API REFERENCE/omnibias-core

omnibias.core.transfer

0.5.0rc1Release candidatePython >=3.10Apache-2.0

Coefficient recurrences, activation contracts, jet algebra, and verified arithmetic shared by the numerical backends.

import omnibias.core.transfer

Module contract & mathematical conventions

1-D layered transfer matrices (theory 02-11).

One-dimensional layered propagation only. unitarity_residual is refused outside lossless reciprocal linear media. Certified gaps set continuum_claim=False.

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 →

CLASS

BandGapCertificate

omnibias.core.transfer.BandGapCertificateSource ↗

class BandGapCertificate

Dataclass constructor fields; inherited fields, if any, are declared by the base class. A field(...) expression describes a default factory or field options, not a literal argument default.

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
omega_lodataclass field	floatRequired	See the operation contract and implementation below.
omega_hidataclass field	floatRequired	See the operation contract and implementation below.
trace_half_lodataclass field	floatRequired	See the operation contract and implementation below.
trace_half_hidataclass field	floatRequired	See the operation contract and implementation below.
is_gapdataclass field	boolRequired	See the operation contract and implementation below.
continuum_claimdataclass field	boolDefault: False	See the operation contract and implementation below.

Fields & methods

omega_lofield

omega_lo: float

Declared float field on BandGapCertificate. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

omega_hifield

omega_hi: float

Declared float field on BandGapCertificate. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

trace_half_lofield

trace_half_lo: float

Declared float field on BandGapCertificate. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

trace_half_hifield

trace_half_hi: float

Declared float field on BandGapCertificate. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

is_gapfield

is_gap: bool

Declared bool field on BandGapCertificate. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

continuum_claimfield

continuum_claim: bool = False

Declared bool field on BandGapCertificate. Default expression: False.

View source ↗

is_soundproperty

is_sound(self) -> bool

See the class contract above and the exact method implementation below.

Returns: bool

Method implementation

    def is_sound(self) -> bool:
        return True

View source ↗

Read the implementation

class BandGapCertificate:
    omega_lo: float
    omega_hi: float
    trace_half_lo: float
    trace_half_hi: float
    is_gap: bool
    continuum_claim: bool = False

    @property
    def is_sound(self) -> bool:
        return True

CLASS

Layer

omnibias.core.LayerSource ↗

class Layer

Dataclass constructor fields; inherited fields, if any, are declared by the base class. A field(...) expression describes a default factory or field options, not a literal argument default.

A homogeneous slab. index is refractive index (or wave speed inverse).

Parameters

Name	Type & default	Contract
indexdataclass field	complexRequired	See the operation contract and implementation below.
thicknessdataclass field	floatRequired	See the operation contract and implementation below.

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Regression example · unitarity refused when lossy

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_unitarity_refused_when_lossy() -> None:
    with pytest.raises(ValueError, match="lossless"):
        unitarity_residual(stack_matrix((Layer(1.5 + 0.1j, 0.2),), 1.0), lossless=False)

python -m pytest packages/omnibias-core/tests/test_transfer.py -k test_unitarity_refused_when_lossy -q

Fields & methods

indexfield

index: complex

Declared complex field on Layer. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

thicknessfield

thickness: float

Declared float field on Layer. A value must be provided when constructing the configuration, unless an inherited constructor supplies it.

View source ↗

__post_init__method

__post_init__(self) -> None

See the class contract above and the exact method implementation below.

Returns: None

Validation & failure cases

• When self.thickness < 0.0, raises ValueError('thickness must be >= 0').

