o Me@sPddlZddlZddlZddlZddlZddlZddlZddlmm Z ddl m Z m Z mZmZgdZGdddejZGdddeZGdd d eZGd d d eZGd d d eZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZ dS) N) constraint distributiontransformed_distributionvariable) Transform AbsTransformAffineTransformChainTransform ExpTransformIndependentTransformPowerTransformReshapeTransformSigmoidTransformSoftmaxTransformStackTransformStickBreakingTransform TanhTransformc@s,eZdZdZdZdZdZdZeddZ dS) Typez!Mapping type of a transformation.Z bijectionZ injectionZ surjectionothercCs||j|jfvS)z3Both bijection and injection are injective mapping.) BIJECTION INJECTION)cls_typerMD:\Projects\ConvertPro\env\Lib\site-packages\paddle/distribution/transform.py is_injective8szType.is_injectiveN) __name__ __module__ __qualname____doc__rr SURJECTIONOTHER classmethodrrrrrr0srcseZdZdZejZfddZeddZ ddZ dd Z d d Z d d Z ddZddZddZeddZeddZddZddZddZddZd d!Zd"d#ZZS)$ra Base class for the transformations of random variables. ``Transform`` can be used to represent any differentiable and injective function from the subset of :math:`R^n` to subset of :math:`R^m`, generally used for transforming a random sample generated by ``Distribution`` instance. Suppose :math:`X` is a K-dimensional random variable with probability density function :math:`p_X(x)`. A new random variable :math:`Y = f(X)` may be defined by transforming :math:`X` with a suitably well-behaved funciton :math:`f`. It suffices for what follows to note that if `f` is one-to-one and its inverse :math:`f^{-1}` have a well-defined Jacobian, then the density of :math:`Y` is .. math:: p_Y(y) = p_X(f^{-1}(y)) |det J_{f^{-1}}(y)| where det is the matrix determinant operation and :math:`J_{f^{-1}}(y)` is the Jacobian matrix of :math:`f^{-1}` evaluated at :math:`y`. Taking :math:`x = f^{-1}(y)`, the Jacobian matrix is defined by .. math:: J(y) = \begin{bmatrix} {\frac{\partial x_1}{\partial y_1}} &{\frac{\partial x_1}{\partial y_2}} &{\cdots} &{\frac{\partial x_1}{\partial y_K}} \\ {\frac{\partial x_2}{\partial y_1}} &{\frac{\partial x_2} {\partial y_2}}&{\cdots} &{\frac{\partial x_2}{\partial y_K}} \\ {\vdots} &{\vdots} &{\ddots} &{\vdots}\\ {\frac{\partial x_K}{\partial y_1}} &{\frac{\partial x_K}{\partial y_2}} &{\cdots} &{\frac{\partial x_K}{\partial y_K}} \end{bmatrix} A ``Transform`` can be characterized by three operations: #. forward Forward implements :math:`x \rightarrow f(x)`, and is used to convert one random outcome into another. #. inverse Undoes the transformation :math:`y \rightarrow f^{-1}(y)`. #. log_det_jacobian The log of the absolute value of the determinant of the matrix of all first-order partial derivatives of the inverse function. Subclass typically implement follow methods: * _forward * _inverse * _forward_log_det_jacobian * _inverse_log_det_jacobian (optional) If the transform changes the shape of the input, you must also implemented: * _forward_shape * _inverse_shape ctt|dSN)superr__init__self __class__rrr&{zTransform.__init__cCs t|jS)zIs the transformation type one-to-one or not. Returns: bool: ``True`` denotes injective. ``False`` denotes non-injective. )rrr)rrrr _is_injective~s zTransform._is_injectivecCs:t|tjr t||gSt|trt||gS|tS)ahMake this instance as a callable object. The return value is depening on the input type. * If the input is a ``Tensor`` instance, return ``self.forward(input)`` . * If the input is a ``Distribution`` instance, return ``TransformedDistribution(base=input, transforms=[self])`` . * If the input is a ``Transform`` instance, return ``ChainTransform([self, input])`` . Args: input (Tensor|Distribution|Transform): The input value. Returns: [Tensor|TransformedDistribution|ChainTransform]: The return value. ) isinstancer DistributionrZTransformedDistributionrr forwardx)r(inputrrr__call__s    zTransform.