Added sampling methods of crv_types

[Smit-create]

Added sampling methods of continuous random variables

References to other Issues or PRs

Closes #17057
Related to #19061

Brief description of what is fixed or changed

Other comments

Release Notes

• stats
  • Added sampling methods for continuous variables
  • Added library option in sample
  • sample returns an iterator object since version 1.7

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• stats

  • Added sampling methods for continuous variables (#18754 by @Smit-create)

  • Added library option in sample (#18754 by @Smit-create)

  • sample returns an iterator object since version 1.7 (#18754 by @Smit-create)

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<!-- Your title above should be a short description of what
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Added sampling methods of continuous random variables
#### References to other Issues or PRs
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Closes #17057 
Related to #19061
#### Brief description of what is fixed or changed


#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* stats
   * Added sampling methods for continuous variables
   * Added `library` option in `sample`
   *  `sample` returns an iterator object since version 1.7
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[Smit-create]

Please review.

[Smit-create]

This is ready for review. @czgdp1807

[czgdp1807]

The diff coverage is quite low. Can you add more tests or modify current tests to or merge master to increase the coverage?

[Smit-create]

Code coverage now increases to 100%

[Smit-create]

@czgdp1807 Does it look good to go?

[czgdp1807]

LGTM. Will merge if no one raises objections.

[oscarbenjamin]

The code here is very repetitive. It would be better to make a data structure that stores the different functions like in lambdify and the code printers.

Would it make more sense to handle this as part of lambdify and the code printers?

[Smit-create]

Would it make more sense to handle this as part of lambdify and the code printers?

I will look into this suggestion.

[oscarbenjamin]

It probably makes more sense to group the code together in one class for each of the libraries and have a mapping from sympy types to the other library types rather than having each of the sympy classes repeat the boiler plate for calling into the external library. That is what I mean by saying that it is repetitive. If we have m other libraries and k sympy distribution classes then we will end up having to add m*k methods for connecting them all. Since m is smaller than k it makes more sense to have m classes for the output each of which can have a mapping of size k that efficiently describes how to connect between them.

[Smit-create]

Thanks! @oscarbenjamin, I get your point. I will think of some way to work upon that.

[Smit-create]

I have designed another way. I will explain with an example of sample_scipy.

We will create 5 dictionaries, one which will import the corresponding random variable from scipy, other four will map scipy arguments with sympy arguments. Generally, scipy has 4 main arguments, i.e, a , b, loc, scale. The other four dictionaries will map these arguments using attributes of the corresponding class of random variable.
Then, finally, return the sample using mapped random variable from first dictionary and arguments from other 4 dictionaries.

[Smit-create]

I have designed a function that works fine with scipy:

def _sample_scipy(dist, size):

    dist_list =  ['BetaDistribution', 'BetaPrimeDistribution',
    'CauchyDistribution', 'ChiDistribution', 'ChiSquaredDistribution',
    'ExponentialDistribution', 'GammaDistribution', 'GammaInverseDistribution',
    'LogNormalDistribution', 'NormalDistribution', 'GaussianInverseDistribution',
    'ParetoDistribution', 'UniformDistribution']

    if dist.__class__.__name__ not in dist_list:
        return None
    from scipy.stats import (beta, betaprime, cauchy, chi, chi2, expon, gamma,
                             invgamma, lognorm, norm, invgauss, pareto, uniform)

    scipy_rv_map = {
            'BetaDistribution': lambda dist, size: beta.rvs(a=float(dist.a), b=float(dist.b),
                                    size=size),
            'BetaPrimeDistribution':lambda dist, size: betaprime.rvs(a=float(dist.alpha),
                                    b=float(dist.beta), size=size),
            'CauchyDistribution': lambda dist, size: cauchy.rvs(loc=float(dist.x0),
                                    scale=float(dist.gamma), size=size),
            'ChiDistribution': lambda dist, size: chi.rvs(df=float(dist.k), size=size),
            'ChiSquaredDistribution': lambda dist, size: chi2.rvs(df=float(dist.k), size=size),
            'ExponentialDistribution': lambda dist, size: expon.rvs(loc=0, scale=1/float(dist.rate),
                                    size=size),
            'GammaDistribution': lambda dist, size: gamma.rvs(a=float(dist.k), loc=0,
                                    scale=float(dist.theta), size=size),
            'GammaInverseDistribution': lambda dist, size: invgamma.rvs(a=float(dist.a), loc=0,
                                    scale=float(dist.b), size=size),
            'LogNormalDistribution': lambda dist, size: lognorm.rvs(s=std, loc=0,
                                    scale=exp(float(dist.mean), size=size)),
            'NormalDistribution': lambda dist, size: norm.rvs(float(dist.mean), float(dist.std), size=size),
            'GaussianInverseDistribution': lambda dist, size: invgauss.rvs(
                mu=float(dist.mean)/float(dist.shape), scale=float(dist.shape), size=size),
            'ParetoDistribution': lambda dist, size: pareto.rvs(b=float(dist.alpha),
                                    scale=float(dist.xm), size=size),
            'UniformDistribution': lambda dist, size: uniform.rvs(loc=float(dist.left),
                            scale=float(dist.right)-float(dist.left), size=size),
        }
    return scipy_rv_map[dist.__class__.__name__](dist, size)

This will remove all _sample_scipy methods from individual classes, and just a single function will be used.
@oscarbenjamin @czgdp1807 Does this look good to commit for all libraries?

[oscarbenjamin]

That looks better. There's probably a way to organise this nicely into one class for each external library and perhaps factor some code out to a base class.

[Smit-create]

Can anyone please have a look at the failing test https://travis-ci.org/github/sympy/sympy/jobs/677325425?

[Smit-create]

Please review this.

[czgdp1807]

LGTM. Ready for merge.

[Smit-create]

@czgdp1807 I think we can merge this if no-one has objection?

[czgdp1807]

Let's merge this after, 1.6 branch is created. Some public API change is made in this PR, and various changes made in the coming months to the sampling APIs, so 1.7 will be more appropriate to have this change.

[czgdp1807]

Finally, it's good to go in. Will merge it by tonight.

[Upabjojr]

What is the purpose of substituting () with (1,) or 1 ? The tuple notation should represent the dimensions of an N-dimensional array you want to be returned.