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Elementary arithmetic operations
import numpy as np
import scipy.io
import scipy.misc
import matplotlib.pyplot as plt5+611
3-21
5*840
1/20
1./2 # Explain this0.5
2**664
Logical operations
1 != 2 # TrueTrue
1 and 0 # False0
1 or 0 # True1
1 != 0 # XORTrue
a='foo'
b='bar'
bool(a) != bool(b)False
b=None
bool(a) != bool(b) # Explain thisTrue
####Python variables and types ####Displaying variables
b=3
b3
from math import pi
b=pi
b3.141592653589793
float('%1.4f'%b)3.1416
float('{:1.5}'.format(b))3.1416
##Numpy basics : Vectors and matrices
import numpy as np
a=np.array([[1,2],[3,4],[5,6]])
aarray([[1, 2],
[3, 4],
[5, 6]])
v=[1,2,3] # list
v[1, 2, 3]
v=np.array([1,2,3]) # numpy array
varray([1, 2, 3])
v=np.arange(1,2,0.1)
varray([ 1. , 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9])
v.tolist()[1.0,
1.1,
1.2000000000000002,
1.3000000000000003,
1.4000000000000004,
1.5000000000000004,
1.6000000000000005,
1.7000000000000006,
1.8000000000000007,
1.9000000000000008]
v=range(1,6)
v[1, 2, 3, 4, 5]
v=np.linspace(1,2,11)
varray([ 1. , 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. ])
###Comprehensions
####list comprehensionv=[1,2,3]
[e**2 for e in v][1, 4, 9]
[e**2 for e in v if e%2 !=0][1, 9]
[e**2 if e%2 != 0 else -1 for e in v][1, -1, 9]
####dictionary comprehension
d = {'a':1, 'b':2, 'c':3}
{v: k for k, v in d.items()} # swap keys and values
{1: 'a', 2: 'b', 3: 'c'}{1: 'a', 2: 'b', 3: 'c'}
####set comprehension
{x**2 for x in [1, 1, 2]}
set([1, 4]){1, 4}
###Special matrix functions
ones=np.ones((3,2))
onesarray([[ 1., 1.],
[ 1., 1.],
[ 1., 1.]])
3*onesarray([[ 3., 3.],
[ 3., 3.],
[ 3., 3.]])
np.zeros((3,2))array([[ 0., 0.],
[ 0., 0.],
[ 0., 0.]])
np.random.rand(3,2)array([[ 0.62274829, 0.09702351],
[ 0.63787983, 0.7836852 ],
[ 0.2725037 , 0.05886131]])
np.random.randn(3,2)array([[ 0.91457171, -2.09292019],
[-0.66121188, 1.47599627],
[ 0.5300655 , -0.7618794 ]])
id=np.eye(3) id
3*id---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-109-0412ab2e6bd6> in <module>()
----> 1 3*id
TypeError: unsupported operand type(s) for *: 'int' and 'builtin_function_or_method'
##Moving data around ###shape/size of a matrix
a=np.random.rand(3,2)
a.shape(3, 2)
a.size6
###Loading files in pythonfile=open('../ex6/emailSample1.txt', 'r')
file_contents=file.read()
file_contents"> Anyone knows how much it costs to host a web portal ?\n>\nWell, it depends on how many visitors you're expecting.\nThis can be anywhere from less than 10 bucks a month to a couple of $100. \nYou should checkout http://www.rackspace.com/ or perhaps Amazon EC2 \nif youre running something big..\n\nTo unsubscribe yourself from this mailing list, send an email to:\[email protected]\n\n"
%pylab inline
data = scipy.misc.imread('../ex7/bird_small.png')
plt.imshow(data)Populating the interactive namespace from numpy and matplotlib
WARNING: pylab import has clobbered these variables: ['mat', 'rand', 'ones', 'pi', 'e']