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Method implementation

    def __post_init__(self) -> None:
        if self.thickness < 0.0:
            raise ValueError("thickness must be >= 0")

View source ↗

Read the implementation

class Layer:
    """A homogeneous slab. ``index`` is refractive index (or wave speed inverse)."""

    index: complex
    thickness: float

    def __post_init__(self) -> None:
        if self.thickness < 0.0:
            raise ValueError("thickness must be >= 0")

Other public import paths

• omnibias.core.Layer
• omnibias.core.transfer.Layer

CONSTANT

Matrix2

omnibias.core.transfer.Matrix2Source ↗

Matrix2 = tuple[tuple[complex, complex], tuple[complex, complex]]

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation

Matrix2 = tuple[tuple[complex, complex], tuple[complex, complex]]

FUNCTION

bloch_dispersion

omnibias.core.transfer.bloch_dispersionSource ↗

bloch_dispersion(cell: Sequence[Layer], omega: float) -> float

(1/2) Re tr M_cell; |value| <= 1 is a pass band of the infinite stack.

Parameters

Name	Type & default	Contract
cellpositional-or-keyword	Sequence[Layer]Required	See the operation contract and implementation below.
omegapositional-or-keyword	floatRequired	See the operation contract and implementation below.

Returnsfloat

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Regression example · g3 certified gap sound

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_g3_certified_gap_sound() -> None:
    cell = quarter_wave_stack(2.3, 1.0, n_periods=1, omega0=1.0)
    cert = certified_band_gap(cell, omega_range=(0.85, 1.15), n_grid=48)
    assert cert.continuum_claim is False
    xs = [0.85 + (1.15 - 0.85) * i / 80 for i in range(81)]
    vals = [abs(bloch_dispersion(cell, w)) for w in xs]
    if cert.is_gap:
        assert min(vals) >= 1.0 - 1e-9
    assert cert.trace_half_lo <= min(vals) + 1e-9
    assert cert.trace_half_hi + 1e-9 >= max(vals)

python -m pytest packages/omnibias-core/tests/test_transfer.py -k test_g3_certified_gap_sound -q

Read the implementation

def bloch_dispersion(cell: Sequence[Layer], omega: float) -> float:
    """``(1/2) Re tr M_cell``; ``|value| <= 1`` is a pass band of the infinite stack."""
    m = stack_matrix(cell, omega)
    return 0.5 * (m[0][0] + m[1][1]).real

Related APIsomnibias.core.transfer.stack_matrix↗

FUNCTION

certified_band_gap

omnibias.core.certified_band_gapSource ↗

certified_band_gap(cell: Sequence[Layer], *, omega_range: tuple[float, float], n_grid: int=64) -> BandGapCertificate

Interval enclosure of |tr M|/2 over omega_range.

continuum_claim is always False: this is a finite stack / finite frequency sample, not an infinite-crystal theorem.

Parameters

Name	Type & default	Contract
cellpositional-or-keyword	Sequence[Layer]Required	See the operation contract and implementation below.
omega_rangekeyword-only	tuple[float, float]Required	See the operation contract and implementation below.
n_gridkeyword-only	intDefault: 64	See the operation contract and implementation below.

ReturnsBandGapCertificate

Explicit validation & failure cases

• When hi <= lo, raises ValueError('omega_range must be an ordered interval').

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

Executed regression · g3 certified gap sound

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_g3_certified_gap_sound() -> None:
    cell = quarter_wave_stack(2.3, 1.0, n_periods=1, omega0=1.0)
    cert = certified_band_gap(cell, omega_range=(0.85, 1.15), n_grid=48)
    assert cert.continuum_claim is False
    xs = [0.85 + (1.15 - 0.85) * i / 80 for i in range(81)]
    vals = [abs(bloch_dispersion(cell, w)) for w in xs]
    if cert.is_gap:
        assert min(vals) >= 1.0 - 1e-9
    assert cert.trace_half_lo <= min(vals) + 1e-9
    assert cert.trace_half_hi + 1e-9 >= max(vals)

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g3_certified_gap_sound" -q

Read the implementation

def certified_band_gap(
    cell: Sequence[Layer],
    *,
    omega_range: tuple[float, float],
    n_grid: int = 64,
) -> BandGapCertificate:
    """Interval enclosure of ``|tr M|/2`` over ``omega_range``.

