Module decomposition 

Tensor Decomposition Tools

This module provides various tensor decomposition algorithms as the foundation for Lie group optimization and tensor ring compression.

Algorithms

• QR Decomposition (orthogonalization)
• SVD Decomposition (baseline comparison)
• Tensor Ring Decomposition (core algorithm)
• CP Decomposition (optional)
• Tucker Decomposition (optional)

Example

use god_gragh::tensor::decomposition::{qr_decompose, svd_decompose, tensor_ring_decompose};
use god_gragh::tensor::DenseTensor;

// Create a test tensor
let tensor = DenseTensor::from_vec(
    vec![1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0],
    vec![4, 2],
);

// QR decomposition
let (q, r) = qr_decompose(&tensor)?;

// SVD decomposition
let (u, s, v) = svd_decompose(&tensor, None)?;

// Tensor ring decomposition
let cores = tensor_ring_decompose(&tensor, &[2, 2])?;

Re-exports

pub use qr::qr_decompose;

pub use svd::svd_decompose;

pub use tensor_ring::tensor_ring_decompose;

pub use lie_algebra::lie_exponential;

pub use lie_algebra::lie_logarithm;

pub use lie_algebra::skew_symmetric_projection;

Modules

lie_algebra

Lie Algebra Utilities

qr

QR Decomposition for tensor orthogonalization

svd

SVD Decomposition for tensor analysis

tensor_ring

Tensor Ring Decomposition