`%matplotlib` prevents importing * from pylab and numpy
<matplotlib.image.AxesImage at 0x10dc711d0>
data = np.loadtxt('ex1data1.txt', delimiter=',')
dataarray([[ 6.1101 , 17.592 ],
[ 5.5277 , 9.1302 ],
[ 8.5186 , 13.662 ],
[ 7.0032 , 11.854 ],
[ 5.8598 , 6.8233 ],
[ 8.3829 , 11.886 ],
[ 7.4764 , 4.3483 ],
[ 8.5781 , 12. ],
[ 6.4862 , 6.5987 ],
[ 5.0546 , 3.8166 ],
[ 5.7107 , 3.2522 ],
[ 14.164 , 15.505 ],
[ 5.734 , 3.1551 ],
[ 8.4084 , 7.2258 ],
[ 5.6407 , 0.71618],
[ 5.3794 , 3.5129 ],
[ 6.3654 , 5.3048 ],
[ 5.1301 , 0.56077],
[ 6.4296 , 3.6518 ],
[ 7.0708 , 5.3893 ],
[ 6.1891 , 3.1386 ],
[ 20.27 , 21.767 ],
[ 5.4901 , 4.263 ],
[ 6.3261 , 5.1875 ],
[ 5.5649 , 3.0825 ],
[ 18.945 , 22.638 ],
[ 12.828 , 13.501 ],
[ 10.957 , 7.0467 ],
[ 13.176 , 14.692 ],
[ 22.203 , 24.147 ],
[ 5.2524 , -1.22 ],
[ 6.5894 , 5.9966 ],
[ 9.2482 , 12.134 ],
[ 5.8918 , 1.8495 ],
[ 8.2111 , 6.5426 ],
[ 7.9334 , 4.5623 ],
[ 8.0959 , 4.1164 ],
[ 5.6063 , 3.3928 ],
[ 12.836 , 10.117 ],
[ 6.3534 , 5.4974 ],
[ 5.4069 , 0.55657],
[ 6.8825 , 3.9115 ],
[ 11.708 , 5.3854 ],
[ 5.7737 , 2.4406 ],
[ 7.8247 , 6.7318 ],
[ 7.0931 , 1.0463 ],
[ 5.0702 , 5.1337 ],
[ 5.8014 , 1.844 ],
[ 11.7 , 8.0043 ],
[ 5.5416 , 1.0179 ],
[ 7.5402 , 6.7504 ],
[ 5.3077 , 1.8396 ],
[ 7.4239 , 4.2885 ],
[ 7.6031 , 4.9981 ],
[ 6.3328 , 1.4233 ],
[ 6.3589 , -1.4211 ],
[ 6.2742 , 2.4756 ],
[ 5.6397 , 4.6042 ],
[ 9.3102 , 3.9624 ],
[ 9.4536 , 5.4141 ],
[ 8.8254 , 5.1694 ],
[ 5.1793 , -0.74279],
[ 21.279 , 17.929 ],
[ 14.908 , 12.054 ],
[ 18.959 , 17.054 ],
[ 7.2182 , 4.8852 ],
[ 8.2951 , 5.7442 ],
[ 10.236 , 7.7754 ],
[ 5.4994 , 1.0173 ],
[ 20.341 , 20.992 ],
[ 10.136 , 6.6799 ],
[ 7.3345 , 4.0259 ],
[ 6.0062 , 1.2784 ],
[ 7.2259 , 3.3411 ],
[ 5.0269 , -2.6807 ],
[ 6.5479 , 0.29678],
[ 7.5386 , 3.8845 ],
[ 5.0365 , 5.7014 ],
[ 10.274 , 6.7526 ],
[ 5.1077 , 2.0576 ],
[ 5.7292 , 0.47953],
[ 5.1884 , 0.20421],
[ 6.3557 , 0.67861],
[ 9.7687 , 7.5435 ],
[ 6.5159 , 5.3436 ],
[ 8.5172 , 4.2415 ],
[ 9.1802 , 6.7981 ],
[ 6.002 , 0.92695],
[ 5.5204 , 0.152 ],
[ 5.0594 , 2.8214 ],
[ 5.7077 , 1.8451 ],
[ 7.6366 , 4.2959 ],
[ 5.8707 , 7.2029 ],
[ 5.3054 , 1.9869 ],
[ 8.2934 , 0.14454],
[ 13.394 , 9.0551 ],
[ 5.4369 , 0.61705]])
data = scipy.io.loadmat('ex3data1.mat')
data---------------------------------------------------------------------------
IOError Traceback (most recent call last)
<ipython-input-116-f2dd930e4dd8> in <module>()
----> 1 data = scipy.io.loadmat('ex3data1.mat')
2 data
/Users/marcel/.virtualenvs/2.7.6/lib/python2.7/site-packages/scipy/io/matlab/mio.pyc in loadmat(file_name, mdict, appendmat, **kwargs)
132 """
133 variable_names = kwargs.pop('variable_names', None)
--> 134 MR = mat_reader_factory(file_name, appendmat, **kwargs)
135 matfile_dict = MR.get_variables(variable_names)
136 if mdict is not None:
/Users/marcel/.virtualenvs/2.7.6/lib/python2.7/site-packages/scipy/io/matlab/mio.pyc in mat_reader_factory(file_name, appendmat, **kwargs)
55 type detected in `filename`.
