Implementation:Scikit learn Scikit learn ExtendedMath

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Linear Algebra, Numerical Computing
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete utility module for optimized mathematical operations provided by scikit-learn.

Description

The extmath module provides a collection of mathematical utility functions optimized for machine learning workloads. Key functions include safe_sparse_dot for matrix multiplication with sparse support, randomized_svd for truncated SVD via randomized methods, row_norms for efficient norm computation, softmax, stable_cumsum, and weighted_mode among others.

Usage

Use these functions when you need efficient mathematical operations that handle both dense and sparse matrices, or when you need randomized linear algebra for dimensionality reduction and matrix decomposition.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/utils/extmath.py

Signature

def squared_norm(x):
    ...

def row_norms(X, squared=False):
    ...

def fast_logdet(A):
    ...

def density(w):
    ...

def safe_sparse_dot(a, b, *, dense_output=False):
    ...

def randomized_svd(M, n_components, *, n_oversamples=10, n_iter="auto",
                   power_iteration_normalizer="auto", transpose="auto",
                   flip_sign=True, random_state="warn", svd_lapack_driver="gesdd"):
    ...

def softmax(X, copy=True):
    ...

def stable_cumsum(arr, axis=None, rtol=1e-05, atol=1e-08):
    ...

def weighted_mode(a, w, *, axis=0):
    ...

Import

from sklearn.utils.extmath import safe_sparse_dot, randomized_svd, softmax, row_norms

I/O Contract

Inputs

Name	Type	Required	Description
x	array-like	Yes	Input array for norm computation
a	array-like or sparse matrix	Yes	First matrix for dot product
b	array-like or sparse matrix	Yes	Second matrix for dot product
M	array-like or sparse matrix	Yes	Matrix to decompose (for randomized_svd)
n_components	int	Yes	Number of SVD components to compute
random_state	int or RandomState	No	Random state for reproducibility

Outputs

Name	Type	Description
result	ndarray	Result of the mathematical operation
U, Sigma, VT	ndarrays	SVD decomposition components (for randomized_svd)

Usage Examples

Basic Usage

import numpy as np
from sklearn.utils.extmath import safe_sparse_dot, randomized_svd, softmax

# Safe dot product (works with sparse and dense)
A = np.random.rand(100, 50)
B = np.random.rand(50, 30)
C = safe_sparse_dot(A, B)

# Randomized SVD
U, Sigma, VT = randomized_svd(A, n_components=5, random_state=42)

# Softmax
logits = np.array([[1.0, 2.0, 3.0]])
probs = softmax(logits)
print(probs.sum())  # 1.0

Related Pages

• Principle:Scikit_learn_Scikit_learn_Dimensionality_Reduction