[GSoC] Simplification for the solutions of systems of ODEs

[mijo2]

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• solvers
  • Added simplification strategies for simplifying the solutions of systems of ODEs

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• solvers
  • Added simplification strategies for simplifying the solutions of systems of ODEs (#19998 by @mijo2 and @oscarbenjamin)

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* solvers
  * Added simplification strategies for simplifying the solutions of systems of ODEs
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Update

The release notes on the wiki have been updated.

[czgdp1807]

I hope this was for debugging(similarly other such statements)?

[mijo2]

Yes, I have removed these lines locally. Forgot to fix up these statements

[mijo2]

I have created a set of functions that can be used to print the test case given a system. Along with that, I have also created a basic structure to replace any rationals in a solution with Rational(a, b). I am not sure if it will always work but the below is what I have created:

In [113]: def filldedent_string_to_tab(string): 
     ...:     string = filldedent(string, w=100) 
     ...:     string = string.split("\n") 
     ...:     if len(string[0]) == 0: del string[0] 
     ...:     string = ['  ' + s if i != 0 else s for i, s in enumerate(string)] 
     ...:     return "\n".join(string)

In [114]: def add_more_spaces(string, more_spaces=10, ignore_first=False): 
     ...:     string = string.split("\n") 
     ...:     string = [more_spaces * ' ' + s if i != 0 or not ignore_first else s for i, s in enumerate(string)] 
     ...:     return "\n".join(string) 
     ...:                             

In [114]: def replace_rationals(str):  
     ...:     array = re.findall(r'[0-9]+/[0-9]+', str)  
     ...:     for expr in array: 
     ...:         str = str.replace(expr, "Rational({}, {})".format(*expr.split('/'))) 
     ...:     return str 
     ...:                                                                                                                                                                                                   

In [115]: def print_eqs(sol, initial_string="sol = {}"): 
     ...:     base = len(initial_string) 
     ...:     print(initial_string, end="") 
     ...:     for i, eq in enumerate(sol): 
     ...:         print((i==0)*'[' + replace_rationals(add_more_spaces(filldedent_string_to_tab(str(eq)), more_spaces=base, ignore_first=(i == 0))) + (i == len(sol)-1) * ']') 
     ...:                           

In [116]: def print_one_sol(eqs, n=1): 
     ...:     sol = dsolve(eqs) 
     ...:     print_eqs(eqs, "eqs{} = ".format(n)) 
     ...:     print_eqs(sol, "sol{} = ".format(n)) 
     ...:     print("assert dsolve(eqs{}) == sol{}".format(n, n)) 
     ...:     print("assert checksysodesol(eqs{}, sol{}) == (True, {})".format(n, n, n*[0])) 
     ...:    
                                                                                                                                                                                                                                                                                                                                                                       

[oscarbenjamin]

@mijo2 what's the status of this?

Did you cancel the tests yourself?

[mijo2]

@oscarbenjamin I cancelled the tests. I want to complete this PR, but due to some commitments, I won't be able to work for atleast the first half of this month. I do intend to complete this PR in this month itself

[oscarbenjamin]

I've pushed a few commits on here to finish off the simplification. This involved changing many of the tests because the output from dsolve changed. Some tests were too slow so I've reorganised some to mark some as slow or perhaps too slow.

@mijo2 Can you review this?

[codecov]

Codecov Report

Merging #19998 into master will decrease coverage by 11.368%.
The diff coverage is 87.671%.

@@              Coverage Diff               @@
##            master    #19998        +/-   ##
==============================================
- Coverage   75.847%   64.478%   -11.369%     
==============================================
  Files          671       671                
  Lines       173810    173874        +64     
  Branches     41048     41069        +21     
==============================================
- Hits        131830    112112     -19718     
- Misses       36222     55335     +19113     
- Partials      5758      6427       +669     

[mijo2]

I've pushed a few commits on here to finish off the simplification. This involved changing many of the tests because the output from dsolve changed. Some tests were too slow so I've reorganised some to mark some as slow or perhaps too slow.

@mijo2 Can you review this?

Sure, I will review it soon, at max by tomorrow. Thanks for the commits.

[mijo2]

Looks good to me. Really liked how you implemented the simplification part along with optimizing the integral computations.

[oscarbenjamin]

Thanks @mijo2. I think with this in the new systems code is ready for release. It would be great if you could write a new page in the docs to describe the systems that can be solved and the new functions though. At the moment none of this is really visible to users except that dsolve might give better answers for many systems.

[mijo2]

It would be great if you could write a new page in the docs to describe the systems that can be solved and the new functions though.

I would love to write a page showing all the examples that can be solved but I am currently very busy. Can you tell me a tentative date for the release so that I can make proper arrangements and plan accordingly to write the doc page?

[oscarbenjamin]

This PR was the main blocker for the release so now it should be fairly soon although I haven't announced anything yet.