B `AU@sdZddlmZddlmZddlmZddlZddlmZ ddl m Z ddl mZdd l mZdd lmZdd lmZdd lmZdd lmZddlmZddlmZddlmZdgZddZddZdddZGdddejZdS)a4Lewandowski-Kurowicka-Joe distribution on correlation matrices. The sampler follows the 'onion' method from [1] Daniel Lewandowski, Dorota Kurowicka, and Harry Joe, 'Generating random correlation matrices based on vines and extended onion method,' Journal of Multivariate Analysis 100 (2009), pp 1989-2001. )absolute_import)division)print_functionN)v2)_numpy)beta) distribution) assert_util) dtype_util) prefer_static)reparameterization)samplers) tensor_util)tensorshape_utilLKJcCsBtjtj||ggdd||d}|tj|ddddtjf}|S)zEReturns a batch of points chosen uniformly from the unit hypersphere.r)axis)shapeseeddtype)ordr.)r normaltfconcatnormnewaxis) dimensionrrrrawZ unit_normre/home/dcms/DCMS/lib/python3.7/site-packages/tensorflow_probability/python/distributions/_numpy/lkj.py_uniform_unit_norm1sr!cCs:tj|gtjt|g|jdgdd}t|tj|S)zAReplicate the input tensor n times along a new (major) dimension.)rr)r)rronesZrankrZtiler)nZtensorZ multiplesrrr _replicate;s r$Fc Cs|dkrtdddtd|d}ttj||dd}tdpD|vt|}t |j sxt d t |j t||}t|}|dkrtj|||ggdd} tj| |j d S||d d } tj| | d } d | j|d d } tjt| dtjft| dtjfgdd} tj| dtjftd| ddtjfgdd}tj| dtjddf|dtjddfgdd}xtd|D]}| d} tj|d | d j|d }t|dtjf}t|||j |d }||}tj|td |dtjfgdd}tj|t|ddtjfgdd}tj||dtjddfgdd}qW|rztdt||r|Stj||dd}tj |tjt|dd|j d }|SQRXdS)a!Returns a Tensor of samples from an LKJ distribution. Args: num_samples: Python `int`. The number of samples to draw. dimension: Python `int`. The dimension of correlation matrices. concentration: `Tensor` representing the concentration of the LKJ distribution. cholesky_space: Python `bool`. Whether to take samples from LKJ or Chol(LKJ). seed: Python integer seed for RNG name: Python `str` name prefixed to Ops created by this function. Returns: samples: A Tensor of correlation matrices (or Cholesky factors of correlation matrices if `cholesky_space = True`) with shape `[n] + B + [D, D]`, where `B` is the shape of the `concentration` parameter, and `D` is the `dimension`. Raises: ValueError: If `dimension` is negative. rz6Cannot sample negative-dimension correlation matrices.r sample_lkj)r#ZsaltzThe LKJ distribution on correlation matrices. This is a one-parameter family of distributions on correlation matrices. The probability density is proportional to the determinant raised to the power of the parameter: `pdf(X; eta) = Z(eta) * det(X) ** (eta - 1)`, where `Z(eta)` is a normalization constant. The uniform distribution on correlation matrices is the special case `eta = 1`. The distribution is named after Lewandowski, Kurowicka, and Joe, who gave a sampler for the distribution in [(Lewandowski, Kurowicka, Joe, 2009)][1]. Note: For better numerical stability, it is recommended that you use `CholeskyLKJ` instead. #### Examples ```python # Initialize a single 3x3 LKJ with concentration parameter 1.5 dist = tfp.distributions.LKJ(dimension=3, concentration=1.5) # Evaluate this at a batch of two observations, each in R^{3x3}. x = ... # Shape is [2, 3, 3]. dist.prob(x) # Shape is [2]. # Draw 6 LKJ-distributed 3x3 correlation matrices ans = dist.sample(sample_shape=[2, 3], seed=42) # shape of ans is [2, 3, 3, 3] ``` FTc s|dkrtdtt}||_t|Pt|gtj}t j |d|d|_ ||_ t t|j|j j||tj||dWdQRXdS)ayConstruct LKJ distributions. Args: dimension: Python `int`. The dimension of the correlation matrices to sample. concentration: `float` or `double` `Tensor`. The positive concentration parameter of the LKJ distributions. The pdf of a sample matrix `X` is proportional to `det(X) ** (concentration - 1)`. input_output_cholesky: Python `bool`. If `True`, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is `True`, input to `log_prob` is presumed of Cholesky form and output from `sample` is of Cholesky form. Setting this argument to `True` is purely a computational optimization and does not change the underlying distribution. Additionally, validation checks which are only defined on the multiplied-out form are omitted, even if `validate_args` is `True`. Default value: `False` (i.e., input/output does not have Cholesky semantics). WARNING: Do not set this boolean to true, when using `tfp.mcmc`. The density is not the density of Cholesky factors of correlation matrices drawn via LKJ. 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. 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. name: Python `str` name prefixed to Ops created by this class. Raises: ValueError: If `dimension` is negative. rz5There are no negative-dimension correlation matrices.r;)r/r)r validate_argsallow_nan_statsZreparameterization_type parametersr/N)r(dictlocals_input_output_choleskyrr+r Z common_dtypefloat32rZconvert_nonref_to_tensor_concentration _dimensionsuperr__init__rr ZNOT_REPARAMETERIZED) selfrr;input_output_choleskyr?r@r/rAr) __class__rr rIs"(   z LKJ.__init__cCs tddS)Nr)r;)rB)clsrrr _params_event_ndims+szLKJ._params_event_ndimscCs|jS)z+Dimension of returned correlation matrices.)rG)rJrrr r/sz LKJ.dimensioncCs|jS)zConcentration parameter.)rF)rJrrr r;4szLKJ.concentrationcCs|jS)zEBoolean indicating if `Tensor` input/outputs are Cholesky factorized.)rD)rJrrr rK9szLKJ.input_output_choleskycCs t|jS)N)r rr;)rJrrr _batch_shape_tensor>szLKJ._batch_shape_tensorcCs|jjS)N)r;r)rJrrr _batch_shapeAszLKJ._batch_shapecCstj|j|jgtjdS)N)r)rZconstantrint32)rJrrr _event_shape_tensorDszLKJ._event_shape_tensorcCst|j|jgS)N)rZ TensorShaper)rJrrr _event_shapeGszLKJ._event_shapeNcCst||j|j|j||dS)aReturns a Tensor of samples from an LKJ distribution. Args: num_samples: Python `int`. The number of samples to draw. seed: Python integer seed for RNG name: Python `str` name prefixed to Ops created by this function. Returns: samples: A Tensor of correlation matrices with shape `[n, B, D, D]`, where `B` is the shape of the `concentration` parameter, and `D` is the `dimension`. Raises: ValueError: If `dimension` is negative. )r:rr;r<rr/)r&rr;rK)rJr:rr/rrr _sample_nJsz LKJ._sample_ncCs(t|j}|j|d}||||S)N)r;)rr,r;_log_normalization_log_unnorm_prob)rJxr;Z normalizerrrr _log_probbs  z LKJ._log_probc Cstt|p d\tj|dd}|jrJdtjtjtj|dgd}ntj |\}}|d|}|SQRXdS) aReturns the unnormalized log density of an LKJ distribution. Args: x: `float` or `double` `Tensor` of correlation matrices. The shape of `x` must be `B + [D, D]`, where `B` broadcasts with the shape of `concentration`. concentration: `float` or `double` `Tensor`. The positive concentration parameter of the LKJ distributions. name: Python `str` name prefixed to Ops created by this function. Returns: log_p: A Tensor of the unnormalized log density of each matrix element of `x`, with respect to an LKJ distribution with parameter the corresponding element of `concentration`. Zlog_unnorm_prob_lkjrW)r/g@r)rg?N) rr+r,rKZ reduce_summathlogr9 diag_partZslogdet)rJrWr;r/Zlogdet_answerrrr rVjs  zLKJ._log_unnorm_problog_normalizationc Cst|p dt|dkr"|jn|}tttj}t|}xNt d|j D]>}|||d}||j d|d}|t |d|}qPW|SQRXdS)aReturns the log normalization of an LKJ distribution. Args: concentration: `float` or `double` `Tensor`. The positive concentration parameter of the LKJ distributions. name: Python `str` name prefixed to Ops created by this function. Returns: log_z: A Tensor of the same shape and dtype as `concentration`, containing the corresponding log normalizers. 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