__call__cCZt|tjjjstdt|d||jj kr(t d|d|jj | |S)aCForward transformation with mapping :math:`y = f(x)`. Useful for turning one random outcome into another. Args: x (Tensos): Input parameter, generally is a sample generated from ``Distribution``. Returns: Tensor: Outcome of forward transformation. z*Expected 'x' is a Tensor or Real, but got .The dimensions of x($) should be grater than or equal to ) r-paddlefluid frameworkVariable TypeErrortypedim_domain event_rank ValueError_forwardr(r0rrrr/s   zTransform.forwardcCr3)a2Inverse transformation :math:`x = f^{-1}(y)`. It's useful for "reversing" a transformation to compute one probability in terms of another. Args: y (Tensor): Input parameter for inverse transformation. Returns: Tensor: Outcome of inverse transform. *Expected 'y' is a Tensor or Real, but got r4The dimensions of y(r6) r-r7r8r9r:r;r<r= _codomainr?r@_inverser(yrrrinverses   zTransform.inversecCszt|tjjjstdt|dt|tjjjr0||jj kr0t d|d|jj | s8t d| |S)agThe log of the absolute value of the determinant of the matrix of all first-order partial derivatives of the inverse function. Args: x (Tensor): Input tensor, generally is a sample generated from ``Distribution`` Returns: Tensor: The log of the absolute value of Jacobian determinant. rCr4r5r6zJforward_log_det_jacobian can't be implemented for non-injectivetransforms.)r-r7r8r9r:r;r<r=r>r?r@r,NotImplementedError_call_forward_log_det_jacobianrBrrrforward_log_det_jacobians"   z"Transform.forward_log_det_jacobiancCr3)aqCompute :math:`log|det J_{f^{-1}}(y)|`. Note that ``forward_log_det_jacobian`` is the negative of this function, evaluated at :math:`f^{-1}(y)`. Args: y (Tensor): The input to the ``inverse`` Jacobian determinant evaluation. Returns: Tensor: The value of :math:`log|det J_{f^{-1}}(y)|`. z"Expected 'y' is a Tensor, but got r4rDr6) r-r7r8r9r:r;r<r=rEr?r@_call_inverse_log_det_jacobianrGrrrinverse_log_det_jacobians   z"Transform.inverse_log_det_jacobiancC*t|tjstdt|d||S)zInfer the shape of forward transformation. Args: shape (Sequence[int]): The input shape. Returns: Sequence[int]: The output shape. .Expected shape is Sequence[int] type, but got r4)r-typingSequencer;r<_forward_shaper(shaperrr forward_shape  zTransform.forward_shapecCrO)zInfer the shape of inverse transformation. Args: shape (Sequence[int]): The input shape of inverse transformation. Returns: Sequence[int]: The output shape of inverse transformation. rPr4)r-rQrRr;r<_inverse_shaperTrrr inverse_shaperWzTransform.inverse_shapecCtjS)z!The domain of this transformationrrealr'rrrr>zTransform._domaincCrZ)z#The codomain of this transformationr[r'rrrrE#r]zTransform._codomaincCtd)zInner method for publid API ``forward``, subclass should overwrite this method for supporting forward transformation. zForward not implementedrJrBrrrrA(zTransform._forwardcCr^)zInner method of public API ``inverse``, subclass should overwrite this method for supporting inverse transformation. zInverse not implementedr_rGrrrrF.r`zTransform._inversecCs8t|dr ||St|dr||t Std)z4Inner method called by ``forward_log_det_jacobian``._forward_log_det_jacobian_inverse_log_det_jacobianzgNeither _forward_log_det_jacobian nor _inverse_log_det_jacobianis implemented. One of them is required.)hasattrrarbr/rHrJrBrrrrK4   z(Transform._call_forward_log_det_jacobiancCs8t|dr ||St|dr||| Std)z3Inner method called by ``inverse_log_det_jacobian``rbrazgNeither _forward_log_det_jacobian nor _inverse_log_det_jacobian is implemented. One of them is required)rcrbrarFrJrGrrrrM?rdz(Transform._call_inverse_log_det_jacobiancC|S)zInner method called by ``forward_shape``, which is used to infer the forward shape. Subclass should overwrite this method for supporting ``forward_shape``. rrTrrrrSJzTransform._forward_shapecCre)zInner method called by ``inverse_shape``, whic is used to infer the invese shape. Subclass should overwrite this method for supporting ``inverse_shape``. rrTrrrrXQrfzTransform._inverse_shape)rrrrrrrr&r"r,r2r/rIrLrNrVrYpropertyr>rErArFrKrMrSrX __classcell__rrr)rr>s.:      rc@sFeZdZdZejZddZddZddZ e dd Z e d d Z d S) ra Absolute transformation with formula :math:`y = f(x) = abs(x)`, element-wise. This non-injective transformation allows for transformations of scalar distributions with the absolute value function, which maps ``(-inf, inf)`` to ``[0, inf)`` . * For ``y`` in ``(0, inf)`` , ``AbsTransform.inverse(y)`` returns the set invese ``{x in (-inf, inf) : |x| = y}`` as a tuple, ``-y, y`` . * For ``y`` equal ``0`` , ``AbsTransform.inverse(0)`` returns ``0, 0``, which is not the set inverse (the set inverse is the singleton {0}), but "works" in conjunction with ``TransformedDistribution`` to produce a left semi-continuous pdf. * For ``y`` in ``(-inf, 0)`` , ``AbsTransform.inverse(y)`` returns the wrong thing ``-y, y``. This is done for efficiency. Examples: .. code-block:: python import paddle abs = paddle.distribution.AbsTransform() print(abs.forward(paddle.to_tensor([-1., 0., 1.]))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 0., 1.]) print(abs.inverse(paddle.to_tensor(1.))) # (Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [-1.]), Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1.])) # The |dX/dY| is constant 1. So Log|dX/dY| == 0 print(abs.inverse_log_det_jacobian(paddle.to_tensor(1.))) # (Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True, # 0.), Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True, # 0.)) #Special case handling of 0. print(abs.inverse(paddle.to_tensor(0.))) # (Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.]), Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.])) print(abs.inverse_log_det_jacobian(paddle.to_tensor(0.))) # (Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True, # 0.), Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True, # 0.)) cC|Sr$)absrBrrrrAzAbsTransform._forwardcCs | |fSr$rrGrrrrF zAbsTransform._inversecCstjdg|jd}||fSN)dtype)r7zerosro)r(rHzerorrrrbsz&AbsTransform._inverse_log_det_jacobiancCrZr$r[r'rrrr>zAbsTransform._domaincCrZr$rZpositiver'rrrrErrzAbsTransform._codomainN) rrrrrr rrArFrbrgr>rErrrrrYs2 rcs~eZdZdZejZfddZeddZ eddZ dd Z d d Z d d Z ddZddZeddZeddZZS)raAffine transformation with mapping :math:`y = \text{loc} + \text{scale} \times x`. Args: loc (Tensor): The location parameter. scale (Tensor): The scale parameter. Examples: .. code-block:: python import paddle x = paddle.to_tensor([1., 2.]) affine = paddle.distribution.AffineTransform(paddle.to_tensor(0.), paddle.to_tensor(1.)) print(affine.forward(x)) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 2.]) print(affine.inverse(affine.forward(x))) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 2.]) print(affine.forward_log_det_jacobian(x)) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.]) csbt|tjjjstdt|t|tjjjs"tdt|||_||_t t | dS)Nz$Expected 'loc' is a Tensor, but got z$Expected scale is a Tensor, but got ) r-r7r8r9r:r;r<_loc_scaler%rr&)r(locscaler)rrr&s zAffineTransform.