[GSoC] Concrete: Implemented Raabe's Test #18656

sachin-4099 · 2020-02-14T18:40:33Z

Reference: #12352
Fixes: #19379
Fixes: #10973

Brief description of what is fixed or changed

This pull request adds Raabe's Test. It is an enhancement of ratio test that is intended for the case where it is inconclusive.

Other comments

Regression Test added

Release Notes

concrete
- Implemented Raabe's Test

sympy-bot · 2020-02-14T18:40:35Z

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- Implemented Raabe's Test (#18656 by @sachin-4099)

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Reference: https://github.com/sympy/sympy/pull/12352
Fixes: #19379 
Fixes: #10973 

#### Brief description of what is fixed or changed
This pull request adds Raabe's Test.  It is an enhancement of ratio test that is intended for the case where it is inconclusive.

#### Other comments
Regression Test added

#### Release Notes


<!-- BEGIN RELEASE NOTES -->
* concrete
  * Implemented Raabe's Test
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

sachin-4099 · 2020-02-14T18:40:58Z

Please suggest some regression tests which could be added.

asmeurer · 2020-02-14T21:25:42Z

sympy/concrete/summations.py

@@ -512,6 +512,21 @@ def is_convergent(self):
        except NotImplementedError:
            pass

+        ### ---------- Raabe's test -------------- ###
+        if lim_ratio == 1:  # ratio test inconclusive


There was a discussion in the other pull request about whether or not this is needed.

imo it is necessary...

Why is it necessary?

Are you talking about raabe's test or the condition??

The condition. Your answer above says "imo it is necessary". I am sure that I agree but I would prefer it if you write an explicit reason (an opinion is not a reason).

We implement Raabe's test only after ratio test fails, and the condition when ratio test fails is when it is 1, so definitely it is necessary, otherwise how will we come to know when to implement raabe's test.

asmeurer · 2020-02-14T21:27:01Z

sympy/concrete/summations.py

+            try:
+                lim_val = limit_seq(test_val, sym)
+                if lim_val is not None and lim_val.is_number:
+                    if lim_val > 1:


I think we can check (lim_val - 1).is_positive here, to allow it to potentially work for symbols with the proper assumptions.

OK will change the line if lim_value > 1:

sachin-4099 · 2020-02-14T21:33:17Z

Please suggest some regression tests which could be added.

What about this @asmeurer

asmeurer · 2020-02-14T22:32:35Z

I don't know. You might need to google around for some examples. I did find https://arxiv.org/abs/1801.07584, which has some. You can also look for series that are known to fail the ratio test.

sachin-4099 · 2020-02-15T05:22:24Z

Series like these are giving maximum recursion depth exceeded:
Sum(Product((3*m-3),(m,2,n))/Product((3*m+1),(m,2,n)),(n,2,oo)).is_convergent()

But they should pass with raabe's test. The point is they are not able to reach up to the point where raabe's test is implemented as the depth is exceeded in the divergence tests itself.

sachin-4099 · 2020-02-15T05:51:11Z

Series like these are giving maximum recursion depth exceeded:
Sum(Product((3*m-3),(m,2,n))/Product((3*m+1),(m,2,n)),(n,2,oo)).is_convergent()

But they should pass with raabe's test. The point is they are not able to reach up to the point where raabe's test is implemented as the depth is exceeded in the divergence tests itself.

Moreover limit_seq is not able to work on sequence_term generated in these series.

sympy/concrete/summations.py

sachin-4099 · 2020-02-15T10:11:35Z

Series like these are giving maximum recursion depth exceeded:
Sum(Product((3*m-3),(m,2,n))/Product((3*m+1),(m,2,n)),(n,2,oo)).is_convergent()
But they should pass with raabe's test. The point is they are not able to reach up to the point where raabe's test is implemented as the depth is exceeded in the divergence tests itself.

Moreover limit_seq is not able to work on sequence_term generated in these series.

