https://docs.scipy.org/doc/numpy-dev/user/quickstart.html 에 내용 중 Shape Manipulation과 Copies And Views 부분에 대한 발표자료.

1. 2016.03.02
Numpy Tutorial
이남기 (beohemian@gmail.com)

2. Shape Manipulation (1)
u Changing the shape of an array
• An Array has a shape given by the number of elements along
each axis:
>>> a = np.floor(10*np.random.random((3,4)))
>>> a
array([[ 2., 8., 0., 6.],
[ 4., 5., 1., 1.],
[ 8., 9., 3., 6.]
])
>>> a.shape
(3, 4)
2
numpy.floor
• 소수점 버리고 반올림

3. Shape Manipulation (2)
u The shape of an array can be changed with various
commands:
>>> a.ravel() # flatten the array
array([ 2., 8., 0., 6., 4., 5., 1., 1., 8., 9., 3., 6.])
>>> a.shape = (6, 2)
>>> a.T
array([[ 2., 0., 4., 1., 8., 3.],
[ 8., 6., 5., 1., 9., 6.]])
3
2 8
0 6
4 5
1 1
8 9
3 6
2 0 4 1 8 3
8 6 5 1 9 6
2 8 0 6 4 5 1 1 8 9 3 6
a.shape = (6, 2) a.T

4. Shape Manipulation (3)
u Stacking together different arrays
4
>>> a = np.array([1,2,3])
>>> a
array([1,2,3])
>>> b = np.array([4,5,6])
>>> b
array([4,5,6])
>>> np.vstack((a,b))
array([[1,2,3],
[4,5,6]])
>>> np.hstack((a,b))
array([1,2,3,4,5,6])

5. Shape Manipulation (4)
u Stacking together different arrays
• The function column_stack stacks 1D arrays as columns into a 2D array. It is
equivalent to vstack only for 1D arrays:
5
>>> from numpy import newaxis
>>> np.column_stack((a,b)) # With 2D arrays
array([[ 8., 8., 1., 8.],
[ 0., 0., 0., 4.]])
1 2 3 4 5 6
a b 1 4
2 5
3 6
np.column_stack((a,b))

6. Shape Manipulation (5)
u Stacking together different arrays
• The function newaxis add an axis to N-dimensional array
6
>>> a = np.array( [[1,2]
[3,4]])
>>> a[0,newaxis]
array([[1,2]])
>>> a[1,newaxis]
array([[3,4]])
>>> a[:,newaxis,:]
array( [[[1,2]], #shape
[[3,4]]] #(2,1,2)
>>> a[newaxis,:,:]
array( [[[1,2], #shape
[3,4]]]) #(1,2,2)
a[:,newaxis,:]
= a[range(0,1), newaxis, range(0,1)
a
[[1,2],
[3,4]]
a[0]
[1,2]
a[1]
[3,4]
Adding
an axis
Adding
an axis
[[3,4]]
[[1,2]]
a[:,newaxis,:]
array( [ [[1,2]],
[[3,4]] ])

7. Shape Manipulation (6)
u Stacking together different arrays
• The function newaxis add an axis to N-dimensional array
7
>>> a = np.array( [[1,2]
[3,4]])
>>> a[0,newaxis]
array([[1,2]])
>>> a[1,newaxis]
array([[3,4]])
>>> a[:,newaxis,:]
array( [[[1,2]], #shape
[[3,4]]] #(2,1,2)
>>> a[newaxis,:,:]
array( [[[1,2], #shape
[3,4]]]) #(1,2,2)
a
[[1,2],
[3,4]]
shape
(2,2)
a
[[[1,2]],
[[3,4]]]
a[:,newaxis,:]
shape
(2,1,2)

8. Shape Manipulation (7)
u Stacking together different arrays
• The function column_stack stacks 1D arrays as columns into a 2D array. It is
equivalent to vstack only for 1D arrays:
8
>>> np.column_stack((a[:,newaxis],b[:,newaxis]))
array([[ 4., 2.],
[ 2., 8.]])
>>> np.vstack((a[:,newaxis],b[:,newaxis]))
# The behavior of vstack is different
array([[ 4.],
[ 2.],
[ 2.],
[ 8.]])
4
2
2
8
a[:,newaxis]
b[:,newaxis]
4
2
2
8
np.vstack

9. Shape Manipulation (8)
u Splitting one array into several smaller ones
9
>>> a = np.floor(10*np.random.random((2,12)))
>>> a
array([[ 9., 5., 6., 3., 6., 8., 0., 7., 9., 7., 2., 7.],
[ 1., 4., 9., 2., 2., 1., 0., 6., 2., 2., 4., 0.]])
>>> np.hsplit(a,3)
[array([[ 9., 5., 6., 3.],
[ 1., 4., 9., 2.]]), array([[ 6., 8., 0., 7.],
[ 2., 1., 0., 6.]]), array([[ 9., 7., 2., 7.],
[ 2., 2., 4., 0.]])]
9 5 6 3 6 8 0 7 9 7 2 7
1 4 9 2 2 1 0 6 2 2 4 0
9 5 6 3
1 4 9 2
6 8 0 7
2 1 0 6
9 7 2 7
2 2 4 0
Split a into 3

