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ckpts/universal/global_step120/zero/7.attention.query_key_value.weight/exp_avg.pt

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+version https://git-lfs.github.com/spec/v1
+oid sha256:14abea4c43e48d1f4affe5a9d8d7b0feee8ca83a5ed9f53867d7ae700ebd5487
+size 50332828

venv/lib/python3.10/site-packages/torch/distributions/beta.py

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+from numbers import Number, Real
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.dirichlet import Dirichlet
+from torch.distributions.exp_family import ExponentialFamily
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Beta"]
+
+
+class Beta(ExponentialFamily):
+    r"""
+    Beta distribution parameterized by :attr:`concentration1` and :attr:`concentration0`.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Beta(torch.tensor([0.5]), torch.tensor([0.5]))
+        >>> m.sample()  # Beta distributed with concentration concentration1 and concentration0
+        tensor([ 0.1046])
+
+    Args:
+        concentration1 (float or Tensor): 1st concentration parameter of the distribution
+            (often referred to as alpha)
+        concentration0 (float or Tensor): 2nd concentration parameter of the distribution
+            (often referred to as beta)
+    """
+    arg_constraints = {
+        "concentration1": constraints.positive,
+        "concentration0": constraints.positive,
+    }
+    support = constraints.unit_interval
+    has_rsample = True
+
+    def __init__(self, concentration1, concentration0, validate_args=None):
+        if isinstance(concentration1, Real) and isinstance(concentration0, Real):
+            concentration1_concentration0 = torch.tensor(
+                [float(concentration1), float(concentration0)]
+            )
+        else:
+            concentration1, concentration0 = broadcast_all(
+                concentration1, concentration0
+            )
+            concentration1_concentration0 = torch.stack(
+                [concentration1, concentration0], -1
+            )
+        self._dirichlet = Dirichlet(
+            concentration1_concentration0, validate_args=validate_args
+        )
+        super().__init__(self._dirichlet._batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Beta, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new._dirichlet = self._dirichlet.expand(batch_shape)
+        super(Beta, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def mean(self):
+        return self.concentration1 / (self.concentration1 + self.concentration0)
+
+    @property
+    def mode(self):
+        return self._dirichlet.mode[..., 0]
+
+    @property
+    def variance(self):
+        total = self.concentration1 + self.concentration0
+        return self.concentration1 * self.concentration0 / (total.pow(2) * (total + 1))
+
+    def rsample(self, sample_shape=()):
+        return self._dirichlet.rsample(sample_shape).select(-1, 0)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        heads_tails = torch.stack([value, 1.0 - value], -1)
+        return self._dirichlet.log_prob(heads_tails)
+
+    def entropy(self):
+        return self._dirichlet.entropy()
+
+    @property
+    def concentration1(self):
+        result = self._dirichlet.concentration[..., 0]
+        if isinstance(result, Number):
+            return torch.tensor([result])
+        else:
+            return result
+
+    @property
+    def concentration0(self):
+        result = self._dirichlet.concentration[..., 1]
+        if isinstance(result, Number):
+            return torch.tensor([result])
+        else:
+            return result
+
+    @property
+    def _natural_params(self):
+        return (self.concentration1, self.concentration0)
+
+    def _log_normalizer(self, x, y):
+        return torch.lgamma(x) + torch.lgamma(y) - torch.lgamma(x + y)

venv/lib/python3.10/site-packages/torch/distributions/categorical.py

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+import torch
+from torch import nan
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import lazy_property, logits_to_probs, probs_to_logits
+
+__all__ = ["Categorical"]
+
+
+class Categorical(Distribution):
+    r"""
+    Creates a categorical distribution parameterized by either :attr:`probs` or
+    :attr:`logits` (but not both).
+
+    .. note::
+        It is equivalent to the distribution that :func:`torch.multinomial`
+        samples from.
+
+    Samples are integers from :math:`\{0, \ldots, K-1\}` where `K` is ``probs.size(-1)``.
+
+    If `probs` is 1-dimensional with length-`K`, each element is the relative probability
+    of sampling the class at that index.
+
+    If `probs` is N-dimensional, the first N-1 dimensions are treated as a batch of
+    relative probability vectors.
+
+    .. note:: The `probs` argument must be non-negative, finite and have a non-zero sum,
+              and it will be normalized to sum to 1 along the last dimension. :attr:`probs`
+              will return this normalized value.
+              The `logits` argument will be interpreted as unnormalized log probabilities
+              and can therefore be any real number. It will likewise be normalized so that
+              the resulting probabilities sum to 1 along the last dimension. :attr:`logits`
+              will return this normalized value.
+
+    See also: :func:`torch.multinomial`
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Categorical(torch.tensor([ 0.25, 0.25, 0.25, 0.25 ]))
+        >>> m.sample()  # equal probability of 0, 1, 2, 3
+        tensor(3)
+
+    Args:
+        probs (Tensor): event probabilities
+        logits (Tensor): event log probabilities (unnormalized)
+    """
+    arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector}
+    has_enumerate_support = True
+
+    def __init__(self, probs=None, logits=None, validate_args=None):
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            if probs.dim() < 1:
+                raise ValueError("`probs` parameter must be at least one-dimensional.")
+            self.probs = probs / probs.sum(-1, keepdim=True)
+        else:
+            if logits.dim() < 1:
+                raise ValueError("`logits` parameter must be at least one-dimensional.")
+            # Normalize
+            self.logits = logits - logits.logsumexp(dim=-1, keepdim=True)
+        self._param = self.probs if probs is not None else self.logits
+        self._num_events = self._param.size()[-1]
+        batch_shape = (
+            self._param.size()[:-1] if self._param.ndimension() > 1 else torch.Size()
+        )
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Categorical, _instance)
+        batch_shape = torch.Size(batch_shape)
+        param_shape = batch_shape + torch.Size((self._num_events,))
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(param_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(param_shape)
+            new._param = new.logits
+        new._num_events = self._num_events
+        super(Categorical, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    @constraints.dependent_property(is_discrete=True, event_dim=0)
+    def support(self):
+        return constraints.integer_interval(0, self._num_events - 1)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits)
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    @property
+    def mean(self):
+        return torch.full(
+            self._extended_shape(),
+            nan,
+            dtype=self.probs.dtype,
+            device=self.probs.device,
+        )
+
+    @property
+    def mode(self):
+        return self.probs.argmax(axis=-1)
+
+    @property
+    def variance(self):
+        return torch.full(
+            self._extended_shape(),
+            nan,
+            dtype=self.probs.dtype,
+            device=self.probs.device,
+        )
+
+    def sample(self, sample_shape=torch.Size()):
+        if not isinstance(sample_shape, torch.Size):
+            sample_shape = torch.Size(sample_shape)
+        probs_2d = self.probs.reshape(-1, self._num_events)
+        samples_2d = torch.multinomial(probs_2d, sample_shape.numel(), True).T
+        return samples_2d.reshape(self._extended_shape(sample_shape))
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        value = value.long().unsqueeze(-1)
+        value, log_pmf = torch.broadcast_tensors(value, self.logits)
+        value = value[..., :1]
+        return log_pmf.gather(-1, value).squeeze(-1)
+
+    def entropy(self):
+        min_real = torch.finfo(self.logits.dtype).min
+        logits = torch.clamp(self.logits, min=min_real)
+        p_log_p = logits * self.probs
+        return -p_log_p.sum(-1)
+
+    def enumerate_support(self, expand=True):
+        num_events = self._num_events
+        values = torch.arange(num_events, dtype=torch.long, device=self._param.device)
+        values = values.view((-1,) + (1,) * len(self._batch_shape))
+        if expand:
+            values = values.expand((-1,) + self._batch_shape)
+        return values

venv/lib/python3.10/site-packages/torch/distributions/cauchy.py

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+import math
+from numbers import Number
+
+import torch
+from torch import inf, nan
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Cauchy"]
+
+
+class Cauchy(Distribution):
+    r"""
+    Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of
+    independent normally distributed random variables with means `0` follows a
+    Cauchy distribution.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Cauchy(torch.tensor([0.0]), torch.tensor([1.0]))
+        >>> m.sample()  # sample from a Cauchy distribution with loc=0 and scale=1
+        tensor([ 2.3214])
+
+    Args:
+        loc (float or Tensor): mode or median of the distribution.
+        scale (float or Tensor): half width at half maximum.
+    """
+    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
+    support = constraints.real
+    has_rsample = True
+
+    def __init__(self, loc, scale, validate_args=None):
+        self.loc, self.scale = broadcast_all(loc, scale)
+        if isinstance(loc, Number) and isinstance(scale, Number):
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self.loc.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Cauchy, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.loc = self.loc.expand(batch_shape)
+        new.scale = self.scale.expand(batch_shape)
+        super(Cauchy, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def mean(self):
+        return torch.full(
+            self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device
+        )
+
+    @property
+    def mode(self):
+        return self.loc
+
+    @property
+    def variance(self):
+        return torch.full(
+            self._extended_shape(), inf, dtype=self.loc.dtype, device=self.loc.device
+        )
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        eps = self.loc.new(shape).cauchy_()
+        return self.loc + eps * self.scale
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        return (
+            -math.log(math.pi)
+            - self.scale.log()
+            - (((value - self.loc) / self.scale) ** 2).log1p()
+        )
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        return torch.atan((value - self.loc) / self.scale) / math.pi + 0.5
+
+    def icdf(self, value):
+        return torch.tan(math.pi * (value - 0.5)) * self.scale + self.loc
+
+    def entropy(self):
+        return math.log(4 * math.pi) + self.scale.log()

venv/lib/python3.10/site-packages/torch/distributions/chi2.py

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+from torch.distributions import constraints
+from torch.distributions.gamma import Gamma
+
+__all__ = ["Chi2"]
+
+
+class Chi2(Gamma):
+    r"""
+    Creates a Chi-squared distribution parameterized by shape parameter :attr:`df`.
+    This is exactly equivalent to ``Gamma(alpha=0.5*df, beta=0.5)``
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Chi2(torch.tensor([1.0]))
+        >>> m.sample()  # Chi2 distributed with shape df=1
+        tensor([ 0.1046])
+
+    Args:
+        df (float or Tensor): shape parameter of the distribution
+    """
+    arg_constraints = {"df": constraints.positive}
+
+    def __init__(self, df, validate_args=None):
+        super().__init__(0.5 * df, 0.5, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Chi2, _instance)
+        return super().expand(batch_shape, new)
+
+    @property
+    def df(self):
+        return self.concentration * 2