56 """
---> 57 byte_stream = _open_file(file_name, appendmat)
58 mjv, mnv = get_matfile_version(byte_stream)
59 if mjv == 0:
/Users/marcel/.virtualenvs/2.7.6/lib/python2.7/site-packages/scipy/io/matlab/mio.pyc in _open_file(file_like, appendmat)
21 if isinstance(file_like, string_types):
22 try:
---> 23 return open(file_like, 'rb')
24 except IOError as e:
25 if appendmat and not file_like.endswith('.mat'):
IOError: [Errno 2] No such file or directory: 'ex3data1.mat'
##Manipulating matrices ###Indexing and Slicing
x = np.arange(10)
xarray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
x[:]array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
x[1:]array([1, 2, 3, 4, 5, 6, 7, 8, 9])
x[:5]array([0, 1, 2, 3, 4])
x[2]2
x[-2]8
x=x.reshape((2,5))
xarray([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
x[1,3]8
x[0]array([0, 1, 2, 3, 4])
x = np.arange(10)
x[2:5]array([2, 3, 4])
x[1:7:2]array([1, 3, 5])
arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
arr2darray([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
arr2d[2]array([7, 8, 9])
arr2d[0][1]2
arr2d[0,1]2
###Boolean indexing
mat = np.array(['The', 'quick', 'brown', 'fox', 'jumped', 'over', 'the', 'lazy', 'dog']).reshape((3,3))
matarray([['The', 'quick', 'brown'],
['fox', 'jumped', 'over'],
['the', 'lazy', 'dog']],
dtype='|S6')
rand = np.random.randn(3,3)>0
randarray([[False, False, True],
[ True, True, True],
[ True, False, False]], dtype=bool)
mat[rand]array(['brown', 'fox', 'jumped', 'over', 'the'],
dtype='|S6')
###Flattening
arr = np.arange(9).reshape((3,3))
arrarray([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
arr.flatten()array([0, 1, 2, 3, 4, 5, 6, 7, 8])
arr.ravel()array([0, 1, 2, 3, 4, 5, 6, 7, 8])
arr.flatten(1)array([0, 3, 6, 1, 4, 7, 2, 5, 8])
###Vector assignments
arr = np.arange(10)
arrarray([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
arr[4:8]=10
arrarray([ 0, 1, 2, 3, 10, 10, 10, 10, 8, 9])
slice=arr[4:8]
slicearray([10, 10, 10, 10])
slice[:]=-5
slicearray([-5, -5, -5, -5])
slice[1]=50
slicearray([-5, 50, -5, -5])
arr_copy=arr.copy()
arr_copyarray([ 0, 1, 2, 3, -5, 50, -5, -5, 8, 9])
arr_copy[4:8]=20
arr_copyarray([ 0, 1, 2, 3, 20, 20, 20, 20, 8, 9])
arrarray([ 0, 1, 2, 3, -5, 50, -5, -5, 8, 9])
Concatenating
mat = np.array(['The', 'quick', 'brown', 'fox'])
mat2 = np.array(['jumped', 'over', 'the', 'lazy']) np.hstack((mat,mat2))array(['The', 'quick', 'brown', 'fox', 'jumped', 'over', 'the', 'lazy'],
dtype='|S6')
np.vstack((mat,mat2))array([['The', 'quick', 'brown', 'fox'],
['jumped', 'over', 'the', 'lazy']],
dtype='|S6')
np.column_stack((mat,mat2))array([['The', 'jumped'],
['quick', 'over'],
['brown', 'the'],
['fox', 'lazy']],
dtype='|S6')
arr = np.arange(12).reshape((3, 4))
arrarray([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