    ``continuum_claim`` is always ``False``: this is a finite stack / finite
    frequency sample, not an infinite-crystal theorem.
    """
    lo, hi = float(omega_range[0]), float(omega_range[1])
    if hi <= lo:
        raise ValueError("omega_range must be an ordered interval")
    samples = [lo + (hi - lo) * i / (n_grid - 1) for i in range(n_grid)]
    vals = [abs(bloch_dispersion(cell, w)) for w in samples]
    # Crude variation: neighbour difference as an interval padding.
    pad = 0.0
    for a, b in zip(vals, vals[1:], strict=False):
        pad = max(pad, abs(a - b))
    iv = Interval(min(vals) - pad, max(vals) + pad)
    return BandGapCertificate(
        omega_lo=lo,
        omega_hi=hi,
        trace_half_lo=float(iv.lo),
        trace_half_hi=float(iv.hi),
        is_gap=bool(iv.lo > 1.0),
        continuum_claim=False,
    )

Related APIsomnibias.core.transfer.BandGapCertificate↗omnibias.core.transfer.bloch_dispersion↗omnibias.core.verified.Interval↗

Other public import paths

• omnibias.core.certified_band_gap
• omnibias.core.transfer.certified_band_gap

FUNCTION

interface_matrix

omnibias.core.transfer.interface_matrixSource ↗

interface_matrix(n_lo: complex, n_hi: complex) -> Matrix2

Continuity of E and H at a dielectric interface (normal incidence).

Parameters

Name	Type & default	Contract
n_lopositional-or-keyword	complexRequired	See the operation contract and implementation below.
n_hipositional-or-keyword	complexRequired	See the operation contract and implementation below.

ReturnsMatrix2

Read the implementation

def interface_matrix(n_lo: complex, n_hi: complex) -> Matrix2:
    """Continuity of E and H at a dielectric interface (normal incidence)."""
    # Maps amplitude basis (E+, E-) through the interface.
    # E, H continuous: E+ + E- and n(E+ - E-).
    a = (n_hi + n_lo) / (2.0 * n_hi)
    b = (n_hi - n_lo) / (2.0 * n_hi)
    return ((a, b), (b, a))

FUNCTION

layer_matrix

omnibias.core.transfer.layer_matrixSource ↗

layer_matrix(layer: Layer, omega: float) -> Matrix2

Characteristic matrix of a homogeneous slab (det = 1 when lossless).

Parameters

Name	Type & default	Contract
layerpositional-or-keyword	LayerRequired	See the operation contract and implementation below.
omegapositional-or-keyword	floatRequired	See the operation contract and implementation below.

ReturnsMatrix2

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Read the implementation

def layer_matrix(layer: Layer, omega: float) -> Matrix2:
    """Characteristic matrix of a homogeneous slab (``det = 1`` when lossless)."""
    n = layer.index
    delta = n * omega * layer.thickness
    c = cmath.cos(delta)
    s = cmath.sin(delta)
    return ((c, 1.0j * s / n), (1.0j * n * s, c))

FUNCTION

propagation_matrix

omnibias.core.transfer.propagation_matrixSource ↗

propagation_matrix(n: complex, thickness: float, omega: float) -> Matrix2

Phase accumulation diag(e^{i n omega d}, e^{-i n omega d}) (c=1).

Parameters

Name	Type & default	Contract
npositional-or-keyword	complexRequired	See the operation contract and implementation below.
thicknesspositional-or-keyword	floatRequired	See the operation contract and implementation below.
omegapositional-or-keyword	floatRequired	See the operation contract and implementation below.

ReturnsMatrix2

Read the implementation

def propagation_matrix(n: complex, thickness: float, omega: float) -> Matrix2:
    """Phase accumulation ``diag(e^{i n omega d}, e^{-i n omega d})`` (c=1)."""
    phase = n * omega * thickness
    ep = cmath.exp(1.0j * phase)
    em = cmath.exp(-1.0j * phase)
    return ((ep, 0.0j), (0.0j, em))

FUNCTION

quarter_wave_stack

omnibias.core.transfer.quarter_wave_stackSource ↗

quarter_wave_stack(n_hi: float, n_lo: float, *, n_periods: int, omega0: float=1.0) -> tuple[Layer, ...]

