2.7. Array Axis¶
2.7.1. Rationale¶
axisis an index ina.shapeColumns are always last
Figure 2.5. Visualizing Multi-Dimensional Arrays [NumpyCL19b]¶
2.7.2. Axis¶
New dimensions are added at the beginning of
shapeOld axes numbers are pushed to the right
One Dimensions:
a = np.array([1,2,3])
a.shape # (3,)
a.ndim # 1
axis=0 # columns
axis=-0 # columns
Two Dimensions:
a = np.array([[1,2,3],
[4,5,6]])
a.shape # (2,3)
a.ndim # 2
axis=0 # rows
axis=1 # columns
axis=-0 # rows
axis=-1 # columns
Three Dimensions:
a = np.array([[[1,2,3],
[4,5,6]],
[[11,22,33],
[44,55,66]]])
a.shape # (2,2,3)
a.ndim # 3
axis=0 # depth
axis=1 # rows
axis=2 # columns
axis=-0 # depth
axis=-1 # columns
axis=-2 # rows
Four Dimensions:
a = np.array([[[[1,2,3],
[4,5,6]],
[[11,22,33],
[44,55,66]]],
[[[1,2,3],
[4,5,6]],
[[11,22,33],
[44,55,66]]]])
a.shape # (2,2,3)
a.ndim # 3
axis=0 # depth
axis=1 # rows
axis=2 # columns
axis=-0 # depth
axis=-1 # columns
axis=-2 # rows
2.7.3. Take¶
One Dimensional:
import numpy
a = np.array([1, 2, 3])
a.shape # (3,)
a[0] # 1
a[1] # 2
a[2] # 3
a.take(0, axis=0) # 1
a.take(1, axis=0) # 2
a.take(2, axis=0) # 3
a.take(0, axis=-1) # 1
a.take(1, axis=-1) # 2
a.take(2, axis=-1) # 3
a[:, 1] # IndexError: too many indices for array
a.take(0, axis=1) # AxisError: axis 1 is out of bounds for array of dimension 1
Two Dimensional - Rows:
import numpy
a = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
a.shape # (3, 3)
a[0, :] # array([1, 2, 3])
a[1, :] # array([4, 5, 6])
a[2, :] # array([7, 8, 9])
a.take(0, axis=0) # array([1, 2, 3])
a.take(1, axis=0) # array([4, 5, 6])
a.take(2, axis=0) # array([7, 8, 9])
Two Dimensional - Columns:
import numpy
a = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
a.shape # (3, 3)
a[:, 0] # array([1, 4, 7])
a[:, 1] # array([2, 5, 8])
a[:, 2] # array([3, 6, 9])
a.take(0, axis=1) # array([1, 4, 7])
a.take(1, axis=1) # array([2, 5, 8])
a.take(2, axis=1) # array([3, 6, 9])
a.take(0, axis=-1) # array([1, 4, 7])
a.take(1, axis=-1) # array([2, 5, 8])
a.take(2, axis=-1) # array([3, 6, 9])
Three Dimensional - Depth:
import numpy
a = np.array([[[ 1, 2, 3],
[ 4, 5, 6],
[ 5, 6, 7]],
[[11, 22, 33],
[44, 55, 66],
[77, 88, 99]]])
a.shape
# (2, 3, 3)
a[0,:,:]
# array([[1, 2, 3],
# [4, 5, 6],
# [5, 6, 7]])
a[1,:,:]
# array([[11, 22, 33],
# [44, 55, 66],
# [77, 88, 99]])
a[2,:,:]
# Traceback (most recent call last):
# IndexError: index 2 is out of bounds for axis 0 with size 2
a.take(0, axis=0)
# array([[1, 2, 3],
# [4, 5, 6],
# [5, 6, 7]])
a.take(1, axis=0)
# array([[11, 22, 33],
# [44, 55, 66],
# [77, 88, 99]])
a.take(2, axis=0)
# Traceback (most recent call last):
# IndexError: index 2 is out of bounds for size 2
Three Dimensional - Rows:
import numpy
a = np.array([[[ 1, 2, 3],
[ 4, 5, 6],
[ 5, 6, 7]],
[[11, 22, 33],
[44, 55, 66],
[77, 88, 99]]])
a.shape
# (2, 3, 3)
a[:,0,:]
# array([[ 1, 2, 3],
# [11, 22, 33]])
a[:,1,:]
# array([[ 4, 5, 6],
# [44, 55, 66]])
a[:,2,:]
# array([[ 5, 6, 7],
# [77, 88, 99]])
a.take(0, axis=1)
# array([[ 1, 2, 3],
# [11, 22, 33]])
a.take(1, axis=1)
# array([[ 4, 5, 6],
# [44, 55, 66]])
a.take(2, axis=1)
# array([[ 5, 6, 7],
# [77, 88, 99]])
Three Dimensional - Columns:
import numpy
a = np.array([[[ 1, 2, 3],
[ 4, 5, 6],
[ 5, 6, 7]],
[[11, 22, 33],
[44, 55, 66],
[77, 88, 99]]])
a.shape
# (2, 3, 3)
a[:,:,0]
# array([[ 1, 4, 5],
# [11, 44, 77]])
a[:,:,1]
# array([[ 2, 5, 6],
# [22, 55, 88]])
a[:,:,2]
# array([[ 3, 6, 7],
# [33, 66, 99]])
a.take(0, axis=2)
# array([[ 1, 4, 5],
# [11, 44, 77]])
a.take(1, axis=2)
# array([[ 2, 5, 6],
# [22, 55, 88]])
a.take(2, axis=2)
# array([[ 3, 6, 7],
# [33, 66, 99]])
a.take(0, axis=-1)
# array([[ 1, 4, 5],
# [11, 44, 77]])
a.take(1, axis=-1)
# array([[ 2, 5, 6],
# [22, 55, 88]])
a.take(2, axis=-1)
# array([[ 3, 6, 7],
# [33, 66, 99]])