[Python] NumPy 学习笔记

[yangruihan]

NumPy 学习笔记

相关资源

• NumPy Documentation including a basic introduction: NumPy.org
• A challenging feature topic: NumPy Broadcasting

创建 Vector

使用长度创建 Vector

# NumPy routines which allocate memory and fill arrays with value
a = np.zeros(4);                print(f"np.zeros(4) :   a = {a}, a shape = {a.shape}, a data type = {a.dtype}")
a = np.zeros((4,));             print(f"np.zeros(4,) :  a = {a}, a shape = {a.shape}, a data type = {a.dtype}")
a = np.random.random_sample(4); print(f"np.random.random_sample(4): a = {a}, a shape = {a.shape}, a data type = {a.dtype}")

# Output
# np.zeros(4) :   a = [0. 0. 0. 0.], a shape = (4,), a data type = float64
# np.zeros(4,) :  a = [0. 0. 0. 0.], a shape = (4,), a data type = float64
# np.random.random_sample(4): a = [0.43275971 0.78989577 0.39071854 0.3555822 ], a shape = (4,), a data type = float64

# NumPy routines which allocate memory and fill arrays with value but do not accept shape as input argument
a = np.arange(4.);              print(f"np.arange(4.):     a = {a}, a shape = {a.shape}, a data type = {a.dtype}")
a = np.random.rand(4);          print(f"np.random.rand(4): a = {a}, a shape = {a.shape}, a data type = {a.dtype}")

# Output
# np.arange(4.):     a = [0. 1. 2. 3.], a shape = (4,), a data type = float64
# np.random.rand(4): a = [0.11359497 0.04380214 0.84767525 0.06349301], a shape = (4,), a data type = float64

使用元素创建 Vector

# NumPy routines which allocate memory and fill with user specified values
a = np.array([5,4,3,2]);  print(f"np.array([5,4,3,2]):  a = {a},     a shape = {a.shape}, a data type = {a.dtype}")
a = np.array([5.,4,3,2]); print(f"np.array([5.,4,3,2]): a = {a}, a shape = {a.shape}, a data type = {a.dtype}")

# Output
# np.array([5,4,3,2]):  a = [5 4 3 2],     a shape = (4,), a data type = int32
# np.array([5.,4,3,2]): a = [5. 4. 3. 2.], a shape = (4,), a data type = float64

Vector 操作

索引访问

#vector indexing operations on 1-D vectors
a = np.arange(10)
print(a)
# [0 1 2 3 4 5 6 7 8 9]

#access an element
print(f"a[2].shape: {a[2].shape} a[2]  = {a[2]}, Accessing an element returns a scalar")
# a[2].shape: () a[2]  = 2, Accessing an element returns a scalar

# access the last element, negative indexes count from the end
print(f"a[-1] = {a[-1]}")
# a[-1] = 9

切片访问

#vector slicing operations
a = np.arange(10)
print(f"a         = {a}")

#access 5 consecutive elements (start:stop:step)
c = a[2:7:1];     print("a[2:7:1] = ", c)

# access 3 elements separated by two 
c = a[2:7:2];     print("a[2:7:2] = ", c)

# access all elements index 3 and above
c = a[3:];        print("a[3:]    = ", c)

# access all elements below index 3
c = a[:3];        print("a[:3]    = ", c)

# access all elements
c = a[:];         print("a[:]     = ", c)

# Output
# a         = [0 1 2 3 4 5 6 7 8 9]
# a[2:7:1] =  [2 3 4 5 6]
# a[2:7:2] =  [2 4 6]
# a[3:]    =  [3 4 5 6 7 8 9]
# a[:3]    =  [0 1 2]
# a[:]     =  [0 1 2 3 4 5 6 7 8 9]

对一整个 Vector 操作

a = np.array([1,2,3,4])
print(f"a             : {a}")
# negate elements of a
b = -a 
print(f"b = -a        : {b}")

# sum all elements of a, returns a scalar
b = np.sum(a) 
print(f"b = np.sum(a) : {b}")

b = np.mean(a)
print(f"b = np.mean(a): {b}")

b = a**2
print(f"b = a**2      : {b}")

# Output
# a             : [1 2 3 4]
# b = -a        : [-1 -2 -3 -4]
# b = np.sum(a) : 10
# b = np.mean(a): 2.5
# b = a**2      : [ 1  4  9 16]


a = np.array([ 1, 2, 3, 4])
b = np.array([-1,-2, 3, 4])
print(f"Binary operators work element wise: {a + b}")