@jksuom @asmeurer ?? And these are the sort of examples where raabe's test becomes useful.

jksuom · 2020-02-15T12:09:13Z

It looks like divergence test should be fixed first so it won't return false when limit_seq returns an unevaluated limit. (limit_seq should also be improved.)

Then Raabe's test should be able to handle sums of rf(a, n)/rf(c, n) for real a, c. It should also work with hypegeometric sums evaluated at x = 1 with terms rf(a, n)*rf(b, n)/(rf(c, n)*factorial(n)).

sachin-4099 · 2020-02-15T19:21:40Z

Now imo, most of the series should no longer cause any RecursionError but I feel there are chances of wrong answers as limit_seq sometimes returns wrong limit values (Ex:#16735)

sympy/concrete/summations.py

codecov · 2020-08-16T17:23:43Z

Codecov Report

Merging #18656 into master will decrease coverage by 16.246%.
The diff coverage is 58.823%.

@@              Coverage Diff               @@
##            master    #18656        +/-   ##
==============================================
- Coverage   75.814%   59.567%   -16.247%     
==============================================
  Files          669       669                
  Lines       173463    173475        +12     
  Branches     40907     40911         +4     
==============================================
- Hits        131510    103335     -28175     
- Misses       36230     64290     +28060     
- Partials      5723      5850       +127

`

jksuom · 2020-08-17T10:29:42Z

Thanks, I think this is ready to go.

Implemented Raabe's Test

c02ece9

sachin-4099 requested a review from jksuom February 14, 2020 20:55

asmeurer reviewed Feb 14, 2020

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jksuom reviewed Feb 15, 2020

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sachin-4099 requested a review from jksuom February 15, 2020 10:08

czgdp1807 mentioned this pull request Feb 15, 2020

Implemented Raabe's Test : Eliminated XFAIL #12352

Closed

czgdp1807 added the concrete label Feb 15, 2020

sachin-4099 requested a review from asmeurer February 15, 2020 10:47

Added test and some simplifications to get rid of RecursionError

d5c27a4

sachin-4099 force-pushed the raabe branch from f933f95 to d5c27a4 Compare February 15, 2020 19:16

sachin-4099 added 3 commits February 16, 2020 01:34

Made a bit fast

553f35a

Added more testcases and made some modifications

5313914

Made some modifications to testcases

32bd957

sachin-4099 closed this Feb 16, 2020

sachin-4099 reopened this Feb 16, 2020

sachin-4099 added 2 commits February 16, 2020 23:38

Merge branch 'master' into raabe

7c863b8

New testcase

91a4b4d

sachin-4099 changed the title ~~Concrete: Implemented Raabe's Test~~ [WIP] Concrete: Implemented Raabe's Test Feb 16, 2020

czgdp1807 reviewed Feb 18, 2020

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czgdp1807 reviewed Feb 18, 2020

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Merge branch 'master' into raabe

e1dd2bd

sachin-4099 force-pushed the raabe branch 2 times, most recently from 6372519 to b45bc4f Compare August 16, 2020 17:29

sachin-4099 requested review from jksuom and removed request for asmeurer and jksuom August 16, 2020 17:35

sachin-4099 added the GSoC label Aug 16, 2020

sachin-4099 changed the title ~~[WIP] Concrete: Implemented Raabe's Test~~ [GSoC] Concrete: Implemented Raabe's Test Aug 16, 2020

Made some modifications and added a testcase

5de4028

`

sachin-4099 force-pushed the raabe branch from b45bc4f to 5de4028 Compare August 17, 2020 08:21

jksuom merged commit e456dba into sympy:master Aug 17, 2020

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[GSoC] Concrete: Implemented Raabe's Test #18656

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[GSoC] Concrete: Implemented Raabe's Test #18656

[GSoC] Concrete: Implemented Raabe's Test #18656

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Brief description of what is fixed or changed

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Release Notes

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