venv/lib/python3.10/site-packages/torch/distributions/independent.py

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+from typing import Dict
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import _sum_rightmost
+
+__all__ = ["Independent"]
+
+
+class Independent(Distribution):
+    r"""
+    Reinterprets some of the batch dims of a distribution as event dims.
+
+    This is mainly useful for changing the shape of the result of
+    :meth:`log_prob`. For example to create a diagonal Normal distribution with
+    the same shape as a Multivariate Normal distribution (so they are
+    interchangeable), you can::
+
+        >>> from torch.distributions.multivariate_normal import MultivariateNormal
+        >>> from torch.distributions.normal import Normal
+        >>> loc = torch.zeros(3)
+        >>> scale = torch.ones(3)
+        >>> mvn = MultivariateNormal(loc, scale_tril=torch.diag(scale))
+        >>> [mvn.batch_shape, mvn.event_shape]
+        [torch.Size([]), torch.Size([3])]
+        >>> normal = Normal(loc, scale)
+        >>> [normal.batch_shape, normal.event_shape]
+        [torch.Size([3]), torch.Size([])]
+        >>> diagn = Independent(normal, 1)
+        >>> [diagn.batch_shape, diagn.event_shape]
+        [torch.Size([]), torch.Size([3])]
+
+    Args:
+        base_distribution (torch.distributions.distribution.Distribution): a
+            base distribution
+        reinterpreted_batch_ndims (int): the number of batch dims to
+            reinterpret as event dims
+    """
+    arg_constraints: Dict[str, constraints.Constraint] = {}
+
+    def __init__(
+        self, base_distribution, reinterpreted_batch_ndims, validate_args=None
+    ):
+        if reinterpreted_batch_ndims > len(base_distribution.batch_shape):
+            raise ValueError(
+                "Expected reinterpreted_batch_ndims <= len(base_distribution.batch_shape), "
+                f"actual {reinterpreted_batch_ndims} vs {len(base_distribution.batch_shape)}"
+            )
+        shape = base_distribution.batch_shape + base_distribution.event_shape
+        event_dim = reinterpreted_batch_ndims + len(base_distribution.event_shape)
+        batch_shape = shape[: len(shape) - event_dim]
+        event_shape = shape[len(shape) - event_dim :]
+        self.base_dist = base_distribution
+        self.reinterpreted_batch_ndims = reinterpreted_batch_ndims
+        super().__init__(batch_shape, event_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Independent, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.base_dist = self.base_dist.expand(
+            batch_shape + self.event_shape[: self.reinterpreted_batch_ndims]
+        )
+        new.reinterpreted_batch_ndims = self.reinterpreted_batch_ndims
+        super(Independent, new).__init__(
+            batch_shape, self.event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def has_rsample(self):
+        return self.base_dist.has_rsample
+
+    @property
+    def has_enumerate_support(self):
+        if self.reinterpreted_batch_ndims > 0:
+            return False
+        return self.base_dist.has_enumerate_support
+
+    @constraints.dependent_property
+    def support(self):
+        result = self.base_dist.support
+        if self.reinterpreted_batch_ndims:
+            result = constraints.independent(result, self.reinterpreted_batch_ndims)
+        return result
+
+    @property
+    def mean(self):
+        return self.base_dist.mean
+
+    @property
+    def mode(self):
+        return self.base_dist.mode
+
+    @property
+    def variance(self):
+        return self.base_dist.variance
+
+    def sample(self, sample_shape=torch.Size()):
+        return self.base_dist.sample(sample_shape)
+
+    def rsample(self, sample_shape=torch.Size()):
+        return self.base_dist.rsample(sample_shape)
+
+    def log_prob(self, value):
+        log_prob = self.base_dist.log_prob(value)
+        return _sum_rightmost(log_prob, self.reinterpreted_batch_ndims)
+
+    def entropy(self):
+        entropy = self.base_dist.entropy()
+        return _sum_rightmost(entropy, self.reinterpreted_batch_ndims)
+
+    def enumerate_support(self, expand=True):
+        if self.reinterpreted_batch_ndims > 0:
+            raise NotImplementedError(
+                "Enumeration over cartesian product is not implemented"
+            )
+        return self.base_dist.enumerate_support(expand=expand)
+
+    def __repr__(self):
+        return (
+            self.__class__.__name__
+            + f"({self.base_dist}, {self.reinterpreted_batch_ndims})"
+        )

venv/lib/python3.10/site-packages/torch/distributions/lkj_cholesky.py

@@ -0,0 +1,142 @@
+"""
+This closely follows the implementation in NumPyro (https://github.com/pyro-ppl/numpyro).
+
+Original copyright notice:
+
+# Copyright: Contributors to the Pyro project.
+# SPDX-License-Identifier: Apache-2.0
+"""
+
+import math
+
+import torch
+from torch.distributions import Beta, constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["LKJCholesky"]
+
+
+class LKJCholesky(Distribution):
+    r"""
+    LKJ distribution for lower Cholesky factor of correlation matrices.
+    The distribution is controlled by ``concentration`` parameter :math:`\eta`
+    to make the probability of the correlation matrix :math:`M` generated from
+    a Cholesky factor proportional to :math:`\det(M)^{\eta - 1}`. Because of that,
+    when ``concentration == 1``, we have a uniform distribution over Cholesky
+    factors of correlation matrices::
+
+        L ~ LKJCholesky(dim, concentration)
+        X = L @ L' ~ LKJCorr(dim, concentration)
+
+    Note that this distribution samples the
+    Cholesky factor of correlation matrices and not the correlation matrices
+    themselves and thereby differs slightly from the derivations in [1] for
+    the `LKJCorr` distribution. For sampling, this uses the Onion method from
+    [1] Section 3.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> l = LKJCholesky(3, 0.5)
+        >>> l.sample()  # l @ l.T is a sample of a correlation 3x3 matrix
+        tensor([[ 1.0000,  0.0000,  0.0000],
+                [ 0.3516,  0.9361,  0.0000],
+                [-0.1899,  0.4748,  0.8593]])
+
+    Args:
+        dimension (dim): dimension of the matrices
+        concentration (float or Tensor): concentration/shape parameter of the
+            distribution (often referred to as eta)
+
+    **References**
+
+    [1] `Generating random correlation matrices based on vines and extended onion method` (2009),
+    Daniel Lewandowski, Dorota Kurowicka, Harry Joe.
+    Journal of Multivariate Analysis. 100. 10.1016/j.jmva.2009.04.008
+    """
+    arg_constraints = {"concentration": constraints.positive}
+    support = constraints.corr_cholesky
+
+    def __init__(self, dim, concentration=1.0, validate_args=None):
+        if dim < 2:
+            raise ValueError(
+                f"Expected dim to be an integer greater than or equal to 2. Found dim={dim}."
+            )
+        self.dim = dim
+        (self.concentration,) = broadcast_all(concentration)
+        batch_shape = self.concentration.size()
+        event_shape = torch.Size((dim, dim))
+        # This is used to draw vectorized samples from the beta distribution in Sec. 3.2 of [1].
+        marginal_conc = self.concentration + 0.5 * (self.dim - 2)
+        offset = torch.arange(
+            self.dim - 1,
+            dtype=self.concentration.dtype,
+            device=self.concentration.device,
+        )
+        offset = torch.cat([offset.new_zeros((1,)), offset])
+        beta_conc1 = offset + 0.5
+        beta_conc0 = marginal_conc.unsqueeze(-1) - 0.5 * offset
+        self._beta = Beta(beta_conc1, beta_conc0)
+        super().__init__(batch_shape, event_shape, validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(LKJCholesky, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.dim = self.dim
+        new.concentration = self.concentration.expand(batch_shape)
+        new._beta = self._beta.expand(batch_shape + (self.dim,))
+        super(LKJCholesky, new).__init__(
+            batch_shape, self.event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    def sample(self, sample_shape=torch.Size()):
+        # This uses the Onion method, but there are a few differences from [1] Sec. 3.2:
+        # - This vectorizes the for loop and also works for heterogeneous eta.
+        # - Same algorithm generalizes to n=1.
+        # - The procedure is simplified since we are sampling the cholesky factor of
+        #   the correlation matrix instead of the correlation matrix itself. As such,
+        #   we only need to generate `w`.
+        y = self._beta.sample(sample_shape).unsqueeze(-1)
+        u_normal = torch.randn(
+            self._extended_shape(sample_shape), dtype=y.dtype, device=y.device
+        ).tril(-1)
+        u_hypersphere = u_normal / u_normal.norm(dim=-1, keepdim=True)
+        # Replace NaNs in first row
+        u_hypersphere[..., 0, :].fill_(0.0)
+        w = torch.sqrt(y) * u_hypersphere
+        # Fill diagonal elements; clamp for numerical stability
+        eps = torch.finfo(w.dtype).tiny
+        diag_elems = torch.clamp(1 - torch.sum(w**2, dim=-1), min=eps).sqrt()
+        w += torch.diag_embed(diag_elems)
+        return w
+
+    def log_prob(self, value):
+        # See: https://mc-stan.org/docs/2_25/functions-reference/cholesky-lkj-correlation-distribution.html
+        # The probability of a correlation matrix is proportional to
+        #   determinant ** (concentration - 1) = prod(L_ii ^ 2(concentration - 1))
+        # Additionally, the Jacobian of the transformation from Cholesky factor to
+        # correlation matrix is:
+        #   prod(L_ii ^ (D - i))
+        # So the probability of a Cholesky factor is propotional to
+        #   prod(L_ii ^ (2 * concentration - 2 + D - i)) = prod(L_ii ^ order_i)
+        # with order_i = 2 * concentration - 2 + D - i
+        if self._validate_args:
+            self._validate_sample(value)
+        diag_elems = value.diagonal(dim1=-1, dim2=-2)[..., 1:]
+        order = torch.arange(2, self.dim + 1, device=self.concentration.device)
+        order = 2 * (self.concentration - 1).unsqueeze(-1) + self.dim - order
+        unnormalized_log_pdf = torch.sum(order * diag_elems.log(), dim=-1)
+        # Compute normalization constant (page 1999 of [1])
+        dm1 = self.dim - 1
+        alpha = self.concentration + 0.5 * dm1
+        denominator = torch.lgamma(alpha) * dm1
+        numerator = torch.mvlgamma(alpha - 0.5, dm1)
+        # pi_constant in [1] is D * (D - 1) / 4 * log(pi)
+        # pi_constant in multigammaln is (D - 1) * (D - 2) / 4 * log(pi)
+        # hence, we need to add a pi_constant = (D - 1) * log(pi) / 2
+        pi_constant = 0.5 * dm1 * math.log(math.pi)
+        normalize_term = pi_constant + numerator - denominator
+        return unnormalized_log_pdf - normalize_term

venv/lib/python3.10/site-packages/torch/distributions/log_normal.py

@@ -0,0 +1,62 @@
+from torch.distributions import constraints
+from torch.distributions.normal import Normal
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import ExpTransform
+
+__all__ = ["LogNormal"]
+
+
+class LogNormal(TransformedDistribution):
+    r"""
+    Creates a log-normal distribution parameterized by
+    :attr:`loc` and :attr:`scale` where::
+
+        X ~ Normal(loc, scale)
+        Y = exp(X) ~ LogNormal(loc, scale)
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = LogNormal(torch.tensor([0.0]), torch.tensor([1.0]))
+        >>> m.sample()  # log-normal distributed with mean=0 and stddev=1
+        tensor([ 0.1046])
+
+    Args:
+        loc (float or Tensor): mean of log of distribution
+        scale (float or Tensor): standard deviation of log of the distribution
+    """
+    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
+    support = constraints.positive
+    has_rsample = True
+
+    def __init__(self, loc, scale, validate_args=None):
+        base_dist = Normal(loc, scale, validate_args=validate_args)
+        super().__init__(base_dist, ExpTransform(), validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(LogNormal, _instance)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def loc(self):
+        return self.base_dist.loc
+
+    @property
+    def scale(self):
+        return self.base_dist.scale
+
+    @property
+    def mean(self):
+        return (self.loc + self.scale.pow(2) / 2).exp()
+
+    @property
+    def mode(self):
+        return (self.loc - self.scale.square()).exp()
+
+    @property
+    def variance(self):
+        scale_sq = self.scale.pow(2)
+        return scale_sq.expm1() * (2 * self.loc + scale_sq).exp()
+
+    def entropy(self):
+        return self.base_dist.entropy() + self.loc

