BUG: wrong weights of the 7-point gauss rule in QUADPACK: dqk15w.f

Describe your issue.

QUADPACK: dqk15w.f: line #103, wrong weights of the 7-point gauss rule The weights of wg should be the same as “dqk15.f”: #103: “0.3818300505051889d+00”, should be changed to “0.3818300505051189d+00”. This is a historical typo that commonly exists in every code that embeds netlib-quadpack, which does not necessarily produce an actual numerical error in the calculation of the error of the quadrature using the Gauss-Kronrod rule.

Reproducing Code Example

c     dqk15: #80-#83
      data wg  (  1) / 0.1294849661 6886969327 0611432679 082 d0 /
      data wg  (  2) / 0.2797053914 8927666790 1467771423 780 d0 /
      data wg  (  3) / 0.3818300505 0511894495 0369775488 975 d0 /
      data wg  (  4) / 0.4179591836 7346938775 5102040816 327 d0 /
c     dqk15i: #97-#104
      data wg(1) / 0.0d0 /
      data wg(2) / 0.1294849661 6886969327 0611432679 082d0 /
      data wg(3) / 0.0d0 /
      data wg(4) / 0.2797053914 8927666790 1467771423 780d0 /
      data wg(5) / 0.0d0 /
      data wg(6) / 0.3818300505 0511894495 0369775488 975d0 /
      data wg(7) / 0.0d0 /
      data wg(8) / 0.4179591836 7346938775 5102040816 327d0 /
c     dqk15w: #101-#103
      data wg(1),wg(2),wg(3),wg(4)/
     *     0.1294849661688697d+00,    0.2797053914892767d+00,
     *     0.3818300505051889d+00,    0.4179591836734694d+00/

Error message

no error message

SciPy/NumPy/Python version information

Any Version

[charris]

Anyhow, these typos fascinate me.

Reminds me of an incorrect citation (Herzberg something) that was propagated in many papers. It seems that none of the authors actually consulted the original work, they just copied the citation 😃

[certik]

Yes, we plan to maintain QUADPACK at fortran-lang just like we already maintain FFTPACK (https://github.com/fortran-lang/fftpack).

@langou, would you be interested in joining efforts on that? You can be the main maintainer of it. It seems you already de-facto are.