pyvelora 0.3.3

Lightweight mathematical backend for physics libraries.

pyvelora

pyvelora is a lightweight math backend for scientific and simulation workflows. It provides structured Vector, Matrix, and Tensor classes, linear algebra helpers, and an ODE module for differential equation workflows.

What You Get

• Clear, typed array wrappers for vectors, matrices, and tensors
• Loop-based arithmetic with predictable behavior
• Linear algebra helpers for matrix operations, solvers, and decompositions
• Utility helpers for precision control, validation, mesh generation, and plotting
• ODE solving helpers with first-order and second-order system support

Philosophy

• Lightweight abstractions over Python-native containers
• Predictable data containers with explicit operations
• Reusable core infrastructure for physics/simulation libraries

Installation

pip install pyvelora

Optional dependencies:

• SciPy for ODE solving
• Matplotlib for plotting utilities and ODE visualization

Install them with:

pip install scipy matplotlib

Core Quick Start

from pyvelora import Vector, Matrix, Tensor

v = Vector([3, 4])
print(v.magnitude())  # 5.0

m = Matrix([[1, 2], [3, 4]])
print(m.transpose())

t = Tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
print(t.shape)  # (2, 2, 2)

Coordinate Vector Input

Vector supports polar, spherical, and cylindrical coordinate input.

from pyvelora import Vector

# Polar input: [r, theta]
v_polar = Vector([2, 45], type="polar", degrees=True)

# Spherical input: [r, theta, phi]
v_spherical = Vector([1, 90, 30], type="spherical", degrees=True)

# Cylindrical input: [rho, phi, z]
v_cyl = Vector([2, 90, 3], type="cylindrical", degrees=True)

Angles are interpreted as radians unless degrees=True is passed.

Linear Algebra Utilities

from pyvelora import Matrix
from pyvelora import Vector
from pyvelora.linalg import solve

A = Matrix([[2, 1], [5, 3]])
b = Vector([4, 11])

print(A.determinant())
print(A.inverse())
print(solve(A, b, method="lu"))

Utilities and Plotting

pyvelora.utils includes numerical cleanup, tolerance management, mesh generation, and lightweight plotting helpers.

from pyvelora import Matrix
from pyvelora.utils import clean, set_precision, get_precision, heatmap, linspace

set_precision(atol=1e-10, rtol=1e-8)
print(get_precision())

A = Matrix([[1.0, 0.99999999999], [-0.2, 0.3]])
print(clean(A.data))

fig, ax = heatmap(A, annotate=True, show=False)

ODE Module

The ODE API is available under pyvelora.diffeq.ode.

from pyvelora.constants import pi
from pyvelora.diffeq.ode import solve, second_order
from pyvelora.utils import linspace

# First-order system: y' = -y
sol = solve(lambda t, y: -y, (0, 2), [1.0], t_eval=linspace(0, 2, 11))
print(sol.final())

# Convert second-order equation y'' = -y to first-order system
sho = second_order(lambda t, y, v: -y)
sho_sol = solve(sho, (0, 2 * pi), [1.0, 0.0])
print(sho_sol.final())

Error Types

The package provides reusable exception types:

• PyveloraError
• ShapeError
• DimensionError

from pyvelora import Vector, ShapeError

try:
    _ = Vector([1, 2, 3]) + Vector([1, 2])
except ShapeError as exc:
    print(exc)

Development

Run the test suite:

python -m pytest src/pyvelora/tests -q

Build source and wheel distributions:

python -m build --no-isolation

AI Use Disclaimer

AI-assisted tooling was used during development for parts of the test suite, docstrings, and project documentation. Library design, implementation decisions, review, and release validation were still performed manually.

Project Status

pyvelora is currently alpha-stage and actively evolving. Core APIs are usable, but minor interface changes may still happen between releases.