legendre polynomials and gaussian quadrature #313

hsnyder · 2021-02-08T04:29:47Z

Added preliminary implementation for Legendre polynomials
Added preliminary implementation for Legendre polynomial first derivatives
Added preliminary implementation for Gauss-Legendre quadrature points/weights
Added preliminary implementation for Gauss-Legendre-Lobatto quadrature points/weights

link to proposal: #277

- Added preliminary implementation for Legendre polynomial first derivatives - Added preliminary implementation for Gauss-Legendre quadrature points/weights - Added preliminary implementation for Gauss-Legendre-Lobatto quadrature points/weights

src/stdlib_quadrature_gauss.f90

ivan-pi · 2021-02-08T12:05:42Z

src/stdlib_quadrature_gauss.f90

+                w(N+1) =  2._dp/(N*(N+1._dp))
+
+                do i = 1, int(floor((N+1)/2._dp)-1)
+                    x(i+1) = -cos( (i+0.25_dp)*PI/N  - 3/(8*N*PI*(i+0.25_dp)))


A comment containing the source for the initial guess could be helpful.

src/stdlib_quadrature_gauss.f90

certik · 2021-02-08T17:18:07Z

I have a comment regarding the implementation --- what is the accuracy? I had bad experience with higher order (say p=64) that wasn't accurate to machine accuracy with such methods. So we resorted to calculate the weights and points using high precision and generate code that hard codes the numbers valid to all digits. But this comment is an implementation, which is minor.

Let's mainly discuss the API first. I would remove interval as doing [-1, 1] seems like a default?

src/stdlib_quadrature_gauss.f90

ivan-pi · 2021-02-08T18:16:24Z

Let's mainly discuss the API first. I would remove interval as doing [-1, 1] seems like a default?

The interval is an optional argument:

pure module subroutine gauss_legendre_fp64 (x, w, interval)
        real(dp), intent(out) :: x(:), w(:)
        real(dp), intent(in), optional :: interval(2)

The default is [-1,1]. At least in (chemical) engineering problems, shifted Legendre polynomials are sometimes used. I find the interval argument handy for such cases. Of course one could argue, that the user of the quadrature should be responsible for such things.

I am afraid the intent(out) attribute for x, and w is wrong. If these are allocatable arrays in the calling program, then gauss_legendre will not work as intended. Adding an integer variable, and using fixed size arrays would be the most flexible solution.

nncarlson · 2021-02-08T18:22:56Z

I am afraid the intent(out) attribute for x, and w is wrong. If these are allocatable arrays in the calling program, then gauss_legendre will not work as intended.

How so? I think you are mistaken here. Whether the actual arguments are allocatable is irrelevant. Are you thinking that the intent(out) causes them to be deallocated?

Co-authored-by: Sebastian Ehlert <[email protected]>

ivan-pi · 2021-02-08T18:29:36Z

@nncarlson, you are right I am mistaken. The concern would only be valid, if the allocatable attribute was given to the dummy variables.

milancurcic · 2021-02-08T18:47:55Z

Thank you @hsnyder. I didn't do a proper review yet, but two things stood out on a cursory skim through:

stdlib_functions.f90 for the source file and stdlib_functions for the module are not informative IMO. Is there some descriptive name we can use? What kind of functions are these?
Please use lowercase for all variables. I think uppercase is okay for constants (parameter) although we don't have an established position on this yet.

ivan-pi · 2021-02-08T18:58:22Z

Please use lowercase for all variables. I think uppercase is okay for constants (parameter) although we don't have an established position on this yet.

Unfortunately, the lower-case l is sometimes frowned upon due to its potential for mix up with 1. Perhaps p (for the polynomial) and dp (for its derivative) can be used as substitutes.

awvwgk · 2021-02-08T19:06:59Z

Perhaps p (for the polynomial) and dp (for its derivative) can be used as substitutes.

dp will unfortunately clash with the kind parameter for double precision reals. More than one or two letters might be advisable instead.

ivan-pi · 2021-02-08T19:13:02Z

dp will unfortunately clash with the kind parameter for double precision reals. More than one or two letters might be advisable instead.

