#tools

Numpy¶

约 564 个字 119 行代码预计阅读时间 4 分钟

仍在探索！

向量 ¶

初始化 ¶

Python

# 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}")

Text Only

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 = [0.16054681 0.65264985 0.98302218 0.29864795], a shape = (4,), a data type = float64

Python

# 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}")

Text Only

np.arange(4.):     a = [0. 1. 2. 3.], a shape = (4,), a data type = float64
np.random.rand(4): a = [0.04467047 0.14854614 0.24949402 0.02417095], a shape = (4,), a data type = float64

Python

# 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}")

Text Only

np.array([5,4,3,2]):  a = [5 4 3 2],     a shape = (4,), a data type = int64
np.array([5.,4,3,2]): a = [5. 4. 3. 2.], a shape = (4,), a data type = float64

索引 ¶

Python

#vector indexing operations on 1-D vectors
a = np.arange(10)
print(a)

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

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

#indexs must be within the range of the vector or they will produce and error
try:
    c = a[10]
except Exception as e:
    print("The error message you'll see is:")
    print(e)

Text Only

[0 1 2 3 4 5 6 7 8 9]
a[2].shape: () a[2]  = 2, Accessing an element returns a scalar
a[-1] = 9
The error message you'll see is:
index 10 is out of bounds for axis 0 with size 10

切片 ¶

Python

#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)

Text Only

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]

一些操作 ¶

Python

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}")

Text Only

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]

Python

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

Text Only

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

Python

#try a mismatched vector operation
c = np.array([1, 2])
try:
    d = a + c
except Exception as e:
    print("The error message you'll see is:")
    print(e)

Text Only

The error message you'll see is:
operands could not be broadcast together with shapes (4,) (2,)

Python

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

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

Text Only

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

Python

# test 1-D
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} ")

Text Only

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 = ()

向量点乘和循环时间比较 ¶

Text Only

np.random.seed(1)
a = np.random.rand(10000000)  # very large arrays
b = np.random.rand(10000000)

tic = time.time()  # capture start time
c = np.dot(a, b)
toc = time.time()  # capture end time

print(f"np.dot(a, b) =  {c:.4f}")
print(f"Vectorized version duration: {1000*(toc-tic):.4f} ms ")

tic = time.time()  # capture start time
c = my_dot(a,b)
toc = time.time()  # capture end time

print(f"my_dot(a, b) =  {c:.4f}")
print(f"loop version duration: {1000*(toc-tic):.4f} ms ")

del(a);del(b)  #remove these big arrays from memory

矩阵 ¶

初始化 ¶

Python

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}")

Text Only

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

Python

# 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}")

索引 ¶

Python

# 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}")

Text Only

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.int64'> Accessing an element returns a scalar

a[2].shape:   (2,), a[2]   = [4 5], type(a[2])   = <class 'numpy.ndarray'>

关于 reshape
- 2 表示分割成二维向量
- -1 表示自动计算行数
- 这里 reshape(-1,2) 的效果和 reshape(3,2) 相同

切片 ¶

Python

#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")

Text Only

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