venv/lib/python3.10/site-packages/torch/distributions/multinomial.py

@@ -0,0 +1,135 @@
+import torch
+from torch import inf
+from torch.distributions import Categorical, constraints
+from torch.distributions.binomial import Binomial
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Multinomial"]
+
+
+class Multinomial(Distribution):
+    r"""
+    Creates a Multinomial distribution parameterized by :attr:`total_count` and
+    either :attr:`probs` or :attr:`logits` (but not both). The innermost dimension of
+    :attr:`probs` indexes over categories. All other dimensions index over batches.
+
+    Note that :attr:`total_count` need not be specified if only :meth:`log_prob` is
+    called (see example below)
+
+    .. note:: The `probs` argument must be non-negative, finite and have a non-zero sum,
+              and it will be normalized to sum to 1 along the last dimension. :attr:`probs`
+              will return this normalized value.
+              The `logits` argument will be interpreted as unnormalized log probabilities
+              and can therefore be any real number. It will likewise be normalized so that
+              the resulting probabilities sum to 1 along the last dimension. :attr:`logits`
+              will return this normalized value.
+
+    -   :meth:`sample` requires a single shared `total_count` for all
+        parameters and samples.
+    -   :meth:`log_prob` allows different `total_count` for each parameter and
+        sample.
+
+    Example::
+
+        >>> # xdoctest: +SKIP("FIXME: found invalid values")
+        >>> m = Multinomial(100, torch.tensor([ 1., 1., 1., 1.]))
+        >>> x = m.sample()  # equal probability of 0, 1, 2, 3
+        tensor([ 21.,  24.,  30.,  25.])
+
+        >>> Multinomial(probs=torch.tensor([1., 1., 1., 1.])).log_prob(x)
+        tensor([-4.1338])
+
+    Args:
+        total_count (int): number of trials
+        probs (Tensor): event probabilities
+        logits (Tensor): event log probabilities (unnormalized)
+    """
+    arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector}
+    total_count: int
+
+    @property
+    def mean(self):
+        return self.probs * self.total_count
+
+    @property
+    def variance(self):
+        return self.total_count * self.probs * (1 - self.probs)
+
+    def __init__(self, total_count=1, probs=None, logits=None, validate_args=None):
+        if not isinstance(total_count, int):
+            raise NotImplementedError("inhomogeneous total_count is not supported")
+        self.total_count = total_count
+        self._categorical = Categorical(probs=probs, logits=logits)
+        self._binomial = Binomial(total_count=total_count, probs=self.probs)
+        batch_shape = self._categorical.batch_shape
+        event_shape = self._categorical.param_shape[-1:]
+        super().__init__(batch_shape, event_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Multinomial, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.total_count = self.total_count
+        new._categorical = self._categorical.expand(batch_shape)
+        super(Multinomial, new).__init__(
+            batch_shape, self.event_shape, validate_args=False
+        )
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._categorical._new(*args, **kwargs)
+
+    @constraints.dependent_property(is_discrete=True, event_dim=1)
+    def support(self):
+        return constraints.multinomial(self.total_count)
+
+    @property
+    def logits(self):
+        return self._categorical.logits
+
+    @property
+    def probs(self):
+        return self._categorical.probs
+
+    @property
+    def param_shape(self):
+        return self._categorical.param_shape
+
+    def sample(self, sample_shape=torch.Size()):
+        sample_shape = torch.Size(sample_shape)
+        samples = self._categorical.sample(
+            torch.Size((self.total_count,)) + sample_shape
+        )
+        # samples.shape is (total_count, sample_shape, batch_shape), need to change it to
+        # (sample_shape, batch_shape, total_count)
+        shifted_idx = list(range(samples.dim()))
+        shifted_idx.append(shifted_idx.pop(0))
+        samples = samples.permute(*shifted_idx)
+        counts = samples.new(self._extended_shape(sample_shape)).zero_()
+        counts.scatter_add_(-1, samples, torch.ones_like(samples))
+        return counts.type_as(self.probs)
+
+    def entropy(self):
+        n = torch.tensor(self.total_count)
+
+        cat_entropy = self._categorical.entropy()
+        term1 = n * cat_entropy - torch.lgamma(n + 1)
+
+        support = self._binomial.enumerate_support(expand=False)[1:]
+        binomial_probs = torch.exp(self._binomial.log_prob(support))
+        weights = torch.lgamma(support + 1)
+        term2 = (binomial_probs * weights).sum([0, -1])
+
+        return term1 + term2
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        logits, value = broadcast_all(self.logits, value)
+        logits = logits.clone(memory_format=torch.contiguous_format)
+        log_factorial_n = torch.lgamma(value.sum(-1) + 1)
+        log_factorial_xs = torch.lgamma(value + 1).sum(-1)
+        logits[(value == 0) & (logits == -inf)] = 0
+        log_powers = (logits * value).sum(-1)
+        return log_factorial_n - log_factorial_xs + log_powers

venv/lib/python3.10/site-packages/torch/distributions/pareto.py

@@ -0,0 +1,60 @@
+from torch.distributions import constraints
+from torch.distributions.exponential import Exponential
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AffineTransform, ExpTransform
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Pareto"]
+
+
+class Pareto(TransformedDistribution):
+    r"""
+    Samples from a Pareto Type 1 distribution.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Pareto(torch.tensor([1.0]), torch.tensor([1.0]))
+        >>> m.sample()  # sample from a Pareto distribution with scale=1 and alpha=1
+        tensor([ 1.5623])
+
+    Args:
+        scale (float or Tensor): Scale parameter of the distribution
+        alpha (float or Tensor): Shape parameter of the distribution
+    """
+    arg_constraints = {"alpha": constraints.positive, "scale": constraints.positive}
+
+    def __init__(self, scale, alpha, validate_args=None):
+        self.scale, self.alpha = broadcast_all(scale, alpha)
+        base_dist = Exponential(self.alpha, validate_args=validate_args)
+        transforms = [ExpTransform(), AffineTransform(loc=0, scale=self.scale)]
+        super().__init__(base_dist, transforms, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Pareto, _instance)
+        new.scale = self.scale.expand(batch_shape)
+        new.alpha = self.alpha.expand(batch_shape)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def mean(self):
+        # mean is inf for alpha <= 1
+        a = self.alpha.clamp(min=1)
+        return a * self.scale / (a - 1)
+
+    @property
+    def mode(self):
+        return self.scale
+
+    @property
+    def variance(self):
+        # var is inf for alpha <= 2
+        a = self.alpha.clamp(min=2)
+        return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2))
+
+    @constraints.dependent_property(is_discrete=False, event_dim=0)
+    def support(self):
+        return constraints.greater_than_eq(self.scale)
+
+    def entropy(self):
+        return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal())

venv/lib/python3.10/site-packages/torch/distributions/relaxed_bernoulli.py

@@ -0,0 +1,149 @@
+from numbers import Number
+
+import torch
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import SigmoidTransform
+from torch.distributions.utils import (
+    broadcast_all,
+    clamp_probs,
+    lazy_property,
+    logits_to_probs,
+    probs_to_logits,
+)
+
+__all__ = ["LogitRelaxedBernoulli", "RelaxedBernoulli"]
+
+
+class LogitRelaxedBernoulli(Distribution):
+    r"""
+    Creates a LogitRelaxedBernoulli distribution parameterized by :attr:`probs`
+    or :attr:`logits` (but not both), which is the logit of a RelaxedBernoulli
+    distribution.
+
+    Samples are logits of values in (0, 1). See [1] for more details.
+
+    Args:
+        temperature (Tensor): relaxation temperature
+        probs (Number, Tensor): the probability of sampling `1`
+        logits (Number, Tensor): the log-odds of sampling `1`
+
+    [1] The Concrete Distribution: A Continuous Relaxation of Discrete Random
+    Variables (Maddison et al, 2017)
+
+    [2] Categorical Reparametrization with Gumbel-Softmax
+    (Jang et al, 2017)
+    """
+    arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real}
+    support = constraints.real
+
+    def __init__(self, temperature, probs=None, logits=None, validate_args=None):
+        self.temperature = temperature
+        if (probs is None) == (logits is None):
+            raise ValueError(
+                "Either `probs` or `logits` must be specified, but not both."
+            )
+        if probs is not None:
+            is_scalar = isinstance(probs, Number)
+            (self.probs,) = broadcast_all(probs)
+        else:
+            is_scalar = isinstance(logits, Number)
+            (self.logits,) = broadcast_all(logits)
+        self._param = self.probs if probs is not None else self.logits
+        if is_scalar:
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self._param.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(LogitRelaxedBernoulli, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.temperature = self.temperature
+        if "probs" in self.__dict__:
+            new.probs = self.probs.expand(batch_shape)
+            new._param = new.probs
+        if "logits" in self.__dict__:
+            new.logits = self.logits.expand(batch_shape)
+            new._param = new.logits
+        super(LogitRelaxedBernoulli, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    def _new(self, *args, **kwargs):
+        return self._param.new(*args, **kwargs)
+
+    @lazy_property
+    def logits(self):
+        return probs_to_logits(self.probs, is_binary=True)
+
+    @lazy_property
+    def probs(self):
+        return logits_to_probs(self.logits, is_binary=True)
+
+    @property
+    def param_shape(self):
+        return self._param.size()
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        probs = clamp_probs(self.probs.expand(shape))
+        uniforms = clamp_probs(
+            torch.rand(shape, dtype=probs.dtype, device=probs.device)
+        )
+        return (
+            uniforms.log() - (-uniforms).log1p() + probs.log() - (-probs).log1p()
+        ) / self.temperature
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        logits, value = broadcast_all(self.logits, value)
+        diff = logits - value.mul(self.temperature)
+        return self.temperature.log() + diff - 2 * diff.exp().log1p()
+
+
+class RelaxedBernoulli(TransformedDistribution):
+    r"""
+    Creates a RelaxedBernoulli distribution, parametrized by
+    :attr:`temperature`, and either :attr:`probs` or :attr:`logits`
+    (but not both). This is a relaxed version of the `Bernoulli` distribution,
+    so the values are in (0, 1), and has reparametrizable samples.
+
+    Example::
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = RelaxedBernoulli(torch.tensor([2.2]),
+        ...                      torch.tensor([0.1, 0.2, 0.3, 0.99]))
+        >>> m.sample()
+        tensor([ 0.2951,  0.3442,  0.8918,  0.9021])
+
+    Args:
+        temperature (Tensor): relaxation temperature
+        probs (Number, Tensor): the probability of sampling `1`
+        logits (Number, Tensor): the log-odds of sampling `1`
+    """
+    arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real}
+    support = constraints.unit_interval
+    has_rsample = True
+
+    def __init__(self, temperature, probs=None, logits=None, validate_args=None):
+        base_dist = LogitRelaxedBernoulli(temperature, probs, logits)
+        super().__init__(base_dist, SigmoidTransform(), validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(RelaxedBernoulli, _instance)
+        return super().expand(batch_shape, _instance=new)
+
+    @property
+    def temperature(self):
+        return self.base_dist.temperature
+
+    @property
+    def logits(self):
+        return self.base_dist.logits
+
+    @property
+    def probs(self):
+        return self.base_dist.probs