Right... My next suggestion then are pn and dpn, which are unsurprisingly also used in the code by Stroud & Secrest.

hsnyder · 2021-02-08T20:03:48Z

Thanks everyone for the input so far!

Thank you @hsnyder. I didn't do a proper review yet, but two things stood out on a cursory skim through:
1. stdlib_functions.f90 for the source file and `stdlib_functions` for the module are not informative IMO. Is there some descriptive name we can use? What kind of functions are these?

@milancurcic The only thing I can really think of is "special functions". Acceptable?

arjenmarkus · 2021-02-09T08:03:20Z

"Special functions" is the general term that is used for this part of mathematics. So I'd say it is certainly acceptable. Op ma 8 feb. 2021 om 21:04 schreef Harris Snyder <[email protected]>:

…

Thanks everyone for the input so far! Thank you @hsnyder <https://github.com/hsnyder>. I didn't do a proper review yet, but two things stood out on a cursory skim through: 1. stdlib_functions.f90 for the source file and `stdlib_functions` for the module are not informative IMO. Is there some descriptive name we can use? What kind of functions are these? @milancurcic <https://github.com/milancurcic> The only thing I can really think of is "special functions". Acceptable? — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#313 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAN6YR3LY6EDIRWOMNN6FRDS6A7TPANCNFSM4XIIGT3Q> .

…ture points

arjenmarkus

Just a remark: the do-loop at line 33 runs from 0 to newton_iters-1. As the do-loop variable is not explicitly used, I would say: let it run from 1 to newton_iters instead.

hsnyder · 2021-02-10T18:17:04Z

Just a remark: the do-loop at line 33 runs from 0 to newton_iters-1. As the do-loop variable is not explicitly used, I would say: let it run from 1 to newton_iters instead.

haha you can tell I'm a C programmer... I will fix this

…in accordance to a review comment

hsnyder · 2021-03-15T01:37:17Z

sorry for the delay I have been very busy. other than resolving the makefile conflicts, what are the next steps towards getting this merged? I will try to get to the conflicts in the makefiles sometime this week but if I can't and someone else wants to, please feel free :)

src/stdlib_quadrature_gauss.f90

hsnyder · 2021-06-01T03:51:54Z

@awvwgk sorry for the delay. I think test cases and a spec are the outstanding items. In principle anyone could write them but it would obviously be easiest for me to do so. I’ve been very busy for the past few weeks but things are starting to ease up. I think I can finish this off this week. I will post again when I’ve done so.

hsnyder · 2021-06-23T21:56:12Z

Sorry for the delay! I've added some tests and specs for the new quadrature functions and the special functions module. Please let me know if any revisions are required.

note: I wasn't sure how to validate the the spec format is correct. I tried to follow the examples already present but I may have made errors and am not sure how to check it.

awvwgk

Thanks a lot, looks good to me now. Only a few comments regarding the markup.

doc/specs/stdlib_quadrature.md

doc/specs/stdlib_specialfunctions.md

Co-authored-by: Sebastian Ehlert <[email protected]>

doc/specs/stdlib_quadrature.md

Co-authored-by: Sebastian Ehlert <[email protected]>

milancurcic

Thank you @hsnyder and reviewers!

I have one last minute question and suggestion: What do you think about renaming everything that's called stdlib_specialfunctions* to stdlib_special*? I find specialfunctions quite long and a bit hard to read because two words are together, and special is clear enough what it means IMO.

I think this PR can go forward either way, but I'd prefer if we called this just stdlib_special.

hsnyder · 2021-06-28T22:31:39Z

Hi @milancurcic , I prefer specialfunctions because of clarity, but I don't have strong feelings about it. On the one hand, I agree that "special" is shorter, easier to type and read, but on the other hand it's not very descriptive (I don't think "special" on it's own is very clear - the stdlib includes more than just math, so I think "special what?" is a perfectly valid reaction).