10. Shape Manipulation (9)
u Splitting one array into several smaller ones
10
>>> a = np.floor(10*np.random.random((2,12)))
>>> a
array([[ 9., 5., 6., 3., 6., 8., 0., 7., 9., 7., 2., 7.],
[ 1., 4., 9., 2., 2., 1., 0., 6., 2., 2., 4., 0.]])
>>> np.hsplit(a,(3,4))
[array([[ 9., 5., 6.],
[ 1., 4., 9.]]),
array([[ 3.],
[ 2.]]),
array([[ 6., 8., 0., 7., 9., 7., 2., 7.],
[ 2., 1., 0., 6., 2., 2., 4., 0.]])]
9 5 6 3 6 8 0 7 9 7 2 7
1 4 9 2 2 1 0 6 2 2 4 0
9 5 6
1 4 9
3
2
6 8 0 7 9 7 2 7
2 1 0 6 2 2 4 0
# Split a after the third and the fourth column

11. Copies and views (1)
u No copy at all
• Simple assignments make no copy of array objects or of their data.
11
>>> a = np.arange(12)
>>> b = a
>>> b is a
True
>>> b.shape = 3,4
>>> a.shape
(3, 4) a
a.shape
b
b.shape
no new object is created
a and b are two names for the same ndarray object
ndarray
object

12. Copies and views (2)
u No copy at all
• Python passes mutable objects as references, so function calls make no copy.
12
>>> def f(x):
... print(id(x))
...
>>> id(a) # id is a unique identifier of an object
148293216
>>> f(a)
148293216

13. Copies and views (3)
u View or Shallow Copy
• Different array objects can share the same data. The view method creates a
new array object that looks at the same data.
13
a
a.view
c
c.viewc.base
a.base
ndarray
object1
ndarray
object1’
>>> c = a.view()
>>> c is a
False
>>> c.base is a
True
>>> c.flags.owndata
False
>>>
>>> c.shape = 2,6
>>> a.shape
(3, 4)
>>> c[0,4] = 1234
>>> a
array([[ 0, 1, 2, 3],
[1234, 5, 6, 7],
[ 8, 9, 10, 11]])
data
0 1 2 3
4 5 6 7
8 9 10 11
0 1 2 3 4 5
6 7 8 9 10 11
a c

14. Copies and views (4)
u View or Shallow Copy
• Different array objects can share the same data. The view method creates a
new array object that looks at the same data.
14
a
a.view
c
c.viewc.base
a.base
ndarray
object1
ndarray
object1’
ndarray.flags.owndata
• The array owns the memory it uses
or borrows it from another object.
data
>>> c = a.view()
>>> c is a
False
>>> c.base is a
True
>>> c.flags.owndata
False
>>>
>>> c.shape = 2,6
>>> a.shape
(3, 4)
>>> c[0,4] = 1234
>>> a
array([[ 0, 1, 2, 3],
[1234, 5, 6, 7],
[ 8, 9, 10, 11]])

15. Copies and views (5)
u View or Shallow Copy
• Different array objects can share the same data. The view method creates a
new array object that looks at the same data.
15
>>> c = a.view()
>>> c is a
False
>>> c.base is a
True
>>> c.flags.owndata
False
>>>
>>> c.shape = 2,6
>>> a.shape
(3, 4)
>>> c[0,4] = 1234
>>> a
array([[ 0, 1, 2, 3],
[1234, 5, 6, 7],
[ 8, 9, 10, 11]])
a
a.view
c
c.viewc.base
a.base
ndarray
object1
ndarray
object1’
data
0 1 2 3
4 5 6 7
8 9 10 11
0 1 2 3 4 5
6 7 8 9 10 11
a c

16. Copies and views (6)
u View or Shallow Copy
• Slicing an array returns a view of it:
16
>>> a
array([[ 0, 1, 2, 3],
[1234, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> s = a[ : , 1:3]
>>> s[:] = 10
>>> a
array([[ 0, 10, 10, 3],
[1234, 10, 10, 7],
[ 8, 10, 10, 11]])

17. Copies and views (7)
u Deep Copy
• The copy method makes a complete copy of the array and its data.
17
>>> d = a.copy()
>>> d is a
False
>>> d.base is a
False
>>> d[0,0] = 9999
>>> a
array([[ 0, 10, 10, 3],
[1234, 10, 10, 7],
[ 8, 10, 10, 11]])
a
a.shape
d
d.shape
ndarray
object
ndarray
object
# a new array object with new data is created
# d doesn't share anything with a