修心问道

Machine Learning for Trading--1-3 The Power of Numpy

发表于 分类于 ，
  • 创建一个numpy阵列–Creating NumPy Arrays
  • 生成随机数–Generating Random Numbers
  • 阵列属性–Array Attributes
  • 阵列运算–Operations on Arrays
  • 最大值的index–Locate maximum value
  • 使用time函数–Using time function
  • 获取阵列中的元素–Accessing Array Elements
  • 数学运算-Arithmetic Operations

创建一个numpy阵列–Creating NumPy Arrays

  • 一维阵列–np.array([2, 3, 4])
  • 二维阵列–(np.array([(2, 3, 4), (5, 6, 7)])
  • 空阵列–1D: np.empty(5), 2D: np.empty((5,4)), 3D: np.empty((5,4,3))
  • 单位阵列–np.ones((5, 4))
  • 指定数据类型–np.ones((5, 4), dtype=np.int_)

Example:

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import numpy as np

def test_run():
    # List to 1D array
    print (np.array([2, 3, 4]))
    
    # List of tuples to 2D array
    print (np.array([(2, 3, 4), (5, 6, 7)]))
    
    # Empty array
    print (np.empty(5))
    print (np.empty((5,4)))
    print (np.empty((5,4,3)))
    
    # Array of 1s
    print (np.ones((5, 4)))
    
    # Specifying the datatype
    print (np.ones((5, 4), dtype=np.int_))
    
    
if __name__ == "__main__":
    test_run()

生成随机数–Generating Random Numbers

  • 生成0和1之间的随机数–np.random.random((5, 4))或者np.random.rand(5, 4)
  • 生成随机数并且符合正态分布–np.random.normal(50, 10, size=(2, 3)) 注：50为平均值，10为方差
  • 生成0到10之间随机的整数–np.random.randint(1) 或者np.random.randint(0, 10)
  • 生成多个0到10之间的随机数–1D: np.random.randint(0, 10, size=5), 2D: np.random.randint(0, 10, size=(2, 3))

Example:

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def test_run():
    # Generate an array full of random numbers, uniformly samples from [0.0, 1.0)
    print (np.random.random((5, 4))) # pass in a size tuple
    
    # Generate an array full of random numbers, uniformly samples from [0.0, 1.0)
    print (np.random.rand(5, 4)) # function arguments (not a tuple)
    
    # Sample numbers from a Gaussian (normal) distribution
    print (np.random.normal(size=(2, 3))) # "standard normal" (mean = 0, s.d. = 1)
    
    # Sample numbers from a Gaussian (normal) distribution
    print (np.random.normal(50, 10, size=(2, 3))) # change mean to 50 and s.d. to 10
    
    # Random integers
    print (np.random.randint(1)) # a single integer in [0, 10)
    print (np.random.randint(0, 10)) # same as above, specifying [low, high) explicit
    print (np.random.randint(0, 10, size=5)) # 5 random integers as a 1D array
    print (np.random.randint(0, 10, size=(2, 3))) # 2x3 array of random integers
    
if __name__ == "__main__":
    test_run()

阵列属性–Array Attributes

  • 阵列的行列数–a.shape, 行数：a.shape[0]， 列数：a.shape[1]
  • 阵列维度–len(a.shape)
  • 阵列元素数–a.size
  • 数据类型–a.dtype

Example:

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import numpy as np

def test_run():

    a = np.random.random((5, 4))  # 5x4 array of random numbers
    print (a)
    print (a.shape)
    
    print (a.shape[0])  # number of rows
    print (a.shape[1])  # number of columns
    
    print (len(a.shape))  # returns 2 --> 2D
    print (a.size)  # returns number of rows * number of columns --> 20 total elements in the array
    print (a.dtype)  # check the date type

    
if __name__ == "__main__":
    test_run()

阵列运算–Operations on Arrays

  • 求和–a.sum()
  • 最小值–a.min()
  • 最大值–a.max()
  • 平均值–a.mean()

Example:

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import numpy as np

def test_run():

    np.random.seed(693)  # seed the random number generator
    a = np.random.randint(0, 10, size=(5, 4)) # 5x4 random integers in [0, 10)
    print ("Array:\n", a)
    
    # Sum of all elements
    print ("Sum of all elements:", a.sum())
    
    # Iterate over rows, to compute sum of each columns
    print ("Sum of each column:\n", a.sum(axis=0))
    
    # Iterate over columns to compute sume of each rows
    print ("Sum of each row:\n", a.sum(axis=1))
    
    # Statistics: min, max, mean (across rows, cols, and overall)
    print ("Minimum of each colulmn:\n", a.min(axis=0))
    print ("Maximum of each row:\n", a.max(axis=1))
    print ("Mean of all elements:", a.mean()) # leave out axis arg.
    
if __name__ == "__main__":
    test_run()

最大值的index–Locate maximum value

  • 返回最大值的index–a.argmax()

Example:

