# Path: diffrax/custom_types.py
# class Array:
#     def __class_getitem__(cls, item):
#         class X:
#             pass
# 
#         X.__module__ = "builtins"
#         X.__qualname__ = _maybe_tuple_to_str(item)
#         return _Array[X]
# 
# class Scalar:
#     pass
# 
# Path: diffrax/misc/errors.py
# def error_if(
#     pred: Union[_Bool, Callable[[], _Bool]],
#     msg: str,
#     error_cls: Type[Exception] = ValueError,
# ) -> bool:
#     """For use as part of validating inputs.
#     Works even under JIT.
# 
#     Example:
#         @jax.jit
#         def f(x):
#             error_if(x < 0, "x must be >= 0")
# 
#         f(jax.numpy.array(-1))
#     """
#     branched_error_if(pred, 0, [msg], error_cls)
# 
# Path: diffrax/brownian/base.py
# class AbstractBrownianPath(AbstractPath):
#     "Abstract base class for all Brownian paths."
# 
#     @abc.abstractmethod
#     def evaluate(self, t0: Scalar, t1: Scalar, left: bool = True) -> Array:
#         r"""Samples a Brownian increment $w(t_1) - w(t_0)$.
# 
#         Each increment has distribution $\mathcal{N}(0, t_1 - t_0)$.
# 
#         **Arguments:**
# 
#         - `t0`: Start of interval.
#         - `t1`: End of interval.
#         - `left`: Ignored. (This determines whether to treat the path as
#             left-continuous or right-continuous at any jump points, but Brownian
#             motion has no jump points.)
# 
#         **Returns:**
# 
#         A JAX array corresponding to the increment $w(t_1) - w(t_0)$.
# 
#         Some subclasses may allow `t1=None`, in which case just the value $w(t_0)$ is
#         returned.
#         """


from dataclasses import field
from typing import Optional, Tuple
from ..custom_types import Array, Scalar
from ..misc import error_if
from .base import AbstractBrownianPath
import equinox as eqx
import jax
import jax.lax as lax
import jax.numpy as jnp
import jax.random as jrandom
    t0: Scalar = field(init=True)
    t1: Scalar = field(init=True)  # override init=False in AbstractPath
    tol: Scalar
    shape: Tuple[int] = eqx.static_field()
    key: "jax.random.PRNGKey"  # noqa: F821

    @eqx.filter_jit
    def evaluate(
        self, t0: Scalar, t1: Optional[Scalar] = None, left: bool = True
    ) -> Array:
        del left
        if t1 is None:
            return self._evaluate(t0)
        else:
            return self._evaluate(t1) - self._evaluate(t0)

    def _brownian_bridge(self, s, t, u, w_s, w_u, key):
        mean = w_s + (w_u - w_s) * ((t - s) / (u - s))
        var = (u - t) * (t - s) / (u - s)
        std = jnp.sqrt(var)
        return mean + std * jrandom.normal(key, self.shape)

    def _evaluate(self, τ: Scalar) -> Array:
        cond = self.t0 < self.t1
        t0 = jnp.where(cond, self.t0, self.t1)
        t1 = jnp.where(cond, self.t1, self.t0)

        error_if(
            τ < t0, "Cannot evaluate VirtualBrownianTree outside of its range [t0, t1]."
        )

# Path: diffrax/custom_types.py
# class Array:
#     def __class_getitem__(cls, item):
#         class X:
#             pass
# 
#         X.__module__ = "builtins"
#         X.__qualname__ = _maybe_tuple_to_str(item)
#         return _Array[X]
# 
# class Scalar:
#     pass
# 
# Path: diffrax/misc/errors.py
# def error_if(
#     pred: Union[_Bool, Callable[[], _Bool]],
#     msg: str,
#     error_cls: Type[Exception] = ValueError,
# ) -> bool:
#     """For use as part of validating inputs.
#     Works even under JIT.
# 
#     Example:
#         @jax.jit
#         def f(x):
#             error_if(x < 0, "x must be >= 0")
# 
#         f(jax.numpy.array(-1))
#     """
#     branched_error_if(pred, 0, [msg], error_cls)
# 
# Path: diffrax/brownian/base.py
# class AbstractBrownianPath(AbstractPath):
#     "Abstract base class for all Brownian paths."
# 
#     @abc.abstractmethod
#     def evaluate(self, t0: Scalar, t1: Scalar, left: bool = True) -> Array:
#         r"""Samples a Brownian increment $w(t_1) - w(t_0)$.
# 
#         Each increment has distribution $\mathcal{N}(0, t_1 - t_0)$.
# 
#         **Arguments:**
# 
#         - `t0`: Start of interval.
#         - `t1`: End of interval.
#         - `left`: Ignored. (This determines whether to treat the path as
#             left-continuous or right-continuous at any jump points, but Brownian
#             motion has no jump points.)
# 
#         **Returns:**
# 
#         A JAX array corresponding to the increment $w(t_1) - w(t_0)$.
# 
#         Some subclasses may allow `t1=None`, in which case just the value $w(t_0)$ is
#         returned.
#         """


# Path: diffrax/brownian/tree.py
from dataclasses import field
from typing import Optional, Tuple
from ..custom_types import Array, Scalar
from ..misc import error_if
from .base import AbstractBrownianPath
import equinox as eqx
import jax
import jax.lax as lax
import jax.numpy as jnp
import jax.random as jrandom

    t0: Scalar = field(init=True)
    t1: Scalar = field(init=True)  # override init=False in AbstractPath
    tol: Scalar
    shape: Tuple[int] = eqx.static_field()
    key: "jax.random.PRNGKey"  # noqa: F821

    @eqx.filter_jit
    def evaluate(
        self, t0: Scalar, t1: Optional[Scalar] = None, left: bool = True
    ) -> Array:
        del left
        if t1 is None:
            return self._evaluate(t0)
        else:
            return self._evaluate(t1) - self._evaluate(t0)

    def _brownian_bridge(self, s, t, u, w_s, w_u, key):
        mean = w_s + (w_u - w_s) * ((t - s) / (u - s))
        var = (u - t) * (t - s) / (u - s)
        std = jnp.sqrt(var)
        return mean + std * jrandom.normal(key, self.shape)

    def _evaluate(self, τ: Scalar) -> Array:
        cond = self.t0 < self.t1
        t0 = jnp.where(cond, self.t0, self.t1)
        t1 = jnp.where(cond, self.t1, self.t0)

        error_if(
            τ < t0, "Cannot evaluate VirtualBrownianTree outside of its range [t0, t1]."
        )

        error_if(