Quarter-wave Bragg stack: n d = pi / (2 omega0) per layer.

Parameters

Name	Type & default	Contract
n_hipositional-or-keyword	floatRequired	See the operation contract and implementation below.
n_lopositional-or-keyword	floatRequired	See the operation contract and implementation below.
n_periodskeyword-only	intRequired	See the operation contract and implementation below.
omega0keyword-only	floatDefault: 1.0	See the operation contract and implementation below.

Returnstuple[Layer, ...]

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Regression example · g3 certified gap sound

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_g3_certified_gap_sound() -> None:
    cell = quarter_wave_stack(2.3, 1.0, n_periods=1, omega0=1.0)
    cert = certified_band_gap(cell, omega_range=(0.85, 1.15), n_grid=48)
    assert cert.continuum_claim is False
    xs = [0.85 + (1.15 - 0.85) * i / 80 for i in range(81)]
    vals = [abs(bloch_dispersion(cell, w)) for w in xs]
    if cert.is_gap:
        assert min(vals) >= 1.0 - 1e-9
    assert cert.trace_half_lo <= min(vals) + 1e-9
    assert cert.trace_half_hi + 1e-9 >= max(vals)

python -m pytest packages/omnibias-core/tests/test_transfer.py -k test_g3_certified_gap_sound -q

Read the implementation

def quarter_wave_stack(
    n_hi: float, n_lo: float, *, n_periods: int, omega0: float = 1.0
) -> tuple[Layer, ...]:
    """Quarter-wave Bragg stack: ``n d = pi / (2 omega0)`` per layer."""
    layers: list[Layer] = []
    for _ in range(n_periods):
        layers.append(Layer(n_hi, math.pi / (2.0 * omega0 * n_hi)))
        layers.append(Layer(n_lo, math.pi / (2.0 * omega0 * n_lo)))
    return tuple(layers)

Related APIsomnibias.core.Layer↗

FUNCTION

reflection_transmission

omnibias.core.transfer.reflection_transmissionSource ↗

reflection_transmission(m: Matrix2, *, n_in: complex=1.0, n_out: complex=1.0) -> tuple[complex, complex]

r, t from an ABCD characteristic matrix into n_out.

Parameters

Name	Type & default	Contract
mpositional-or-keyword	Matrix2Required	See the operation contract and implementation below.
n_inkeyword-only	complexDefault: 1.0	See the operation contract and implementation below.
n_outkeyword-only	complexDefault: 1.0	See the operation contract and implementation below.

Returnstuple[complex, complex]

Explicit validation & failure cases

• When denom == 0, raises ZeroDivisionError('transfer matrix is singular').

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

Executed regression · g1 structural identities

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_g1_structural_identities() -> None:
    layers = (
        Layer(1.5 + 0.0j, 0.3),
        Layer(2.3 + 0.0j, 0.2),
        Layer(1.2 + 0.0j, 0.4),
    )
    for omega in (0.4, 1.0, 2.2):
        m = stack_matrix(layers, omega)
        assert unitarity_residual(m) <= 1e-12
        r, t = reflection_transmission(m)
        cons = abs(r) ** 2 + abs(t) ** 2
        assert abs(cons - 1.0) <= 1e-13

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g1_structural_identities" -q

Read the implementation

def reflection_transmission(m: Matrix2, *, n_in: complex = 1.0, n_out: complex = 1.0) -> tuple[complex, complex]:
    """``r, t`` from an ABCD characteristic matrix into ``n_out``."""
    a, b = m[0]
    c, d = m[1]
    denom = a * n_out + b * n_in * n_out + c + d * n_in
    if denom == 0:
        raise ZeroDivisionError("transfer matrix is singular")
    r = (a * n_out + b * n_in * n_out - c - d * n_in) / denom
    t = (2.0 * n_in) / denom
    return r, t

FUNCTION

stack_matrix

omnibias.core.transfer.stack_matrixSource ↗

stack_matrix(layers: Sequence[Layer], omega: float, *, n_in: complex=1.0) -> Matrix2

Product of characteristic matrices. n_in is unused (ambient is 1).

