SpaceCore

SpaceCore is a lightweight backend-agnostic library for working with vector spaces and linear operators.

It provides a small set of abstractions for:

• backend-aware numerical operations
• contexts carrying backend and dtype information
• structured vector spaces
• structured linear operators
• conversion between compatible contexts

Installation

Base install:

pip install spacecore

With JAX support:

pip install "spacecore[jax]"

• spacecore[jax]: installs optional JAX support.
• GPU users should install the appropriate CUDA-enabled JAX build first, following the official JAX installation guide.

Main concepts

Context

A Context specifies how objects are represented, in particular:

• backend (NumPy, JAX, etc.)
• dtype
• validation/conversion behavior

Space

A Space describes the structure of objects space, for example:

• VectorSpace - Euclidean space
• HermitianSpace - space of Hermitian (symmetric) matrices
• ProductSpace - Cartesian product of spaces

LinOp

A LinOp represents a linear operator between spaces, for example:

• DenseLinOp - linear operator represented by dense matrix
• SparseLinOp - linear operator represented by sparse matrix
• BlockDiagonalLinOp - linear operator from $X_1 \times \dots \times X_k$ to $Y_1 \times \dots \times Y_k$
• StackedLinOp - linear operator from $X$ to $Y_1 \times \dots \times Y_k$
• SumToSingleLinOp - linear operator from $X_1 \times \dots \times X_k$ to $Y$

Minimal example

import numpy as np
import spacecore as sc

sc.set_context('numpy', dtype='float64')

X = sc.VectorSpace((3,))
Y = sc.VectorSpace((2,))

A = np.array(
    [[1.0, 2.0, 3.0],
     [0.0, 1.0, 0.0]]
)
linop = sc.DenseLinOp(
    A,
    dom=X,
    cod=Y,
)

x = X.ctx.asarray([1.0, 0.0, -1.0])
y = linop.apply(x)

print(y)

Status

SpaceCore is currently experimental and under active development. The public API may still evolve.

Tutorials

See the tutorials/ directory for usage examples and design guidance.

License

Apache License 2.0