-       [ 0.,  0.,  1.]])
-</code>

CS545 fall 2016

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