__init__cC|jSr$)rtr'rrrrvrrzAffineTransform.loccCrxr$)rur'rrrrwrrzAffineTransform.scalecCs|j|j|Sr$rtrurBrrrrAzAffineTransform._forwardcCs||j|jSr$ryrGrrrrFrzzAffineTransform._inversecCst|jSr$)r7rjrulogrBrrrrarzz)AffineTransform._forward_log_det_jacobiancC ttt||jj|jjSr$tupler7broadcast_shapertrUrurTrrrrS zAffineTransform._forward_shapecCr|r$r}rTrrrrXrzAffineTransform._inverse_shapecCrZr$r[r'rrrr>rrzAffineTransform._domaincCrZr$r[r'rrrrErrzAffineTransform._codomain)rrrrrrrr&rgrvrwrArFrarSrXr>rErhrrr)rrs"    rcspeZdZdZfddZddZddZdd Zd d Zd d Z ddZ ddZ e ddZ e ddZZS)r aComposes multiple transforms in a chain. Args: transforms (Sequence[Transform]): A sequence of transformations. Examples: .. code-block:: python import paddle x = paddle.to_tensor([0., 1., 2., 3.]) chain = paddle.distribution.ChainTransform(( paddle.distribution.AffineTransform( paddle.to_tensor(0.), paddle.to_tensor(1.)), paddle.distribution.ExpTransform() )) print(chain.forward(x)) # Tensor(shape=[4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1. , 2.71828175 , 7.38905621 , 20.08553696]) print(chain.inverse(chain.forward(x))) # Tensor(shape=[4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0., 1., 2., 3.]) print(chain.forward_log_det_jacobian(x)) # Tensor(shape=[4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0., 1., 2., 3.]) print(chain.inverse_log_det_jacobian(chain.forward(x))) # Tensor(shape=[4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [ 0., -1., -2., -3.]) csPt|tjstdt|tdd|Dstd||_tt| dS)Nz3Expected type of 'transforms' is Sequence, but got cs|]}t|tVqdSr$r-r.0trrr z*ChainTransform.__init__..z4All elements of transforms should be Transform type.) r-rQrRr;r<all transformsr%r r&)r(rr)rrr&s  zChainTransform.__init__cCtdd|jDS)Ncs|]}|VqdSr$r,rrrrr#z/ChainTransform._is_injective..)rrr'rrrr,"zChainTransform._is_injectivecC|jD]}||}q|Sr$)rr/)r(r0 transformrrrrA%  zChainTransform._forwardcCst|jD]}||}q|Sr$)reversedrrI)r(rHrrrrrF*s zChainTransform._inversecCsXd}|jj}|jD] }||||||jj7}||}||jj|jj7}q |S)N)r>r?r_sum_rightmostrLr/rE)r(r0valuer?rrrrra/s  z(ChainTransform._forward_log_det_jacobiancCrr$)rrVr(rUrrrrrS:rzChainTransform._forward_shapecCrr$)rrYrrrrrX?rzChainTransform._inverse_shapecCs"|dkr|tt| dS|S)zsum value along rightmost n dimr)sumlistrange)r(rnrrrrDs"zChainTransform._sum_rightmostcCs^|jdj}|jdjj}t|jD]}||jj|jj8}t||jj}qt|||jS)Nr)rr>rEr?rmaxr Independent)r(domainr?rrrrr>Hs zChainTransform._domaincCsZ|jdj}|jdjj}|jD]}||jj|jj7}t||jj}qt|||jS)Nrr)rrEr>r?rrr)r(Zcodomainr?rrrrrEds  zChainTransform._codomain)rrrrr&r,rArFrarSrXrrgr>rErhrrr)rr s !   r csVeZdZdZejZfddZeddZ eddZ dd Z d d Z d d Z ZS)r aExponent transformation with mapping :math:`y = \exp(x)`. Examples: .. code-block:: python import paddle exp = paddle.distribution.ExpTransform() print(exp.forward(paddle.to_tensor([1., 2., 3.]))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [2.71828175 , 7.38905621 , 20.08553696]) print(exp.inverse(paddle.to_tensor([1., 2., 3.]))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0. , 0.69314718, 1.09861231]) print(exp.forward_log_det_jacobian(paddle.to_tensor([1., 2., 3.]))