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API REFERENCE/omnibias-fields

omnibias.fields.jax.ops.complex

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.jax.ops.complex
Module contract & mathematical conventions

Complex (Wirtinger) calculus on a split-real field (jax).

Bit-identical twin of omnibias.fields.torch.ops.complex.

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 →
FUNCTION

dz​

omnibias.fields.jax.ops.dzSource ↗
dz(state: FieldState, re_name: str, im_name: str, *, real_axis: int | str='x', imag_axis: int | str='y') -> tuple[Array, Array]

\partial_z f as a (real, imag) pair.

Parameters

NameType & defaultContract
statepositional-or-keywordFieldStateRequiredSee the operation contract and implementation below.
re_namepositional-or-keywordstrRequiredSee the operation contract and implementation below.
im_namepositional-or-keywordstrRequiredSee the operation contract and implementation below.
real_axiskeyword-onlyint | strDefault: 'x'See the operation contract and implementation below.
imag_axiskeyword-onlyint | strDefault: 'y'See the operation contract and implementation below.
Returnstuple[Array, Array]
Executed regression · wirtinger cross backend

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_wirtinger_cross_backend():  # type: ignore[no-untyped-def]
    from omnibias.fields.jax import _ops_dispatch as jd
    from omnibias.fields.jax.ops.complex import dz as jdz
    from omnibias.fields.torch import _ops_dispatch as td
    from omnibias.fields.torch.ops.complex import dz as tdz

    ts = _ExpZField(torch, td)(torch.as_tensor(COORDS, dtype=torch.float64))
    js = _ExpZField(jnp, jd)(jnp.asarray(COORDS, dtype=jnp.float64))
    tre, tim = tdz(ts, "fR", "fI")
    jre, jim = jdz(js, "fR", "fI")
    assert np.allclose(_np(tre), _np(jre), rtol=1e-12, atol=1e-12)
    assert np.allclose(_np(tim), _np(jim), rtol=1e-12, atol=1e-12)
python -m pytest "packages/omnibias-fields/tests/test_wirtinger.py::test_wirtinger_cross_backend" -q
Read the implementation
def dz(
    state: FieldState,
    re_name: str,
    im_name: str,
    *,
    real_axis: int | str = "x",
    imag_axis: int | str = "y",
) -> tuple[Array, Array]:
    r""":math:`\partial_z f` as a ``(real, imag)`` pair."""
    fr_x, fr_y, fi_x, fi_y = _partials(state, re_name, im_name, real_axis, imag_axis)
    return 0.5 * (fr_x + fi_y), 0.5 * (fi_x - fr_y)
Other public import paths
  • omnibias.fields.jax.ops.dz
  • omnibias.fields.jax.ops.complex.dz
FUNCTION

dzbar​

omnibias.fields.jax.ops.dzbarSource ↗
dzbar(state: FieldState, re_name: str, im_name: str, *, real_axis: int | str='x', imag_axis: int | str='y') -> tuple[Array, Array]

\partial_{\bar z} f as a (real, imag) pair (zero if holomorphic).

Parameters

NameType & defaultContract
statepositional-or-keywordFieldStateRequiredSee the operation contract and implementation below.
re_namepositional-or-keywordstrRequiredSee the operation contract and implementation below.
im_namepositional-or-keywordstrRequiredSee the operation contract and implementation below.
real_axiskeyword-onlyint | strDefault: 'x'See the operation contract and implementation below.
imag_axiskeyword-onlyint | strDefault: 'y'See the operation contract and implementation below.
Returnstuple[Array, Array]
Read the implementation
def dzbar(
    state: FieldState,
    re_name: str,
    im_name: str,
    *,
    real_axis: int | str = "x",
    imag_axis: int | str = "y",
) -> tuple[Array, Array]:
    r""":math:`\partial_{\bar z} f` as a ``(real, imag)`` pair (zero if holomorphic)."""
    fr_x, fr_y, fi_x, fi_y = _partials(state, re_name, im_name, real_axis, imag_axis)
    return 0.5 * (fr_x - fi_y), 0.5 * (fi_x + fr_y)
Other public import paths
  • omnibias.fields.jax.ops.dzbar
  • omnibias.fields.jax.ops.complex.dzbar
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