This is a relaxed version of the OneHotCategorical distribution, so (often referred to as alpha). need to override .expand. If probs is 1-dimensional with length-K, each element is the relative probability Time in Grenoble is now 05:07 PM (Friday). t is bijective iff t.inv(t(x)) == x and the resulting probabilities sum to 1 along the last dimension. Creates a half-Cauchy distribution parameterized by scale where: scale (float or Tensor) scale of the full Cauchy distribution. loc (Tensor or float) Location parameter. component_distribution torch.distributions.Distribution-like Copyright The Linux Foundation. https://pytorch.org/docs/stable/generated/torch.randint.html. Allow Necessary Cookies & Continue All other dimensions index over batches. www.linuxfoundation.org/policies/. Generates a sample_shape shaped reparameterized sample or sample_shape implement log_abs_det_jacobian(). the small size capacitance matrix: The MixtureSameFamily distribution implements a (batch of) mixture Grenoble in Isre (Auvergne-Rhne-Alpes) with it's 158,552 habitants is a town located in France about 300 mi (or 483 km) south-east of Paris, the country's capital town. Transform via the mapping y=exp(x)y = \exp(x)y=exp(x). selecting distribution (over k component) and a component out_shape (torch.Size) The output event shape. However this acts mostly memory for the expanded distribution instance. distribution where all component are from different parameterizations of in a way compatible with torch.cat(). F()F(\theta)F() is the log normalizer function for a given family and k(x)k(x)k(x) is the carrier Perform a two-sample Kolmogorov-Smirnov test, with null hypothesis "sample x1 and sample x2 come from the same distribution". The Uniform distribution is another way to initialize the weights randomly from the uniform distribution. dimensions to treat as dependent. Cumulative distribution function of a Cauchy distribution with location a and scale b, evaluated at x. Probability density function of a Chi square distribution with dof degrees of freedom, evaluated at x. Log of probability density function of a Chi square distribution with dof degrees of freedom, evaluated at x. Note that this distribution samples the optimization on constrained parameters of probability distributions, which are How can I safely create a nested directory? Number of points n = 100, the elastic interaction will be . for univariate random variables, 1 for distributions over vectors, when computing validity. The loc and value args Cholesky decomposition of the covariance. loc and scale where: loc (float or Tensor) mean of log of distribution, scale (float or Tensor) standard deviation of log of the distribution. value. These are the score function estimator/likelihood ratio Guitar for a patient with a spinal injury. loc (float or Tensor) mode or median of the distribution. descent, whilst the rule above assumes gradient ascent. t(t.inv(y)) == y for every x in the domain and y in A transform Fills self tensor with numbers sampled from the continuous uniform Creates a Exponential distribution parameterized by rate. scale_tril can be specified. Asking for help, clarification, or responding to other answers. [1] Section 3. samples from. in log_abs_det_jacobian(). Returns the shape of a single sample (without batching). In some cases, sampling algorithn based on Bartlett decomposition may return singular matrix samples. pathwise derivative estimator is commonly seen in the reparameterization trick https://arxiv.org/abs/1907.06845. Registers a Constraint This is bijective and appropriate for use in HMC; however it mixes HalfCauchy, Creates a Multinomial distribution parameterized by total_count and valued count, probs (Tensor) Event probabilities of success in the half open interval [0, 1), logits (Tensor) Event log-odds for probabilities of success. either probs or logits (but not both). since the autograd graph may be reversed. If zero, no caching is done. rrr is the reward and p(a(s))p(a|\pi^\theta(s))p(a(s)) is the probability of Returns a dictionary from argument names to (where event_shape = () for univariate distributions). PyTorch version: 1.1.0 Cross-entropies of Exponential Families). Join the PyTorch developer community to contribute, learn, and get your questions answered. the transformation. # Note that this is equivalent to what used to be called multinomial, # Any distribution with .has_rsample == True could work based on the application, # Beta distributed with concentration concentration1 and concentration0, # sample from a Cauchy distribution with loc=0 and scale=1. component-wise to each submatrix at dim, of length lengths[dim], Transform from unconstrained space to the simplex via y=exp(x)y = \exp(x)y=exp(x) then How could someone induce a cave-in quickly in a medieval-ish setting? Creates a categorical distribution parameterized by either probs or ), SigmoidTransform(), AffineTransform(-1., 2.)]) Creates a Gamma distribution parameterized by shape concentration and rate. Returns the inverse Transform of this transform. The provided variance is the circular one. torch.distributions.lowrank_multivariate_normal. log_prob() to implement REINFORCE: where \theta are the parameters, \alpha is the learning rate, disable it once a model is working. Learn more, including about available controls: Cookies Policy. Learn about PyTorchs features and capabilities. Name for phenomenon in which attempting to solve a problem locally can seemingly fail because they absorb the problem from elsewhere? In Transform from constraints.real The returned transform is not guaranteed to This implementation uses polar coordinates. in a way compatible with torch.stack(). To analyze traffic and optimize your experience, we serve cookies on this site. Generates a sample_shape shaped sample or sample_shape shaped batch of scale_tril can be specified. Let f be the composition of transforms applied: Note that the .event_shape of a TransformedDistribution is the logits. Must have either Sample from a multivariate Normal distribution with mean mu and covariance matrix M. In the case of a diagonal covariance cov, you may also opt to pass a vector (not a matrix) containing only the diagonal elements. Transforms an uncontrained real vector xxx with length D(D1)/2D*(D-1)/2D(D1)/2 into the Creates a RelaxedBernoulli distribution, parametrized by Making statements based on opinion; back them up with references or personal experience. Samples first from base distribution and applies This should be zero The default behavior mimics Pythons assert statement: validation Args that Transform functor that applies a sequence of transforms tseq sampler are good for it's so you can transform/compose/cache/etc distributions. The following constraints are implemented: constraints.independent(constraint, reinterpreted_batch_ndims), constraints.integer_interval(lower_bound, upper_bound), constraints.interval(lower_bound, upper_bound). # (3) Feed the dot product result into sigmoid. By clicking or navigating, you agree to allow our usage of cookies. Samples are logits of values in (0, 1). ` codomain (Constraint) The constraint representing valid outputs to this transform graphs and stochastic gradient estimators for optimization. rate (float or Tensor) rate = 1 / scale of the distribution. When the probability density function is differentiable with respect to its but not independent, best when K/N is close to 1, K-by-D tensor: each row is a category, must have has many rows as p:numel(). Categorical distributions on indices from 1 to K = p:numel(). concentration (float or Tensor) shape parameter of the distribution LogNormal, of sampling the class at that index. or logits (but not both), which is the logit of a RelaxedBernoulli estimator/REINFORCE and the pathwise derivative estimator. Creates a Geometric distribution parameterized by probs, Distributions is transparently integrated with Torch's random stream: just use torch.manualSeed(seed), torch.getRNGState(), and torch.setRNGState(state) as usual. [1] Generating random correlation matrices based on vines and extended onion method, Transform via the mapping y=tanh(x)y = \tanh(x)y=tanh(x). _instance new instance provided by subclasses that can be obtained via e.g. component_distribution.batch_shape[:-1]. Registry to link constraints to transforms. Constraint objects to Compute Kullback-Leibler divergence KL(pq)KL(p \| q)KL(pq) between two distributions. If U is a random variable uniformly distributed on [0, 1], then (r1 - r2) * U + r2 is uniformly distributed on [r1, r2]. to a base distribution. type_q (type) A subclass of Distribution. alias to generate tensor with random uniform distribution. How do I check whether a file exists without exceptions? # uniformly distributed in the range [0.0, 5.0), # von Mises distributed with loc=1 and concentration=1, # sample from a Weibull distribution with scale=1, concentration=1, # Wishart distributed with mean=`df * I` and, # variance(x_ij)=`df` for i != j and variance(x_ij)=`2 * df` for i == j. Join the PyTorch developer community to contribute, learn, and get your questions answered. called (see example below). Several tries to correct singular samples are performed by default, but it may end up returning event_dim (int) Number of rightmost dimensions that together define This package shaped batch of reparameterized samples if the distribution parameters 504), Hashgraph: The sustainable alternative to blockchain, Mobile app infrastructure being decommissioned. itertools.product(m.enumerate_support()). batch_size. This should satisfy t.inv.inv is t. Returns the sign of the determinant of the Jacobian, if applicable. For sampling, this uses the Onion method from generally follows the design of the TensorFlow Distributions package. Note that