o "j{)@sFddlZddlZddlZddlmZddlmZGdddejZ dS)N) framework) distributioncseZdZdZfddZeddZeddZedd Zd d Z d d Z dddZ dddZ ddZ ddZddZZS) GeometricaM Geometric distribution parameterized by probs. In probability theory and statistics, the geometric distribution is one of discrete probability distributions, parameterized by one positive shape parameter, denoted by probs. In n Bernoulli trials, it takes k+1 trials to get the probability of success for the first time. In detail, it is: the probability that the first k times failed and the kth time succeeded. The geometric distribution is a special case of the Pascal distribution when r=1. The probability mass function (pmf) is .. math:: Pr(Y=k)=(1-p)^kp where k is number of trials failed before seeing a success, and p is probability of success for each trial and k=0,1,2,3,4..., p belong to (0,1]. Args: probs (Real|Tensor): Probability parameter. The value of probs must be positive. When the parameter is a tensor, probs is probability of success for each trial. Returns: Geometric distribution for instantiation of probs. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom = Geometric(0.5) >>> print(geom.mean) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.) >>> print(geom.variance) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 2.) >>> print(geom.stddev) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.41421354) cst|tjtjtjfr@t|tjrtjd|tjd}tj|j d|j d}tj|j d|j d}tj|j dt d}||k}||k}n t dt |t||r[t||r[t|j }ntd||_t|dS)N)shapeZ fill_valuedtyperFzIExpected type of probs is Number.Real|Tensor|framework.Variable, but got zvExpected parameter probs of distribution Geometric to satisfy theconstraint Interval(lower_bound=0.0, upper_bound=1.0)) isinstancenumbersRealpaddleZTensorrVariablefullfloat32rrbool TypeErrortypeZ equal_alltuple ValueErrorprobssuper__init__)selfrall_onesZ all_zerosZ all_falseZ lessthen_0Z morethen_1Z batch_shape __class__r^/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/paddle/distribution/geometric.pyrFs8      zGeometric.__init__cCsd|jdS)zMean of geometric distribution.?)rrrrrmeanlszGeometric.meancCs"tjd|jd|j|jjdS)z#Variance of geometric distribution.rr)r Z to_tensorrrrrrrvarianceqszGeometric.variancecCs t|jS)z-Standard deviation of Geometric distribution.)r sqrtr!rrrrstddevys zGeometric.stddevcCs<t|tjtjfrtd|j||jStdt |)aIProbability mass funciotn evaluated at k. .. math:: P(X=k) = (1-p)^{k} p, \quad k=0,1,2,3,\ldots Args: k (int): Value to be evaluated. Returns: Tensor: Probability. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom = Geometric(0.5) >>> print(geom.pmf(2)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.12500000) r>Expected type of k is number.Real|framework.Variable, but got r r Integralrr r powrrrrkrrrpmf~s  z Geometric.pmfcCs4t|tjtjfrt||Stdt |)aFLog probability mass function evaluated at k. .. math:: \log P(X = k) = \log(1-p)^k p Args: k (int): Value to be evaluated. Returns: Tensor: Log probability. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom = Geometric(0.5) >>> print(geom.log_pmf(2)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -2.07944131) r$) r r r&rr r logr*rrr(rrrlog_pmfs  zGeometric.log_pmfrcCs6t ||WdS1swYdS)aSample from Geometric distribution with sample shape. Args: shape (tuple(int)): Sample shape. Returns: Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> paddle.seed(2023) >>> geom = Geometric(0.5) >>> print(geom.sample((2,2))) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[0., 0.], [1., 0.]]) N)r Zno_gradrsample)rrrrrsamples $zGeometric.samplecCsRtjj||d}tj|ttjddjd|j j d}t t |t |j S)aGenerate samples of the specified shape. Args: shape(tuple(int)): The shape of generated samples. Returns: Tensor: A sample tensor that fits the Geometric distribution. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> paddle.seed(2023) >>> geom = Geometric(0.5) >>> print(geom.rsample((2,2))) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[0., 0.], [1., 0.]]) )Z sample_shaperr r)rminmaxr)r DistributionZ _extend_shaper uniformfloatnpZfinfoZtinyrrfloorr+log1p)rrr2rrrr-szGeometric.rsamplecCs<d|jtd|j}|jt|j}|| |jS)aEntropy of dirichlet distribution. .. math:: H(X) = -\left[\frac{1}{p} \log p + \frac{1-p}{p^2} \log (1-p) \right] Returns: Tensor: Entropy. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom = Geometric(0.5) >>> print(geom.entropy()) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.38629425) r)rr r+)rxyrrrentropyszGeometric.entropycCs>t|tjtjfrdtd|j|dStdt |)aDCdf of geometric distribution. .. math:: F(X \leq k) = 1 - (1-p)^(k+1), \quad k=0,1,2,\ldots Args: k: The number of trials performed. Returns: Tensor: Entropy. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom = Geometric(0.5) >>> print(geom.cdf(4)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.96875000) rrr$r%r(rrrcdfs  z Geometric.cdfcCsZt|tr$|j|j}}|t||d|td|d|Stdt|)aCalculate the KL divergence KL(self || other) with two Geometric instances. .. math:: KL(P \| Q) = \frac{p}{q} \log \frac{p}{q} + \log (1-p) - \log (1-q) Args: other (Geometric): An instance of Geometric. Returns: Tensor: The kl-divergence between two geometric distributions. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Geometric >>> geom_p = Geometric(0.5) >>> geom_q = Geometric(0.1) >>> print(geom_p.kl_divergence(geom_q)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.51082563) rz6Exected type of other is geometric.Geometric, but got )r rrr r+rr)rotherpqrrr kl_divergence7s  zGeometric.kl_divergence)r)__name__ __module__ __qualname____doc__rpropertyrr!r#r*r,r.r-r9r:r> __classcell__rrrrrs  -&     % r) r numpyr4r Z paddle.baserZpaddle.distributionrr1rrrrrs