Module decomposition 

Decomposition and embedding algorithms and their shared linear algebra.

Each concrete algorithm lives in its own submodule (pca, factor_analysis, ica, tsne, umap, lle) and is re-exported here so callers name decomposition::<algo> without the submodule path. This module owns the dense linear-algebra primitives the family shares — mean-centering, the covariance matrix, a symmetric-eigenvalue Jacobi solver, and a reconstruction-error measure — operating on row-major f64 buffers.

Components and embedding axes are defined only up to sign (and, for ICA and spectral methods, up to ordering), so the equivalence suite compares the sign/order-invariant quantities — explained variance, reconstruction error, and trustworthiness — rather than raw component values.

Structs

FactorResult

Outcome of a factor-analysis fit.

IcaResult

Outcome of a FastICA fit.

PcaResult

Outcome of a PCA fit.

Functions

at

Reads entry (i, j) from a row-major n×n buffer (0.0 if out of range).

column_means

Computes the per-feature mean (centroid) of a row-major data matrix.

count_to_f64

Widens a usize count to f64 without an as cast.

covariance

Computes the dim×dim sample covariance matrix of centered (already mean-centered) using the unbiased n − 1 denominator, matching scikit-learn.

descending_order

Returns the eigenvalue indices in descending order of eigenvalue.

factor_analysis

Fits a k-factor model to data by SVD-based EM.

fast_ica

Separates the linear mixture mixed into n_components independent sources.

identity

Builds the n×n identity matrix in a row-major buffer.

jacobi_eigen

Computes the eigenvalues and eigenvectors of a symmetric n×n matrix by the cyclic Jacobi rotation method.

lle

Embeds data into n_components dimensions by locally linear embedding.

mean_center

Mean-centers data, returning the centered matrix and the column means.

pca

Fits PCA to data, returning the top n_components principal components.

put

Writes entry (i, j) into a row-major n×n buffer (no-op if out of range).

reconstruction_error

Computes the mean squared reconstruction error between two equal-shaped matrices.

symmetric_inverse

Inverts a small symmetric positive-definite n×n matrix via its eigen- decomposition: A⁻¹ = V diag(1/λ) Vᵀ.

tsne

Embeds data into n_components dimensions by t-SNE.

umap

Embeds data into n_components dimensions by a UMAP-style layout.