1. Numpy (Numerical Python)
John R. Woodward

2. Last Lecture Numeric Python. Fast computation n-dimensional arrays
Creating (zero, random, arange)
Shape (e.g. (2L, 3L)), dtype (e.g. float64), ndim
Operations on arrays (arithmetic, dot product)
Slicing, broadcasting
import numpy as np
Do not forget – this is at the start of each file.

3. Broadcasting - array arr = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8])
print arr
arr[3:8] = -99
OUTPUT
[ ]
[ ]

4. Python list
list = [0, 1, 2, 3, 4, 5, 6, 7, 8] print list list[3] = -99 list[3:8] = -99

5. Python list list = [0, 1, 2, 3, 4, 5, 6, 7, 8] print list
Output
[0, 1, 2, 3, 4, 5, 6, 7, 8]
[0, 1, 2, -99, 4, 5, 6, 7, 8]
Traceback (most recent call last):
File "F:\Previous\Users\jrw\workspace\Python1\slice2.py", line 14, in <module>
TypeError: can only assign an iterable

6. Fast element-wise array functions
arr = np.arange(5)
print arr
print np.sqrt(arr)
print np.exp(arr)
[ ]
[ ]
[ ]

7. element-wise maximum x = randn(4) y = randn(4) print x print y
print np.maximum(x, y)
[ ]
[ ]
[ ]

8. element-wise add x = randn(4) y = randn(4) print x print y
print np.add(x, y)
[ ]
[ ]
[ ]

9. Zip two lists together - python
a = [1,2,3]
b = [10, 20, 30]
zipAB = zip(a,b)
print zipAB
OUTPUT
[(1, 10), (2, 20), (3, 30)]

10. Zip three lists together
a = [1,2,3]
b = [10, 20, 30]
c = [True, False, True]
zipABC = zip(a,b,c)
print zipABC
Output
[(1, 10, True), (2, 20, False), (3, 30, True)]

11. And is the same as a = [1,2,3] b = [10, 20, 30]
c = [True, False, True]
result = [(x,y,z)
for x, y, z in zip(a,b,c)]
print result
Output
[(1, 10, True), (2, 20, False), (3, 30, True)]

12. conditionals result = [(x if z else y) for x, y, z in zip(a,b,c)]
print result
OUTPUT
[1, 20, 3]
NOTE depending on the boolean value, it decides which list to take value from.

13. where an easier way to do this with np a = [1,2,3] b = [10, 20, 30]
c = [True, False, True]
np.where(c,a,b)
Output is [ ]

14. types <type 'list'> <type 'numpy.ndarray'>
result = [(x if z else y)
for x, y, z in zip(a,b,c)]
print type(result)
result = np.where(c,a,b)
<type 'list'>
<type 'numpy.ndarray'>

15. where(arr > 0, 2, -2) #creates random 3 by 2 array
arr = np.random.rand(3,2)
print arr
print np.where(arr > 0.5, 2, -2)
[[-2 2]
[ 2 2]
[-2 -2]]
[[ ]
[ ]
[ ]]

16. where(arr > 0, 2, arr) arr = np.random.rand(3, 2) print arr
print np.where(arr > 0.5, 2, arr)
[[ ]
[ ]
[ ]]
[[ ]
[ ]
[ ]]

17. Mathematical and statistical methods
arr = np.random.randn(2, 2)
print arr
print arr.mean()
print np.mean(arr)
print arr.sum()
[[ ]
[ ]]

18. Axis An array has an axis. These are labelled 0, 1, 2, …
Usually we think of these as x y z axiz, but we soon run out of letters.
What comes after row, column, ???
These are just the dimensions.

19. Mean of rows/columns (axis)
arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
print arr
print arr.mean(axis=0)
print arr.mean(axis=1)
#these are the
#”means in different
#directions”
[[0 1 2]
[3 4 5]
[6 7 8]]
[ ]
[ ]

20. Sum different axis arr = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]])
print arr
print arr.sum(0)
print arr.sum(1)
#we sum
#vertically
#horizonatally
[[0 1 2]
[3 4 5]
[6 7 8]]
[ ]
[ ]

21. Cumulative sum (running total)
[[0 1 2]
[3 4 5]
[6 7 8]]
[[ ]
[ ]
[ ]]
[[ ]
[ ]
[ ]]
arr = np.array(
[[0, 1, 2],
[3, 4, 5], [6, 7, 8]])
print arr
print arr.cumsum(0)
print arr.cumsum(1)
This is across different axis.

