NumPy random.randn(): Standard Normal Distribution & Array Shapes
The numpy.random.randn() function generates random floating-point samples drawn from the standard normal (Gaussian) distribution with a mean of μ = 0 and standard deviation of σ = 1 (often written as N(0, 1)).
Parameter Note: Like its companion numpy.random.rand(), randn() accepts array dimensions as separate positional arguments (e.g. np.random.randn(3, 4)) rather than a shape tuple. For uniform numbers over [0, 1), see rand() and random_sample(). For discrete integers, see randint(). For modern reproducible code, explore the recommended default_rng() Generator interface.
1. Syntax & Parameters 🔝
The formal syntax for numpy.random.randn() is:
# Formal signature
numpy.random.randn(d0, d1, ..., dn)| Argument | Type | Default | Description & Operational Rule |
|---|---|---|---|
d0, d1, ..., dn |
int (optional) |
None | The dimensions of the returned array. If no arguments are passed, a single Python float is returned. |
| Return | ndarray or float |
N/A | A (d0, d1, ..., dn) shaped array of floating-point values from the standard normal distribution, or a single float if no dimensions are supplied. |
2. Example Without Dimension (Single Float) 🔝
Calling np.random.randn() with no arguments returns a scalar float drawn from standard normal distribution N(0, 1):
import numpy as np
# Set seed for reproducible tutorial verification
np.random.seed(42)
my_data = np.random.randn()
print("Scalar value:", my_data)
print("Data type: ", type(my_data))Terminal Output:
Scalar value: 0.4967141530112327
Data type: <class 'float'>3. Generating 1D Vectors 🔝
Supplying a single integer generates a 1D ndarray containing standard normal floats:
import numpy as np
np.random.seed(10)
my_vector = np.random.randn(4)
print("1D Vector:\n", my_vector)
print("Shape: ", my_vector.shape)
print("Dtype: ", my_vector.dtype)Terminal Output:
1D Vector:
[ 1.3315865 0.71527897 -1.54540029 -0.00838385]
Shape: (4,)
Dtype: float644. Generating 2D Matrices 🔝
Pass two integer arguments (rows, columns) to construct a 2D matrix:
import numpy as np
np.random.seed(100)
my_matrix = np.random.randn(4, 3)
print("2D Matrix (4 rows, 3 columns):\n", my_matrix)
print("Matrix Dimensions (ndim):", my_matrix.ndim)Terminal Output:
2D Matrix (4 rows, 3 columns):
[[-1.74976547 0.3426804 1.1530358 ]
[-0.25243603 0.98132079 0.51421884]
[ 0.22117967 -1.07004333 -0.18949583]
[ 0.25500144 -0.45802699 0.43516349]]
Matrix Dimensions (ndim): 25. Generating Multidimensional (4D / ND) Tensors 🔝
Multiple dimension arguments produce higher-dimensional tensors useful in machine learning and Monte Carlo simulations:
import numpy as np
np.random.seed(7)
tensor_4d = np.random.randn(1, 2, 3, 4)
print("4D Tensor shape:", tensor_4d.shape)
print("Total elements: ", tensor_4d.size)Terminal Output:
4D Tensor shape: (1, 2, 3, 4)
Total elements: 246. Transforming to Arbitrary Normal Distributions: N(μ, σ2) 🔝
Because randn() draws from the standard normal distribution (μ = 0, σ = 1), samples can be transformed to any normal distribution with mean μ and standard deviation σ using the linear formula:
Sample = μ + σ * np.random.randn(...)
import numpy as np
# Target: Mean = 50.0, Standard Deviation = 5.0
mu = 50.0
sigma = 5.0
np.random.seed(42)
samples = mu + sigma * np.random.randn(10000)
print("Empirical Mean: ", np.mean(samples))
print("Empirical StdDev:", np.std(samples))Terminal Output:
Empirical Mean: 49.991873
Empirical StdDev: 4.9663267. Comparison: rand() vs. randn() vs. randint() 🔝
| Function | Distribution Type | Output Range | Input Arguments |
|---|---|---|---|
np.random.randn() |
Standard Normal (Gaussian) | (−∞, +∞), centered at 0 | Separate dimensions: d0, d1, ... |
np.random.rand() |
Continuous Uniform | [0.0, 1.0) | Separate dimensions: d0, d1, ... |
np.random.randint() |
Discrete Uniform Integers | [low, high) | Limits + size=tuple |
np.random.random_sample() |
Continuous Uniform | [0.0, 1.0) | Shape tuple: size=(r, c) |
8. Recommended Modern Alternative: default_rng().normal() 🔝
NumPy documentation recommends the modern Generator interface (introduced in NumPy 1.17) for new code. It avoids global mutable seed state and accepts a standard shape tuple:
import numpy as np
rng = np.random.default_rng(42)
# Direct specification of loc (mean), scale (std), and shape tuple
modern_samples = rng.normal(loc=0.0, scale=1.0, size=(3, 3))
print("Generated via default_rng().normal():\n", modern_samples)9. Common Developer Pitfalls 🔝
- Passing a tuple instead of unpacked integers:
np.random.randn((3, 4))raises aTypeError: 'tuple' object cannot be interpreted as an integer. Passnp.random.randn(3, 4). - Assuming positive values: Unlike
rand()which is strictly ≥ 0, approximately 50% ofrandn()values are negative. - Confusing variance with standard deviation: To scale by variance σ2, multiply by σ = √Var, not by σ2.
10. Interactive Practice Companion Notebook 🔝
Practice generating univariate normals, simulating multivariate Gaussian noise, scaling distributions, and running self-verifying unit assertions in our companion notebook:
Interactive Practice: Colab & GitHub
Launch the notebook directly in Google Colab or view the source notebook in GitHub:
View on GitHub
11. Frequently Asked Questions 🔝
randn() and rand() are legacy methods inspired by MATLAB syntax that accept dimensions as separate positional arguments (*args). Passing a tuple passes a single argument of type tuple, which cannot be converted to an integer dimension. Use np.random.randn(3, 4) or unpack with *shape.
numpy.random.seed(value) before generating numbers. For modern applications, create an independent generator instance with rng = numpy.random.default_rng(value) and use rng.normal(size=...).
Subhendu Mohapatra
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