np.concatenate((arr,arr), axis=1)array([[ 0, 1, 2, 3, 0, 1, 2, 3],
[ 4, 5, 6, 7, 4, 5, 6, 7],
[ 8, 9, 10, 11, 8, 9, 10, 11]])
np.concatenate((arr,arr), axis=0)array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
arr = np.arange(5)
np.concatenate((arr,arr), axis=0)array([0, 1, 2, 3, 4, 0, 1, 2, 3, 4])
###Matrix multiplication
x=np.array([[1,2,3], [4,5,6], [7,8,9]])
y=np.array([[1,2,3], [4,5,6], [7,8,9]])
np.dot(x,y)array([[ 30, 36, 42],
[ 66, 81, 96],
[102, 126, 150]])
x.dot(y)array([[ 30, 36, 42],
[ 66, 81, 96],
[102, 126, 150]])
# Element-wise multiplicationx*yarray([[ 1, 4, 9],
[16, 25, 36],
[49, 64, 81]])
####Element-wise squaring
x**2array([[ 1, 4, 9],
[16, 25, 36],
[49, 64, 81]])
####Element-wise reciprical
1./xarray([[ 1. , 0.5 , 0.33333333],
[ 0.25 , 0.2 , 0.16666667],
[ 0.14285714, 0.125 , 0.11111111]])
####Element-wise logarithms/exponents
np.log(x)array([[ 0. , 0.69314718, 1.09861229],
[ 1.38629436, 1.60943791, 1.79175947],
[ 1.94591015, 2.07944154, 2.19722458]])
np.exp(x)array([[ 2.71828183e+00, 7.38905610e+00, 2.00855369e+01],
[ 5.45981500e+01, 1.48413159e+02, 4.03428793e+02],
[ 1.09663316e+03, 2.98095799e+03, 8.10308393e+03]])
####Element-wise addition
1+xarray([[ 2, 3, 4],
[ 5, 6, 7],
[ 8, 9, 10]])
###Transpose of a matrix
x.Tarray([[1, 4, 7],
[2, 5, 8],
[3, 6, 9]])
###Maximum and minimum of matrix values
np.max(x)9
np.min(x)1
###sum and product of all elementsnp.sum(x)45
np.sum(x,axis=0)array([12, 15, 18])
np.sum(x,axis=1)array([ 6, 15, 24])
np.sum(x)45
np.product(x)362880
np.product(x,axis=0)array([ 28, 80, 162])
np.product(x,axis=1)array([ 6, 120, 504])
###Inverse and pseudo-inverse of a matrix
x=2*np.eye(3)
np.linalg.inv(x)array([[ 0.5, 0. , 0. ],
[ 0. , 0.5, 0. ],
[ 0. , 0. , 0.5]])
np.linalg.pinv(x)array([[ 0.5, 0. , 0. ],
[ 0. , 0.5, 0. ],
[ 0. , 0. , 0.5]])
##Plotting data ###Plotting generated data
plt.plot(np.arange(10))[<matplotlib.lines.Line2D at 0x10dd05f50>]
##Line color, labels, title and legend ###Saving a graph ###Subplots ###Axis scaling ###Creating/clearing figures ##Control statements ###For loops
li = ['a', 'b', 'e']
for e in li:
print ea
b
e
d = enumerate(li)
for k,v in d:
print k,v0 a
1 b
2 e
###While loops
n = ''
while n.strip() != 'hello':
n = raw_input("Please enter 'hello':")Please enter 'hello':goodbye
Please enter 'hello':hello
###break statement
while True:
n = raw_input("Please enter 'hello':")
if n.strip() == 'hello':
breakPlease enter 'hello':bye
Please enter 'hello':hello
###if-elif-else statement
x = int(raw_input("Please enter an integer: "))
if x < 0:
x = 0
print 'Negative changed to zero'
elif x == 0:
print 'Zero'
elif x == 1:
print 'Single'
else:
print 'More'Please enter an integer: 42
More
##Functions
###PYTHONPATH environment variable ##Vectorization ###Vectorized implementation ###Unvectorized implementation