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View Code? Open in Web Editor NEWModern Fortran QUADPACK Library for 1D numerical quadrature
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Adaptive quadrature method from MATLAB
It would be nice to add the MATLAB algorithm, which is described in
Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. https://doi.org/10.1016/j.cam.2006.11.021
I believe the algorithm is similar to those in QUADPACK, but with a few small differences in how the error estimate is constructed.
For simplicity it offers a unified interface for both proper and improper integrals.
See also
dqng needs quad-precision coefficients
Need to figure out how to regenerate the remaining coefficients in dqng.
Slatec routines
There are a few quadrature routines in slatec that could be incorporated:
quadpack fails to build on Sonoma (x86_64, arm64): `<ERROR> error: Missing key for table header`
Executing: cd "/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm install --verbose --prefix="/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/opt/local" --profile="release"
DEBUG: system: cd "/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm install --verbose --prefix="/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/opt/local" --profile="release"
<ERROR> error: Missing key for table header
--> fpm.toml:21:3
|
21 | [[ test ]]
| ^ unexpected whitespace
|
STOP 1
Command failed: cd "/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm install --verbose --prefix="/opt/local/var/macports/build/_opt_bblocal_var_buildworker_ports_build_ports_fortran_quadpack/quadpack/work/opt/local" --profile="release"
Exit code: 1
Same error on arm64:
---> Building quadpack
xinstall: mkdir /opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_macports_release_tarballs_ports_fortran_quadpack/quadpack/work/bin
Executing: cd "/opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_macports_release_tarballs_ports_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm install --verbose --prefix="/opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_macports_release_tarballs_ports_fortran_quadpack/quadpack/work/opt/local" --profile="release"
<ERROR> error: Missing key for table header
--> fpm.toml:21:3
|
21 | [[ test ]]
| ^ unexpected whitespace
|
STOP 1
Command failed: cd "/opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_macports_release_tarballs_ports_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm install --verbose --prefix="/opt/local/var/macports/build/_opt_local_var_macports_sources_rsync.macports.org_macports_release_tarballs_ports_fortran_quadpack/quadpack/work/opt/local" --profile="release"
Exit code: 1
Bug in dqawo
I believe this line:
if (Ier == 6) lvl = 0should be :
if (Ier == 6) lvl = 1Which matches all the other routines. This is a bug that has been in there since 1983.
tanh-sinh quadrature
Consider adding fixed-precision versions of David H. Bailey's routines from tquad.f90 in MPFUN2020.
- quadts: tanh-sinh quadrature scheme of Takahashi and Mori, for functions on a finite interval such as (0,1).
- quades: exp-sinh scheme, a variation of tanh-sinh well-suited for functions on a semi-infinite interval such as (0, +infinity).
- quadss: sinh-sinh scheme, a variation of tanh-sinh well-suited for functions on the entire real line.
Regenerate coefficients with more precision for quad precision version
See #5. Maybe we need 36 digits?
Add basic adaptive Simpson and Lobatto
Bug in weight value
In dqk51, the last weight value for the 51-point rule is given as:
0.061580818067832935078759824240066
The last decimal point isn't right. If you compute at a higher resolution, you get:
0.06158081806783293507875982424006455319043693690314
So, for the 33 digit value, it should be:
0.061580818067832935078759824240065
Multidimensional integration
See quadrature-fortran. Can we merge that library into this one? All the routines would need to be made recursive. Could allow the method to be independently-selected for each dimension.
single, double, and quad procedures
What is the best way to export single, double, and quad procedures that:
- is standard fortran
- doesn't duplicate code
- doesn't break IDEs, linters, syntax highlighters
- is backward compatible with the old interface (e.g, qag for single, dqag for double)
- is able to be documented with Ford without confusion or duplicated routines in the docs
See #4
add topic fortran-package-manager
add topic fortran-package-manager
C or cplusplus api request
Thanks for re-implementing the QUADPACK in modern FORTRAN. I would like to know if it is possible to add the C/C++ API (dynamic/static library). As a user of C/C++/JAVA/scala, I do not have any experience in the FORTRAN language.
Replace linpack DGTSL with lapack DGTSV
Consider replacing linpack DGTSL with lapack DGTSV. This was done in the SciPy version. See: scipy/scipy@361468a#diff-3bc2ad4ff04dcd0fd46bde7b0a273a6b453177a8494cbc77f08009db5cb8ad93
CQUAD doubly-adaptive integration
The GNU Scientific Library also contains an implementation of the algorithm from
P. Gonnet, “Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants”, ACM Transactions on Mathematical Software, Volume 37 (2010), Issue 3, Article 26. https://doi.org/10.1145/1824801.1824804
In principle Fortran programmers can use it via the fgsl wrapper library, but it would be nice to have them all in one place.
