python numpy

• Example of exis
  • one axis

     [1, 3, 5]
    

  • 2 axis

     [[1, 3, 5],
      [2, 4, 6]]
    

• create ndarray

   import numpy as np
  
   x = np.arange(3) # array([0, 1, 2])
  
   print(type(x)) # <class 'numpy.ndarray'>
  
   # check if ndarray type
   isinstance(x, np.ndarray)  # True
  
   # be excplicitly 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_arrary = np.array(existed_list)
  
   print(np_arrary) # [18 15 21 10 88 76 29 20]
  

• Attributes of ndarray

   import numpy as np
  
   x = np.arange(3)
  
   # ndim - the number of axes (dimensions) of the array.
   print(x.ndim) # 3
  
   # 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_reshape)  # [[0 1 2]
                       #  [3 4 5]]
   # equivalently 
   new_shape = x.reshape(x, (2, 3))
  
   # 一行搞定!
   y = np.arange(6).reshape(2, 3)                           
  

• Initial placeholder content

  • zeros

     np.zeros(3)  # array([0., 0., 0.])
    
     np.zeros((2, 3))  # array([[0., 0., 0.], 
                       #        [0., 0., 0.]])
    

  • ones

     np.ones((2, 3)) # array([[1., 1., 1.],
                     #        [1., 1., 1.]])
    

  • 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

  • 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) # array([[0, 1, 2],
                                    #        [3, 4, 5]])
     x[0, 2] # 2
     x[1, -1] # 5
    

• Array Slice & Stride

  • 1-D array

     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]
    

  • 2-D array

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

• Boolean / Mask Index

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

• Why called mask ?

   x = np.arange(6)
   condition = x < 3
   condition
   array([ True,  True,  True, False, False, False])
     
   x[condition] = 0
   x            # array([0, 0, 0, 3, 4, 5])
  

• Concatenate 串接

   import numpy as np
  
   a = np.array([[1, 2, 3],[4, 5, 6]])
   b = np.array([[7, 8, 9]])
  
   # axis = 0 , 從 row 的方向串接 
   np.concatenate((a, b), axis = 0)
                                   #　array([[1, 2, 3],
                                   #         [4, 5, 6],
                                   #         [7, 8, 9]])
     
   # axis = 1, 從　column 的方向串接
   c = [[0], [0]]
   np.concatenate((a, c), axis = 1)
                                    # array([[1, 2, 3, 0],
                                    #        [4, 5, 6, 0]])　
  

• Basice Operations

   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) # array([[0, 2],
              #        [1, 3]])
  
     
   # 逆矩陣
   inverse = np.linalg.inv(a)
   print(inverse) # array([[-1.5,  0.5],
                  #        [ 1. ,  0. ]])
  
   # 內積
   np.dot(a, inverse)
                  # array([[1., 0.],
                  #        [0., 1.]])
  

• Vector Stacking

   import numpy as np
  
   a = np.array([[0, 1],
                 [2, 3]])
  
   b = np.array([[4, 5],
                [6, 7]])
  
   c = np.array([[8,  9],
                 [10, 11]])
  
   # vertical
   v = np.vstack((a, b, c))
   print(v.shape)   # (6, 2) 
   print(v)
           # array([[ 0,  1],
           #     [ 2,  3],
           #     [ 4,  5],
           #     [ 6,  7],
           #     [ 8,  9],
           #     [10, 11]])
  
   # horizontal
   h = np.hstack((a, b, c))
   print(h.shape)   # (2, 6)
   print(h)
           # array([[ 0,  1,  4,  5,  8,  9],   
           #        [ 2,  3,  6,  7, 10, 11]])
     
   # stack: axis 想要增加維度的方向
   h = np.stack([a, b, c], axis=0)
   print(s.shape)  # (3, 2, 2) 三個維度的　2*2 array
   print(s)
                 #   array([[[ 0,  1],
                 #        [ 2,  3]],
                 #
                 #       [[ 4,  5],
                 #        [ 6,  7]],
                 #
                 #       [[ 8,  9],
                 #        [10, 11]]])