venv/lib/python3.10/site-packages/torch/distributions/transforms.py

@@ -0,0 +1,1245 @@
+import functools
+import math
+import numbers
+import operator
+import weakref
+from typing import List
+
+import torch
+import torch.nn.functional as F
+from torch.distributions import constraints
+from torch.distributions.utils import (
+    _sum_rightmost,
+    broadcast_all,
+    lazy_property,
+    tril_matrix_to_vec,
+    vec_to_tril_matrix,
+)
+from torch.nn.functional import pad, softplus
+
+__all__ = [
+    "AbsTransform",
+    "AffineTransform",
+    "CatTransform",
+    "ComposeTransform",
+    "CorrCholeskyTransform",
+    "CumulativeDistributionTransform",
+    "ExpTransform",
+    "IndependentTransform",
+    "LowerCholeskyTransform",
+    "PositiveDefiniteTransform",
+    "PowerTransform",
+    "ReshapeTransform",
+    "SigmoidTransform",
+    "SoftplusTransform",
+    "TanhTransform",
+    "SoftmaxTransform",
+    "StackTransform",
+    "StickBreakingTransform",
+    "Transform",
+    "identity_transform",
+]
+
+
+class Transform:
+    """
+    Abstract class for invertable transformations with computable log
+    det jacobians. They are primarily used in
+    :class:`torch.distributions.TransformedDistribution`.
+
+    Caching is useful for transforms whose inverses are either expensive or
+    numerically unstable. Note that care must be taken with memoized values
+    since the autograd graph may be reversed. For example while the following
+    works with or without caching::
+
+        y = t(x)
+        t.log_abs_det_jacobian(x, y).backward()  # x will receive gradients.
+
+    However the following will error when caching due to dependency reversal::
+
+        y = t(x)
+        z = t.inv(y)
+        grad(z.sum(), [y])  # error because z is x
+
+    Derived classes should implement one or both of :meth:`_call` or
+    :meth:`_inverse`. Derived classes that set `bijective=True` should also
+    implement :meth:`log_abs_det_jacobian`.
+
+    Args:
+        cache_size (int): Size of cache. If zero, no caching is done. If one,
+            the latest single value is cached. Only 0 and 1 are supported.
+
+    Attributes:
+        domain (:class:`~torch.distributions.constraints.Constraint`):
+            The constraint representing valid inputs to this transform.
+        codomain (:class:`~torch.distributions.constraints.Constraint`):
+            The constraint representing valid outputs to this transform
+            which are inputs to the inverse transform.
+        bijective (bool): Whether this transform is bijective. A transform
+            ``t`` is bijective iff ``t.inv(t(x)) == x`` and
+            ``t(t.inv(y)) == y`` for every ``x`` in the domain and ``y`` in
+            the codomain. Transforms that are not bijective should at least
+            maintain the weaker pseudoinverse properties
+            ``t(t.inv(t(x)) == t(x)`` and ``t.inv(t(t.inv(y))) == t.inv(y)``.
+        sign (int or Tensor): For bijective univariate transforms, this
+            should be +1 or -1 depending on whether transform is monotone
+            increasing or decreasing.
+    """
+
+    bijective = False
+    domain: constraints.Constraint
+    codomain: constraints.Constraint
+
+    def __init__(self, cache_size=0):
+        self._cache_size = cache_size
+        self._inv = None
+        if cache_size == 0:
+            pass  # default behavior
+        elif cache_size == 1:
+            self._cached_x_y = None, None
+        else:
+            raise ValueError("cache_size must be 0 or 1")
+        super().__init__()
+
+    def __getstate__(self):
+        state = self.__dict__.copy()
+        state["_inv"] = None
+        return state
+
+    @property
+    def event_dim(self):
+        if self.domain.event_dim == self.codomain.event_dim:
+            return self.domain.event_dim
+        raise ValueError("Please use either .domain.event_dim or .codomain.event_dim")
+
+    @property
+    def inv(self):
+        """
+        Returns the inverse :class:`Transform` of this transform.
+        This should satisfy ``t.inv.inv is t``.
+        """
+        inv = None
+        if self._inv is not None:
+            inv = self._inv()
+        if inv is None:
+            inv = _InverseTransform(self)
+            self._inv = weakref.ref(inv)
+        return inv
+
+    @property
+    def sign(self):
+        """
+        Returns the sign of the determinant of the Jacobian, if applicable.
+        In general this only makes sense for bijective transforms.
+        """
+        raise NotImplementedError
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        if type(self).__init__ is Transform.__init__:
+            return type(self)(cache_size=cache_size)
+        raise NotImplementedError(f"{type(self)}.with_cache is not implemented")
+
+    def __eq__(self, other):
+        return self is other
+
+    def __ne__(self, other):
+        # Necessary for Python2
+        return not self.__eq__(other)
+
+    def __call__(self, x):
+        """
+        Computes the transform `x => y`.
+        """
+        if self._cache_size == 0:
+            return self._call(x)
+        x_old, y_old = self._cached_x_y
+        if x is x_old:
+            return y_old
+        y = self._call(x)
+        self._cached_x_y = x, y
+        return y
+
+    def _inv_call(self, y):
+        """
+        Inverts the transform `y => x`.
+        """
+        if self._cache_size == 0:
+            return self._inverse(y)
+        x_old, y_old = self._cached_x_y
+        if y is y_old:
+            return x_old
+        x = self._inverse(y)
+        self._cached_x_y = x, y
+        return x
+
+    def _call(self, x):
+        """
+        Abstract method to compute forward transformation.
+        """
+        raise NotImplementedError
+
+    def _inverse(self, y):
+        """
+        Abstract method to compute inverse transformation.
+        """
+        raise NotImplementedError
+
+    def log_abs_det_jacobian(self, x, y):
+        """
+        Computes the log det jacobian `log |dy/dx|` given input and output.
+        """
+        raise NotImplementedError
+
+    def __repr__(self):
+        return self.__class__.__name__ + "()"
+
+    def forward_shape(self, shape):
+        """
+        Infers the shape of the forward computation, given the input shape.
+        Defaults to preserving shape.
+        """
+        return shape
+
+    def inverse_shape(self, shape):
+        """
+        Infers the shapes of the inverse computation, given the output shape.
+        Defaults to preserving shape.
+        """
+        return shape
+
+
+class _InverseTransform(Transform):
+    """
+    Inverts a single :class:`Transform`.
+    This class is private; please instead use the ``Transform.inv`` property.
+    """
+
+    def __init__(self, transform: Transform):
+        super().__init__(cache_size=transform._cache_size)
+        self._inv: Transform = transform
+
+    @constraints.dependent_property(is_discrete=False)
+    def domain(self):
+        assert self._inv is not None
+        return self._inv.codomain
+
+    @constraints.dependent_property(is_discrete=False)
+    def codomain(self):
+        assert self._inv is not None
+        return self._inv.domain
+
+    @property
+    def bijective(self):
+        assert self._inv is not None
+        return self._inv.bijective
+
+    @property
+    def sign(self):
+        assert self._inv is not None
+        return self._inv.sign
+
+    @property
+    def inv(self):
+        return self._inv
+
+    def with_cache(self, cache_size=1):
+        assert self._inv is not None
+        return self.inv.with_cache(cache_size).inv
+
+    def __eq__(self, other):
+        if not isinstance(other, _InverseTransform):
+            return False
+        assert self._inv is not None
+        return self._inv == other._inv
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({repr(self._inv)})"
+
+    def __call__(self, x):
+        assert self._inv is not None
+        return self._inv._inv_call(x)
+
+    def log_abs_det_jacobian(self, x, y):
+        assert self._inv is not None
+        return -self._inv.log_abs_det_jacobian(y, x)
+
+    def forward_shape(self, shape):
+        return self._inv.inverse_shape(shape)
+
+    def inverse_shape(self, shape):
+        return self._inv.forward_shape(shape)
+
+
+class ComposeTransform(Transform):
+    """
+    Composes multiple transforms in a chain.
+    The transforms being composed are responsible for caching.
+
+    Args:
+        parts (list of :class:`Transform`): A list of transforms to compose.
+        cache_size (int): Size of cache. If zero, no caching is done. If one,
+            the latest single value is cached. Only 0 and 1 are supported.
+    """
+
+    def __init__(self, parts: List[Transform], cache_size=0):
+        if cache_size:
+            parts = [part.with_cache(cache_size) for part in parts]
+        super().__init__(cache_size=cache_size)
+        self.parts = parts
+
+    def __eq__(self, other):
+        if not isinstance(other, ComposeTransform):
+            return False
+        return self.parts == other.parts
+
+    @constraints.dependent_property(is_discrete=False)
+    def domain(self):
+        if not self.parts:
+            return constraints.real
+        domain = self.parts[0].domain
+        # Adjust event_dim to be maximum among all parts.
+        event_dim = self.parts[-1].codomain.event_dim
+        for part in reversed(self.parts):
+            event_dim += part.domain.event_dim - part.codomain.event_dim
+            event_dim = max(event_dim, part.domain.event_dim)
+        assert event_dim >= domain.event_dim
+        if event_dim > domain.event_dim:
+            domain = constraints.independent(domain, event_dim - domain.event_dim)
+        return domain
+
+    @constraints.dependent_property(is_discrete=False)
+    def codomain(self):
+        if not self.parts:
+            return constraints.real
+        codomain = self.parts[-1].codomain
+        # Adjust event_dim to be maximum among all parts.
+        event_dim = self.parts[0].domain.event_dim
+        for part in self.parts:
+            event_dim += part.codomain.event_dim - part.domain.event_dim
+            event_dim = max(event_dim, part.codomain.event_dim)
+        assert event_dim >= codomain.event_dim
+        if event_dim > codomain.event_dim:
+            codomain = constraints.independent(codomain, event_dim - codomain.event_dim)
+        return codomain
+
+    @lazy_property
+    def bijective(self):
+        return all(p.bijective for p in self.parts)
+
+    @lazy_property
+    def sign(self):
+        sign = 1
+        for p in self.parts:
+            sign = sign * p.sign
+        return sign
+
+    @property
+    def inv(self):
+        inv = None
+        if self._inv is not None:
+            inv = self._inv()
+        if inv is None:
+            inv = ComposeTransform([p.inv for p in reversed(self.parts)])
+            self._inv = weakref.ref(inv)
+            inv._inv = weakref.ref(self)
+        return inv
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return ComposeTransform(self.parts, cache_size=cache_size)
+
+    def __call__(self, x):
+        for part in self.parts:
+            x = part(x)
+        return x
+
+    def log_abs_det_jacobian(self, x, y):
+        if not self.parts:
+            return torch.zeros_like(x)
+
+        # Compute intermediates. This will be free if parts[:-1] are all cached.
+        xs = [x]
+        for part in self.parts[:-1]:
+            xs.append(part(xs[-1]))
+        xs.append(y)
+
+        terms = []
+        event_dim = self.domain.event_dim
+        for part, x, y in zip(self.parts, xs[:-1], xs[1:]):
+            terms.append(
+                _sum_rightmost(
+                    part.log_abs_det_jacobian(x, y), event_dim - part.domain.event_dim
+                )
+            )
+            event_dim += part.codomain.event_dim - part.domain.event_dim
+        return functools.reduce(operator.add, terms)
+
+    def forward_shape(self, shape):
+        for part in self.parts:
+            shape = part.forward_shape(shape)
+        return shape
+
+    def inverse_shape(self, shape):
+        for part in reversed(self.parts):
+            shape = part.inverse_shape(shape)
+        return shape
+
+    def __repr__(self):
+        fmt_string = self.__class__.__name__ + "(\n    "
+        fmt_string += ",\n    ".join([p.__repr__() for p in self.parts])
+        fmt_string += "\n)"
+        return fmt_string
+
+
+identity_transform = ComposeTransform([])
+
+
+class IndependentTransform(Transform):
+    """
+    Wrapper around another transform to treat
+    ``reinterpreted_batch_ndims``-many extra of the right most dimensions as
+    dependent. This has no effect on the forward or backward transforms, but
+    does sum out ``reinterpreted_batch_ndims``-many of the rightmost dimensions
+    in :meth:`log_abs_det_jacobian`.
+
+    Args:
+        base_transform (:class:`Transform`): A base transform.
+        reinterpreted_batch_ndims (int): The number of extra rightmost
+            dimensions to treat as dependent.
+    """
+
+    def __init__(self, base_transform, reinterpreted_batch_ndims, cache_size=0):
+        super().__init__(cache_size=cache_size)
+        self.base_transform = base_transform.with_cache(cache_size)
+        self.reinterpreted_batch_ndims = reinterpreted_batch_ndims
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return IndependentTransform(
+            self.base_transform, self.reinterpreted_batch_ndims, cache_size=cache_size
+        )
+
+    @constraints.dependent_property(is_discrete=False)
+    def domain(self):
+        return constraints.independent(
+            self.base_transform.domain, self.reinterpreted_batch_ndims
+        )
+
+    @constraints.dependent_property(is_discrete=False)
