Small dense decompositions on the host: symmetric eigensolver, power iteration, QR and SVD (roadmap FND-4). More...

#include <cstdint>
#include "pulsatrix/tensor.hpp"

Include dependency graph for matrix_decompositions.hpp:

Classes
struct	pulsatrix::EigenResult
	SymmetricEigen()'s result. More...

struct	pulsatrix::DominantEigenResult
	PowerIteration()'s result. More...

struct	pulsatrix::QRResult
	QR()'s result, the thin factorization A = Q R. More...

struct	pulsatrix::SVDResult
	SVD()'s result, the thin factorization A = U diag(S) V^T with k = min(m, n). More...

Functions
EigenResult	pulsatrix::SymmetricEigen (const Tensor &a)
	All eigenvalues and eigenvectors of a symmetric matrix, by Householder reduction to tridiagonal form followed by QL with implicit shifts.

DominantEigenResult	pulsatrix::PowerIteration (const Tensor &a, int64_t max_iterations=1000, float tolerance=1e-6f, uint64_t seed=0)
	The dominant eigenpair of a symmetric matrix by power iteration – cheaper than SymmetricEigen() when only the top eigenpair is needed (spectral norm, stable rank).

QRResult	pulsatrix::QR (const Tensor &a)
	Thin QR factorization by Householder reflections.

SVDResult	pulsatrix::SVD (const Tensor &a)
	Thin singular value decomposition by one-sided (Hestenes) Jacobi rotations.

Detailed Description

Small dense decompositions on the host: symmetric eigensolver, power iteration, QR and SVD (roadmap FND-4).

Note: For the matrices interpretability works with – covariances of activations, weight matrices, Gram matrices – up to a few hundred rows and columns. Inputs are CPU tensors; arithmetic is in double; results are float tensors on the input's backend.; Eigenvector and singular-vector signs are arbitrary mathematically, so every result here is made canonical: in each vector, the largest-magnitude entry (the first, on a tie) is positive. Values come in descending order, ties kept in a fixed order. The same input therefore always gives the same output, which makes vectors comparable across runs and models (PCA directions, intruder-dimension checks).

Classes