I'll wait ~ 24 hours for any additional opinions re: the name change and then I'll merge the request. Thanks very much for reviewing!

arjenmarkus · 2021-06-29T08:45:51Z

An alternative might be "stdlib_specfunc" - though perhaps that is too reminiscent of other packages/libraries in other languages? Op di 29 jun. 2021 om 00:31 schreef Harris Snyder ***@***.***

…

: Hi @milancurcic <https://github.com/milancurcic> , I prefer specialfunctions because of clarity, but I don't have strong feelings about it. On the one hand, I agree that "special" is shorter, easier to type and read, but on the other hand it's not very descriptive (I don't think "special" on it's own is very clear - the stdlib includes more than just math, so I think "special what?" is a perfectly valid reaction). I'll wait ~ 24 hours for any additional opinions re: the name change and then I'll merge the request. Thanks very much for reviewing! — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#313 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAN6YR3EK6PFZU6UA4MZVPTTVDZ5NANCNFSM4XIIGT3Q> .

hsnyder · 2021-06-29T21:10:34Z

So it turns out I cannot merge this myself as I don't have write access. @milancurcic are you able to do so? Feel free to change the name if you want (though I still prefer "specialfunctions", or Arjen's suggestion instead of just "special").

Thanks!

milancurcic · 2021-06-30T21:46:24Z

Thanks, @hsnyder, I'll merge as is.

mjben · 2022-01-13T09:20:09Z

Unless I missed something, there should not be x(1) = interval(1) and x(size(x)) = interval(2) in gauss_legendre subroutines, this would only be relevant for gauss_legendre_lobatto.

ivan-pi reviewed Feb 8, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

ivan-pi reviewed Feb 8, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

ivan-pi reviewed Feb 8, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

ivan-pi reviewed Feb 8, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

awvwgk reviewed Feb 8, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

Update src/stdlib_quadrature_gauss.f90

1a914dd

Co-authored-by: Sebastian Ehlert <[email protected]>

hsnyder added 2 commits February 8, 2021 14:18

Some changes in accorance with preliminary review comments

5937f90

merge

124a2c5

hsnyder added 2 commits February 9, 2021 10:44

changed stdlib_functions to stdlib_specialfunctions

e0add1a

added a comment regarding the initial guess for gauss-legendre quadra…

29ebe9c

…ture points

arjenmarkus reviewed Feb 10, 2021

View reviewed changes

changed newton iteration loop indexing (stdlib_quadrature_gauss.f90) …

7f91f1d

…in accordance to a review comment

milancurcic mentioned this pull request Mar 11, 2021

Proposal for quadrature #112

Closed

Merge branch 'master' into master

6a1945f

awvwgk reviewed Apr 10, 2021

View reviewed changes

src/stdlib_quadrature_gauss.f90 Outdated Show resolved Hide resolved

Fix build for GCC 10.2

56b9423

hsnyder added 5 commits June 1, 2021 23:51

Merge branch 'fortran-lang:master' into master

ce62e1f

added first tests for gaussian quadrature functions

551ec6d

test implementation for gaussian quadrature functions

6f06f69

added spec for gaussian quadrature functions

274f542

Added spec for special functions

f6ac41b

hsnyder requested review from arjenmarkus, ivan-pi and awvwgk June 23, 2021 21:54

awvwgk added reviewers needed This patch requires extra eyes and removed waiting for OP This patch requires action from the OP labels Jun 24, 2021

