API REFERENCE/omnibias-qcalculus

omnibias.qcalculus.jax

0.1.0a2AlphaPython >=3.10Apache-2.0

q-numbers, Jackson derivatives and integrals, q-series, and the ordinary-calculus limit as q approaches one.

import omnibias.qcalculus.jax

Module contract & mathematical conventions

JAX twin of the Jackson q-derivative of an activation.

Bit-identical mirror of omnibias.qcalculus.torch, jit / vmap / grad-safe (name and q are static, only z is traced). q_derivative is the batched Jackson quotient (sigma(qz) - sigma(z)) / ((q-1)z); q_derivative_limit is the closed-form sigma'(z) -- the exact q -> 1 limit (the **distinct** q-limit, not the delta -> 0 founding collapse).

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 →

hybridModule ↗

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
QOMBUConfig	omnibias.qcalculus.QOMBUConfig
q_ombu_forward	omnibias.qcalculus.jax.q_ombu_forward

FUNCTION

q_derivative

omnibias.qcalculus.jax.q_derivativeSource ↗

q_derivative(name: str, z: Array, q: float) -> Array

Batched Jackson q-derivative (sigma(qz) - sigma(z)) / ((q-1)z) (q != 1).

Parameters

Name	Type & default	Contract
namepositional-or-keyword	strRequired	See the operation contract and implementation below.
zpositional-or-keyword	ArrayRequired	See the operation contract and implementation below.
qpositional-or-keyword	floatRequired	See the operation contract and implementation below.

ReturnsArray

Explicit validation & failure cases

• When q == 1.0, raises ValueError('q_derivative needs q != 1 (the q -> 1 limit is q_derivative_limit)').

These are explicit source guards. Backend operations may also raise for invalid shapes, dtypes, or unsupported devices.

Executed regression · jax twin matches torch twin

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_jax_twin_matches_torch_twin() -> None:
    torch = pytest.importorskip("torch")
    jax = pytest.importorskip("jax")
    jax.config.update("jax_enable_x64", True)
    import jax.numpy as jnp
    from omnibias.qcalculus.jax import q_derivative as jq
    from omnibias.qcalculus.torch import q_derivative as tq

    xs = [0.5, 0.9, 1.4, 1.9]
    q = 0.95
    t = tq("sigmoid", torch.tensor(xs, dtype=torch.float64), q).tolist()
    j = jq("sigmoid", jnp.asarray(xs, dtype=jnp.float64), q).tolist()
    for a, b in zip(t, j, strict=False):
        assert a == pytest.approx(b, rel=1e-10, abs=1e-12)

python -m pytest "packages/omnibias-qcalculus/tests/test_package.py::test_jax_twin_matches_torch_twin" -q

Read the implementation

def q_derivative(name: str, z: Array, q: float) -> Array:
    r"""Batched Jackson q-derivative ``(sigma(qz) - sigma(z)) / ((q-1)z)`` (``q != 1``)."""
    if q == 1.0:
        raise ValueError("q_derivative needs q != 1 (the q -> 1 limit is q_derivative_limit)")
    spec = get_activation(name)
    return (spec.forward(q * z) - spec.forward(z)) / ((q - 1.0) * z)

Related APIsomnibias.jax.get_activation↗

FUNCTION

q_derivative_limit

omnibias.qcalculus.jax.q_derivative_limitSource ↗

q_derivative_limit(name: str, z: Array) -> Array

Closed-form sigma'(z) via the backend fastpath -- the exact q -> 1 limit.

Parameters

Name	Type & default	Contract
namepositional-or-keyword	strRequired	See the operation contract and implementation below.
zpositional-or-keyword	ArrayRequired	See the operation contract and implementation below.

ReturnsArray

Explicit validation & failure cases

• When spec.fastpath is None, raises NotImplementedError(f'activation {name!r} has no closed-form derivative kernel').

These are explicit source guards. Backend operations may also raise for invalid shapes, dtypes, or unsupported devices.

Read the implementation

def q_derivative_limit(name: str, z: Array) -> Array:
    r"""Closed-form ``sigma'(z)`` via the backend fastpath -- the exact ``q -> 1`` limit."""
    spec = get_activation(name)
    if spec.fastpath is None:
        raise NotImplementedError(f"activation {name!r} has no closed-form derivative kernel")
    out: Array = spec.fastpath(z, 1)
    return out

Related APIsomnibias.jax.get_activation↗

FUNCTION

q_derivative_residual

omnibias.qcalculus.jax.q_derivative_residualSource ↗

q_derivative_residual(name: str, z: Array, q: float) -> Array

q_derivative - q_derivative_limit; -> 0 as q -> 1.

Parameters

Name	Type & default	Contract
namepositional-or-keyword	strRequired	See the operation contract and implementation below.
zpositional-or-keyword	ArrayRequired	See the operation contract and implementation below.
qpositional-or-keyword	floatRequired	See the operation contract and implementation below.

ReturnsArray

Read the implementation

def q_derivative_residual(name: str, z: Array, q: float) -> Array:
    r"""``q_derivative - q_derivative_limit``; ``-> 0`` as ``q -> 1``."""
    return q_derivative(name, z, q) - q_derivative_limit(name, z)

Related APIsomnibias.qcalculus.jax.q_derivative↗omnibias.qcalculus.jax.q_derivative_limit↗

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