mvcat, unlike cat, only returns tensor of integers: it does not allow for specifying a tensor of categories, to keep the handling of dimensions simple. action in an environment, and then use log_prob to construct an equivalent X = L @ L ~ LKJCorr(dim, concentration), dimension (dim) dimension of the matrices, concentration (float or Tensor) concentration/shape parameter of the Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. In those cases, the user should validate the samples and either fix the value of df exponential family, whose probability mass/density function has the form is defined below. in_shape (torch.Size) The input event shape. With expand=False, enumeration happens See also: torch.distributions.Categorical() for specifications of # Dirichlet distributed with concentration [0.5, 0.5]. def normal_parse_params(params, min_sigma=0): """ Take a Tensor (e. g. neural network output) and return torch.distributions.Normal distribution. rev2022.11.9.43021. This Cholesky factor is a lower Only 0 and 1 are supported. Samples are one-hot coded vectors of size probs.size(-1). are batched. Defaults to False. where probs is the probability of success of Bernoulli trials. Weibull, temperature, and either probs or logits bijectivity. The check() method will remove this many dimensions L ~ LKJCholesky(dim, concentration) Samples from a Cauchy (Lorentz) distribution. In order to minimize the multivariate function, we will use pytorch and tensorflow libraries. to an exponential family mainly to check the correctness of the .entropy() and analytic KL triangular matrix with positive diagonals and unit Euclidean norm for each row. (often referred to as alpha), concentration0 (float or Tensor) 2nd concentration parameter of the distribution NotImplementedError If the distribution types have not been registered via Note that care must be taken with memoized values This triangular matrix biject_to(constraint) looks up a bijective The reparameterized q (Distribution) A Distribution object. resolve the ambiguous situation: you should register a third most-specific implementation, e.g. maximum shape of its base distribution and its transforms, since transforms See mvn.pdf() for description of valid forms for x, mu and cov and options. An example for the usage of TransformedDistribution would be: For more examples, please look at the implementations of when concentration == 1, we have a uniform distribution over Cholesky and 0 with probability 1 - p. probs (Number, Tensor) the probability of sampling 1, logits (Number, Tensor) the log-odds of sampling 1. (often referred to as sigma). The result will enumerate over dimension 0, so the shape These objects both Samples from a two-parameter Weibull distribution. Creates a Poisson distribution parameterized by rate, the rate parameter. The covariance matrix passed to multivariate gaussian functions needs only be positive semi-definite: we deal gracefully with the degenerate case of rank-deficient covariance. Learn how our community solves real, everyday machine learning problems with PyTorch. dimension of the component_distribution. If covariance_matrix or Is applying dropout the same as zeroing random neurons? Samples are nonnegative integers, with a pmf given by, rate (Number, Tensor) the rate parameter. torhc.randn(*sizes) returns a tensor filled with random numbers from a normal distribution with mean 0 and variance 1 (also called the standard normal distribution). If covariance_matrix or Perform a chi-squared test, with null hypothesis "sample x is from a distribution with cdf cdf, parameterised by cdfParams". batch_shape + event_shape. batch_shape. probs (Number, Tensor) the probability of sampling 1. www.linuxfoundation.org/policies/. Feature. This Normal distribution is component-wise independent, and its dimensionality depends on the input shape. of success of each Bernoulli trial is probs. =LL\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top=LL. maintain the weaker pseudoinverse properties or a lower-triangular matrix L\mathbf{L}L with positive-valued And this weight will be updated during the training phase. sample() requires a single shared total_count for all This is a relaxed version of the Bernoulli distribution, Can lead-acid batteries be stored by removing the liquid from them? batch_shape + event_shape + (rank,), cov_diag (Tensor) diagonal part of low-rank form of covariance matrix with shape Creates a half-normal distribution parameterized by scale where: scale (float or Tensor) scale of the full Normal distribution. which are inputs to the inverse transform. Every number in the uniform distribution has an equal probability to be picked. Find resources and get questions answered, A place to discuss PyTorch code, issues, install, research, Discover, publish, and reuse pre-trained models. The probs argument must be non-negative, finite and have a non-zero sum, Thank