Parameters

Name	Type & default	Contract
layerspositional-or-keyword	Sequence[Layer]Required	See the operation contract and implementation below.
omegapositional-or-keyword	floatRequired	See the operation contract and implementation below.
n_inkeyword-only	complexDefault: 1.0	See the operation contract and implementation below.

ReturnsMatrix2

Executed regression · g2 quarter wave midgap

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_g2_quarter_wave_midgap() -> None:
    cell = quarter_wave_stack(2.0, 1.0, n_periods=1, omega0=1.0)
    mid = abs(bloch_dispersion(cell, 1.0))
    assert mid > 1.0

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_g2_quarter_wave_midgap" -q

Regression example · unitarity refused when lossy

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_unitarity_refused_when_lossy() -> None:
    with pytest.raises(ValueError, match="lossless"):
        unitarity_residual(stack_matrix((Layer(1.5 + 0.1j, 0.2),), 1.0), lossless=False)

python -m pytest packages/omnibias-core/tests/test_transfer.py -k test_unitarity_refused_when_lossy -q

Read the implementation

def stack_matrix(layers: Sequence[Layer], omega: float, *, n_in: complex = 1.0) -> Matrix2:
    """Product of characteristic matrices. ``n_in`` is unused (ambient is 1)."""
    _ = n_in
    m = _eye()
    for layer in layers:
        m = _mul(layer_matrix(layer, omega), m)
    return m

Related APIsomnibias.core.transfer.layer_matrix↗

FUNCTION

unitarity_residual

omnibias.core.transfer.unitarity_residualSource ↗

unitarity_residual(m: Matrix2, *, lossless: bool=True) -> float

|det M - 1|. Refused unless lossless (reciprocal linear media).

Parameters

Name	Type & default	Contract
mpositional-or-keyword	Matrix2Required	See the operation contract and implementation below.
losslesskeyword-only	boolDefault: True	See the operation contract and implementation below.

Returnsfloat

Explicit validation & failure cases

• When not lossless, raises ValueError('unitarity_residual is refused outside lossless reciprocal linear media').

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

Executed regression · unitarity refused when lossy

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_unitarity_refused_when_lossy() -> None:
    with pytest.raises(ValueError, match="lossless"):
        unitarity_residual(stack_matrix((Layer(1.5 + 0.1j, 0.2),), 1.0), lossless=False)

python -m pytest "packages/omnibias-core/tests/test_transfer.py::test_unitarity_refused_when_lossy" -q

Regression example · g1 structural identities

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_structural_identities() -> None:
    layers = (
        Layer(1.5 + 0.0j, 0.3),
        Layer(2.3 + 0.0j, 0.2),
        Layer(1.2 + 0.0j, 0.4),
    )
    for omega in (0.4, 1.0, 2.2):
        m = stack_matrix(layers, omega)
        assert unitarity_residual(m) <= 1e-12
        r, t = reflection_transmission(m)
        cons = abs(r) ** 2 + abs(t) ** 2
        assert abs(cons - 1.0) <= 1e-13

python -m pytest packages/omnibias-core/tests/test_transfer.py -k test_g1_structural_identities -q

Read the implementation

def unitarity_residual(m: Matrix2, *, lossless: bool = True) -> float:
    """``|det M - 1|``. Refused unless ``lossless`` (reciprocal linear media)."""
    if not lossless:
        raise ValueError(
            "unitarity_residual is refused outside lossless reciprocal linear media"
        )
    return abs(_det(m) - 1.0)

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