跳轉到

17.Numpy

axis=0 列 axis=1 行

# one axis
[1, 3, 5] # 3 elements, it has a length of 3.

# 2 axes
[[ 1, 3, 5],
[ 2, 4, 6]] # The first axis has a length of 2,
# the second axis has a length of 3.

Create ndarray

import numpy as np
# create 1 axis array
x = np.arange(3) # [0, 1, 2]
print(type(x)) # <class 'numpy.ndarray'>
# check if ndarray type
isinstance(x, np.ndarray) # True
# be explicitly specified type
y = np.arange(3, dtype='float64') # [ 0. 1. 2.]

import numpy as np
existed_list = [18, 15, 21, 10, 88, 76, 29, 20]
np_array = np.array(existed_list)
print(np_array) # [18 15 21 10 88 76 29 20]

Attributes of ndarray

import numpy as np
x = np.arange(3) # [0, 1, 2]
# ndim - the number of axes (dimensions) of the array.
print(x.ndim) # 1 dim
# shape - the dimensions of the array.
print(x.shape) # (3, )
# size - the total number of elements of the array.
print(x.size) # 3
# dtype - the type of the elements in the array.
print(x.dtype) # int64

Axes reshape

x = np.arange(6)
print(x) # [0 1 2 3 4 5]
new_shape = x.reshape(2, 3)
print(new_shape) 
# [[0 1 2]
# [3 4 5]]

# equivalently
new_shape = np.reshape(x, (2, 3))
# also can be one line to create and reshpae
y = np.arange(6).reshape(2, 3)

Initial placeholder content

# np.zeros - full of zeros
np.zeros(3) # array([ 0., 0., 0.])
np.zeros((2, 3)) # array([[ 0., 0., 0.],
# [ 0., 0., 0.]])
# np.ones - full of ones
np.ones((2,3)) # array([[ 1., 1., 1.],
# [ 1., 1., 1.]])
# np.identity - a square array with ones on the main diagonal
np.identity(3) # array([[ 1., 0., 0.],
# [ 0., 1., 0.],
# [ 0., 0., 1.]])

Array Index

import numpy as np
# 1-D array
x = np.arange(6) # array([0, 1, 2, 3, 4, 5])
x[2] # 2
x[-2] # 4
# 2-D array
x = np.arange(6).reshape(2, 3) #[[0, 1, 2],
# [3, 4, 5]])
x[0, 2] # 2
x[1, -1] # 5

Array Slice & Stride (1-D array)

import numpy as np
x = np.arange(6) # array([0, 1, 2, 3, 4, 5])
x[1:5] # [1, 2, 3, 4]
x[:2] # [0, 1]
x[1:5:2] # [1, 3]

Array Slice & Stride (2-D array)

import numpy as np
x = np.arange(6).reshape(2, 3) #[[0, 1, 2],
# [3, 4, 5]])
x[0, 0:2] # [0, 1]
x[:, 1:] # [[1, 2],
# [4, 5]]
x[::1, ::2] # [[0, 2],
# [3, 5]]

Boolean / Mask Index

import numpy as np
x = np.arange(6) # array([0, 1, 2, 3, 4, 5])
condition = x<3
x[condition] # [0, 1, 2]
x[condition] = 0
x # [0, 0, 0, 3, 4, 5]

Concatenate

import numpy as np
a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([[7, 8, 9]])
np.concatenate((a, b), axis=0) # [[1, 2, 3],
# [4, 5, 6],
# [7, 8, 9]]

c = [[0], [0]]
np.concatenate((a, c), axis=1) # [[1, 2, 3, 0],
# [4, 5, 6, 0]]

Basic Operations

可以做一個或兩個array的數學運算

import numpy as np
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6], [7, 8]])
print(a + b) # array([[6, 8], [10, 12]])
print(a - b) # array([[-4, -4], [-4, -4]])
print(a * b) # array([[5, 12], [21, 32]])
print(a / b) # array([[0.2, 0.33333333], [0.42857143, 0.5]]
print(a - 1) # array([[0, 1], [2, 3]])
print(a * 2) # array([[2, 4], [6, 8]])

Basic Linear Algebra

  • 轉置矩陣:m * n 矩陣在向量空間上轉置為 n * m 矩陣
  • 逆矩陣:n * n 矩陣 A 存在一個 n * n 矩陣 B,使得 AB = BA = I
import numpy as np
a = np.array([[0, 1],[2, 3]])

# 轉置矩陣
print(a.T) 
#[[0, 2],
# [1, 3]]

# 逆矩陣
inverse = np.linalg.inv(a)
print(inverse)
# [[-1.5, 0.5]
#   [1, 0]]

# 內積
print(np.dot(a, inverse))
# [[ 1. 0.]
#  [ 0. 1.]]

Test

Q1. Create a vector with values ranging from 10 to 49 by np.arange
Q2. Reverse a vector (first element becomes last)
Q3. Create a 3x3x3 array with random values by np.random.random
Q4. Create a 10x10 array with random values and find the minimum and maximum values
by np.min, np.max
Q5. Add a border (filled with 0's) around an 3 * 3 matrix with 1 by np.pad
Q6. Normalize a 5x5 random matrix by divide max number

#Q1
arr=np.arange(10,50)
print(arr)
#Q2
arr=np.arange(10,50)
arr=arr[::-1]
print(arr)
#Q3
arr=np.random.random((3, 3, 3))
print(arr)
#Q4
arr=np.random.random((10,10))
print(arr)
np.min(arr)
np.max(arr)
#Q5
arr=np.ones((3,3))
arr=np.pad(arr,pad_width=1, mode='constant', constant_values=0)
print(arr)
#Q6
arr=np.random.random((5,5))
print(arr)
max=np.max(arr)
arr=arr/max
print(arr)

Q7. Given a 1D array, negate all elements which are between 3 and 8, in place.
Q8. Extract from the array np.array([3,4,6,10,24,89,45,43,46,99,100]) with Boolean
masking all the number:
(1) which are not divisible by 3
(2) which are divisible by 5
(3) which are divisible by 3 and 5
Q9. Create random vector of size 10 and replace the maximum value by 0 (np.argmax)
Q10. Create a 5x5 matrix with row values ranging from 0 to 4

#Q7
arr=np.arange(11)
arr[(3<=arr)&(8>=arr)]*=-1
print(arr)
#Q8
arr=np.array([3,4,6,10,24,89,45,43,46,99,100])
arr1=arr[arr%3!=0]
print(arr1)
arr2=arr[arr%5==0]
print(arr2)
arr3=arr[(arr%3==0)&(arr%5==0)]
print(arr3)
#Q9
arr=np.random.random(10)
print(arr)
arr[arr.argmax()]=0
print(arr)
#Q10
Z = np.zeros((5, 5))
Z += np.arange(5)
print(Z)

數據拼接

  1. 新增資料
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6]])
np.concatenate((a, b), axis=0)

array([[1, 2],
       [3, 4],
       [5, 6]])
  1. 新增欄位
a = np.array([[1, 2], [3, 4]])
b = np.array([[5, 6]])
np.concatenate((a,b.T),axis = 1)

array([[1, 2, 5],
       [3, 4, 6]])