The same author also published a review of error estimation approaches
Gonnet, P. (2012). A review of error estimation in adaptive quadrature. ACM Computing Surveys (CSUR), 44(4), 1-36. https://dl.acm.org/doi/abs/10.1145/2333112.2333117
Bug in dqnc79 routine
I get the following error when I try to compile the library using the Intel compiler:
./quadpack_generic.F90(7823): warning #6843: A dummy argument with an explicit INTENT(OUT) declaration is not given an explicit value. [ERR]
subroutine dqnc79(fun,a,b,err,ans,ierr,k)
------------------------------^
I believe that err argument is actually an input argument, so the fix would be obviuos.
diff --git a/src/quadpack_generic.F90 b/src/quadpack_generic.F90
index 66344ed..eb8b056 100644
--- a/src/quadpack_generic.F90
+++ b/src/quadpack_generic.F90
@@ -7830 +7830 @@ subroutine dquad(f, a, b, result, epsil, npts, icheck)
- real(wp),intent(out) :: err !! a requested error tolerance. Normally, pick a value
+ real(wp),intent(in) :: err !! a requested error tolerance. Normally, pick a value
Tests on PowerPC: 1 abnormal return from dqag, 1 abnormal return from dqng
---> Testing quadpack
Executing: cd "/opt/local/var/macports/build/_opt_PPCRosettaPorts_fortran_quadpack/quadpack/work/quadpack-2.1.1" && /opt/local/bin/fpm test --flag="-I/opt/local/var/macports/build/_opt_PPCRosettaPorts_fortran_quadpack/quadpack/work/destroot/opt/local/include" --link-flag="-L/opt/local/var/macports/build/_opt_PPCRosettaPorts_fortran_quadpack/quadpack/work/destroot/opt/local/lib" --profile="release"
[ 0%] quadpack_double.F90
[ 7%] quadpack_double.F90 done.
[ 7%] quadpack_quad.F90
[ 15%] quadpack_quad.F90 done.
[ 15%] quadpack_single.F90
[ 23%] quadpack_single.F90 done.
[ 23%] libquadpack.a
[ 30%] libquadpack.a done.
[ 30%] quadpack_test_module_double.F9
[ 38%] quadpack_test_module_double.F9 done.
[ 38%] quadpack_test_module_quad.F90
[ 46%] quadpack_test_module_quad.F90 done.
[ 46%] quadpack_test_module_single.F9
[ 53%] quadpack_test_module_single.F9 done.
[ 53%] quadpack_tests_single.F90
[ 61%] quadpack_tests_single.F90 done.
[ 61%] quadpack_tests_double.F90
[ 69%] quadpack_tests_double.F90 done.
[ 69%] quadpack_tests_quad.F90
[ 76%] quadpack_tests_quad.F90 done.
[ 76%] single
[ 84%] single done.
[ 84%] double
[ 92%] double done.
[ 92%] quad
[100%] quad done.
[100%] Project compiled successfully.
quadpack_tests : Single. tol = 3.45267006E-03
dqag-1 1.154701E+00 0.000000E+00 225
dqag-2 1.154701E+00 0.000000E+00 315
dqag-3 1.154701E+00 1.192093E-07 217
dqag-4 1.154701E+00 0.000000E+00 287
dqag-5 1.154701E+00 0.000000E+00 255
dqagi 3.079725E+00 1.525879E-04 255
dqagp 4.253487E+00 2.007484E-04 819
dqags 2.000000E+00 4.768372E-07 231
dqawc -6.284617E+02 0.000000E+00 225
dqawf 1.422564E+00 1.204014E-05 6990
dqawo -1.776392E-01 4.470348E-08 255
dqaws 5.350192E-01 1.192093E-07 50
dqng 1.270724E+00 1.192093E-07 21
dqag C(1)-1 5.904893E-01 1.192093E-07 15
dqag f1-1 2.500000E-01 1.490116E-08 15
dqag f2-1 2.106572E-01 2.980232E-08 15
dqag f3-1 1.905239E+00 2.384186E-07 15
dqag f4-1 5.140419E-01 5.960464E-08 15
dqag i2-1 8.435118E-01 0.000000E+00 15
dqag i3-1 2.467401E+00 0.000000E+00 45
