NumPy std()

import numpy as np

# create an array
array1 = np.array([0, 1, 2, 3, 4, 5, 6, 7])

# calculate the standard deviation of the array
deviation = np.std(array1)

print(deviation)

# Output: 2.29128784747792

std() 语法

std() 的语法是

numpy.std(array, axis=None, dtype=None, out=None, ddof = 0, keepdims=<no value>, where=<no value>)

std() 参数

std() 方法接受以下参数

• array - 包含需要计算标准差的数字的数组 (可以是 array_like)
• axis (可选) - 计算标准差的轴或轴 (int 或 tuple of int)
• dtype (可选) - 用于计算标准差的数据类型 (datatype)
• out (可选) - 用于存储结果的输出数组 (ndarray)
• ddof (可选) - 自由度增量 (int)
• keepdims (可选) - 指定是否保留原始数组的形状 (bool)
• where (可选) - 过滤包含在标准差计算中的元素 (array of bool)

std() 返回值

std() 方法返回数组的标准差。

示例 1：计算 ndArray 的标准差

import numpy as np

# create an array
array1 = np.array([[[0, 1], [2, 3]],                   
                  	    [[4, 5],  [6, 7]]])

# find the standard deviation of entire array
deviation1 = np.std(array1)

# find the standard deviation across axis 0 (slice wise mean)
deviation2 = np.std(array1, 0)

# find the standard deviation across axis 0 and 1
deviation3 = np.std(array1, (0, 1))

print('\nStandard Deviation of the entire array:', deviation1)
print('\nStandard Deviation across axis 0:\n', deviation2)
print('\nStandard Deviation across axis 0 and 1', deviation3)

输出

Standard Deviation of the entire array: 2.29128784747792

Standard Deviation across axis 0:
[[2. 2.]
 [2. 2.]]

Standard Deviation across axis 0 and 1 [2.23606798 2.23606798]

当未指定 axis 参数时，np.std(array1) 计算整个数组的标准差。

沿 axis=0 计算标准差，得到的是每列的行标准差。

沿 axis=(0, 1) 计算标准差，同时计算行和列的标准差。结果数组是一个 **1**D 数组，包含整个 **2**D 数组的所有元素的标准差。

示例 2：指定 ndArray 的标准差数据类型

我们可以使用 dtype 参数指定输出数组的数据类型。

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# by default int is converted to float
result1 = np.std(array1)

# pass dtype to specify integer output
result2 = np.std(array1, dtype = int)

print('Float deviation:', result1)
print('Integer deviation:', result2)

输出

Float deviation: 1.707825127659933
Integer deviation: 1

注意： 使用较低精度的 dtype，例如 int，可能会导致精度损失。

示例 3：使用可选的 keepdims 参数

如果 keepdims 设置为 True，则保留原始数组的维度并将其传递给结果的标准差数组。

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# keepdims defaults to False
result1 = np.std(array1, axis = 0)

# pass keepdims as True
result2 = np.std(array1, axis = 0, keepdims = True)

print('Original Array Dimension:', array1.ndim)
print('Standard Deviation without keepdims:', result1, 'Dimensions', result1.ndim)
print('Standard Deviation with keepdims:', result2, 'Dimensions', result2.ndim)

输出

Original Array Dimension: 2
Standard Deviation without keepdims: [1.5 1.5 1.5] Dimensions 1
Standard Deviation with keepdims: [[1.5 1.5 1.5]] Dimensions 2

示例 4：使用 where() 计算过滤后数组的标准差

我们可以使用 where 参数过滤数组，并计算过滤后数组的标准差。

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# standard deviation of entire array
result1 = np.std(array1)

# standard deviation of only even elements
result2 = np.std(array1, where = (array1%2==0))

# standard deviation of  numbers greater than 3
result3 = np.std(array1, where = (array1 > 3))

print('Standard Deviation of entire array:', result1)
print('Standard Deviation of only even elements:', result2)
print('Standard Deviation of  numbers greater than 3:', result3)

输出

Standard Deviation of entire array: 1.707825127659933
Standard Deviation of only even elements: 1.632993161855452
Standard Deviation of  numbers greater than 3: 0.816496580927726

示例 5：使用 out 将结果存储在指定位置

out 参数允许指定一个输出数组，结果将存储在该数组中。

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# create an output array
output = np.zeros(3)

# compute standard deviation and store the result in the output array
np.std(array1, out = output, axis = 0)

print('Standard Deviation:', output)

输出

Standard Deviation: [1.5 1.5 1.5]

std = sqrt(sum((arr - arr.mean())**2) / (N - 1))

import numpy as np

array1 = np.array([2, 4, 6, 8, 10])

# calculate standard deviation using np.std()
deviation1 = np.std(array1)

# calculate standard deviation without using np.std()
mean = np.mean(array1)
diff_squared = (array1 - mean) ** 2
variance = np.mean(diff_squared)
deviation2 = np.sqrt(variance)

print('Standard Deviation with np.std():', deviation1)
print('Standard Deviation without np.std():', deviation2)

Standard Deviation with np.std(): 2.8284271247461903
Standard Deviation without np.std(): 2.8284271247461903

std = sqrt(sum((arr - arr.mean())**2) / (N - ddof))

import numpy as np

array1 = np.array([1, 2, 3, 4, 5])

# calculate standard deviation with the default ddof=0
deviation1 = np.std(array1)

# calculate standard deviation with ddof=1
deviation2 = np.std(array1, ddof=1)

print('Standard Deviation (default ddof=0):', deviation1)
print('Standard Deviation (ddof=1):', deviation2)

Standard Deviation (default ddof=0): 1.4142135623730951
Standard Deviation (ddof=1): 1.5811388300841898