+    def codomain(self):
+        return constraints.independent(
+            self.base_transform.codomain, self.reinterpreted_batch_ndims
+        )
+
+    @property
+    def bijective(self):
+        return self.base_transform.bijective
+
+    @property
+    def sign(self):
+        return self.base_transform.sign
+
+    def _call(self, x):
+        if x.dim() < self.domain.event_dim:
+            raise ValueError("Too few dimensions on input")
+        return self.base_transform(x)
+
+    def _inverse(self, y):
+        if y.dim() < self.codomain.event_dim:
+            raise ValueError("Too few dimensions on input")
+        return self.base_transform.inv(y)
+
+    def log_abs_det_jacobian(self, x, y):
+        result = self.base_transform.log_abs_det_jacobian(x, y)
+        result = _sum_rightmost(result, self.reinterpreted_batch_ndims)
+        return result
+
+    def __repr__(self):
+        return f"{self.__class__.__name__}({repr(self.base_transform)}, {self.reinterpreted_batch_ndims})"
+
+    def forward_shape(self, shape):
+        return self.base_transform.forward_shape(shape)
+
+    def inverse_shape(self, shape):
+        return self.base_transform.inverse_shape(shape)
+
+
+class ReshapeTransform(Transform):
+    """
+    Unit Jacobian transform to reshape the rightmost part of a tensor.
+
+    Note that ``in_shape`` and ``out_shape`` must have the same number of
+    elements, just as for :meth:`torch.Tensor.reshape`.
+
+    Arguments:
+        in_shape (torch.Size): The input event shape.
+        out_shape (torch.Size): The output event shape.
+    """
+
+    bijective = True
+
+    def __init__(self, in_shape, out_shape, cache_size=0):
+        self.in_shape = torch.Size(in_shape)
+        self.out_shape = torch.Size(out_shape)
+        if self.in_shape.numel() != self.out_shape.numel():
+            raise ValueError("in_shape, out_shape have different numbers of elements")
+        super().__init__(cache_size=cache_size)
+
+    @constraints.dependent_property
+    def domain(self):
+        return constraints.independent(constraints.real, len(self.in_shape))
+
+    @constraints.dependent_property
+    def codomain(self):
+        return constraints.independent(constraints.real, len(self.out_shape))
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return ReshapeTransform(self.in_shape, self.out_shape, cache_size=cache_size)
+
+    def _call(self, x):
+        batch_shape = x.shape[: x.dim() - len(self.in_shape)]
+        return x.reshape(batch_shape + self.out_shape)
+
+    def _inverse(self, y):
+        batch_shape = y.shape[: y.dim() - len(self.out_shape)]
+        return y.reshape(batch_shape + self.in_shape)
+
+    def log_abs_det_jacobian(self, x, y):
+        batch_shape = x.shape[: x.dim() - len(self.in_shape)]
+        return x.new_zeros(batch_shape)
+
+    def forward_shape(self, shape):
+        if len(shape) < len(self.in_shape):
+            raise ValueError("Too few dimensions on input")
+        cut = len(shape) - len(self.in_shape)
+        if shape[cut:] != self.in_shape:
+            raise ValueError(
+                f"Shape mismatch: expected {shape[cut:]} but got {self.in_shape}"
+            )
+        return shape[:cut] + self.out_shape
+
+    def inverse_shape(self, shape):
+        if len(shape) < len(self.out_shape):
+            raise ValueError("Too few dimensions on input")
+        cut = len(shape) - len(self.out_shape)
+        if shape[cut:] != self.out_shape:
+            raise ValueError(
+                f"Shape mismatch: expected {shape[cut:]} but got {self.out_shape}"
+            )
+        return shape[:cut] + self.in_shape
+
+
+class ExpTransform(Transform):
+    r"""
+    Transform via the mapping :math:`y = \exp(x)`.
+    """
+    domain = constraints.real
+    codomain = constraints.positive
+    bijective = True
+    sign = +1
+
+    def __eq__(self, other):
+        return isinstance(other, ExpTransform)
+
+    def _call(self, x):
+        return x.exp()
+
+    def _inverse(self, y):
+        return y.log()
+
+    def log_abs_det_jacobian(self, x, y):
+        return x
+
+
+class PowerTransform(Transform):
+    r"""
+    Transform via the mapping :math:`y = x^{\text{exponent}}`.
+    """
+    domain = constraints.positive
+    codomain = constraints.positive
+    bijective = True
+
+    def __init__(self, exponent, cache_size=0):
+        super().__init__(cache_size=cache_size)
+        (self.exponent,) = broadcast_all(exponent)
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return PowerTransform(self.exponent, cache_size=cache_size)
+
+    @lazy_property
+    def sign(self):
+        return self.exponent.sign()
+
+    def __eq__(self, other):
+        if not isinstance(other, PowerTransform):
+            return False
+        return self.exponent.eq(other.exponent).all().item()
+
+    def _call(self, x):
+        return x.pow(self.exponent)
+
+    def _inverse(self, y):
+        return y.pow(1 / self.exponent)
+
+    def log_abs_det_jacobian(self, x, y):
+        return (self.exponent * y / x).abs().log()
+
+    def forward_shape(self, shape):
+        return torch.broadcast_shapes(shape, getattr(self.exponent, "shape", ()))
+
+    def inverse_shape(self, shape):
+        return torch.broadcast_shapes(shape, getattr(self.exponent, "shape", ()))
+
+
+def _clipped_sigmoid(x):
+    finfo = torch.finfo(x.dtype)
+    return torch.clamp(torch.sigmoid(x), min=finfo.tiny, max=1.0 - finfo.eps)
+
+
+class SigmoidTransform(Transform):
+    r"""
+    Transform via the mapping :math:`y = \frac{1}{1 + \exp(-x)}` and :math:`x = \text{logit}(y)`.
+    """
+    domain = constraints.real
+    codomain = constraints.unit_interval
+    bijective = True
+    sign = +1
+
+    def __eq__(self, other):
+        return isinstance(other, SigmoidTransform)
+
+    def _call(self, x):
+        return _clipped_sigmoid(x)
+
+    def _inverse(self, y):
+        finfo = torch.finfo(y.dtype)
+        y = y.clamp(min=finfo.tiny, max=1.0 - finfo.eps)
+        return y.log() - (-y).log1p()
+
+    def log_abs_det_jacobian(self, x, y):
+        return -F.softplus(-x) - F.softplus(x)
+
+
+class SoftplusTransform(Transform):
+    r"""
+    Transform via the mapping :math:`\text{Softplus}(x) = \log(1 + \exp(x))`.
+    The implementation reverts to the linear function when :math:`x > 20`.
+    """
+    domain = constraints.real
+    codomain = constraints.positive
+    bijective = True
+    sign = +1
+
+    def __eq__(self, other):
+        return isinstance(other, SoftplusTransform)
+
+    def _call(self, x):
+        return softplus(x)
+
+    def _inverse(self, y):
+        return (-y).expm1().neg().log() + y
+
+    def log_abs_det_jacobian(self, x, y):
+        return -softplus(-x)
+
+
+class TanhTransform(Transform):
+    r"""
+    Transform via the mapping :math:`y = \tanh(x)`.
+
+    It is equivalent to
+    ```
+    ComposeTransform([AffineTransform(0., 2.), SigmoidTransform(), AffineTransform(-1., 2.)])
+    ```
+    However this might not be numerically stable, thus it is recommended to use `TanhTransform`
+    instead.
+
+    Note that one should use `cache_size=1` when it comes to `NaN/Inf` values.
+
+    """
+    domain = constraints.real
+    codomain = constraints.interval(-1.0, 1.0)
+    bijective = True
+    sign = +1
+
+    def __eq__(self, other):
+        return isinstance(other, TanhTransform)
+
+    def _call(self, x):
+        return x.tanh()
+
+    def _inverse(self, y):
+        # We do not clamp to the boundary here as it may degrade the performance of certain algorithms.
+        # one should use `cache_size=1` instead
+        return torch.atanh(y)
+
+    def log_abs_det_jacobian(self, x, y):
+        # We use a formula that is more numerically stable, see details in the following link
+        # https://github.com/tensorflow/probability/blob/master/tensorflow_probability/python/bijectors/tanh.py#L69-L80
+        return 2.0 * (math.log(2.0) - x - softplus(-2.0 * x))
+
+
+class AbsTransform(Transform):
+    r"""
+    Transform via the mapping :math:`y = |x|`.
+    """
+    domain = constraints.real
+    codomain = constraints.positive
+
+    def __eq__(self, other):
+        return isinstance(other, AbsTransform)
+
+    def _call(self, x):
+        return x.abs()
+
+    def _inverse(self, y):
+        return y
+
+
+class AffineTransform(Transform):
+    r"""
+    Transform via the pointwise affine mapping :math:`y = \text{loc} + \text{scale} \times x`.
+
+    Args:
+        loc (Tensor or float): Location parameter.
+        scale (Tensor or float): Scale parameter.
+        event_dim (int): Optional size of `event_shape`. This should be zero
+            for univariate random variables, 1 for distributions over vectors,
+            2 for distributions over matrices, etc.
+    """
+    bijective = True
+
+    def __init__(self, loc, scale, event_dim=0, cache_size=0):
+        super().__init__(cache_size=cache_size)
+        self.loc = loc
+        self.scale = scale
+        self._event_dim = event_dim
+
+    @property
+    def event_dim(self):
+        return self._event_dim
+
+    @constraints.dependent_property(is_discrete=False)
+    def domain(self):
+        if self.event_dim == 0:
+            return constraints.real
+        return constraints.independent(constraints.real, self.event_dim)
+
+    @constraints.dependent_property(is_discrete=False)
+    def codomain(self):
+        if self.event_dim == 0:
+            return constraints.real
+        return constraints.independent(constraints.real, self.event_dim)
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return AffineTransform(
+            self.loc, self.scale, self.event_dim, cache_size=cache_size
+        )
+
+    def __eq__(self, other):
+        if not isinstance(other, AffineTransform):
+            return False
+
+        if isinstance(self.loc, numbers.Number) and isinstance(
+            other.loc, numbers.Number
+        ):
+            if self.loc != other.loc:
+                return False
+        else:
+            if not (self.loc == other.loc).all().item():
+                return False
+
+        if isinstance(self.scale, numbers.Number) and isinstance(
+            other.scale, numbers.Number
+        ):
+            if self.scale != other.scale:
+                return False
+        else:
+            if not (self.scale == other.scale).all().item():
+                return False
+
+        return True
+
+    @property
+    def sign(self):
+        if isinstance(self.scale, numbers.Real):
+            return 1 if float(self.scale) > 0 else -1 if float(self.scale) < 0 else 0
+        return self.scale.sign()
+
+    def _call(self, x):
+        return self.loc + self.scale * x
+
+    def _inverse(self, y):
+        return (y - self.loc) / self.scale
+
+    def log_abs_det_jacobian(self, x, y):
+        shape = x.shape
+        scale = self.scale
+        if isinstance(scale, numbers.Real):
+            result = torch.full_like(x, math.log(abs(scale)))
+        else:
+            result = torch.abs(scale).log()
+        if self.event_dim:
+            result_size = result.size()[: -self.event_dim] + (-1,)
+            result = result.view(result_size).sum(-1)
+            shape = shape[: -self.event_dim]
+        return result.expand(shape)
+
+    def forward_shape(self, shape):
+        return torch.broadcast_shapes(
+            shape, getattr(self.loc, "shape", ()), getattr(self.scale, "shape", ())
+        )
+
+    def inverse_shape(self, shape):
+        return torch.broadcast_shapes(
+            shape, getattr(self.loc, "shape", ()), getattr(self.scale, "shape", ())
+        )
+
+
+class CorrCholeskyTransform(Transform):
+    r"""
+    Transforms an uncontrained real vector :math:`x` with length :math:`D*(D-1)/2` into the
+    Cholesky factor of a D-dimension correlation matrix. This Cholesky factor is a lower
+    triangular matrix with positive diagonals and unit Euclidean norm for each row.
+    The transform is processed as follows:
+
+        1. First we convert x into a lower triangular matrix in row order.
+        2. For each row :math:`X_i` of the lower triangular part, we apply a *signed* version of
+           class :class:`StickBreakingTransform` to transform :math:`X_i` into a
+           unit Euclidean length vector using the following steps:
+           - Scales into the interval :math:`(-1, 1)` domain: :math:`r_i = \tanh(X_i)`.
+           - Transforms into an unsigned domain: :math:`z_i = r_i^2`.
+           - Applies :math:`s_i = StickBreakingTransform(z_i)`.
+           - Transforms back into signed domain: :math:`y_i = sign(r_i) * \sqrt{s_i}`.
+    """
+    domain = constraints.real_vector
+    codomain = constraints.corr_cholesky
+    bijective = True
+
+    def _call(self, x):
+        x = torch.tanh(x)
+        eps = torch.finfo(x.dtype).eps
+        x = x.clamp(min=-1 + eps, max=1 - eps)
+        r = vec_to_tril_matrix(x, diag=-1)
+        # apply stick-breaking on the squared values
+        # Note that y = sign(r) * sqrt(z * z1m_cumprod)
+        #             = (sign(r) * sqrt(z)) * sqrt(z1m_cumprod) = r * sqrt(z1m_cumprod)
+        z = r**2
+        z1m_cumprod_sqrt = (1 - z).sqrt().cumprod(-1)
+        # Diagonal elements must be 1.
+        r = r + torch.eye(r.shape[-1], dtype=r.dtype, device=r.device)
+        y = r * pad(z1m_cumprod_sqrt[..., :-1], [1, 0], value=1)
+        return y
+
+    def _inverse(self, y):
+        # inverse stick-breaking
+        # See: https://mc-stan.org/docs/2_18/reference-manual/cholesky-factors-of-correlation-matrices-1.html
+        y_cumsum = 1 - torch.cumsum(y * y, dim=-1)
+        y_cumsum_shifted = pad(y_cumsum[..., :-1], [1, 0], value=1)
+        y_vec = tril_matrix_to_vec(y, diag=-1)
+        y_cumsum_vec = tril_matrix_to_vec(y_cumsum_shifted, diag=-1)
+        t = y_vec / (y_cumsum_vec).sqrt()
+        # inverse of tanh
