Method gamma

imperative/python/megengine/random/rng.py:376–433

r"""Random variable with Gamma distribution :math:`\Gamma(k, \theta)`. The corresponding probability density function is .. math:: p(x)=x^{k-1} \frac{e^{-x / \theta}}{\theta^{k} \Gamma(k)} \quad \text { for } x>0 \quad k, \theta>0, where :math:`\Ga

(
        self,
        shape: Union[Tensor, float],
        scale: Union[Tensor, float] = 1,
        size: Optional[Iterable[int]] = None,
    )

        )

    def gamma(
        self,
        shape: Union[Tensor, float],
        scale: Union[Tensor, float] = 1,
        size: Optional[Iterable[int]] = None,
    ):
        r"""Random variable with Gamma distribution :math:`\Gamma(k, \theta)`.

        The corresponding probability density function is

        .. math::

            p(x)=x^{k-1} \frac{e^{-x / \theta}}{\theta^{k} \Gamma(k)}
            \quad \text { for } x>0 \quad k, \theta>0,

        where :math:`\Gamma(k)` is the gamma function,

        .. math::
            \Gamma(k)=(k-1) !  \quad \text { for } \quad k \quad \text{is positive integer}.

        Args:
            shape(Union[Tensor, float]): the shape parameter (sometimes designated "k") of the distribution.
                Must be positive.
            scale(Union[Tensor, float]): the scale parameter (sometimes designated "theta") of the distribution.
                Must be positive. Default: 1.
            size(Optional[Iterable[int]]): the size of output tensor. If shape and scale are scalars and given size is, e.g.,
                `(m, n)`, then the output shape is `(m, n)`. If shape or scale is a Tensor and given size
                is, e.g., `(m, n)`, then the output shape is `(m, n) + broadcast(shape, scale).shape`.
                The broadcast rules are consistent with `numpy.broadcast`. Default: None.

        Returns:
            Return type: tensor. The random variable with Gamma distribution.

        Examples:
            >>> import megengine.random as rand
            >>> x = rand.gamma(shape=2, scale=1, size=(2, 2))
            >>> x.numpy()   # doctest: +SKIP
            array([[0.97447544, 1.5668875 ],
                   [1.0069491 , 0.3078318 ]], dtype=float32)
            >>> shape = mge.Tensor([[ 1],
            ...                     [10]], dtype="float32")
            >>> scale = mge.Tensor([1,5], dtype="float32")
            >>> x = rand.gamma(shape=shape, scale=scale)
            >>> x.numpy()   # doctest: +SKIP
            array([[ 0.11312152,  3.0799196 ],
                   [10.973469  , 29.596972  ]], dtype=float32)
            >>> x = rand.gamma(shape=shape, scale=scale, size=2)
            >>> x.numpy()   # doctest: +SKIP
            array([[[4.35868073e+00, 1.22415285e+01],
                    [1.02696848e+01, 4.19773598e+01]],

                   [[7.73875117e-02, 6.06766164e-01],
                    [1.22881927e+01, 8.13445740e+01]]], dtype=float32)
        """
        _seed = self._seed() if callable(self._seed) else self._seed
        return _gamma(
            shape=shape, scale=scale, size=size, seed=_seed, handle=self._handle
        )