o "j21@sFddlZddlZddlZddlmZddlmZGdddejZ dS)N) framework) distributioncseZdZdZfddZeddZeddZedd Zd d Z d d Z ddZ ddZ ddZ dddZddZddZddZZS)Laplacea Creates a Laplace distribution parameterized by :attr:`loc` and :attr:`scale`. Mathematical details The probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{2 * \sigma} * e^{\frac{-|x - \mu|}{\sigma}} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: loc (scalar|Tensor): The mean of the distribution. scale (scalar|Tensor): The scale of the distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.sample() # Laplace distributed with loc=0, scale=1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.31554604) cst|tjtjfstdt|t|tjtjfs$tdt|t|tjr1tjd|d}t|tjr>tjd|d}t |j dksLt |j dkr^|j |j kr^t ||g\|_ |_n|||_ |_t|j j dS)Nz/Expected type of loc is Real|Variable, but got z1Expected type of scale is Real|Variable, but got shapeZ fill_valuer) isinstancenumbersRealrVariable TypeErrortypepaddlefulllenrdtypebroadcast_tensorslocscalesuper__init__)selfrr __class__r\/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/paddle/distribution/laplace.pyr8s"     zLaplace.__init__cCs|jS)zTMean of distribution. Returns: Tensor: The mean value. )rrrrrmeanRsz Laplace.meancCs d|jS)zStandard deviation. The stddev is .. math:: stddev = \sqrt{2} * \sigma In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: The std value. g;f?)rrrrrstddev[s zLaplace.stddevcCs |jdS)aVariance of distribution. The variance is .. math:: variance = 2 * \sigma^2 In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: The variance value. )rpowrrrrvariancems zLaplace.variancecCst|tjr tjd|d}|j|jjkrt||jj}t|jj dks3t|j j dks3t|j dkrAt |j |j|g\}}}n|j |j}}|||fS)aHArgument dimension check for distribution methods such as `log_prob`, `cdf` and `icdf`. Args: value (Tensor|Scalar): The input value, which can be a scalar or a tensor. Returns: loc, scale, value: The broadcasted loc, scale and value, with the same dimension and data type. rrr) rr r rrrrcastrrrr)rvaluerrrrr_validate_values    zLaplace._validate_valuecCs6||\}}}td| }|t|||S)aLog probability density/mass function. The log_prob is .. math:: log\_prob(value) = \frac{-log(2 * \sigma) - |value - \mu|}{\sigma} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor|Scalar): The input value, can be a scalar or a tensor. Returns: Tensor: The log probability, whose data type is same with value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.log_prob(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -0.79314721) r)r#rlogabs)rr"rrZ log_scalerrrlog_probszLaplace.log_probcCsdtd|jS)amEntropy of Laplace distribution. The entropy is: .. math:: entropy() = 1 + log(2 * \sigma) In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: The entropy of distribution. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.entropy() Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.69314718) r)rr$rrrrrentropyszLaplace.entropycCs@||\}}}d||t|| |}d|S)aZCumulative distribution function. The cdf is .. math:: cdf(value) = 0.5 - 0.5 * sign(value - \mu) * e^\frac{-|(\mu - \sigma)|}{\sigma} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor): The value to be evaluated. Returns: Tensor: The cumulative probability of value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.cdf(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.54758132) ?)r#signrexpm1r%)rr"rrZitermrrrcdfs z Laplace.cdfcCs:||\}}}|d}|||td|S)a`Inverse Cumulative distribution function. The icdf is .. math:: cdf^{-1}(value)= \mu - \sigma * sign(value - 0.5) * ln(1 - 2 * |value-0.5|) In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor): The value to be evaluated. Returns: Tensor: The cumulative probability of value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.icdf(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -1.60943794) r))r#r*rlog1pr%)rr"rrtermrrricdfs"z Laplace.icdfrcCsLt|tr|nt|}t ||WdS1swYdS)azGenerate samples of the specified shape. Args: shape(tuple[int]): The shape of generated samples. Returns: Tensor: A sample tensor that fits the Laplace distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.sample() # Laplace distributed with loc=0, scale=1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.31554604) N)rtuplerZno_gradrsample)rrrrrsample"s $zLaplace.samplecCsh|}||}tj|ttdd|dd|d|jjd}|j|j | t | S)azReparameterized sample. Args: shape(tuple[int]): The shape of generated samples. Returns: Tensor: A sample tensor that fits the Laplace distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m.rsample((1,)) # Laplace distributed with loc=0, scale=1 Tensor(shape=[1, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.31554604]]) r'rg?)rminmaxr) _get_epsZ _extend_shaperuniformfloatnp nextafterrrrr*r.r%)rrepsr8rrrr29s  zLaplace.rsamplecCs(d}|jjtjks|jjtjkrd}|S)z Get the eps of certain data type. Note: Since paddle.finfo is temporarily unavailable, we use hard-coding style to get eps value. Returns: Float: An eps value by different data types. gy>gǝ<)rrrZfloat64Z complex128)rr<rrrr7Ys  zLaplace._get_epscCsV|j|j}t|j|j}|jt| |j||j}t|}||dS)aCalculate the KL divergence KL(self || other) with two Laplace instances. The kl_divergence between two Laplace distribution is .. math:: KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\frac{diff}{\sigma_1})^2 - 1 - 2 \ln {ratio}) .. math:: ratio = \frac{\sigma_0}{\sigma_1} .. math:: diff = \mu_1 - \mu_0 In the above equation: * :math:`loc = \mu`: is the location parameter of self. * :math:`scale = \sigma`: is the scale parameter of self. * :math:`loc = \mu_1`: is the location parameter of the reference Laplace distribution. * :math:`scale = \sigma_1`: is the scale parameter of the reference Laplace distribution. * :math:`ratio`: is the ratio between the two distribution. * :math:`diff`: is the difference between the two distribution. Args: other (Laplace): An instance of Laplace. Returns: Tensor: The kl-divergence between two laplace distributions. Examples: .. code-block:: python >>> import paddle >>> m1 = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m2 = paddle.distribution.Laplace(paddle.to_tensor([1.0]), paddle.to_tensor([0.5])) >>> m1.kl_divergence(m2) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.04261160]) r')rrr%rexpr$)rotherZ var_ratiotZterm1Zterm2rrr kl_divergencems )"  zLaplace.kl_divergence)r)__name__ __module__ __qualname____doc__rpropertyrrr r#r&r(r,r0r3r2r7r@ __classcell__rrrrrs$    $' " r) r numpyr:rZ paddle.baserZpaddle.distributionr Distributionrrrrrs