B `,.@sdZddlmZddlmZddlmZddlZddlmZ ddl m Z ddl m Zdd l mZdd lmZdd lmZdd lmZdd lmZddlmZddlmZddlmZddlmZddlmZGdddejZe eedddZ!dS)zThe Pareto distribution class.)absolute_import)division)print_functionN)v2)chain)shift)softplus) distribution)kullback_leibler) assert_util)distribution_util) dtype_util)reparameterization)samplers) tensor_util)DeferredTensorcseZdZdZd.fdd ZeddZed d Zed d Z d/ddZ ddZ ddZ d0ddZ ddZddZddZddZddZed d!d"Zed#d$d%Zd&d'Zd(d)Zd*d+Zd,d-ZZS)1ParetoaPareto distribution. The Pareto distribution is parameterized by a `scale` and a `concentration` parameter. #### Mathematical Details The probability density function (pdf) is, ```none pdf(x; alpha, scale, x >= scale) = alpha * scale ** alpha / x ** (alpha + 1) ``` where `concentration = alpha`. Note that `scale` acts as a scaling parameter, since `Pareto(c, scale).pdf(x) == Pareto(c, 1.).pdf(x / scale)`. The support of the distribution is defined on `[scale, infinity)`. ?FTc s~tt}t|`tj||gtjd}tj|d|d|_ tj|d|d|_ t t |j |j jtj||||dWdQRXdS)aGConstruct Pareto distribution with `concentration` and `scale`. Args: concentration: Floating point tensor. Must contain only positive values. scale: Floating point tensor, equivalent to `mode`. `scale` also restricts the domain of this distribution to be in `[scale, inf)`. Must contain only positive values. Default value: `1`. validate_args: Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs. Default value: `False` (i.e. do not validate args). allow_nan_stats: Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value '`NaN`' to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined. Default value: `True`. name: Python `str` name prefixed to Ops created by this class. Default value: 'Pareto'. )Z dtype_hint concentration)namedtypescale)rZreparameterization_type validate_argsallow_nan_stats parametersrN)dictlocalstf name_scoper Z common_dtypefloat32rZconvert_nonref_to_tensor_concentration_scalesuperr__init__rrZFULLY_REPARAMETERIZED)selfrrrrrrr) __class__h/home/dcms/DCMS/lib/python3.7/site-packages/tensorflow_probability/python/distributions/_numpy/pareto.pyr#>s     zPareto.__init__cCs tdddS)Nr)rr)r)clsr&r&r'_params_event_ndimsgszPareto._params_event_ndimscCs|jS)z8Scale parameter and also the lower bound of the support.)r!)r$r&r&r'rksz Pareto.scalecCs|jS)z.Concentration parameter for this distribution.)r )r$r&r&r'rpszPareto.concentrationNcCs4tt|dkr|jn|t|dkr,|jn|S)N)rZbroadcast_dynamic_shapeshaperr)r$rrr&r&r'_batch_shape_tensoruszPareto._batch_shape_tensorcCst|jj|jjS)N)rZbroadcast_static_shaperr*r)r$r&r&r' _batch_shape{szPareto._batch_shapecCs tgS)N)rZ TensorShape)r$r&r&r' _event_shape~szPareto._event_shapecCsrt|j}t|j}tj|g|j||dgdd}tj|d||jd}tj |tj | |}t |S)N)rrr)Zaxisg?)maxvalseedr) rconvert_to_tensorrrconcatr+runiformrmathloglog1pexp)r$nr/rrr*ZsampledZ log_sampler&r&r' _sample_ns  zPareto._sample_nc sjt|jt|jt|jr4tj|ddgng&fdd}|j||t j dSQRXdS)Nz.`x` is not in the support of the distribution.)messagecs0tjtjdtj|S)Ng?)rr3r4)z)rrr&r'log_prob_on_supportsz-Pareto._log_prob..log_prob_on_support)alt) rr0rrcontrol_dependenciesrr assert_greater_equal_extend_supportnpinf)r$xr;r&)rrr' _log_probs   zPareto._log_probc sft|jt|jt|jr4tj|ddgng"fdd}|j||ddSQRXdS)Nz.