+        x = (t.log1p() - t.neg().log1p()) / 2
+        return x
+
+    def log_abs_det_jacobian(self, x, y, intermediates=None):
+        # Because domain and codomain are two spaces with different dimensions, determinant of
+        # Jacobian is not well-defined. We return `log_abs_det_jacobian` of `x` and the
+        # flattened lower triangular part of `y`.
+
+        # See: https://mc-stan.org/docs/2_18/reference-manual/cholesky-factors-of-correlation-matrices-1.html
+        y1m_cumsum = 1 - (y * y).cumsum(dim=-1)
+        # by taking diagonal=-2, we don't need to shift z_cumprod to the right
+        # also works for 2 x 2 matrix
+        y1m_cumsum_tril = tril_matrix_to_vec(y1m_cumsum, diag=-2)
+        stick_breaking_logdet = 0.5 * (y1m_cumsum_tril).log().sum(-1)
+        tanh_logdet = -2 * (x + softplus(-2 * x) - math.log(2.0)).sum(dim=-1)
+        return stick_breaking_logdet + tanh_logdet
+
+    def forward_shape(self, shape):
+        # Reshape from (..., N) to (..., D, D).
+        if len(shape) < 1:
+            raise ValueError("Too few dimensions on input")
+        N = shape[-1]
+        D = round((0.25 + 2 * N) ** 0.5 + 0.5)
+        if D * (D - 1) // 2 != N:
+            raise ValueError("Input is not a flattend lower-diagonal number")
+        return shape[:-1] + (D, D)
+
+    def inverse_shape(self, shape):
+        # Reshape from (..., D, D) to (..., N).
+        if len(shape) < 2:
+            raise ValueError("Too few dimensions on input")
+        if shape[-2] != shape[-1]:
+            raise ValueError("Input is not square")
+        D = shape[-1]
+        N = D * (D - 1) // 2
+        return shape[:-2] + (N,)
+
+
+class SoftmaxTransform(Transform):
+    r"""
+    Transform from unconstrained space to the simplex via :math:`y = \exp(x)` then
+    normalizing.
+
+    This is not bijective and cannot be used for HMC. However this acts mostly
+    coordinate-wise (except for the final normalization), and thus is
+    appropriate for coordinate-wise optimization algorithms.
+    """
+    domain = constraints.real_vector
+    codomain = constraints.simplex
+
+    def __eq__(self, other):
+        return isinstance(other, SoftmaxTransform)
+
+    def _call(self, x):
+        logprobs = x
+        probs = (logprobs - logprobs.max(-1, True)[0]).exp()
+        return probs / probs.sum(-1, True)
+
+    def _inverse(self, y):
+        probs = y
+        return probs.log()
+
+    def forward_shape(self, shape):
+        if len(shape) < 1:
+            raise ValueError("Too few dimensions on input")
+        return shape
+
+    def inverse_shape(self, shape):
+        if len(shape) < 1:
+            raise ValueError("Too few dimensions on input")
+        return shape
+
+
+class StickBreakingTransform(Transform):
+    """
+    Transform from unconstrained space to the simplex of one additional
+    dimension via a stick-breaking process.
+
+    This transform arises as an iterated sigmoid transform in a stick-breaking
+    construction of the `Dirichlet` distribution: the first logit is
+    transformed via sigmoid to the first probability and the probability of
+    everything else, and then the process recurses.
+
+    This is bijective and appropriate for use in HMC; however it mixes
+    coordinates together and is less appropriate for optimization.
+    """
+
+    domain = constraints.real_vector
+    codomain = constraints.simplex
+    bijective = True
+
+    def __eq__(self, other):
+        return isinstance(other, StickBreakingTransform)
+
+    def _call(self, x):
+        offset = x.shape[-1] + 1 - x.new_ones(x.shape[-1]).cumsum(-1)
+        z = _clipped_sigmoid(x - offset.log())
+        z_cumprod = (1 - z).cumprod(-1)
+        y = pad(z, [0, 1], value=1) * pad(z_cumprod, [1, 0], value=1)
+        return y
+
+    def _inverse(self, y):
+        y_crop = y[..., :-1]
+        offset = y.shape[-1] - y.new_ones(y_crop.shape[-1]).cumsum(-1)
+        sf = 1 - y_crop.cumsum(-1)
+        # we clamp to make sure that sf is positive which sometimes does not
+        # happen when y[-1] ~ 0 or y[:-1].sum() ~ 1
+        sf = torch.clamp(sf, min=torch.finfo(y.dtype).tiny)
+        x = y_crop.log() - sf.log() + offset.log()
+        return x
+
+    def log_abs_det_jacobian(self, x, y):
+        offset = x.shape[-1] + 1 - x.new_ones(x.shape[-1]).cumsum(-1)
+        x = x - offset.log()
+        # use the identity 1 - sigmoid(x) = exp(-x) * sigmoid(x)
+        detJ = (-x + F.logsigmoid(x) + y[..., :-1].log()).sum(-1)
+        return detJ
+
+    def forward_shape(self, shape):
+        if len(shape) < 1:
+            raise ValueError("Too few dimensions on input")
+        return shape[:-1] + (shape[-1] + 1,)
+
+    def inverse_shape(self, shape):
+        if len(shape) < 1:
+            raise ValueError("Too few dimensions on input")
+        return shape[:-1] + (shape[-1] - 1,)
+
+
+class LowerCholeskyTransform(Transform):
+    """
+    Transform from unconstrained matrices to lower-triangular matrices with
+    nonnegative diagonal entries.
+
+    This is useful for parameterizing positive definite matrices in terms of
+    their Cholesky factorization.
+    """
+
+    domain = constraints.independent(constraints.real, 2)
+    codomain = constraints.lower_cholesky
+
+    def __eq__(self, other):
+        return isinstance(other, LowerCholeskyTransform)
+
+    def _call(self, x):
+        return x.tril(-1) + x.diagonal(dim1=-2, dim2=-1).exp().diag_embed()
+
+    def _inverse(self, y):
+        return y.tril(-1) + y.diagonal(dim1=-2, dim2=-1).log().diag_embed()
+
+
+class PositiveDefiniteTransform(Transform):
+    """
+    Transform from unconstrained matrices to positive-definite matrices.
+    """
+
+    domain = constraints.independent(constraints.real, 2)
+    codomain = constraints.positive_definite  # type: ignore[assignment]
+
+    def __eq__(self, other):
+        return isinstance(other, PositiveDefiniteTransform)
+
+    def _call(self, x):
+        x = LowerCholeskyTransform()(x)
+        return x @ x.mT
+
+    def _inverse(self, y):
+        y = torch.linalg.cholesky(y)
+        return LowerCholeskyTransform().inv(y)
+
+
+class CatTransform(Transform):
+    """
+    Transform functor that applies a sequence of transforms `tseq`
+    component-wise to each submatrix at `dim`, of length `lengths[dim]`,
+    in a way compatible with :func:`torch.cat`.
+
+    Example::
+
+       x0 = torch.cat([torch.range(1, 10), torch.range(1, 10)], dim=0)
+       x = torch.cat([x0, x0], dim=0)
+       t0 = CatTransform([ExpTransform(), identity_transform], dim=0, lengths=[10, 10])
+       t = CatTransform([t0, t0], dim=0, lengths=[20, 20])
+       y = t(x)
+    """
+
+    transforms: List[Transform]
+
+    def __init__(self, tseq, dim=0, lengths=None, cache_size=0):
+        assert all(isinstance(t, Transform) for t in tseq)
+        if cache_size:
+            tseq = [t.with_cache(cache_size) for t in tseq]
+        super().__init__(cache_size=cache_size)
+        self.transforms = list(tseq)
+        if lengths is None:
+            lengths = [1] * len(self.transforms)
+        self.lengths = list(lengths)
+        assert len(self.lengths) == len(self.transforms)
+        self.dim = dim
+
+    @lazy_property
+    def event_dim(self):
+        return max(t.event_dim for t in self.transforms)
+
+    @lazy_property
+    def length(self):
+        return sum(self.lengths)
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return CatTransform(self.transforms, self.dim, self.lengths, cache_size)
+
+    def _call(self, x):
+        assert -x.dim() <= self.dim < x.dim()
+        assert x.size(self.dim) == self.length
+        yslices = []
+        start = 0
+        for trans, length in zip(self.transforms, self.lengths):
+            xslice = x.narrow(self.dim, start, length)
+            yslices.append(trans(xslice))
+            start = start + length  # avoid += for jit compat
+        return torch.cat(yslices, dim=self.dim)
+
+    def _inverse(self, y):
+        assert -y.dim() <= self.dim < y.dim()
+        assert y.size(self.dim) == self.length
+        xslices = []
+        start = 0
+        for trans, length in zip(self.transforms, self.lengths):
+            yslice = y.narrow(self.dim, start, length)
+            xslices.append(trans.inv(yslice))
+            start = start + length  # avoid += for jit compat
+        return torch.cat(xslices, dim=self.dim)
+
+    def log_abs_det_jacobian(self, x, y):
+        assert -x.dim() <= self.dim < x.dim()
+        assert x.size(self.dim) == self.length
+        assert -y.dim() <= self.dim < y.dim()
+        assert y.size(self.dim) == self.length
+        logdetjacs = []
+        start = 0
+        for trans, length in zip(self.transforms, self.lengths):
+            xslice = x.narrow(self.dim, start, length)
+            yslice = y.narrow(self.dim, start, length)
+            logdetjac = trans.log_abs_det_jacobian(xslice, yslice)
+            if trans.event_dim < self.event_dim:
+                logdetjac = _sum_rightmost(logdetjac, self.event_dim - trans.event_dim)
+            logdetjacs.append(logdetjac)
+            start = start + length  # avoid += for jit compat
+        # Decide whether to concatenate or sum.
+        dim = self.dim
+        if dim >= 0:
+            dim = dim - x.dim()
+        dim = dim + self.event_dim
+        if dim < 0:
+            return torch.cat(logdetjacs, dim=dim)
+        else:
+            return sum(logdetjacs)
+
+    @property
+    def bijective(self):
+        return all(t.bijective for t in self.transforms)
+
+    @constraints.dependent_property
+    def domain(self):
+        return constraints.cat(
+            [t.domain for t in self.transforms], self.dim, self.lengths
+        )
+
+    @constraints.dependent_property
+    def codomain(self):
+        return constraints.cat(
+            [t.codomain for t in self.transforms], self.dim, self.lengths
+        )
+
+
+class StackTransform(Transform):
+    """
+    Transform functor that applies a sequence of transforms `tseq`
+    component-wise to each submatrix at `dim`
+    in a way compatible with :func:`torch.stack`.
+
+    Example::
+
+       x = torch.stack([torch.range(1, 10), torch.range(1, 10)], dim=1)
+       t = StackTransform([ExpTransform(), identity_transform], dim=1)
+       y = t(x)
+    """
+
+    transforms: List[Transform]
+
+    def __init__(self, tseq, dim=0, cache_size=0):
+        assert all(isinstance(t, Transform) for t in tseq)
+        if cache_size:
+            tseq = [t.with_cache(cache_size) for t in tseq]
+        super().__init__(cache_size=cache_size)
+        self.transforms = list(tseq)
+        self.dim = dim
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return StackTransform(self.transforms, self.dim, cache_size)
+
+    def _slice(self, z):
+        return [z.select(self.dim, i) for i in range(z.size(self.dim))]
+
+    def _call(self, x):
+        assert -x.dim() <= self.dim < x.dim()
+        assert x.size(self.dim) == len(self.transforms)
+        yslices = []
+        for xslice, trans in zip(self._slice(x), self.transforms):
+            yslices.append(trans(xslice))
+        return torch.stack(yslices, dim=self.dim)
+
+    def _inverse(self, y):
+        assert -y.dim() <= self.dim < y.dim()
+        assert y.size(self.dim) == len(self.transforms)
+        xslices = []
+        for yslice, trans in zip(self._slice(y), self.transforms):
+            xslices.append(trans.inv(yslice))
+        return torch.stack(xslices, dim=self.dim)
+
+    def log_abs_det_jacobian(self, x, y):
+        assert -x.dim() <= self.dim < x.dim()
+        assert x.size(self.dim) == len(self.transforms)
+        assert -y.dim() <= self.dim < y.dim()
+        assert y.size(self.dim) == len(self.transforms)
+        logdetjacs = []
+        yslices = self._slice(y)
+        xslices = self._slice(x)
+        for xslice, yslice, trans in zip(xslices, yslices, self.transforms):
+            logdetjacs.append(trans.log_abs_det_jacobian(xslice, yslice))
+        return torch.stack(logdetjacs, dim=self.dim)
+
+    @property
+    def bijective(self):
+        return all(t.bijective for t in self.transforms)
+
+    @constraints.dependent_property
+    def domain(self):
+        return constraints.stack([t.domain for t in self.transforms], self.dim)
+
+    @constraints.dependent_property
+    def codomain(self):
+        return constraints.stack([t.codomain for t in self.transforms], self.dim)
+
+
+class CumulativeDistributionTransform(Transform):
+    """
+    Transform via the cumulative distribution function of a probability distribution.
+
+    Args:
+        distribution (Distribution): Distribution whose cumulative distribution function to use for
+            the transformation.
+
+    Example::
+
+        # Construct a Gaussian copula from a multivariate normal.
+        base_dist = MultivariateNormal(
+            loc=torch.zeros(2),
+            scale_tril=LKJCholesky(2).sample(),
+        )
+        transform = CumulativeDistributionTransform(Normal(0, 1))
+        copula = TransformedDistribution(base_dist, [transform])
+    """
+
+    bijective = True
+    codomain = constraints.unit_interval
+    sign = +1
+
+    def __init__(self, distribution, cache_size=0):
+        super().__init__(cache_size=cache_size)
+        self.distribution = distribution
+
+    @property
+    def domain(self):
+        return self.distribution.support
+
+    def _call(self, x):
+        return self.distribution.cdf(x)
+
+    def _inverse(self, y):
+        return self.distribution.icdf(y)
+
+    def log_abs_det_jacobian(self, x, y):
+        return self.distribution.log_prob(x)
+
+    def with_cache(self, cache_size=1):
+        if self._cache_size == cache_size:
+            return self
+        return CumulativeDistributionTransform(self.distribution, cache_size=cache_size)

