API REFERENCE/omnibias-fields

omnibias.fields.weak

0.2.0rc1Release candidatePython >=3.10Apache-2.0

Structured scalar, vector, and tensor fields with derivative caches, calculus operators, and coordinate conventions.

import omnibias.fields.weak

Module contract & mathematical conventions

Weak-form VPINN test functions (theory 02-04, gated).

Import assembly kernels from omnibias.fields.weak.torch or omnibias.fields.weak.jax. Exact integrals only for polynomial coefficients on boxes; the boundary bound is on by default.

Shared formulas do not imply universal floating-point identity. Verify dtype, shape, derivative-order support, and the stated numerical assumptions for the path you use.

Module source ↗Source revision 9a2d73df0573Running reference examples →

jaxModule ↗torchModule ↗

Imports & aliases

These names share a definition with another public module. Follow a name for its full contract, parameters, and examples.

Import from this module	Canonical reference
TestFunctionSpace	omnibias.fields.TestFunctionSpace
WeakForm	omnibias.fields.WeakForm
boundary_bound	omnibias.fields.boundary_bound
exact_moment	omnibias.fields.exact_moment

FUNCTION

eval_test

omnibias.fields.weak.eval_testSource ↗

eval_test(space: TestFunctionSpace, index: int, x: float, *, deriv: int=0) -> float

v^{(deriv)}(x) for test function index.

Parameters

Name	Type & default	Contract
spacepositional-or-keyword	TestFunctionSpaceRequired	See the operation contract and implementation below.
indexpositional-or-keyword	intRequired	See the operation contract and implementation below.
xpositional-or-keyword	floatRequired	See the operation contract and implementation below.
derivkeyword-only	intDefault: 0	See the operation contract and implementation below.

Returnsfloat

Executed regression · path recording quadrature for callable source

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_path_recording_quadrature_for_callable_source() -> None:
    torch.set_default_dtype(torch.float64)
    space = _space()
    op = WeakForm(diffusion=(1.0,))
    quad = gauss_legendre(((0.0, 1.0),), 8)

    def source(x: torch.Tensor) -> torch.Tensor:
        return torch.sin(math.pi * x.reshape(-1)).reshape(x.shape)

    _res, terms = weak_residual(
        (0.0, 1.0, -1.0), space, operator=op, source=source, quadrature=quad
    )
    load_paths = {t.path for t in terms if t.name.startswith("load")}
    stiff_paths = {t.path for t in terms if t.name.startswith("stiffness")}
    assert "quadrature" in load_paths
    assert "exact" in stiff_paths

python -m pytest "packages/omnibias-fields/tests/test_weak.py::test_path_recording_quadrature_for_callable_source" -q

Regression example · g1 exact moment vs gauss

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_exact_moment_vs_gauss() -> None:
    space = TestFunctionSpace(
        BankSpec.uniform(0.3, 0.7, 3, scales=(2.0,)),
        orders=(2,),
        base="tanh",
        window=(0.0, 1.0),
    )
    exact = exact_moment(space, 0, 0)
    hi = gauss_legendre(((0.0, 1.0),), 48)
    lo = gauss_legendre(((0.0, 1.0),), 2)
    v_hi = np.array([eval_test(space, 0, float(x), deriv=0) for x in hi.nodes[:, 0]])
    v_lo = np.array([eval_test(space, 0, float(x), deriv=0) for x in lo.nodes[:, 0]])
    g_hi = float(np.dot(hi.weights, v_hi))
    g_lo = float(np.dot(lo.weights, v_lo))
    rel = abs(exact - g_hi) / max(abs(g_hi), 1e-16)
    assert rel <= 1e-13
    assert abs(g_lo - exact) > abs(g_hi - exact)

python -m pytest packages/omnibias-fields/tests/test_weak.py -k test_g1_exact_moment_vs_gauss -q

Read the implementation

def eval_test(space: TestFunctionSpace, index: int, x: float, *, deriv: int = 0) -> float:
    """``v^{(deriv)}(x)`` for test function ``index``."""
    n = space.order_at(index) + int(deriv)
    alpha = space.scale_at(index)
    mu = space.offset_at(index)
    z = alpha * (x - mu)
    return (alpha ** deriv) * _sigma_n(space.base, z, n)

FUNCTION

poly_eval

omnibias.fields.weak.poly_evalSource ↗

poly_eval(coeffs: tuple[float, ...], x: float) -> float

The module contract describes the context for this operation. Its signature, explicit validation, return expressions, and implementation are recorded below.

Parameters

Name	Type & default	Contract
coeffspositional-or-keyword	tuple[float, ...]Required	See the operation contract and implementation below.
xpositional-or-keyword	floatRequired	See the operation contract and implementation below.

Returnsfloat

Read the implementation

def poly_eval(coeffs: tuple[float, ...], x: float) -> float:
    acc = 0.0
    for c in reversed(coeffs):
        acc = acc * x + c
    return acc

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