zj{E"UddlmZddlZddlmZmZddlmZddlZ ddl mZ ddl Z ddl mZmZddlmZddlmZddlmZdd lmZerdd lmZdd lmZdd l mZmZdd lmZeee fZ!de"d<ee j#e j$e j%e j&fZ'de"d<ee!ee!ee!e j(e'efZ)de"d<eeeeeee j(ee j#e j$fefZ*de"d<Gddej+Z,dS)) annotationsN)IterableSequence) TYPE_CHECKING) check_type convert_dtype)Variable) distribution)in_dynamic_mode)random)Union) TypeAlias)Tensordtype)NestedSequencer_NormalLocBase_NormalLocNDArray _NormalLoc _NormalScaleceZdZUdZded<ded<ded<ded< ddfd Zed dZed dZgdfd!dZ gfd"dZ d dZ d#dZ d#dZ d$dZxZS)%Normala The Normal distribution with location `loc` and `scale` parameters. Mathematical details If 'loc' is real number, the probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{Z}e^{\frac {-0.5 (x - \mu)^2} {\sigma^2} } .. math:: Z = (2 \pi \sigma^2)^{0.5} If 'loc' is complex number, the probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{Z}e^{\frac {-(x - \mu)^2} {\sigma^2} } .. math:: Z = \pi \sigma^2 In the above equations: * :math:`loc = \mu`: is the mean. * :math:`scale = \sigma`: is the std. * :math:`Z`: is the normalization constant. Args: loc(int|float|complex|list|tuple|numpy.ndarray|Tensor): The mean of normal distribution.The data type is float32, float64, complex64 and complex128. scale(int|float|list|tuple|numpy.ndarray|Tensor): The std of normal distribution.The data type is float32 and float64. name(str|None, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Normal >>> # Define a single scalar Normal distribution. >>> dist = Normal(loc=0., scale=3.) >>> # Define a batch of two scalar valued Normals. >>> # The first has mean 1 and standard deviation 11, the second 2 and 22. >>> dist = Normal(loc=[1., 2.], scale=[11., 22.]) >>> # Get 3 samples, returning a 3 x 2 tensor. >>> dist.sample([3]) >>> # Define a batch of two scalar valued Normals. >>> # Both have mean 1, but different standard deviations. >>> dist = Normal(loc=1., scale=[11., 22.]) >>> # Complete example >>> value_tensor = paddle.to_tensor([0.8], dtype="float32") >>> normal_a = Normal([0.], [1.]) >>> normal_b = Normal([0.5], [2.]) >>> sample = normal_a.sample([2]) >>> # a random tensor created by normal distribution with shape: [2, 1] >>> entropy = normal_a.entropy() >>> print(entropy) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.41893852]) >>> lp = normal_a.log_prob(value_tensor) >>> print(lp) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [-1.23893857]) >>> p = normal_a.probs(value_tensor) >>> print(p) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.28969154]) >>> kl = normal_a.kl_divergence(normal_b) >>> print(kl) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.34939718]) rlocscalestrnamerNrr str | NonereturnNonec  tst|dtttt jttj j ttfdt|dttt jttj j ttfdd|_ ||nd|_d|_d|_t#|trt|}t#|trt|}t#|ttfrht j|}|jt jkr|d}|jt jkr|d}t#|ttfr t j|t j}t#|tsdt#|t jr|jt jt jfvs+||r|rd|_t#|trt#|trd|_ t#|t jr|jt jkrdnd }|jt jkrdnd }tj|j|}tj|j|}tj|||_nmt#|trQtj|jd}tj|jd}tj|||_n||_t#|t jr!tj||j|_n8t#|trtj|d|_n||_t?|jj|_nx|||r)||_||_t?|j|_n9t#|trt#|trd|_ t#|t jr#tA|jd vr |j|_n>>##C((?-0^^-=-=?&*D "#w'' -Jue,D,D -(,%#rz** !$bl!:!:II "%bl!:!:II '*=='*==!>$55C)) ' BBB' BBB!>$55%,, ##-e5;GGG E5)) ##-e9EEE " &tx~66DJJ""3.. K" *3955 c5))1j.F.F1,0D)c2:.. -3sy>>F44"%DJJrz22-s5;7G7GL88"'DJ'+sE'B'B$$*:tx~!>!>>>%{484:FFFDH!'TZtz!J!J!JDJ (((((c|jS)zWMean of normal distribution. Returns: Tensor: mean value. )rr>s rBmeanz Normal.means xrCc6|jdS)z_Variance of normal distribution. Returns: Tensor: variance value. )rpowrEs rBvariancezNormal.variance sz~~a   rCrr= Sequence[int]seedr$ct|tstdtst |dt dt |}t |j|jzj }|j dz}d|vr||z}t ||z}tj |j|jzd |d<tj |d|j}tj||}tj |} t!j| |jrdndd ||j } | ||jzz} tj| |j| } | S||z}t!j||jrdndd ||j tj||j |jzz} tj| |j| } |jrtj| || S| S) a&Generate samples of the specified shape. Args: shape (Sequence[int], optional): Shape of the generated samples. seed (int): Python integer number. Returns: Tensor, A tensor with prepended dimensions shape.The data type is float32. %sample shape must be Iterable object.rLsample_sampler?)rFstdrLrrr")r0r TypeErrorr rr$r,rrr=rr)itemfullrreshaper gaussianr/addzerosr.) r>r=rL batch_shaper output_shape fill_shapezero_tmpzero_tmp_reshapezero_tmp_shapenormal_random_tmpoutputs rBrOz Normal.samples %** ECDD D   6 tVcH 5 5 5U DHtz1899 y9$    ;.LkE122J"LDJ)>??BGGIIJqM{:sDJ??H%~h EE #\*:;;N &%)%;Djjj !!! '*:TZ*GHFZt<<r=epss rBrsamplezNormal.rsampleHs|%** ECDD D""5<<00m!