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--- python_getting_started [2013/08/14 11:10]
asa created
+++ python_getting_started [2016/08/09 10:25] (current)
@@ Line 105: / Line 105: @@
 To plot the data, first import the ''pyplot'' module.
-<code>
+<code python>
 In [6]: import matplotlib.pyplot as plt
@@ Line 148: / Line 148: @@
 <code python>
 In [14]: x = np.arange(10, 0.1)
-In [15]: plt.pl
-plt.plot       plt.plot_date  plt.plotfile   plt.plotting
 In [15]: plt.plot(x, x**2, 'ob')
 Out[15]: [<matplotlib.lines.Line2D at 0x1054162d0>]
 </code>
-{{ Notes:plot2.png?400  }}
+/* {{ Notes:plot2.png?400  }}*/
-We can add a second plot to the same axes by calling //plot// again without the call to //clf()//.
+We can add a second plot to the same axes by calling //plot// again:
-<code>
+<code python>
-In [47]: plt.plot(x,x**2)
+In [16]: plt.plot(x, x, 'dr')
-Out[47]: [<matplotlib.lines.Line2D object at 0x3608990>]
+Out[16]: [<matplotlib.lines.Line2D object at 0x3608990>]
 </code>
-{{ Notes:plot3.png?400  }}
+/*{{ Notes:plot3.png?400  }}*/
@@ Line 173: / Line 169: @@
 Of course!  No data analysis tool is worth the bytes it burns if it
-doesn't. The python  //numpy// module provides the magic to work with matrices as
+doesn't. The ''numpy'' package provides the required magic.
-//ndarray//'s.
+Let's create an array that represents the following matrix:
-We have several ways to create an array.  Make this array
 \[\left ( \begin{array}{cc}
 & 2\\
@@ Line 196: / Line 189: @@
 </code>
-This array can be copied and reshaped by
+Let's construct the matrices
-<code>
-In [22]: m.reshape(1,6)
-Out[22]: array([[1, 2, 3, 4, 5, 6]])
-In [23]: m
-array([[1, 2],
-       [3, 4],
-       [5, 6]])
-</code>
-To change m, you must assign it or use resize.
-<code>
-In [24]: m = m.reshape(1,6)
-In [7]: m
-Out[7]: array([[1, 2, 3, 4, 5, 6]])
-In [8]: m.resize((2,3))
-In [9]: m
-Out[9]:
-array([[1, 2, 3],
-       [4, 5, 6]])
-</code>
-We could use the //numpy// function //arange// followed by //reshape//:
-<code>
-In [26]: np.arange(10)
-Out[26]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
-In [27]: np.arange(10).reshape(2,5)
-Out[27]:
-array([[0, 1, 2, 3, 4],
-       [5, 6, 7, 8, 9]])
-</code>
-Want to know more?  Try
-  np.reshape?
-Let's make the matrices
 \[a = \left ( \begin{array}{cc}
 & 2 & 2\\
@@ Line 245: / Line 201: @@
 & 8 & 9
 	\end{array} \right ) \]
-We can use //resize// for the first one, and //resize// or //reshape//
+<code python>
-for the second.  (//resize// changes the array it is applied to;
+In [16]: a = np.ones((3,3)) * 2
-//reshape// makes a new version)
-<code>
-In [65]: a = np.resize(2,(3,3))
-In [66]: a
+In [17]: a
-Out[66]:
+Out[17]:
-array([[2, 2, 2],
+array([[ 2.,  2.,  2.],
-       [2, 2, 2],
+       [ 2.,  2.,  2.],
-       [2, 2, 2]])
+       [ 2.,  2.,  2.]])
-In [67]: b = np.resize(np.arange(9)+1,(3,3))
+In [18]: b = np.resize(np.arange(9)+1,(3,3))
-In [68]: b
+In [19]: b
-Out[68]:
+Out[19]:
 array([[1, 2, 3],
        [4, 5, 6],
@@ Line 267: / Line 220: @@
 What is the value of $a * b$?