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import numpy as np

def get_max_index(a):
    """Return the index of the maximum value in given 1D array."""
    # Quiz: Your code here
    return np.argmax(a)

def test_run():
    a = np.array([9, 6, 2, 3, 12, 14, 7, 10], dtype=np.int32)  # 32-bit integer array
    print( "Array:", a)
    
    # Find the maximum and its index in array
    print ("Maximum value:", a.max())
    print ("Index of max.:", get_max_index(a))
    
if __name__ == "__main__":
    test_run()

使用time函数–Using time function

time函数–time.time()

Example 1:

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import numpy as np
import time 
    
def test_run():
    t1 = time.time()
    print ("ML4T")
    t2 = time.time()
    print ("The time taken by print statement is ", t2 - t1, " seconds")
    
if __name__ == "__main__":
    test_run()

Example 2:

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import numpy as np
from time import time


def how_long(func, *args):
    """Execute function with given arguments, and measure execution time."""
    t0 = time()
    result = func(*args) # all argument are passed in as-is
    t1 = time()
    return result, t1 - t0

def manual_mean(arr):
    """Compute mean (average) of all elements in the given 2D array."""
    sum = 0
    for i in range(0, arr.shape[0]):
        for j in range(0, arr.shape[1]):
            sum = sum + arr[i, j]
    return sum / arr.size

def numpy_mean(arr):
    """Compute mean(average) using Numpy"""
    return arr.mean()

def test_run():
    """Function called by Test Run."""
    nd1 = np.random.random((1000, 10000)) # use a sufficiently large array

    # Time the two functions, retrieving results and execution times
    res_manual, t_manual = how_long(manual_mean, nd1)
    res_numpy, t_numpy = how_long(numpy_mean, nd1)
    print ("Manual: {:.6f} ({:.3f} secs.) vs. Numpy: {:.6f} ({:.3f} secs.)".format(res_manual, t_manual, res_numpy, t_numpy))

    # Make sure both give us the same answer (upto some precision)
    assert abs(res_manual - res_numpy) <= 10e-6, "Results aren't equal!"

    # Compute speedup
    speedup = t_manual / t_numpy
    print ("Numpy mean is", speedup, "times faster than manual for loops.")


if __name__ == "__main__":
    test_run()

获取阵列中的元素–Accessing Array Elements

  • 获取特定元素–a[3, 2]
  • 获取特定范围内的元素–a[0, 1:3], a[:, 0:3:2]
  • 使用包含指针的list来获取元素–indices = np.array([1,2,3,3]) –> a[indices]
  • 使用mask对数据进行处理—-a[a<mean]

Example 1:

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import numpy as np

def test_run():
    a = np.random.rand(5, 4)
    print ("array:\n", a)

    # Accessing element at position (3, 2)
    element = a[3, 2]
    print (element)

    # Element in defined range
    print (a[0, 1:3])

    # Top-left corner
    print (a[0:2, 0:2])

    # Slicing
    # Note: Slice n:m:t specifies a range that starts n, and stops before m, in
    print( a[:, 0:3:2]) # will select columns 0, 2 for every row

    # Assigning a value to a particular location
    a[0, 0] = 1
    print ("\nModified (replaced one element):\n", a)

    # Assigning a single value to an entire row
    a[0,:] = 2
    print ("\nModified (replaced a row with a single value):\n", a)

    # Assigning a list to a column in an array
    a[:, 3] = [1, 2, 3, 4, 5]
    print ("\nModified (replaced a column with a list):\n", a)

if __name__ == "__main__":
    test_run()

Example 2:

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import numpy as np

def test_run():
    a = np.random.rand(5)
    
    # accessing using list of indices
    indices = np.array([1,2,3,3])
    print (a[indices])
    
    a = np.array([(20,25,10,23,26,32,10,5,0),(0,2,50,20,0,1,28,5,0)])
    print (a)
    
    # calculating mean
    mean = a.mean()
    print (mean)
    
    # masking
    print (a[a<mean])
    
    # masking2
    a[a<mean]= mean
    print (a)

if __name__ == "__main__":
    test_run()

数学运算-Arithmetic Operations

Example:

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import numpy as np

def test_run():
    a = np.array([(1, 2, 3, 4, 5), (10, 20, 30, 40, 50)])
    print ("Original array a:\n", a)
    
    # Multiple a by 2
    print ("\nMultiply a by 2:\n", 2 * a)
    
    # Divide a by 2
    print ("\nDivide a by 2:\n", a / 2)
    
    # Divide a by 2
    print ("\nDivide a by 2:\n", a / 2.0)
    
    b = np.array([(100, 200, 300, 400, 500), (1, 2, 3, 4, 5)])
    print ("\nOriginal array b:\n", b)
    
    # Add the two arrays
    print ("\nAdd a + b:\n", a + b)
    
    # Multiply a and b
    print ("\nMultiply a and b:\n", a * b)
    
    # Divide a by b
    print ("\nDivide a by b:\n", a / b)
    
if __name__ == "__main__":
    test_run()
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