TTNumPy documentationΒΆ

TTNumPy is a tensor-train toolbox for numerical linear algebra. It provides tools for solving optimization problems in the tensor-train formalism. Problems that this formalism handles efficiently include systems of linear equations, black-box function interpolation and numerical integration.

The library works with tensor trains (TT) and tensor train matrices (TTM), known in the physics literature as matrix product states and matrix product operators. It is written in Python on top of NumPy and SciPy and pulls in no other runtime dependencies.

Features

  • Tensor train container. TensorTrain holds both the TT and the TTM format, tracking bond dimensions, canonical form and the position of the orthogonality centre.

  • Constructors. TT-SVD decomposition of a full tensor, plus ones, zeros, eye, rand and canonical_tt.

  • Arithmetic. Addition, element-wise and scalar multiplication, matrix-by-vector and matrix-by-matrix products, transposition and conjugation, each with optional rounding.

  • Quantization. Conversion between TT and quantized tensor train (QTT) form, which turns a grid of \(2^n\) points into \(n\) cores of mode size 2.

  • Linear solvers. ALS, MALS and AMEn for \(A x = b\) in TT format, sharing environments, local solvers and stopping criteria.

  • Benchmarks. A runner that measures the TT solvers against SciPy CG, PyAMG and PETSc on the Poisson equation.

At a glance

import ttnumpy as tt

A = tt.eye([2, 2, 2])                      # TTM operator
b = tt.rand([2, 2, 2], ranks=2, seed=0)    # TT right-hand side

x, info = tt.amen(A, b, residual_tol=1e-8, return_info=True)
print(info.stop_reason, info.residuals[-1])

Start with Installation, then follow Getting Started for a tour of the main features. The User guide covers tensor trains and the algorithms in depth, and API Reference documents every public entry point.

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