VI. NumPy Random Sampling (随机抽样)#

numpy.random generates pseudo-random numbers (伪随机数) following various distributions (分布). Always set a seed (随机种子) for reproducible experiments.

1. Setting the Seed (设置随机种子)#

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import numpy as np
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np.random.seed(42)   # All subsequent random calls are reproducible

Note: The modern recommended way is rng = np.random.default_rng(42), then use rng.random() etc. (NumPy 1.17+).

2. `random.rand()` — Uniform Distribution (均匀分布)#

Core idea: Floats uniformly distributed in [0, 1).

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np.random.rand(3)        # 1-D: 3 random floats
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np.random.rand(2, 4)     # 2-D: shape (2, 4)
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# Scale to [a, b]: a + (b - a) * rand()
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np.random.rand(5) * 10   # uniform in [0, 10)

3. `random.randn()` — Standard Normal Distribution (标准正态分布)#

Core idea: Floats from a distribution with mean=0, std=1 (Bell curve / 钟形曲线).

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np.random.randn(4)         # 1-D: 4 values near 0
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np.random.randn(3, 3)      # 2-D: 3×3 matrix
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# Scale to mean=μ, std=σ
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mu, sigma = 5, 2
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mu + sigma * np.random.randn(100)

4. `random.randint()` — Random Integers (随机整数)#

Core idea: Random integers in [low, high) — high is excluded.

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np.random.randint(0, 10)           # single integer, 0–9
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np.random.randint(1, 7, size=5)    # five dice rolls
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np.random.randint(0, 100, size=(3, 4))  # 3×4 matrix

5. `random.choice()` — Sample from Array (从数组中抽取)#

Core idea: Randomly pick elements from a 1-D array — with or without replacement (有/无放回).

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arr = np.array([10, 20, 30, 40, 50])
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np.random.choice(arr, 3)                # 3 samples WITH replacement
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np.random.choice(arr, 3, replace=False) # 3 samples WITHOUT replacement
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# Weighted sampling (带权重抽取)
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np.random.choice(arr, 3, p=[0.1, 0.2, 0.4, 0.2, 0.1])

6. `random.normal()` — Custom Normal Distribution (自定义正态分布)#

Core idea: Generate samples from a normal distribution with any mean (均值) and standard deviation (标准差).

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np.random.normal(loc=0, scale=1, size=5)   # = randn(5)
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np.random.normal(loc=170, scale=10, size=1000)  # heights in cm

7. Other Useful Distributions (其他常用分布)#

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np.random.uniform(low=1, high=6, size=10)   # Continuous uniform (连续均匀)
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np.random.binomial(n=10, p=0.5, size=5)     # Binomial (二项分布)
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np.random.poisson(lam=3, size=10)           # Poisson (泊松分布)
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np.random.shuffle(arr)                       # Shuffle in-place (原地打乱)
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np.random.permutation(arr)                  # Shuffled copy (打乱副本)

8. Quick Comparison Table#

Function (函数)	Distribution	Output Range
`rand(*shape)`	Uniform	[0, 1) floats
`randn(*shape)`	Standard Normal	≈ [-3, 3] floats
`randint(lo, hi, size)`	Discrete Uniform	[lo, hi) integers
`choice(a, n)`	Custom array	Elements of `a`
`normal(μ, σ, size)`	Normal	Floats near μ
`uniform(lo, hi, size)`	Continuous Uniform	[lo, hi) floats

💡 One-line Takeaway
Always call np.random.seed(n) at the start of experiments for reproducibility, and use replace=False in choice() when sampling without repetition.

VI. NumPy Random Sampling (随机抽样)#

1. Setting the Seed (设置随机种子)#

2. random.rand() — Uniform Distribution (均匀分布)#

3. random.randn() — Standard Normal Distribution (标准正态分布)#

4. random.randint() — Random Integers (随机整数)#

5. random.choice() — Sample from Array (从数组中抽取)#

6. random.normal() — Custom Normal Distribution (自定义正态分布)#