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kronos-venv/lib/python3.12/site-packages/torch/distributions/von_mises.py

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+# mypy: allow-untyped-defs
+import math
+
+import torch
+import torch.jit
+from torch import Tensor
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import broadcast_all, lazy_property
+
+
+__all__ = ["VonMises"]
+
+
+def _eval_poly(y, coef):
+    coef = list(coef)
+    result = coef.pop()
+    while coef:
+        result = coef.pop() + y * result
+    return result
+
+
+_I0_COEF_SMALL = [
+    1.0,
+    3.5156229,
+    3.0899424,
+    1.2067492,
+    0.2659732,
+    0.360768e-1,
+    0.45813e-2,
+]
+_I0_COEF_LARGE = [
+    0.39894228,
+    0.1328592e-1,
+    0.225319e-2,
+    -0.157565e-2,
+    0.916281e-2,
+    -0.2057706e-1,
+    0.2635537e-1,
+    -0.1647633e-1,
+    0.392377e-2,
+]
+_I1_COEF_SMALL = [
+    0.5,
+    0.87890594,
+    0.51498869,
+    0.15084934,
+    0.2658733e-1,
+    0.301532e-2,
+    0.32411e-3,
+]
+_I1_COEF_LARGE = [
+    0.39894228,
+    -0.3988024e-1,
+    -0.362018e-2,
+    0.163801e-2,
+    -0.1031555e-1,
+    0.2282967e-1,
+    -0.2895312e-1,
+    0.1787654e-1,
+    -0.420059e-2,
+]
+
+_COEF_SMALL = [_I0_COEF_SMALL, _I1_COEF_SMALL]
+_COEF_LARGE = [_I0_COEF_LARGE, _I1_COEF_LARGE]
+
+
+def _log_modified_bessel_fn(x, order=0):
+    """
+    Returns ``log(I_order(x))`` for ``x > 0``,
+    where `order` is either 0 or 1.
+    """
+    if order != 0 and order != 1:
+        raise AssertionError(f"order must be 0 or 1, got {order}")
+
+    # compute small solution
+    y = x / 3.75
+    y = y * y
+    small = _eval_poly(y, _COEF_SMALL[order])
+    if order == 1:
+        small = x.abs() * small
+    small = small.log()
+
+    # compute large solution
+    y = 3.75 / x
+    large = x - 0.5 * x.log() + _eval_poly(y, _COEF_LARGE[order]).log()
+
+    result = torch.where(x < 3.75, small, large)
+    return result
+
+
+@torch.jit.script_if_tracing
+def _rejection_sample(loc, concentration, proposal_r, x):
+    done = torch.zeros(x.shape, dtype=torch.bool, device=loc.device)
+    # pyrefly: ignore [bad-assignment, missing-attribute]
+    while not done.all():
+        u = torch.rand((3,) + x.shape, dtype=loc.dtype, device=loc.device)
+        u1, u2, u3 = u.unbind()
+        z = torch.cos(math.pi * u1)
+        f = (1 + proposal_r * z) / (proposal_r + z)
+        c = concentration * (proposal_r - f)
+        accept = ((c * (2 - c) - u2) > 0) | ((c / u2).log() + 1 - c >= 0)
+        if accept.any():
+            # pyrefly: ignore [no-matching-overload]
+            x = torch.where(accept, (u3 - 0.5).sign() * f.acos(), x)
+            done = done | accept
+    return (x + math.pi + loc) % (2 * math.pi) - math.pi
+
+
+class VonMises(Distribution):
+    """
+    A circular von Mises distribution.
+
+    This implementation uses polar coordinates. The ``loc`` and ``value`` args
+    can be any real number (to facilitate unconstrained optimization), but are
+    interpreted as angles modulo 2 pi.
+
+    Example::
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = VonMises(torch.tensor([1.0]), torch.tensor([1.0]))
+        >>> m.sample()  # von Mises distributed with loc=1 and concentration=1
+        tensor([1.9777])
+
+    :param torch.Tensor loc: an angle in radians.
+    :param torch.Tensor concentration: concentration parameter
+    """
+
+    # pyrefly: ignore [bad-override]
+    arg_constraints = {"loc": constraints.real, "concentration": constraints.positive}
+    support = constraints.real
+    has_rsample = False
+
+    def __init__(
+        self,
+        loc: Tensor,
+        concentration: Tensor,
+        validate_args: bool | None = None,
+    ) -> None:
+        self.loc, self.concentration = broadcast_all(loc, concentration)
+        batch_shape = self.loc.shape
+        event_shape = torch.Size()
+        super().__init__(batch_shape, event_shape, validate_args)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        log_prob = self.concentration * torch.cos(value - self.loc)
+        log_prob = (
+            log_prob
+            - math.log(2 * math.pi)
+            - _log_modified_bessel_fn(self.concentration, order=0)
+        )
+        return log_prob
+
+    @lazy_property
+    def _loc(self) -> Tensor:
+        return self.loc.to(torch.double)
+
+    @lazy_property
+    def _concentration(self) -> Tensor:
+        return self.concentration.to(torch.double)
+
+    @lazy_property
+    def _proposal_r(self) -> Tensor:
+        kappa = self._concentration
+        tau = 1 + (1 + 4 * kappa**2).sqrt()
+        rho = (tau - (2 * tau).sqrt()) / (2 * kappa)
+        _proposal_r = (1 + rho**2) / (2 * rho)
+        # second order Taylor expansion around 0 for small kappa
+        _proposal_r_taylor = 1 / kappa + kappa
+        return torch.where(kappa < 1e-5, _proposal_r_taylor, _proposal_r)
+
+    @torch.no_grad()
+    def sample(self, sample_shape=torch.Size()):
+        """
+        The sampling algorithm for the von Mises distribution is based on the
+        following paper: D.J. Best and N.I. Fisher, "Efficient simulation of the
+        von Mises distribution." Applied Statistics (1979): 152-157.
+
+        Sampling is always done in double precision internally to avoid a hang
+        in _rejection_sample() for small values of the concentration, which
+        starts to happen for single precision around 1e-4 (see issue #88443).
+        """
+        shape = self._extended_shape(sample_shape)
+        x = torch.empty(shape, dtype=self._loc.dtype, device=self.loc.device)
+        return _rejection_sample(
+            self._loc, self._concentration, self._proposal_r, x
+        ).to(self.loc.dtype)
+
+    def expand(self, batch_shape, _instance=None):
+        try:
+            return super().expand(batch_shape)
+        except NotImplementedError:
+            validate_args = self.__dict__.get("_validate_args")
+            loc = self.loc.expand(batch_shape)
+            concentration = self.concentration.expand(batch_shape)
+            return type(self)(loc, concentration, validate_args=validate_args)
+
+    @property
+    def mean(self) -> Tensor:
+        """
+        The provided mean is the circular one.
+        """
+        return self.loc
+
+    @property
+    def mode(self) -> Tensor:
+        return self.loc
+
+    @lazy_property
+    def variance(self) -> Tensor:  # type: ignore[override]
+        """
+        The provided variance is the circular one.
+        """
+        return (
+            1
+            - (
+                _log_modified_bessel_fn(self.concentration, order=1)
+                - _log_modified_bessel_fn(self.concentration, order=0)
+            ).exp()
+        )