venv/lib/python3.10/site-packages/torch/distributions/uniform.py

@@ -0,0 +1,99 @@
+from numbers import Number
+
+import torch
+from torch import nan
+from torch.distributions import constraints
+from torch.distributions.distribution import Distribution
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Uniform"]
+
+
+class Uniform(Distribution):
+    r"""
+    Generates uniformly distributed random samples from the half-open interval
+    ``[low, high)``.
+
+    Example::
+
+        >>> m = Uniform(torch.tensor([0.0]), torch.tensor([5.0]))
+        >>> m.sample()  # uniformly distributed in the range [0.0, 5.0)
+        >>> # xdoctest: +SKIP
+        tensor([ 2.3418])
+
+    Args:
+        low (float or Tensor): lower range (inclusive).
+        high (float or Tensor): upper range (exclusive).
+    """
+    # TODO allow (loc,scale) parameterization to allow independent constraints.
+    arg_constraints = {
+        "low": constraints.dependent(is_discrete=False, event_dim=0),
+        "high": constraints.dependent(is_discrete=False, event_dim=0),
+    }
+    has_rsample = True
+
+    @property
+    def mean(self):
+        return (self.high + self.low) / 2
+
+    @property
+    def mode(self):
+        return nan * self.high
+
+    @property
+    def stddev(self):
+        return (self.high - self.low) / 12**0.5
+
+    @property
+    def variance(self):
+        return (self.high - self.low).pow(2) / 12
+
+    def __init__(self, low, high, validate_args=None):
+        self.low, self.high = broadcast_all(low, high)
+
+        if isinstance(low, Number) and isinstance(high, Number):
+            batch_shape = torch.Size()
+        else:
+            batch_shape = self.low.size()
+        super().__init__(batch_shape, validate_args=validate_args)
+
+        if self._validate_args and not torch.lt(self.low, self.high).all():
+            raise ValueError("Uniform is not defined when low>= high")
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Uniform, _instance)
+        batch_shape = torch.Size(batch_shape)
+        new.low = self.low.expand(batch_shape)
+        new.high = self.high.expand(batch_shape)
+        super(Uniform, new).__init__(batch_shape, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @constraints.dependent_property(is_discrete=False, event_dim=0)
+    def support(self):
+        return constraints.interval(self.low, self.high)
+
+    def rsample(self, sample_shape=torch.Size()):
+        shape = self._extended_shape(sample_shape)
+        rand = torch.rand(shape, dtype=self.low.dtype, device=self.low.device)
+        return self.low + rand * (self.high - self.low)
+
+    def log_prob(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        lb = self.low.le(value).type_as(self.low)
+        ub = self.high.gt(value).type_as(self.low)
+        return torch.log(lb.mul(ub)) - torch.log(self.high - self.low)
+
+    def cdf(self, value):
+        if self._validate_args:
+            self._validate_sample(value)
+        result = (value - self.low) / (self.high - self.low)
+        return result.clamp(min=0, max=1)
+
+    def icdf(self, value):
+        result = value * (self.high - self.low) + self.low
+        return result
+
+    def entropy(self):
+        return torch.log(self.high - self.low)

venv/lib/python3.10/site-packages/torch/distributions/utils.py

@@ -0,0 +1,177 @@
+from functools import update_wrapper
+from numbers import Number
+from typing import Any, Dict
+
+import torch
+import torch.nn.functional as F
+from torch.overrides import is_tensor_like
+
+euler_constant = 0.57721566490153286060  # Euler Mascheroni Constant
+
+__all__ = [
+    "broadcast_all",
+    "logits_to_probs",
+    "clamp_probs",
+    "probs_to_logits",
+    "lazy_property",
+    "tril_matrix_to_vec",
+    "vec_to_tril_matrix",
+]
+
+
+def broadcast_all(*values):
+    r"""
+    Given a list of values (possibly containing numbers), returns a list where each
+    value is broadcasted based on the following rules:
+      - `torch.*Tensor` instances are broadcasted as per :ref:`_broadcasting-semantics`.
+      - numbers.Number instances (scalars) are upcast to tensors having
+        the same size and type as the first tensor passed to `values`.  If all the
+        values are scalars, then they are upcasted to scalar Tensors.
+
+    Args:
+        values (list of `numbers.Number`, `torch.*Tensor` or objects implementing __torch_function__)
+
+    Raises:
+        ValueError: if any of the values is not a `numbers.Number` instance,
+            a `torch.*Tensor` instance, or an instance implementing __torch_function__
+    """
+    if not all(is_tensor_like(v) or isinstance(v, Number) for v in values):
+        raise ValueError(
+            "Input arguments must all be instances of numbers.Number, "
+            "torch.Tensor or objects implementing __torch_function__."
+        )
+    if not all(is_tensor_like(v) for v in values):
+        options: Dict[str, Any] = dict(dtype=torch.get_default_dtype())
+        for value in values:
+            if isinstance(value, torch.Tensor):
+                options = dict(dtype=value.dtype, device=value.device)
+                break
+        new_values = [
+            v if is_tensor_like(v) else torch.tensor(v, **options) for v in values
+        ]
+        return torch.broadcast_tensors(*new_values)
+    return torch.broadcast_tensors(*values)
+
+
+def _standard_normal(shape, dtype, device):
+    if torch._C._get_tracing_state():
+        # [JIT WORKAROUND] lack of support for .normal_()
+        return torch.normal(
+            torch.zeros(shape, dtype=dtype, device=device),
+            torch.ones(shape, dtype=dtype, device=device),
+        )
+    return torch.empty(shape, dtype=dtype, device=device).normal_()
+
+
+def _sum_rightmost(value, dim):
+    r"""
+    Sum out ``dim`` many rightmost dimensions of a given tensor.
+
+    Args:
+        value (Tensor): A tensor of ``.dim()`` at least ``dim``.
+        dim (int): The number of rightmost dims to sum out.
+    """
+    if dim == 0:
+        return value
+    required_shape = value.shape[:-dim] + (-1,)
+    return value.reshape(required_shape).sum(-1)
+
+
+def logits_to_probs(logits, is_binary=False):
+    r"""
+    Converts a tensor of logits into probabilities. Note that for the
+    binary case, each value denotes log odds, whereas for the
+    multi-dimensional case, the values along the last dimension denote
+    the log probabilities (possibly unnormalized) of the events.
+    """
+    if is_binary:
+        return torch.sigmoid(logits)
+    return F.softmax(logits, dim=-1)
+
+
+def clamp_probs(probs):
+    eps = torch.finfo(probs.dtype).eps
+    return probs.clamp(min=eps, max=1 - eps)
+
+
+def probs_to_logits(probs, is_binary=False):
+    r"""
+    Converts a tensor of probabilities into logits. For the binary case,
+    this denotes the probability of occurrence of the event indexed by `1`.
+    For the multi-dimensional case, the values along the last dimension
+    denote the probabilities of occurrence of each of the events.
+    """
+    ps_clamped = clamp_probs(probs)
+    if is_binary:
+        return torch.log(ps_clamped) - torch.log1p(-ps_clamped)
+    return torch.log(ps_clamped)
+
+
+class lazy_property:
+    r"""
+    Used as a decorator for lazy loading of class attributes. This uses a
+    non-data descriptor that calls the wrapped method to compute the property on
+    first call; thereafter replacing the wrapped method into an instance
+    attribute.
+    """
+
+    def __init__(self, wrapped):
+        self.wrapped = wrapped
+        update_wrapper(self, wrapped)
+
+    def __get__(self, instance, obj_type=None):
+        if instance is None:
+            return _lazy_property_and_property(self.wrapped)
+        with torch.enable_grad():
+            value = self.wrapped(instance)
+        setattr(instance, self.wrapped.__name__, value)
+        return value
+
+
+class _lazy_property_and_property(lazy_property, property):
+    """We want lazy properties to look like multiple things.
+
+    * property when Sphinx autodoc looks
+    * lazy_property when Distribution validate_args looks
+    """
+
+    def __init__(self, wrapped):
+        property.__init__(self, wrapped)
+
+
+def tril_matrix_to_vec(mat: torch.Tensor, diag: int = 0) -> torch.Tensor:
+    r"""
+    Convert a `D x D` matrix or a batch of matrices into a (batched) vector
+    which comprises of lower triangular elements from the matrix in row order.
+    """
+    n = mat.shape[-1]
+    if not torch._C._get_tracing_state() and (diag < -n or diag >= n):
+        raise ValueError(f"diag ({diag}) provided is outside [{-n}, {n-1}].")
+    arange = torch.arange(n, device=mat.device)
+    tril_mask = arange < arange.view(-1, 1) + (diag + 1)
+    vec = mat[..., tril_mask]
+    return vec
+
+
+def vec_to_tril_matrix(vec: torch.Tensor, diag: int = 0) -> torch.Tensor:
+    r"""
+    Convert a vector or a batch of vectors into a batched `D x D`
+    lower triangular matrix containing elements from the vector in row order.
+    """
+    # +ve root of D**2 + (1+2*diag)*D - |diag| * (diag+1) - 2*vec.shape[-1] = 0
+    n = (
+        -(1 + 2 * diag)
+        + ((1 + 2 * diag) ** 2 + 8 * vec.shape[-1] + 4 * abs(diag) * (diag + 1)) ** 0.5
+    ) / 2
+    eps = torch.finfo(vec.dtype).eps
+    if not torch._C._get_tracing_state() and (round(n) - n > eps):
+        raise ValueError(
+            f"The size of last dimension is {vec.shape[-1]} which cannot be expressed as "
+            + "the lower triangular part of a square D x D matrix."
+        )
+    n = round(n.item()) if isinstance(n, torch.Tensor) else round(n)
+    mat = vec.new_zeros(vec.shape[:-1] + torch.Size((n, n)))
+    arange = torch.arange(n, device=vec.device)
+    tril_mask = arange < arange.view(-1, 1) + (diag + 1)
+    mat[..., tril_mask] = vec
+    return mat

venv/lib/python3.10/site-packages/torch/distributions/von_mises.py

@@ -0,0 +1,209 @@
+import math
+
+import torch
+import torch.jit
+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.
+    """
+    assert order == 0 or order == 1
+
+    # 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)
+    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():
+            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
+    """
+
+    arg_constraints = {"loc": constraints.real, "concentration": constraints.positive}
+    support = constraints.real
+    has_rsample = False
+
+    def __init__(self, loc, concentration, validate_args=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):
+        return self.loc.to(torch.double)
+
+    @lazy_property
+    def _concentration(self):
+        return self.concentration.to(torch.double)
+
+    @lazy_property
+    def _proposal_r(self):
+        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):
+        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):
+        """
+        The provided mean is the circular one.
+        """
+        return self.loc
+
+    @property
+    def mode(self):
+        return self.loc
+
+    @lazy_property
+    def variance(self):
+        """
+        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()
+        )