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 2., 3.]) print(exp.inverse_log_det_jacobian(paddle.to_tensor([1., 2., 3.]))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [ 0. , -0.69314718, -1.09861231]) cr#r$)r%r r&r'r)rrr&r+zExpTransform.__init__cCrZr$r[r'rrrr>rrzExpTransform._domaincCrZr$rsr'rrrrErrzExpTransform._codomaincCrir$)exprBrrrrArkzExpTransform._forwardcCrir$r{rGrrrrFrkzExpTransform._inversecCrer$rrBrrrrasz&ExpTransform._forward_log_det_jacobian)rrrrrrrr&rgr>rErArFrarhrrr)rr ps   r csheZdZdZfddZddZddZdd Zd d Zd d Z ddZ e ddZ e ddZ ZS)r a[ ``IndependentTransform`` wraps a base transformation, reinterprets some of the rightmost batch axes as event axes. Generally, it is used to expand the event axes. This has no effect on the forward or inverse transformaion, but does sum out the ``reinterpretd_bach_rank`` rightmost dimensions in computing the determinant of Jacobian matrix. To see this, consider the ``ExpTransform`` applied to a Tensor which has sample, batch, and event ``(S,B,E)`` shape semantics. Suppose the Tensor's paritioned-shape is ``(S=[4], B=[2, 2], E=[3])`` , reinterpreted_batch_rank is 1. Then the reinterpreted Tensor's shape is ``(S=[4], B=[2], E=[2, 3])`` . The shape returned by ``forward`` and ``inverse`` is unchanged, ie, ``[4,2,2,3]`` . However the shape returned by ``inverse_log_det_jacobian`` is ``[4,2]``, because the Jacobian determinant is a reduction over the event dimensions. Args: base (Transform): The base transformation. reinterpreted_batch_rank (int): The num of rightmost batch rank that will be reinterpreted as event rank. Examples: .. code-block:: python import paddle x = paddle.to_tensor([[1., 2., 3.], [4., 5., 6.]]) # Exponential transform with event_rank = 1 multi_exp = paddle.distribution.IndependentTransform( paddle.distribution.ExpTransform(), 1) print(multi_exp.forward(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[2.71828175 , 7.38905621 , 20.08553696 ], # [54.59814835 , 148.41316223, 403.42880249]]) print(multi_exp.forward_log_det_jacobian(x)) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [6. , 15.]) csPt|tstdt||dkrtd|||_||_tt| dS)Nz+Expected 'base' is Transform type, but get rzAExpected 'reinterpreted_batch_rank' is grater than zero, but got ) r-rr;r<r@_base_reinterpreted_batch_rankr%r r&)r(baseZreinterpreted_batch_rankr)rrr&s  zIndependentTransform.__init__cCs |jSr$)rr,r'rrrr,rlz"IndependentTransform._is_injectivecC$||jjkr td|j|SNz/Input dimensions is less than event dimensions.)r=r>r?r@rr/rBrrrrA zIndependentTransform._forwardcCrr)r=rEr?r@rrIrGrrrrFrzIndependentTransform._inversecCs |j|tt|j dS)Nr)rrLrrrrrBrrrras z.IndependentTransform._forward_log_det_jacobiancC |j|Sr$)rrVrTrrrrS z#IndependentTransform._forward_shapecCrr$)rrYrTrrrrXrz#IndependentTransform._inverse_shapecCt|jj|jSr$)rrrr>rr'rrrr> zIndependentTransform._domaincCrr$)rrrrErr'rrrrErzIndependentTransform._codomain)rrrrr&r,rArFrarSrXrgr>rErhrrr)rr s + r csreZdZdZejZfddZeddZ eddZ edd Z d d Z d d Z ddZddZddZZS)r aC Power transformation with mapping :math:`y = x^{\text{power}}`. Args: power (Tensor): The power parameter. Examples: .. code-block:: python import paddle x = paddle.to_tensor([1., 2.]) power = paddle.distribution.PowerTransform(paddle.to_tensor(2.)) print(power.forward(x)) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 4.]) print(power.inverse(power.forward(x))) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [1., 2.]) print(power.forward_log_det_jacobian(x)) # Tensor(shape=[2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.69314718, 1.38629436]) cs:t|tjjjstdt|||_tt | dS)Nz&Expected 'power' is a tensor, but got ) r-r7r8r9r:r;r<_powerr%r r&)r(powerr)rrr&s  zPowerTransform.