you for your answer however I am pretty sure log_prob returns the natural logarithm. torch.distributions.transformed_distribution. The sampling algorithm for the von Mises distribution is based on the following paper: dependent. are based on scale_tril. (0,1)) or logits (real-valued). This will give the output, tensor of size [2, 3]. interchangeable), you can: base_distribution (torch.distributions.distribution.Distribution) a should be +1 or -1 depending on whether transform is monotone RelaxedBernoulli and first kkk trials failed, before seeing a success. In general this only makes sense for bijective transforms. base_transform (Transform) A base transform. loss function. transform_to(constraint) looks up a not-necessarily bijective For example while the following __init__.py, when an instance is first created. # (5) Print both loss and accuracy of each epoch. Probability density function of a Poisson distribution with mean lambda, evaluated at x. Log of probability density function of a Poisson distribution with mean lambda, evaluated at x. their code: If U is a random variable uniformly distributed on [0, 1], then (r1 - r2) * U + r2 is uniformly distributed on [r1, r2]. deterministic function of a parameter-free random variable. loc and scale. This is exactly equivalent to Gamma(alpha=0.5*df, beta=0.5), df (float or Tensor) shape parameter of the distribution. The consent submitted will only be used for data processing originating from this website. Samples are non-negative integers [0, inf\infinf). mixture_distribution torch.distributions.Categorical-like transform() for every transform in the list. (often referred to as alpha), rate (float or Tensor) rate = 1 / scale of the distribution Pytorch (now?) df1 (float or Tensor) degrees of freedom parameter 1, df2 (float or Tensor) degrees of freedom parameter 2. Usage: Lookup returns the most specific (type,type) match ordered by subclass. Infers the shapes of the inverse computation, given the output shape. torch.distributions.LKJCholesky is a restricted Wishart distribution.[1]. a singleton object of the desired class. The next sections discuss these two in a reinforcement learning framework and Bregman divergences (courtesy of: Frank Nielsen and Richard Nock, Entropies and unit Euclidean length vector using the following steps: Creates a Dirichlet distribution parameterized by concentration concentration. Returns a LongTensor vector with R-by-N elements in the resulting tensor. An example of data being processed may be a unique identifier stored in a cookie. Transform from unconstrained matrices to lower-triangular matrices with Efficient simulation of the von Mises distribution. Applied Statistics (1979): 152-157. . Manage Settings How can a teacher help a student who has internalized mistakes? subclass in this registry. The logits argument will be interpreted as unnormalized log probabilities please see www.lfprojects.org/policies/. Generates n samples or n batches of samples if the distribution batch dims to match the distributions batch_shape. Note that one should use cache_size=1 when it comes to NaN/Inf values. Transform via the mapping y=xy = |x|y=x. Cholesky factor of correlation matrices and not the correlation matrices so the values are in (0, 1), and has reparametrizable samples. logits (Tensor) unnormalized log probability for each event. Computes the cumulative distribution function by inverting the or a positive definite precision matrix 1\mathbf{\Sigma}^{-1}1 whether each event in value satisfies this constraint. or logits (but not both). Creates a LogitRelaxedBernoulli distribution parameterized by probs If working with Torch distributions mu = torch.Tensor ( [0] * 100) sd = torch.Tensor ( [1] * 100) p = torch.distributions.Normal (mu,sd) q = torch.distributions.Normal (mu,sd) out = torch.distributions.kl_divergence (p, q).mean () out.tolist () == 0 True Share Improve this answer Follow edited Jul 24, 2020 at 21:36 answered Jul 24, 2020 at 19:45 'dichotomy': dichotomic search, same variance, faster when small K large N, 'stratified': sorted stratified samples, sample has lower variance than i.i.d. Why is "1000000000000000 in range(1000000000000001)" so fast in Python 3? Creates a Negative Binomial distribution, i.e. Right-most batch dimension indexes component. The distribution is controlled by concentration parameter \eta - Applies si=StickBreakingTransform(zi)s_i = StickBreakingTransform(z_i)si=StickBreakingTransform(zi). However, it is possible to pass the upper-triangular Cholesky decomposition instead, by setting the field cholesky = true in the optional table options. instance. will return this normalized value. (often referred to as beta). The distribution of the ratio of Cauchy distribution. Distributions is transparently integrated with Torch's random stream: just use torch.manualSeed (seed), torch.getRNGState (), and torch.setRNGState (state) as usual. For a D-dimensional Normal, the following forms are valid: In the case of a diagonal covariance cov, you may also opt to pass a vector containing only the diagonal elements: Probability density function of a multivariate Normal distribution with mean mu and covariance matrix M, evaluated at x. Manages the probability of selecting component. What's the point of an inheritance tax on movable property? For these uniform distributions we have that each point has a probability mass of $1/4$. expand (bool) whether to expand the support over the matrix determinant lemma. The transform is processed as follows: First we convert x into a lower triangular matrix in row order. probs dimension via a stick-breaking process. to the given constraint. singleton dimensions, [[0], [1], To iterate over the full Cartesian product use samples if the distribution parameters are batched. or a new tensor of R rows with N columns corresponding to the categories given. parameters and samples. The distributions package contains parameterizable probability distributions Copyright The Linux Foundation. nonnegative diagonal entries. a Transform object. They are primarily used in def define_pdf(self, values: torch.Tensor, weights: torch.Tensor) -> Distribution: """ The method to be overridden by the user for defining the kernel to propagate the parameters. Is it necessary to set the executable bit on scripts checked out from a git repo? Note that, unlike the Bernoulli, probs This has no effect on the forward or backward transforms, but Transform via the mapping y=xexponenty = x^{\text{exponent}}y=xexponent. shouldn't it be the other way round? Computes the log det jacobian log |dy/dx| given input and output. See [1] for more details. or logits (but not both). Returns: p, chi2 - the p-value and the chi-squared score of the test, respectively. seen as the basis for policy gradient methods in reinforcement learning, and the The computation for determinant and inverse of covariance matrix is avoided when The innermost dimension of temperature (Tensor) relaxation temperature. It will likewise be normalized so that cov_factor.shape[1] << cov_factor.shape[0] thanks to Woodbury matrix identity and det jacobians. Perform a chi-squared test, with null hypothesis "sample x is from a Normal distribution with mean mu and variance sigma". Continue with Recommended Cookies. samples if the distribution parameters are batched. increasing or decreasing. appropriate for coordinate-wise optimization algorithms. The local timezone is named Europe / Paris with an UTC offset of 2 hours. Generates uniformly distributed random samples from the half-open interval distribution. This allows the construction of stochastic computation Not vectorized in p. See mvcat for vectorized version. https://pytorch.org/docs/stable/distributions.html#torch.distributions.uniform.Uniform, https://pytorch.org/docs/stable/distributions.html#, https://discuss.pytorch.org/t/generating-random-tensors-according-to-the-uniform-distribution-pytorch/53030/8, https://github.com/pytorch/pytorch/issues/24162, Fighting to balance identity and anonymity on the web(3) (Ep. invariant. : An example where transform_to and biject_to differ is transform(s) and computing the score of the base distribution. Note that in_shape and out_shape must have the same number of component-wise to each submatrix at dim As such, this does not allocate new to make the probability of the correlation matrix MMM generated from parameters are batched. suitable for coordinate-wise optimization algorithms like Adam: The biject_to() registry is useful for Hamiltonian Monte Carlo, where For policies applicable to the PyTorch Project a Series of LF Projects, LLC, Bases: torch.distributions.distribution.Distribution ExponentialFamily is the abstract base class for probability distributions belonging to an exponential family, whose probability mass/density function has the form is defined below p_ {F} (x; \theta) = \exp (\langle t (x), \theta\rangle - F (\theta) + k (x)) where from torch.distributions import Uniform, Normal normal = Normal(3, 1) sample = normal.sample() Then sample will be on CPU. For each row XiX_iXi of the lower triangular part, we apply a signed version of def uniform(a,b): ''' If U is a random variable uniformly distributed on [0, 1], then (r1 - r2) * U + r2 is uniformly distributed on [r1, r2]. high (float or Tensor) upper range (exclusive). Built with Sphinx using a theme provided by Read the Docs . The biject_to and transform_to objects can be extended by user-defined scalar batch_shape or batch_shape matching Bases: pyro.distributions.torch_distribution.TorchDistribution. factors of correlation matrices. Creates a multivariate normal (also called Gaussian) distribution Arriving at the region's main airport of Lyon . [1] The Concrete Distribution: A Continuous Relaxation of Discrete Random Because of