Initial import: grid-bot — grid trading bot for BTC-USDT on Cifra Markets

2026-09-24 13:22:23 +07:00
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+# mypy: allow-untyped-defs
+import math
+
+import torch
+from torch import inf, nan, Tensor
+from torch.distributions import Chi2, constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import _standard_normal, broadcast_all
+from torch.types import _size
+
+
+__all__ = ["StudentT"]
+
+
+class StudentT(Distribution):
+    r"""
+    Creates a Student's t-distribution parameterized by degree of
+    freedom :attr:`df`, mean :attr:`loc` and scale :attr:`scale`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = StudentT(torch.tensor([2.0]))
+        >>> m.sample()  # Student's t-distributed with degrees of freedom=2
+        tensor([ 0.1046])
+
+    Args:
+        df (float or Tensor): degrees of freedom
+        loc (float or Tensor): mean of the distribution
+        scale (float or Tensor): scale of the distribution
+    """
+
+    # pyrefly: ignore [bad-override]
+    arg_constraints = {
+        "df": constraints.positive,
+        "loc": constraints.real,
+        "scale": constraints.positive,
+    }
+    support = constraints.real
+    has_rsample = True
+
+    @property
+    def mean(self) -> Tensor:
+        m = self.loc.clone(memory_format=torch.contiguous_format)
+        m[self.df <= 1] = nan
+        return m
+
+    @property
+    def mode(self) -> Tensor:
+        return self.loc
+
+    @property
+    def variance(self) -> Tensor:
+        m = self.df.clone(memory_format=torch.contiguous_format)
+        m[self.df > 2] = (
+            self.scale[self.df > 2].pow(2)
+            * self.df[self.df > 2]
+            / (self.df[self.df > 2] - 2)
+        )
+        m[(self.df <= 2) & (self.df > 1)] = inf
+        m[self.df <= 1] = nan
+        return m
+
+    def __init__(
+        self,
+        df: Tensor | float,
+        loc: Tensor | float = 0.0,
+        scale: Tensor | float = 1.0,
+        validate_args: bool | None = None,
+    ) -> None:
+        self.df, self.loc, self.scale = broadcast_all(df, loc, scale)
+        self._chi2 = Chi2(self.df)
+        batch_shape = self.df.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(StudentT, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.df = self.df.expand(batch_shape)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        new._chi2 = self._chi2.expand(batch_shape)
+        super(StudentT, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def rsample(self, sample_shape: _size = torch.Size()) -> Tensor:
+        # NOTE: This does not agree with scipy implementation as much as other distributions.
+        # (see https://github.com/fritzo/notebooks/blob/master/debug-student-t.ipynb). Using DoubleTensor
+        # parameters seems to help.
+
+        #   X ~ Normal(0, 1)
+        #   Z ~ Chi2(df)
+        #   Y = X / sqrt(Z / df) ~ StudentT(df)
+        shape = self._extended_shape(sample_shape)
+        X = _standard_normal(shape, dtype=self.df.dtype, device=self.df.device)
+        Z = self._chi2.rsample(sample_shape)
+        Y = X * torch.rsqrt(Z / self.df)
+        return self.loc + self.scale * Y
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        y = (value - self.loc) / self.scale
+        Z = (
+            self.scale.log()
+            + 0.5 * self.df.log()
+            + 0.5 * math.log(math.pi)
+            + torch.lgamma(0.5 * self.df)
+            - torch.lgamma(0.5 * (self.df + 1.0))
+        )
+        return -0.5 * (self.df + 1.0) * torch.log1p(y**2.0 / self.df) - Z
+
+    def entropy(self):
+        lbeta = (
+            torch.lgamma(0.5 * self.df)
+            + math.lgamma(0.5)
+            - torch.lgamma(0.5 * (self.df + 1))
+        )
+        return (
+            self.scale.log()
+            + 0.5
+            * (self.df + 1)
+            * (torch.digamma(0.5 * (self.df + 1)) - torch.digamma(0.5 * self.df))
+            + 0.5 * self.df.log()
+            + lbeta
+        )