__init__cCrxr$)rr'rrrr$rrzPowerTransform.powercCrZr$r[r'rrrr>(rrzPowerTransform._domaincCrZr$rsr'rrrrE,rrzPowerTransform._codomaincCs ||jSr$powrrBrrrrA0rzPowerTransform._forwardcCs|d|jSNrnrrGrrrrF3rzzPowerTransform._inversecCs|j||jdSr)rrrjr{rBrrrra6sz(PowerTransform._forward_log_det_jacobiancCtt||jjSr$r~r7rrrUrTrrrrS9rzPowerTransform._forward_shapecCrr$rrTrrrrX<rzPowerTransform._inverse_shape)rrrrrrrr&rgrr>rErArFrarSrXrhrrr)rr s    r cs~eZdZdZejZfddZeddZ eddZ edd Z ed d Z d d Z ddZddZddZddZZS)r aReshape the event shape of a tensor. Note that ``in_event_shape`` and ``out_event_shape`` must have the same number of elements. Args: in_event_shape(Sequence[int]): The input event shape. out_event_shape(Sequence[int]): The output event shape. Examples: .. code-block:: python import paddle x = paddle.ones((1,2,3)) reshape_transform = paddle.distribution.ReshapeTransform((2, 3), (3, 2)) print(reshape_transform.forward_shape((1,2,3))) # (5, 2, 6) print(reshape_transform.forward(x)) # Tensor(shape=[1, 3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[[1., 1.], # [1., 1.], # [1., 1.]]]) print(reshape_transform.inverse(reshape_transform.forward(x))) # Tensor(shape=[1, 2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[[1., 1., 1.], # [1., 1., 1.]]]) print(reshape_transform.forward_log_det_jacobian(x)) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.]) cst|tjr t|tjstd|d|ttj|ttj|kr8tdttj|dttj|t ||_ t ||_ t t |dS)NzcExpected type of 'in_event_shape' and 'out_event_shape' is Squence[int], but got 'in_event_shape': z, 'out_event_shape': zCThe numel of 'in_event_shape' should be 'out_event_shape', but got z!=)r-rQrRr; functoolsreduceoperatormulr@r~_in_event_shape_out_event_shaper%r r&)r(in_event_shapeout_event_shaper)rrr&cs.    zReshapeTransform.__init__cCrxr$)rr'rrrrxrrzReshapeTransform.in_event_shapecCrxr$)rr'rrrr|rrz ReshapeTransform.out_event_shapecCttjt|jSr$)rrr\lenrr'rrrr>zReshapeTransform._domaincCrr$)rrr\rrr'rrrrErzReshapeTransform._codomaincC,|t|jd|t|j|jSr$)reshaper~rUr=rrrrBrrrrA zReshapeTransform._forwardcCrr$)rr~rUr=rrrrGrrrrFrzReshapeTransform._inversecCt|t|jkrtdt|jdt||t|j d|jkr8td|jd|t|j dt|dt|j |jS)Nz,Expected length of 'shape' is not less than , but got Event shape mismatch, expected: )rrr@r~rrTrrrrS zReshapeTransform._forward_shapecCr)Nz)Expected 'shape' length is not less than rr)rrr@r~rrTrrrrXrzReshapeTransform._inverse_shapecCs2|jd|t|jpdg}tj||jdSrm)rUr=rrr7rpro)r(r0rUrrrras"z*ReshapeTransform._forward_log_det_jacobian)rrrrrrrr&rgrrr>rErArFrSrXrarhrrr)rr @s"       r c@s@eZdZdZeddZeddZddZdd Zd d Z d S) ra Sigmoid transformation with mapping :math:`y = \frac{1}{1 + \exp(-x)}` and :math:`x = \text{logit}(y)`. Examples: .. code-block:: python import paddle x = paddle.ones((2,3)) t = paddle.distribution.SigmoidTransform() print(t.forward(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[0.73105860, 0.73105860, 0.73105860], # [0.73105860, 0.73105860, 0.73105860]]) print(t.inverse(t.forward(x))) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[1.00000012, 1.00000012, 1.00000012], # [1.00000012, 1.00000012, 