%!7@**S   x# ***rCc |jdz}t|j|jzj}|jrd|vrnt|}t j|j|jzd|d<|jj}t j |d|}n t j |d|jj}t j d|ztj tj dt j |j|zzz|Sd|vrvt|}t j|j|jzd|d<|j|jzj}t j |d|}nt j |d|j}t j d|zdtj d tj zzt j |j|zz|S) aShannon entropy in nats. If non-complex, the entropy is .. math:: entropy(\sigma) = 0.5 \log (2 \pi e \sigma^2) If complex gaussian, the entropy is .. math:: entropy(\sigma) = \log (\pi e \sigma^2) + 1 In the above equation: * :math:`scale = \sigma`: is the std. Returns: Tensor, Shannon entropy of normal distribution.The data type is float32. _entropyrQrrRrT@rV?rH)rr,rrr=r/r)rXrrYr\mathlogpi)r>rr^r` fill_dtyperas rBentropyzNormal.entropy[s.y:%DHtz1899  ! [  !+.. & TX -B C CA F K K M M 1 !Z- !;z3 CC!;{C9IJJ:h!!C&*TZ(5J*K*K$KK  [  !+.. & TX -B C CA F K K M M 1 "h3: !;z3 CC!;{CDD:hdhq47{+++fjh9N.O.OO rCvaluec @|jdz}||j|}|j|jz}t j|j}|jrdt jd||jz ||jz zz|z d|ztjtj z|St jd||jz ||jz zzd|zz |tjtj dtj zz|S)zLog probability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability.The data type is same with :attr:`value` . _log_probrmrV) r_check_values_dtype_in_probsrrr)rpr/subtractconjrorqsqrt)r>rtrvar log_scales rBlog_probzNormal.log_probsy;&11$(EBBj4:%Jtz**  ! ?)//11UTX5EFG3Oi$(47"3"33  ?)edh.>?@C#INDHTYsTW}%=%=>>> rCc|jdz}||j|}|j|jz}|jrat jt jd||jz ||jz zz|z tj |z|St jt jd||jz ||jz zzd|zz tj dtj z|jz|S)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor, probability. The data type is same with :attr:`value` . _probsrwrVrmrH) rrxrrr/r)divideexprzrorqr{)r>rtrr|s rBprobsz Normal.probssy8#11$(EBBj4:%  ! = (..00EDH4DEG 3 = (UTX-=>@Sy" 1tw;''$*4 rCotherctst|dtd|j|jkrt d|jdz}|j|jz }||z}|j|jz |jz }|jr4||z}||zdz tj |z S||z}tj d|zd|dz tj |z z|S)aThe KL-divergence between two normal distributions. If non-complex, the KL-divergence 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}) If complex gaussian: .. math:: KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 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_0`: is the mean of current Normal distribution. * :math:`scale = \sigma_0`: is the std of current Normal distribution. * :math:`loc = \mu_1`: is the mean of other Normal distribution. * :math:`scale = \sigma_1`: is the std of other Normal distribution. * :math:`ratio`: is the ratio of scales. * :math:`diff`: is the difference between means. Args: other (Normal): instance of Normal. Returns: Tensor, kl-divergence between two normal distributions.The data type is float32. r kl_divergencezVThe kl divergence must be computed between two distributions in the same number field._kl_divergencerTrnrV) r rrr/ ValueErrorrrrrzr)rpr\)r>rr var_ratiot1s rBrzNormal.kl_divergences N   @ ugv ? ? ?  !U%< < <h y++J,  ) h"ek 1  ! RBr>C'&*Y*?*?? ?bB:irCx&*Y"7"778 rC)N)rrrrrrrr)rr)r=rKrLr$rr)r=rKrr)rtrrr)rrrr)__name__ __module__ __qualname____doc____annotations__r<propertyrFrJrOrjrsr~rr __classcell__)rAs@rBrr:sWLL\KKKMMM IIILLLHLq)q)q)q)q)q)q)fX!!!X!-/A33333j.0+++++&3333j8!!!!F;;;;;;;;rCr)- __future__rrocollections.abcrrtypingrnumpyr' numpy.typingnptr)paddle.base.data_feederrrpaddle.base.frameworkr paddle.distributionr paddle.frameworkr paddle.tensorr r typing_extensionsrrrpaddle._typingrr%r&rrr r#r!r3rNDArrayrr DistributionrrCrBrsR#"""""" ........  ========******,,,,,,,,,,,, ++++++$$$$$$$$------ %eWn 5N5555#( BJ bm;$" ~& %&  J$ u E"*bj012  LPPPPP\ &PPPPPrC