awvwgk approved these changes Jun 24, 2021

View reviewed changes

hsnyder and others added 5 commits June 24, 2021 10:05

Update doc/specs/stdlib_quadrature.md

4dbd769

Co-authored-by: Sebastian Ehlert <[email protected]>

Update doc/specs/stdlib_quadrature.md

259482a

Co-authored-by: Sebastian Ehlert <[email protected]>

Update doc/specs/stdlib_specialfunctions.md

7225987

Co-authored-by: Sebastian Ehlert <[email protected]>

Update doc/specs/stdlib_specialfunctions.md

6647e9b

Co-authored-by: Sebastian Ehlert <[email protected]>

made spec examples (guassian quadrature) standalone programs

f3d43b3

awvwgk reviewed Jun 24, 2021

View reviewed changes

doc/specs/stdlib_quadrature.md Outdated Show resolved Hide resolved

awvwgk reviewed Jun 24, 2021

View reviewed changes

doc/specs/stdlib_quadrature.md Outdated Show resolved Hide resolved

hsnyder and others added 2 commits June 24, 2021 10:20

Update doc/specs/stdlib_quadrature.md

6f9d7e4

Co-authored-by: Sebastian Ehlert <[email protected]>

Update doc/specs/stdlib_quadrature.md

5c53579

Co-authored-by: Sebastian Ehlert <[email protected]>

milancurcic approved these changes Jun 28, 2021

View reviewed changes

milancurcic merged commit 9fb85ff into fortran-lang:master Jun 30, 2021

awvwgk removed the reviewers needed This patch requires extra eyes label Jul 4, 2021

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

legendre polynomials and gaussian quadrature #313

legendre polynomials and gaussian quadrature #313

hsnyder commented Feb 8, 2021

ivan-pi Feb 8, 2021

certik commented Feb 8, 2021

ivan-pi commented Feb 8, 2021 •

edited

Loading

nncarlson commented Feb 8, 2021

ivan-pi commented Feb 8, 2021 •

edited

Loading

milancurcic commented Feb 8, 2021

ivan-pi commented Feb 8, 2021

awvwgk commented Feb 8, 2021

ivan-pi commented Feb 8, 2021

hsnyder commented Feb 8, 2021 •

edited

Loading

arjenmarkus commented Feb 9, 2021 via email

arjenmarkus left a comment

hsnyder commented Feb 10, 2021

hsnyder commented Mar 15, 2021

hsnyder commented Jun 1, 2021

hsnyder commented Jun 23, 2021

awvwgk left a comment

milancurcic left a comment

hsnyder commented Jun 28, 2021

arjenmarkus commented Jun 29, 2021 via email

hsnyder commented Jun 29, 2021

milancurcic commented Jun 30, 2021

mjben commented Jan 13, 2022

legendre polynomials and gaussian quadrature #313

legendre polynomials and gaussian quadrature #313

Conversation

hsnyder commented Feb 8, 2021

ivan-pi Feb 8, 2021

Choose a reason for hiding this comment

certik commented Feb 8, 2021

ivan-pi commented Feb 8, 2021 • edited Loading

nncarlson commented Feb 8, 2021

ivan-pi commented Feb 8, 2021 • edited Loading

milancurcic commented Feb 8, 2021

ivan-pi commented Feb 8, 2021

awvwgk commented Feb 8, 2021

ivan-pi commented Feb 8, 2021

hsnyder commented Feb 8, 2021 • edited Loading

arjenmarkus commented Feb 9, 2021 via email

arjenmarkus left a comment

Choose a reason for hiding this comment

hsnyder commented Feb 10, 2021

hsnyder commented Mar 15, 2021

hsnyder commented Jun 1, 2021

hsnyder commented Jun 23, 2021

awvwgk left a comment

Choose a reason for hiding this comment

milancurcic left a comment

Choose a reason for hiding this comment

hsnyder commented Jun 28, 2021

arjenmarkus commented Jun 29, 2021 via email

hsnyder commented Jun 29, 2021

milancurcic commented Jun 30, 2021

mjben commented Jan 13, 2022

ivan-pi commented Feb 8, 2021 •

edited

Loading

ivan-pi commented Feb 8, 2021 •

edited

Loading

hsnyder commented Feb 8, 2021 •

edited

Loading