1.00000012]]) print(t.forward_log_det_jacobian(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[-1.62652326, -1.62652326, -1.62652326], # [-1.62652326, -1.62652326, -1.62652326]]) cCrZr$r[r'rrrr>rrzSigmoidTransform._domaincCtddtddS)NFrr?rr:rRanger'rrrrEzSigmoidTransform._codomaincCs t|Sr$)FsigmoidrBrrrrArlzSigmoidTransform._forwardcCs|| Sr$)r{log1prGrrrrFr+zSigmoidTransform._inversecCst|  t|Sr$)rsoftplusrBrrrrasz*SigmoidTransform._forward_log_det_jacobianN) rrrrrgr>rErArFrarrrrrs   rc@sNeZdZdZejZeddZeddZ ddZ dd Z d d Z d d Z dS)raSoftmax transformation with mapping :math:`y=\exp(x)` then normalizing. It's generally used to convert unconstrained space to simplex. This mapping is not injective, so ``forward_log_det_jacobian`` and ``inverse_log_det_jacobian`` are not implemented. Examples: .. code-block:: python import paddle x = paddle.ones((2,3)) t = paddle.distribution.SoftmaxTransform() print(t.forward(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[0.33333334, 0.33333334, 0.33333334], # [0.33333334, 0.33333334, 0.33333334]]) print(t.inverse(t.forward(x))) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[-1.09861231, -1.09861231, -1.09861231], # [-1.09861231, -1.09861231, -1.09861231]]) cCttjdSrrrr\r'rrrr>zSoftmaxTransform._domaincCtddtjSNFrnrr:rZsimplexr'rrrrEzSoftmaxTransform._codomaincCs,||jdddd}||jdddS)NrT)Zkeepdimr)rrrrBrrrrAszSoftmaxTransform._forwardcCrir$rrGrrrrFrkzSoftmaxTransform._inversecC"t|dkrtdt||SNrnz3Expected length of shape is grater than 1, but got rr@rTrrrrS  zSoftmaxTransform._forward_shapecCrrrrTrrrrXrzSoftmaxTransform._inverse_shapeN)rrrrrr!rrgr>rErArFrSrXrrrrrs   rc@sreZdZdZdddZddZeddZed d Zd d Z d dZ ddZ ddZ eddZ eddZdS)ra``StackTransform`` applies a sequence of transformations along the specific axis. Args: transforms (Sequence[Transform]): The sequence of transformations. axis (int, optional): The axis along which will be transformed. default value is 0. Examples: .. code-block:: python import paddle x = paddle.stack( (paddle.to_tensor([1., 2., 3.]), paddle.to_tensor([1, 2., 3.])), 1) t = paddle.distribution.StackTransform( (paddle.distribution.ExpTransform(), paddle.distribution.PowerTransform(paddle.to_tensor(2.))), 1 ) print(t.forward(x)) # Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[2.71828175 , 1. ], # [7.38905621 , 4. ], # [20.08553696, 9. ]]) print(t.inverse(t.forward(x))) # Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[1., 1.], # [2., 2.], # [3., 3.]]) print(t.forward_log_det_jacobian(x)) # Tensor(shape=[3, 2], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[1. , 0.69314718], # [2. , 1.38629436], # [3. , 1.79175949]]) rcCsl|rt|tjstdt|dtdd|Dstdt|ts.tdt|d||_||_dS)Nz6Expected 'transforms' is Sequence[Transform], but got r4csrr$rrrrrrErz*StackTransform.__init__..z5Expected all element in transforms is Transform Type.zExpected 'axis' is int, but got) r-rQrRr;r<rint _transforms_axis)r(raxisrrrr&@s  zStackTransform.__init__cCr)Ncsrr$rrrrrrPrz/StackTransform._is_injective..)rrr'rrrr,OrzStackTransform._is_injectivecCrxr$)rr'rrrrRrrzStackTransform.transformscCrxr$)rr'rrrrVrrzStackTransform.axiscC4||tddtt||j|jD|jS)NcSg|] \}}||qSr)r/rvrrrr ]z+StackTransform._forward.. _check_sizer7stackzipZunstackrrrBrrrrAZ zStackTransform._forwardcCr)NcSrr)rIrrrrrgrz+StackTransform._inverse..rrGrrrrFdrzStackTransform._inversecCr)NcSrr)rLrrrrrqrz.rrBrrrranrz(StackTransform._forward_log_det_jacobiancCsj| |jkr|ksntd|d|jd|j|jt|jkr3td|jddS)NzInput dimensions