venv/lib/python3.10/site-packages/torch/distributions/weibull.py

@@ -0,0 +1,83 @@
+import torch
+from torch.distributions import constraints
+from torch.distributions.exponential import Exponential
+from torch.distributions.gumbel import euler_constant
+from torch.distributions.transformed_distribution import TransformedDistribution
+from torch.distributions.transforms import AffineTransform, PowerTransform
+from torch.distributions.utils import broadcast_all
+
+__all__ = ["Weibull"]
+
+
+class Weibull(TransformedDistribution):
+    r"""
+    Samples from a two-parameter Weibull distribution.
+
+    Example:
+
+        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
+        >>> m = Weibull(torch.tensor([1.0]), torch.tensor([1.0]))
+        >>> m.sample()  # sample from a Weibull distribution with scale=1, concentration=1
+        tensor([ 0.4784])
+
+    Args:
+        scale (float or Tensor): Scale parameter of distribution (lambda).
+        concentration (float or Tensor): Concentration parameter of distribution (k/shape).
+    """
+    arg_constraints = {
+        "scale": constraints.positive,
+        "concentration": constraints.positive,
+    }
+    support = constraints.positive
+
+    def __init__(self, scale, concentration, validate_args=None):
+        self.scale, self.concentration = broadcast_all(scale, concentration)
+        self.concentration_reciprocal = self.concentration.reciprocal()
+        base_dist = Exponential(
+            torch.ones_like(self.scale), validate_args=validate_args
+        )
+        transforms = [
+            PowerTransform(exponent=self.concentration_reciprocal),
+            AffineTransform(loc=0, scale=self.scale),
+        ]
+        super().__init__(base_dist, transforms, validate_args=validate_args)
+
+    def expand(self, batch_shape, _instance=None):
+        new = self._get_checked_instance(Weibull, _instance)
+        new.scale = self.scale.expand(batch_shape)
+        new.concentration = self.concentration.expand(batch_shape)
+        new.concentration_reciprocal = new.concentration.reciprocal()
+        base_dist = self.base_dist.expand(batch_shape)
+        transforms = [
+            PowerTransform(exponent=new.concentration_reciprocal),
+            AffineTransform(loc=0, scale=new.scale),
+        ]
+        super(Weibull, new).__init__(base_dist, transforms, validate_args=False)
+        new._validate_args = self._validate_args
+        return new
+
+    @property
+    def mean(self):
+        return self.scale * torch.exp(torch.lgamma(1 + self.concentration_reciprocal))
+
+    @property
+    def mode(self):
+        return (
+            self.scale
+            * ((self.concentration - 1) / self.concentration)
+            ** self.concentration.reciprocal()
+        )
+
+    @property
+    def variance(self):
+        return self.scale.pow(2) * (
+            torch.exp(torch.lgamma(1 + 2 * self.concentration_reciprocal))
+            - torch.exp(2 * torch.lgamma(1 + self.concentration_reciprocal))
+        )
+
+    def entropy(self):
+        return (
+            euler_constant * (1 - self.concentration_reciprocal)
+            + torch.log(self.scale * self.concentration_reciprocal)
+            + 1
+        )

venv/lib/python3.10/site-packages/torch/mps/__init__.py

@@ -0,0 +1,130 @@
+r"""
+This package enables an interface for accessing MPS (Metal Performance Shaders) backend in Python.
+Metal is Apple's API for programming metal GPU (graphics processor unit). Using MPS means that increased
+performance can be achieved, by running work on the metal GPU(s).
+See https://developer.apple.com/documentation/metalperformanceshaders for more details.
+"""
+import torch
+from .. import Tensor
+
+_is_in_bad_fork = getattr(torch._C, "_mps_is_in_bad_fork", lambda: False)
+_default_mps_generator: torch._C.Generator = None  # type: ignore[assignment]
+
+
+# local helper function (not public or exported)
+def _get_default_mps_generator() -> torch._C.Generator:
+    global _default_mps_generator
+    if _default_mps_generator is None:
+        _default_mps_generator = torch._C._mps_get_default_generator()
+    return _default_mps_generator
+
+
+def synchronize() -> None:
+    r"""Waits for all kernels in all streams on a MPS device to complete."""
+    return torch._C._mps_deviceSynchronize()
+
+
+def get_rng_state() -> Tensor:
+    r"""Returns the random number generator state as a ByteTensor."""
+    return _get_default_mps_generator().get_state()
+
+
+def set_rng_state(new_state: Tensor) -> None:
+    r"""Sets the random number generator state.
+
+    Args:
+        new_state (torch.ByteTensor): The desired state
+    """
+    new_state_copy = new_state.clone(memory_format=torch.contiguous_format)
+    _get_default_mps_generator().set_state(new_state_copy)
+
+
+def manual_seed(seed: int) -> None:
+    r"""Sets the seed for generating random numbers.
+
+    Args:
+        seed (int): The desired seed.
+    """
+    # the torch.mps.manual_seed() can be called from the global
+    # torch.manual_seed() in torch/random.py. So we need to make
+    # sure mps is available (otherwise we just return without
+    # erroring out)
+    if not torch._C._has_mps:
+        return
+    seed = int(seed)
+    _get_default_mps_generator().manual_seed(seed)
+
+
+def seed() -> None:
+    r"""Sets the seed for generating random numbers to a random number."""
+    _get_default_mps_generator().seed()
+
+
+def empty_cache() -> None:
+    r"""Releases all unoccupied cached memory currently held by the caching
+    allocator so that those can be used in other GPU applications.
+    """
+    torch._C._mps_emptyCache()
+
+
+def set_per_process_memory_fraction(fraction) -> None:
+    r"""Set memory fraction for limiting process's memory allocation on MPS device.
+    The allowed value equals the fraction multiplied by recommended maximum device memory
+    (obtained from Metal API device.recommendedMaxWorkingSetSize).
+    If trying to allocate more than the allowed value in a process, it will raise an out of
+    memory error in allocator.
+
+    Args:
+        fraction(float): Range: 0~2. Allowed memory equals total_memory * fraction.
+
+    .. note::
+       Passing 0 to fraction means unlimited allocations
+       (may cause system failure if out of memory).
+       Passing fraction greater than 1.0 allows limits beyond the value
+       returned from device.recommendedMaxWorkingSetSize.
+    """
+
+    if not isinstance(fraction, float):
+        raise TypeError("Invalid type for fraction argument, must be `float`")
+    if fraction < 0 or fraction > 2:
+        raise ValueError(f"Invalid fraction value: {fraction}. Allowed range: 0~2")
+
+    torch._C._mps_setMemoryFraction(fraction)
+
+
+def current_allocated_memory() -> int:
+    r"""Returns the current GPU memory occupied by tensors in bytes.
+
+    .. note::
+       The returned size does not include cached allocations in
+       memory pools of MPSAllocator.
+    """
+    return torch._C._mps_currentAllocatedMemory()
+
+
+def driver_allocated_memory() -> int:
+    r"""Returns total GPU memory allocated by Metal driver for the process in bytes.
+
+    .. note::
+       The returned size includes cached allocations in MPSAllocator pools
+       as well as allocations from MPS/MPSGraph frameworks.
+    """
+    return torch._C._mps_driverAllocatedMemory()
+
+
+from . import profiler
+from .event import Event
+
+__all__ = [
+    "get_rng_state",
+    "manual_seed",
+    "seed",
+    "set_rng_state",
+    "synchronize",
+    "empty_cache",
+    "set_per_process_memory_fraction",
+    "current_allocated_memory",
+    "driver_allocated_memory",
+    "Event",
+    "profiler",
+]

venv/lib/python3.10/site-packages/torch/mps/event.py

@@ -0,0 +1,45 @@
+import torch
+
+
+class Event:
+    r"""Wrapper around an MPS event.
+
+    MPS events are synchronization markers that can be used to monitor the
+    device's progress, to accurately measure timing, and to synchronize MPS streams.
+
+    Args:
+        enable_timing (bool, optional): indicates if the event should measure time
+            (default: ``False``)
+    """
+
+    def __init__(self, enable_timing=False):
+        self.__eventId = torch._C._mps_acquireEvent(enable_timing)
+
+    def __del__(self):
+        # checks if torch._C is already destroyed
+        if hasattr(torch._C, "_mps_releaseEvent") and self.__eventId > 0:
+            torch._C._mps_releaseEvent(self.__eventId)
+
+    def record(self):
+        r"""Records the event in the default stream."""
+        torch._C._mps_recordEvent(self.__eventId)
+
+    def wait(self):
+        r"""Makes all future work submitted to the default stream wait for this event."""
+        torch._C._mps_waitForEvent(self.__eventId)
+
+    def query(self):
+        r"""Returns True if all work currently captured by event has completed."""
+        return torch._C._mps_queryEvent(self.__eventId)
+
+    def synchronize(self):
+        r"""Waits until the completion of all work currently captured in this event.
+        This prevents the CPU thread from proceeding until the event completes.
+        """
+        torch._C._mps_synchronizeEvent(self.__eventId)
+
+    def elapsed_time(self, end_event):
+        r"""Returns the time elapsed in milliseconds after the event was
+        recorded and before the end_event was recorded.
+        """
+        return torch._C._mps_elapsedTimeOfEvents(self.__eventId, end_event.__eventId)

venv/lib/python3.10/site-packages/torch/mps/profiler.py

@@ -0,0 +1,59 @@
+import contextlib
+
+import torch
+
+__all__ = ["start", "stop", "profile"]
+
+
+def start(mode: str = "interval", wait_until_completed: bool = False) -> None:
+    r"""Start OS Signpost tracing from MPS backend.
+
+    The generated OS Signposts could be recorded and viewed in
+    XCode Instruments Logging tool.
+
+    Args:
+        mode(str): OS Signpost tracing mode could be "interval", "event",
+            or both "interval,event".
+            The interval mode traces the duration of execution of the operations,
+            whereas event mode marks the completion of executions.
+            See document `Recording Performance Data`_ for more info.
+        wait_until_completed(bool): Waits until the MPS Stream complete
+            executing each encoded GPU operation. This helps generating single
+            dispatches on the trace's timeline.
+            Note that enabling this option would affect the performance negatively.
+
+    .. _Recording Performance Data:
+       https://developer.apple.com/documentation/os/logging/recording_performance_data
+    """
+    mode_normalized = mode.lower().replace(" ", "")
+    torch._C._mps_profilerStartTrace(mode_normalized, wait_until_completed)
+
+
+def stop():
+    r"""Stops generating OS Signpost tracing from MPS backend."""
+    torch._C._mps_profilerStopTrace()
+
+
+@contextlib.contextmanager
+def profile(mode: str = "interval", wait_until_completed: bool = False):
+    r"""Context Manager to enabling generating OS Signpost tracing from MPS backend.
+
+    Args:
+        mode(str): OS Signpost tracing mode could be "interval", "event",
+            or both "interval,event".
+            The interval mode traces the duration of execution of the operations,
+            whereas event mode marks the completion of executions.
+            See document `Recording Performance Data`_ for more info.
+        wait_until_completed(bool): Waits until the MPS Stream complete
+            executing each encoded GPU operation. This helps generating single
+            dispatches on the trace's timeline.
+            Note that enabling this option would affect the performance negatively.
+
+    .. _Recording Performance Data:
+       https://developer.apple.com/documentation/os/logging/recording_performance_data
+    """
+    try:
+        start(mode, wait_until_completed)
+        yield
+    finally:
+        stop()

venv/lib/python3.10/site-packages/torch/package/__init__.py

@@ -0,0 +1,12 @@
+from .analyze.is_from_package import is_from_package
+from .file_structure_representation import Directory
+from .glob_group import GlobGroup
+from .importer import (
+    Importer,
+    ObjMismatchError,
+    ObjNotFoundError,
+    OrderedImporter,
+    sys_importer,
+)
+from .package_exporter import EmptyMatchError, PackageExporter, PackagingError
+from .package_importer import PackageImporter