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Inverse problems

frontx.InterpolatedSolution

Bases: Module, AbstractSolution

Source code in frontx/__init__.py 
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class InterpolatedSolution(eqx.Module, AbstractSolution):
    _sol: PchipInterpolator
    _do_dtheta: PchipInterpolator
    _Iodtheta: PchipInterpolator
    _c: float
    _oi: float

    def __init__(
        self,
        o: jax.Array | np.ndarray[Any, Any],
        theta: jax.Array | np.ndarray[Any, Any],
        /,
        *,
        b: float | None = None,
        i: float | None = None,
    ) -> None:
        self._sol = PchipInterpolator(x=o, y=theta, check=False)

        if b is not None:
            o = jnp.insert(o, 0, 0)
            theta = jnp.insert(theta, 0, b)

        if i is not None:
            o = jnp.append(o, o[-1] + 1)
            theta = jnp.append(theta, i)
        else:
            i = theta[-1]  # type: ignore[assignment]

        self._oi: float = o[-1]  # type: ignore[assignment]

        theta, indices = jnp.unique(theta, return_index=True)
        o = o[indices]

        inverse = PchipInterpolator(x=theta, y=o, extrapolate=False, check=False)
        self._do_dtheta = inverse.derivative()
        self._Iodtheta = inverse.antiderivative()
        self._c = self._Iodtheta(i)

    @boltzmannmethod
    def __call__(
        self,
        o: float | jax.Array | np.ndarray[Any, Any],
    ) -> float | jax.Array | np.ndarray[Any, Any]:
        return self._sol(o)  # type: ignore[no-any-return]

    def D(  # noqa: N802
        self,
        theta: float | jax.Array | np.ndarray[Any, Any],
        /,
    ) -> float | jax.Array | np.ndarray[Any, Any]:
        Iodtheta = self._Iodtheta(theta) - self._c  # noqa: N806
        do_dtheta = self._do_dtheta(theta)

        return jnp.squeeze(-(do_dtheta * Iodtheta) / 2)

    def sorptivity(
        self, o: float | jax.Array | np.ndarray[Any, Any] = 0
    ) -> float | jax.Array | np.ndarray[Any, Any]:
        Ithetado = self._sol.antiderivative()  # noqa: N806
        return (Ithetado(self._oi) - Ithetado(o)) - self.i * (self._oi - o)  # type: ignore[no-any-return]

    @property
    def oi(self) -> float:
        return self._oi

oi: float property

D(theta: float | jax.Array | np.ndarray[Any, Any]) -> float | jax.Array | np.ndarray[Any, Any]

Source code in frontx/__init__.py 
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def D(  # noqa: N802
    self,
    theta: float | jax.Array | np.ndarray[Any, Any],
    /,
) -> float | jax.Array | np.ndarray[Any, Any]:
    Iodtheta = self._Iodtheta(theta) - self._c  # noqa: N806
    do_dtheta = self._do_dtheta(theta)

    return jnp.squeeze(-(do_dtheta * Iodtheta) / 2)

__call__(o: float | jax.Array | np.ndarray[Any, Any]) -> float | jax.Array | np.ndarray[Any, Any]

Source code in frontx/__init__.py 
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@boltzmannmethod
def __call__(
    self,
    o: float | jax.Array | np.ndarray[Any, Any],
) -> float | jax.Array | np.ndarray[Any, Any]:
    return self._sol(o)  # type: ignore[no-any-return]

__init__(o: jax.Array | np.ndarray[Any, Any], theta: jax.Array | np.ndarray[Any, Any], /, *, b: float | None = None, i: float | None = None) -> None

Source code in frontx/__init__.py 
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def __init__(
    self,
    o: jax.Array | np.ndarray[Any, Any],
    theta: jax.Array | np.ndarray[Any, Any],
    /,
    *,
    b: float | None = None,
    i: float | None = None,
) -> None:
    self._sol = PchipInterpolator(x=o, y=theta, check=False)

    if b is not None:
        o = jnp.insert(o, 0, 0)
        theta = jnp.insert(theta, 0, b)

    if i is not None:
        o = jnp.append(o, o[-1] + 1)
        theta = jnp.append(theta, i)
    else:
        i = theta[-1]  # type: ignore[assignment]

    self._oi: float = o[-1]  # type: ignore[assignment]

    theta, indices = jnp.unique(theta, return_index=True)
    o = o[indices]

    inverse = PchipInterpolator(x=theta, y=o, extrapolate=False, check=False)
    self._do_dtheta = inverse.derivative()
    self._Iodtheta = inverse.antiderivative()
    self._c = self._Iodtheta(i)

sorptivity(o: float | jax.Array | np.ndarray[Any, Any] = 0) -> float | jax.Array | np.ndarray[Any, Any]

Source code in frontx/__init__.py 
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def sorptivity(
    self, o: float | jax.Array | np.ndarray[Any, Any] = 0
) -> float | jax.Array | np.ndarray[Any, Any]:
    Ithetado = self._sol.antiderivative()  # noqa: N806
    return (Ithetado(self._oi) - Ithetado(o)) - self.i * (self._oi - o)  # type: ignore[no-any-return]