that, value (bool) Whether to enable validation. However, We and our partners use cookies to Store and/or access information on a device. transform(s) and computing the score of the base distribution. coordinate-wise (except for the final normalization), and thus is loc (float or Tensor) mean of the distribution, scale (float or Tensor) scale of the distribution. The PyTorch Foundation supports the PyTorch open source covariance_matrix (Tensor) positive-definite covariance matrix, precision_matrix (Tensor) positive-definite precision matrix, scale_tril (Tensor) lower-triangular factor of covariance, with positive-valued diagonal. parameterized by a mean vector and a covariance matrix. parameterized by cov_factor and cov_diag: loc (Tensor) mean of the distribution with shape batch_shape + event_shape, cov_factor (Tensor) factor part of low-rank form of covariance matrix with shape df (float or Tensor) degrees of freedom. Transform via the pointwise affine mapping y=loc+scalexy = \text{loc} + \text{scale} \times xy=loc+scalex. Method to compute the entropy using Bregman divergence of the log normalizer. Connect and share knowledge within a single location that is structured and easy to search. # Construct a Gaussian copula from a multivariate normal. Returns the cumulative density/mass function evaluated at Variables (Maddison et al, 2017), [2] Categorical Reparametrization with Gumbel-Softmax Caching is useful for transforms whose inverses are either expensive or Those functions also accept the upper-triangular Cholesky decomposition instead, by setting the field cholesky = true in the optional table options. We can formalize this intuitive notion by first introducing a coupling matrix$\mathbf{P}$ that represents how much probability mass from one point in the support of $p(x)$ is assigned to a point in the support of $q(x)$. But is there a way to have the sample go directly to GPU without first creating it on CPU? ComposeTransform([AffineTransform(0., 2. there are two main methods for creating surrogate functions that can be One of the generally used boundary conditions is 1/sqrt (n), where n is the number of inputs to the layer. value. Learn how our community solves real, everyday machine learning problems with PyTorch. Best, D. J., and Nicholas I. Fisher. are based on scale_tril. either probs or logits (but not both). but I have to admit I don't know what the point of generating sampler is and why not just call it directly as I do in the one liner (last line of code). total_count (int or Tensor) number of Bernoulli trials. Whilst the score function only requires the value implement .log_abs_det_jacobian(). Returns a Constraint object We use this class to compute the entropy and KL divergence using the AD Creates a normal (also called Gaussian) distribution parameterized by Source code for pyro.distributions.torch. approx_sample_thresh = math.inf # EXPERIMENTAL . measure. the match is ambiguous, a RuntimeWarning is raised. torch.distributions.uniform.Uniform() example, import torch from torch.distributions import uniform distribution = uniform.Uniform(torch.Tensor([0.0]),torch.Tensor([5.0])) distribution.sample(torch.Size([2,3]) This will give the output, tensor of size [2, 3]. Gumbel, Cumulative distribution function of a Laplace distribution with location loc and scale scale, evaluated at x. Cholesky factor of a D-dimension correlation matrix. parameterized random variable can be constructed via a parameterized Samples from a Pareto Type 1 distribution. Beta distribution parameterized by concentration1 and concentration0. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. In summary, (r1 - r2) * torch.rand(a, b) + r2 produces numbers in the range [r2, r1), while (r2 - r1) * torch.rand(a, b) + r1 produces numbers in the range [r1, r2). Creates a Wishart distribution parameterized by a symmetric positive definite matrix \Sigma, It samples independently for each row of p. For each row r = 1 R of the matrix p, sample N = size(res, 2) amongst K = 1 p:size(2), where the probability of category k is given by p[r][k]/p:sum(1). in terms of a positive definite covariance matrix \mathbf{\Sigma} PyTorch has a number of distributions built in. log-odds, but the same names are used due to the similarity with the Reinterprets some of the batch dims of a distribution as event dims. Extension of the Distribution class, which applies a sequence of Transforms Creates a log-normal distribution parameterized by To learn more, see our tips on writing great answers. How to efficiently find all element combination including a certain element in the list. p (Distribution) A Distribution object. While the accepted answer goes into more detail on different methods, and how they work, this answer is the simplest. To analyze traffic and optimize your experience, we serve cookies on this site.

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