-<code>
+<code python>
-In [69]: a * b
+In [20]: a * b
-Out[69]:
+Out[21]:
 array([[ 2,  4,  6],
        [ 8, 10, 12],
        [14, 16, 18]])
 </code>
-The //*// operator does a component-wise multiplication.  Use the
+The ''*'' operator does a component-wise multiplication.  Use the
-//numpy// function //dot// to do matrix multiplication.
+''numpy'' function ''dot'' to do matrix multiplication.
-<code>
-In [70]: np.dot(a,b)
+<code python>
-Out[70]:
+In [22]: np.dot(a,b)
+Out[22]:
 array([[24, 30, 36],
        [24, 30, 36],
@@ Line 285: / Line 239: @@
 An array is transposed by
-<code>
+<code python>
-In [75]: b.transpose()
+In [23]: b.transpose()
-Out[75]:
+Out[23]:
-array([[1, 4, 7],
-       [2, 5, 8],
-       [3, 6, 9]])
-In [76]: b.T
-Out[76]:
 array([[1, 4, 7],
        [2, 5, 8],
        [3, 6, 9]])
-In [77]: np.transpose(b)
+In [24]: b.T
-Out[77]:
+Out[24]:
 array([[1, 4, 7],
        [2, 5, 8],
@@ Line 305: / Line 253: @@
 </code>
-What is $a b^T$?
+Elements and sub-matrices are easily extracted:
-<code>
+<code python>
-In [78]: np.dot(a,b.T)
+In [25]: b
-Out[78]:
+Out[25]:
-array([[12, 30, 48],
-       [12, 30, 48],
-       [12, 30, 48]])
-</code>
-Elements and sub-matrices are easily extracted. Given the previous
-assignment of $b$,
-<code>
-In [79]: b
-Out[79]:
 array([[1, 2, 3],
        [4, 5, 6],
        [7, 8, 9]])
-In [80]: b[0,0]
+In [26]: b[0,0]
-Out[80]: 1
+Out[26]: 1
-In [81]: b[0,1]
+In [27]: b[0,1]
-Out[81]: 2
+Out[27]: 2
-In [82]: b[0:1,0:1]
+In [28]: b[0:2, 1:3]
-Out[82]: array([[1]])
+Out[28]:
-In [83]: b[0:2,0:1]
-Out[83]:
-array([[1],
-       [4]])
-In [84]: b[0:2,1:2]
-Out[84]:
-array([[2],
-       [5]])
-In [85]: b[0:2,1:3]
-Out[85]:
 array([[2, 3],
        [5, 6]])
 </code>
-Let's multiply $a$ by the first column of $b$.
+Let's multiply the first row of a $a$ by the second column of $b$.
-<code>
+<code python>
-In [89]: a
+In [29]: np.dot(a[0], b[:,1])
-Out[89]:
+Out[29]: 30.0
-array([[2, 2, 2],
-       [2, 2, 2],
-       [2, 2, 2]])
-In [91]: b
-Out[91]:
-array([[1, 2, 3],
-       [4, 5, 6],
-       [7, 8, 9]])
-In [92]: b[:,0]
-Out[92]: array([1, 4, 7])
-In [93]: np.dot(a,b[:,0])
+In [30]: np.dot(a[0],b.T[1])
-Out[93]: array([24, 24, 24])
+Out[30]: 30.0
 </code>
-What happenend?  This should be a 3x3 times 3x1 operation, resulting
-in a 3x1 matrix, but the answer shows a 1x3 matrix.
-While ''b'' is two-dimensonal, ''b[:,0]'' is one-dimensional.  It is the
+How do I find the inverse of a matrix?
-first column, but as a vector.  To keep the two-dimensional nature,
+<code python>
-use ''b[:,0:1]'' or just ''b[:,:1]''.
-<code>
-In [94]: b[:,:1]
-Out[94]:
-array([[1],
-       [4],
-       [7]])
-In [95]: np.dot(a,b[:,:1])
-Out[95]:
-array([[24],
-       [24],
-       [24]])
-</code>
-How do I find the inverse of a matrix?  Search the net for //numpy
-inverse//.
-<code>
 In [2]: z = np.array([[2,1,1],[1,2,2],[2,3,4]])

CS545 fall 2016

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