z, should be grater than stack transform axis r4zInput size along z- should be equal to the length of transforms.)r=rr@rUrr)r(rrrrrxs"  zStackTransform._check_sizecCtdd|jD|jS)NcSg|]}|jqSr)r>rrrrrz*StackTransform._domain..rStackrrr'rrrr>szStackTransform._domaincCr)NcSrr)rErrrrrrz,StackTransform._codomain..rr'rrrrEszStackTransform._codomainN)r)rrrrr&r,rgrrrArFrarr>rErrrrrs  (      rc@sVeZdZdZejZddZddZddZ dd Z d d Z e d d Z e ddZdS)raVConvert an unconstrained vector to the simplex with one additional dimension by the stick-breaking construction. Examples: .. code-block:: python import paddle x = paddle.to_tensor([1.,2.,3.]) t = paddle.distribution.StickBreakingTransform() print(t.forward(x)) # Tensor(shape=[4], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.47536686, 0.41287899, 0.10645414, 0.00530004]) print(t.inverse(t.forward(x))) # Tensor(shape=[3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [0.99999988, 2. , 2.99999881]) print(t.forward_log_det_jacobian(x)) # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [-9.10835075]) cCs|jddt|jdgd}t||}d|d}tj|dgdt |jdddgddtj|dgdt |jdddgddS)Nrrnr)r) rUr7onescumsumrrr{Zcumprodpadr)r(r0offsetzZ z_cumprodrrrrAs &."zStickBreakingTransform._forwardcCs\|dddf}|jdt|jdgd}d|d}|||}|S)N.rrn)rUr7rrr{)r(rHZy_croprZsfr0rrrrFs "zStickBreakingTransform._inversecCsf||}|jddt|jdgd}||}| t||dddfdS)Nrrn.) r/rUr7rrr{rZ log_sigmoidr)r(r0rHrrrrras & *z0StickBreakingTransform._forward_log_det_jacobiancCs,|s td||dd|ddfSNz'Expected 'shape' is not empty, but got rrnr@rTrrrrSz%StickBreakingTransform._forward_shapecCs,|s td||dd|ddfSrrrTrrrrXrz%StickBreakingTransform._inverse_shapecCrrrr'rrrr>rzStickBreakingTransform._domaincCrrrr'rrrrErz StickBreakingTransform._codomainN)rrrrrrrrArFrarSrXrgr>rErrrrrs rc@sFeZdZdZejZeddZeddZ ddZ dd Z d d Z d S) ra&Tanh transformation with mapping :math:`y = \tanh(x)`. Examples: .. code-block:: python import paddle tanh = paddle.distribution.TanhTransform() x = paddle.to_tensor([[1., 2., 3.], [4., 5., 6.]]) print(tanh.forward(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[0.76159418, 0.96402758, 0.99505478], # [0.99932933, 0.99990922, 0.99998772]]) print(tanh.inverse(tanh.forward(x))) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[1.00000012, 2. , 3.00000286], # [4.00002146, 5.00009823, 6.00039864]]) print(tanh.forward_log_det_jacobian(x)) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[-0.86756170 , -2.65000558 , -4.61865711 ], # [-6.61437654 , -8.61379623 , -10.61371803]]) print(tanh.inverse_log_det_jacobian(tanh.forward(x))) # Tensor(shape=[2, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True, # [[0.86756176 , 2.65000558 , 4.61866283 ], # [6.61441946 , 8.61399269 , 10.61451530]]) cCrZr$r[r'rrrr>rrzTanhTransform._domaincCr)NFrgrrr'rrrrErzTanhTransform._codomaincCrir$)tanhrBrrrrArkzTanhTransform._forwardcCrir$)atanhrGrrrrFrkzTanhTransform._inversecCs dtd|td|S)aaWe implicitly rely on _forward_log_det_jacobian rather than explicitly implement ``_inverse_log_det_jacobian`` since directly using ``-tf.math.log1p(-tf.square(y))`` has lower numerical precision. See details: https://github.com/tensorflow/probability/blob/master/tensorflow_probability/python/bijectors/tanh.py#L69-L80 g@g)mathr{rrrBrrrras z'TanhTransform._forward_log_det_jacobianN) rrrrrrrrgr>rErArFrarrrrrs   r)!enumrrnumbersrrQr7Zpaddle.nn.functionalnnZ functionalrZpaddle.distributionrrrr__all__Enumrobjectrrrr r r r r rrrrrrrrrs4HR}1_@t+8xB