22. Cumulative product “running product”
[[0 1 2]
[3 4 5]
[6 7 8]]
[[ ]
[ ]
[ ]]
[[ ]
[ ]
[ ]]
arr = np.array(
[[0, 1, 2],
[3, 4, 5], [6, 7, 8]])
print arr
print arr.cumsum(0)
print arr.cumsum(1)
This is across different axis.

23. Methods for Boolean arrays
arr = np.random.randn(5)
print arr
print (arr > 0).sum()
1/ makes a random array
2/ counts only the positive entries.
[ ] 2

24. Methods for Boolean arrays
bools = np.array(
[False, False, True, False])
print bools.any()
print bools.all()
This asks if all/any in bools is true.
output
True
False

25. Sorting 1 arr = randn(4) print arr arr.sort() OUTPUT
[ ]
[ ]

26. SORTING 2 [[1 3 2] [8 4 9] [3 5 8]] [3 4 8] [8 5 9]] [[1 2 3] [5 8 9]]
arr = randn(2, 3) print arr arr.sort(0) arr.sort(1) sorting on different axis

27. Unique and other set logic
names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])
print np.unique(names)
print sorted(set(names))
OUTPUT
['Bob' 'Joe' 'Will']
['Bob', 'Joe', 'Will']

28. Testing Membership Test if something is in an array.
values = np.array([6, 0, 0, 3, 2, 5, 6])
print np.in1d(values, [2, 3, 6])
Output
[ True False False True True False True]
#asks is 6 in [2,3,6], is 0 in [2,3,6], ....

29. Storing arrays on disk in binary format
Lets save and load a file
arr = np.arange(10)
print arr
np.save('some_array', arr)
arr1 = np.load('some_array.npy')
print arr1
NOTE THE file extension is npy

30. Saving multiple arrays
arr3 = np.arange(3)
arr5 = np.arange(5)
np.savez('array_archive.npz', a=arr3, b=arr5)
arch = np.load('array_archive.npz')
print type(arch)
print arch['a']
print arch['b']
print dict(arch)

31. arr3 = np.arange(3)
arr5 = np.arange(5)
np.savez('array_archive.npz', a=arr3, b=arr5)
arch = np.load('array_archive.npz')
print type(arch)
print arch['a']
print arch['b']
print dict(arch)

32. np.load returns dict-like object
<class 'numpy.lib.npyio.NpzFile'>
[0 1 2]
[ ]
{'a': array([0, 1, 2]), 'b': array([0, 1, 2, 3, 4])}

33. Saving and loading text files
arr = np.loadtxt('array_ex.txt', delimiter=',')
print arr
print type(arr)
OUTPUT
[[ ]
[ ]]
<type 'numpy.ndarray'>
array_ex.txt
1,2,3,4
3,4,5,6

34. Indexing elements in a NumPy array
Axis 0 is rows
Axis 1 is colmuns.
Axis 3 is ???

35. Indexing elements in a NumPy array

36. Two- dimensional array slicing

37. Ask questions on board first.

38. 3d 2x2x2
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3

39. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0]

40. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[1]

41. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0][0]

42. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0][0][0]

43. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0][1]

44. Indexing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[1][0]

45. Slicing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0,0,0]

46. Slicing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[0,1,0]

47. Slicing
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[:,0]

48. a[:,:,0] Slicing 2,4 3,1 3,3 4,3 Both slices, both rows, column 0
a=np.array([ [ [3, 1],[4, 3] ], [2, 4],[3, 3] ] ])
2,4
3,3
3,1
4,3
a[:,:,0]
Both slices, both rows, column 0

49. Slicing
Remember, slicing range:
a:b
Means elements from a up to b-1

50. Data Types Every element in an ndarray has the same type Basic types:
int
float
complex
bool
object
string
unicode

51. Data Types Types also have a defined size in bytes, e.g.
int32
float64
The size defines storage size and accuracy
To set the type:
a=np.array([1,2], dtype=np.int32)
print a.dtype
OUTPUT IS dtype('int32')

52. Iterating and Processing
You can iterate through a ndarray if you like:
for e in a:
print e or
for e in a[0]:
etc. but this is complicated an not advised
There is a better way ...

53. Element-wise Operations
a=a*2
a=a+5
a=a+b
etc.
Functions:
a.sum()
a.max()
a.mean()
a.round()

54. Slices and Indexes
a[0]=a[0]/2
a[0,0,0]+=1
a[:,1,1].sum()