`x` is not in the support of the distribution.)r9cs|dS)Nr&)r:)rrr&r'prob_on_supportsz%Pareto._prob..prob_on_supportg)r<) rr0rrr=rr r>r?)r$rBrEr&)rrr'_probs    z Pareto._probcs,tjj|fddtj dS)Ncstj|j S)N)rr3r5r)rB)rr$r&r'z!Pareto._log_cdf..)r<)rr0rr?r@rA)r$rBr&)rr$r'_log_cdfs   zPareto._log_cdfcs(tjj|fddddS)Ncs tjjtj| S)N)rr3expm1rr4)rB)rr$r&r'rGrHzPareto._cdf..g)r<)rr0rr?)r$rBr&)rr$r'_cdfs   z Pareto._cdfcs*tjj|fddtjdS)Ncsjtj|S)N)rrr3r4)rB)rr$r&r'rGrHz/Pareto._log_survival_function..)r<)rr0rr?r@rA)r$rBr&)rr$r'_log_survival_functions   zPareto._log_survival_functionzTThe mean of Pareto is defined` if `concentration > 1.`, otherwise it is `Inf`.cCs:t|j}t|dk||j|dt|jtj S)Ng?rD) rr0rwhererr as_numpy_dtyperr@rA)r$rr&r&r'_means  z Pareto._meanzXThe variance of Pareto is defined` if `concentration > 2.`, otherwise it is `Inf`.cCsNt|j}|jd||dd|d}t|dk|t|jtj S)Ng?g@) rr0rrrMr rNrr@rA)r$rZvalid_variancer&r&r' _variances    zPareto._variancecCs t|j}t||j|dS)N)r)rr0rZ broadcast_tor+)r$rr&r&r'_modes z Pareto._modecCs|jr||S|dkr"t|jn|}||k}|t|||}|dkrZtjg|jd}n*|dkrttjg|jd}nt |j|}t|||S)aReturns `f(x)` if x is in the support, and `alt` otherwise. Given `f` which is defined on the support of this distribution (e.g. x > scale), extend the function definition to the real line by defining `f(x) = alt` for `x < scale`. Args: x: Floating-point Tensor to evaluate `f` at. scale: Floating-point Tensor by which to verify `x` validity. f: Lambda that takes in a tensor and returns a tensor. This represents the function who we want to extend the domain of definition. alt: Python or numpy literal representing the value to use for extending the domain. Returns: Tensor representing an extension of `f(x)`. Ng)rg?) rrr0rrMzerosrZonesr rN)r$rBrfr<Z is_invalidyr&r&r'r?szPareto._extend_supportcCs^|js gSg}|t|jkr4|tj|jdd|t|jkrZ|tj|jdd|S)Nz!`concentration` must be positive.)r9z`scale` must be positive.)rrZis_refrappendr Zassert_positiver)r$Zis_initZ assertionsr&r&r'_parameter_control_dependenciessz&Pareto._parameter_control_dependenciescCs:t|jdd}tjtj||jdtj|jdg|jdS)NcSs|S)Nr&)rBr&r&r'rGrHz6Pareto._default_event_space_bijector..)rr)r) rrchain_bijectorZChainshift_bijectorZShiftrsoftplus_bijectorZSoftplus)r$Zdeferred_scaler&r&r'_default_event_space_bijectors  z$Pareto._default_event_space_bijector)rFTr)NN)N)__name__ __module__ __qualname____doc__r# classmethodr)propertyrrr+r,r-r8rCrFrIrKrLr ZAppendDocstringrOrQrRr?rWr[ __classcell__r&r&)r%r'r(s2$        rc Cst|p dt|j}t|j}t|j}t|j}t||k|tj|tj|tj|tj|||dt |j t j SQRXdS)a4Calculate the batched KL divergence KL(a || b) with a and b Pareto. Args: a: instance of a Pareto distribution object. b: instance of a Pareto distribution object. name: (optional) Name to use for created operations. default is 'kl_pareto_pareto'. Returns: Batchwise KL(a || b) Zkl_pareto_paretog?N) rrr0rrrMr3r4r rNrr@rA)abrZa_scaleZb_scaleZa_concentrationZb_concentrationr&r&r'_kl_pareto_paretos     >re)N)"r_ __future__rrrnumpyr@Z;tensorflow_probability.python.internal.backend.numpy.compatrrZ.tensorflow_probability.python.bijectors._numpyrrXrrYrrZZ2tensorflow_probability.python.distributions._numpyr r Z-tensorflow_probability.python.internal._numpyr r r Z&tensorflow_probability.python.internalrrrZ9tensorflow_probability.python.util._numpy.deferred_tensorr DistributionrZ RegisterKLrer&r&r&r's*                g