[Bug-gsl] [bug #32233] Gauss-Legendre routine does not work in gsl-1.14

[Rhys Ulerich]

Update of bug #32233 (project gsl):

                  Status:                    None => Need Info              
             Assigned to:                    None => rhysu                  

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Follow-up Comment #1:

Good morning Jussi,

Three comments:

1) You've filed a bug report on an internal implementation detail-- you'll
note that the GSL manual says nothing definite about the contents of
gsl_integration_glfixed_table.  That was deliberate.

I believe that if you check the code against a 2nd order polynomial it will
behave correctly.  The GSL source code contains exactly such a test within
integration/test.c near a comment saying "Test the fixed-order Gauss-Legendre
rules with a monomial".

2) The weights and points are symmetric about zero leading to only about half
of the points needing to be stored.  That 0.57735 value you show is used
twice, once at 0.57735 and once at -0.57735 each time with weight 1.  This
sums to 2.  The point x = 1 has w = 0, as your table shows, and does not
contribute to such a sum.  But again, this is an implementation detail.

3) If you have a need to access the points and weights, please consider
filing a feature request.  It should be easy to provide an API call that will
return the values that MathWorld lists.

Does this address your concerns about the correctness?  May I close this
bug?

- Rhys

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