[GSoC] Added symbolic Expectation, Variance and CrossCovariance matrix

[Smit-create]

Added symbolic Expectation, Variance and Covariance matrix

References to other Issues or PRs

References from #19299

Brief description of what is fixed or changed

Other comments

• Add classses
• Add docs and tests

Release Notes

• stats
  • Added Expectation Matrix, Variance Matrix and CrossCovariance Matrix

ping @czgdp1807 @Upabjojr

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• stats
  • Added Expectation Matrix, Variance Matrix and CrossCovariance Matrix (#19529 by @Smit-create)

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<!-- Your title above should be a short description of what
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Added symbolic Expectation, Variance and Covariance matrix
#### References to other Issues or PRs
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References from #19299 

#### Brief description of what is fixed or changed


#### Other comments
- [x] Add classses
- [x] Add docs and tests 

#### Release Notes

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* stats
  * Added Expectation Matrix, Variance Matrix and CrossCovariance Matrix
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ping @czgdp1807  @Upabjojr

Update

The release notes on the wiki have been updated.

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The following commits add new files:

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  • sympy/stats/symbolic_multivariate_probability.py
• 3117bbf:
  • sympy/stats/tests/test_symbolic_multivariate.py

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[Upabjojr]

There are various name possibilities to choose, from wikipedia:

1. https://en.wikipedia.org/wiki/Covariance_matrix

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix)

2. OTOH, the cross-covariance matrix: https://en.wikipedia.org/wiki/Cross-covariance_matrix

In principle, 1 and 2 are the generalizations of variance and covariance to vector random variables. There are problems with the terminology though, as the covariance matrix is the generalization of the variance (not the covariance), while the cross-covariance matrix is the generalization of the covariance.

[czgdp1807]

Tests?

[Smit-create]

I am writing them currently, and push by tonight.

[Smit-create]

I have added docs and tests for VarianceMatrix and CrossCovarianceMatrix. I am currently trying to resolve the following error with ExpectationMatrix.

>>> A = MatrixSymbol("A", k, k)
>>> X = RandomMatrixSymbol("X", k, 1)
>>> Expectation((Mul.fromiter([A*X]))) # correct
ExpectationMatrix(A*X)
>>> Expectation((Mul.fromiter([X])))
ExpectationMatrix(X)
>>> A*Expectation((Mul.fromiter([X]))) # this looks incorrect
A*X  # Expected as: A*ExpectationMatrix(X)

@oscarbenjamin @sylee957 Can you please have a look at this?

[czgdp1807]

The problem is with doit of ExpectationMatrix,

>>> r = Expectation((Mul.fromiter([X])))
>>> r
ExpectationMatrix(X)
>>> r.doit()
X

[codecov]

Codecov Report

Merging #19529 into master will increase coverage by 0.046%.
The diff coverage is 87.820%.

@@              Coverage Diff              @@
##            master    #19529       +/-   ##
=============================================
+ Coverage   75.621%   75.667%   +0.046%     
=============================================
  Files          652       655        +3     
  Lines       169813    170092      +279     
  Branches     40061     40110       +49     
=============================================
+ Hits        128415    128705      +290     
+ Misses       35789     35770       -19     
- Partials      5609      5617        +8     

[Smit-create]

The problem is with doit of ExpectationMatrix,

Opps, got it, MatMul will call doit, so for ExpecationMatrix, Expectation's doit is called, so need to fix it. Thanks!!

[czgdp1807]

LGTM. Any thoughts @Upabjojr @jmig5776 ?

[Smit-create]

ping @Upabjojr

[Upabjojr]

maybe also an assert isinstance(expr, VarianceMatrix)?

[Upabjojr]

This looks good to me.