# Output
# Binary operators work element wise: [0 0 6 8]


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

# multiply a by a scalar
b = 5 * a 
print(f"b = 5 * a : {b}")

# Output
# b = 5 * a : [ 5 10 15 20]


a = np.array([1, 2, 3, 4])
b = np.array([-1, 4, 3, 2])
c = np.dot(a, b)
print(f"NumPy 1-D np.dot(a, b) = {c}, np.dot(a, b).shape = {c.shape} ") 
c = np.dot(b, a)
print(f"NumPy 1-D np.dot(b, a) = {c}, np.dot(a, b).shape = {c.shape} ")

# Output
# NumPy 1-D np.dot(a, b) = 24, np.dot(a, b).shape = () 
# NumPy 1-D np.dot(b, a) = 24, np.dot(a, b).shape = () 

创建矩阵

a = np.zeros((1, 5))                                       
print(f"a shape = {a.shape}, a = {a}")                     

a = np.zeros((2, 1))                                                                   
print(f"a shape = {a.shape}, a = {a}") 

a = np.random.random_sample((1, 1))  
print(f"a shape = {a.shape}, a = {a}") 

# Output
# a shape = (1, 5), a = [[0. 0. 0. 0. 0.]]
# a shape = (2, 1), a = [[0.]
# [0.]]
# a shape = (1, 1), a = [[0.44236513]]


# NumPy routines which allocate memory and fill with user specified values
a = np.array([[5], [4], [3]]);   print(f" a shape = {a.shape}, np.array: a = {a}")
a = np.array([[5],   # One can also
              [4],   # separate values
              [3]]); #into separate rows
print(f" a shape = {a.shape}, np.array: a = {a}")

# Output
# a shape = (3, 1), np.array: a = [[5]
#  [4]
#  [3]]
#  a shape = (3, 1), np.array: a = [[5]
#  [4]
#  [3]]

矩阵操作

索引访问

#vector indexing operations on matrices
a = np.arange(6).reshape(-1, 2)   #reshape is a convenient way to create matrices
print(f"a.shape: {a.shape}, \na= {a}")

#access an element
print(f"\na[2,0].shape:   {a[2, 0].shape}, a[2,0] = {a[2, 0]},     type(a[2,0]) = {type(a[2, 0])} Accessing an element returns a scalar\n")

#access a row
print(f"a[2].shape:   {a[2].shape}, a[2]   = {a[2]}, type(a[2])   = {type(a[2])}")

# Output
# a.shape: (3, 2), 
# a= [[0 1]
#  [2 3]
#  [4 5]]
# 
# a[2,0].shape:   (), a[2,0] = 4,     type(a[2,0]) = <class 'numpy.int32'> Accessing an element returns a scalar
# 
# a[2].shape:   (2,), a[2]   = [4 5], type(a[2])   = <class 'numpy.ndarray'>

切片访问

#vector 2-D slicing operations
a = np.arange(20).reshape(-1, 10)
print(f"a = \n{a}")

#access 5 consecutive elements (start:stop:step)
print("a[0, 2:7:1] = ", a[0, 2:7:1], ",  a[0, 2:7:1].shape =", a[0, 2:7:1].shape, "a 1-D array")

#access 5 consecutive elements (start:stop:step) in two rows
print("a[:, 2:7:1] = \n", a[:, 2:7:1], ",  a[:, 2:7:1].shape =", a[:, 2:7:1].shape, "a 2-D array")

# access all elements
print("a[:,:] = \n", a[:,:], ",  a[:,:].shape =", a[:,:].shape)

# access all elements in one row (very common usage)
print("a[1,:] = ", a[1,:], ",  a[1,:].shape =", a[1,:].shape, "a 1-D array")
# same as
print("a[1]   = ", a[1],   ",  a[1].shape   =", a[1].shape, "a 1-D array")

# Output
# a = 
# [[ 0  1  2  3  4  5  6  7  8  9]
#  [10 11 12 13 14 15 16 17 18 19]]
# a[0, 2:7:1] =  [2 3 4 5 6] ,  a[0, 2:7:1].shape = (5,) a 1-D array
# a[:, 2:7:1] = 
#  [[ 2  3  4  5  6]
#  [12 13 14 15 16]] ,  a[:, 2:7:1].shape = (2, 5) a 2-D array
# a[:,:] = 
#  [[ 0  1  2  3  4  5  6  7  8  9]
#  [10 11 12 13 14 15 16 17 18 19]] ,  a[:,:].shape = (2, 10)
# a[1,:] =  [10 11 12 13 14 15 16 17 18 19] ,  a[1,:].shape = (10,) a 1-D array
# a[1]   =  [10 11 12 13 14 15 16 17 18 19] ,  a[1].shape   = (10,) a 1-D array