dqag C(1)-2 5.904893E-01 1.192093E-07 21
dqag f1-2 2.500000E-01 1.490116E-08 21
dqag f2-2 2.106572E-01 1.490116E-08 21
dqag f3-2 1.905239E+00 2.384186E-07 21
dqag f4-2 5.140419E-01 5.960464E-08 21
dqag i2-2 8.435118E-01 0.000000E+00 21
dqag i3-2 2.467401E+00 2.384186E-07 21
dqag C(1)-3 5.904893E-01 1.192093E-07 31
dqag f1-3 2.500000E-01 0.000000E+00 31
dqag f2-3 2.106573E-01 0.000000E+00 31
dqag f3-3 1.905239E+00 3.576279E-07 31
dqag f4-3 5.140419E-01 5.960464E-08 31
dqag i2-3 8.435118E-01 0.000000E+00 31
dqag i3-3 2.467401E+00 2.384186E-07 31
dqag C(1)-4 5.904893E-01 1.788139E-07 41
dqag f1-4 2.500000E-01 0.000000E+00 41
dqag f2-4 2.106572E-01 1.490116E-08 41
dqag f3-4 1.905239E+00 3.576279E-07 41
dqag f4-4 5.140419E-01 5.960464E-08 41
dqag i2-4 8.435118E-01 0.000000E+00 41
dqag i3-4 2.467401E+00 2.384186E-07 41
dqag C(1)-5 5.904893E-01 1.192093E-07 51
dqag f1-5 2.500000E-01 1.490116E-08 51
dqag f2-5 2.106573E-01 0.000000E+00 51
dqag f3-5 1.905239E+00 0.000000E+00 51
dqag f4-5 5.140419E-01 5.960464E-08 51
dqag i2-5 8.435119E-01 1.192093E-07 51
dqag i3-5 2.467401E+00 2.384186E-07 51
dqng C(1)-6 5.904893E-01 1.192093E-07 21
dquad C(1)-6 5.904893E-01 1.192093E-07 7
dgauss8 C(1)-6 5.904893E-01 1.192093E-07 7
simpson C(1)-6 5.906193E-01 1.301765E-04 7
lobatto C(1)-6 5.904893E-01 1.192093E-07 7
dqng f1-6 2.500000E-01 1.490116E-08 21
dquad f1-6 2.500000E-01 0.000000E+00 7
dgauss8 f1-6 2.500000E-01 0.000000E+00 7
simpson f1-6 2.500083E-01 8.314848E-06 7
lobatto f1-6 2.500000E-01 2.980232E-08 7
dqng f2-6 2.106572E-01 1.490116E-08 21
dquad f2-6 2.106572E-01 1.490116E-08 7
dgauss8 f2-6 2.106572E-01 1.490116E-08 7
simpson f2-6 2.106856E-01 2.838671E-05 7
lobatto f2-6 2.106573E-01 0.000000E+00 7
dqng f3-6 1.905239E+00 2.384186E-07 21
dquad f3-6 1.905239E+00 2.384186E-07 7
dgauss8 f3-6 1.905239E+00 2.384186E-07 7
simpson f3-6 1.905397E+00 1.577139E-04 7
lobatto f3-6 1.905239E+00 2.384186E-07 7
dqng f4-6 5.140419E-01 5.960464E-08 21
dquad f4-6 5.140419E-01 5.960464E-08 7
dgauss8 f4-6 5.140419E-01 5.960464E-08 7
simpson f4-6 5.141450E-01 1.029968E-04 7
lobatto f4-6 5.140419E-01 5.960464E-08 7
dqng i2-6 8.435118E-01 0.000000E+00 21
dquad i2-6 8.435118E-01 0.000000E+00 7
dgauss8 i2-6 8.435119E-01 1.192093E-07 7
dqng i3-6 2.467401E+00 2.384186E-07 21
dquad i3-6 2.467405E+00 3.576279E-06 15
dgauss8 i3-6 2.467401E+00 0.000000E+00 15
simpson i3-6 2.467587E+00 1.862049E-04 15
lobatto i3-6 2.467401E+00 0.000000E+00 15
davint square 1.600000E+01 0.000000E+00 0
quadpack_tests : Double. tol = 1.4901161193847664E-007
dqag-1 1.154701E+00 2.597922E-14 465
dqag-2 1.154701E+00 1.998401E-15 483
dqag-3 1.154701E+00 0.000000E+00 465
dqag-4 1.154701E+00 1.100453E-12 287
dqag-5 1.154701E+00 1.776357E-15 357
dqagi 3.079572E+00 2.655209E-12 645
dqagp 4.253688E+00 3.223368E-10 1365
dqags 2.000000E+00 1.554312E-15 231
dqawc -6.284617E+02 1.500666E-11 425
dqawf 1.422552E+00 9.672154E-10 20220
dqawo -1.776392E-01 3.053113E-15 285
dqaws 5.350191E-01 2.220446E-16 50
dqng 1.270724E+00 0.000000E+00 21
dqag C(1)-1 5.904893E-01 4.440892E-16 15
dqag f1-1 2.500000E-01 0.000000E+00 15
dqag f2-1 2.106573E-01 0.000000E+00 15
dqag f3-1 1.905239E+00 2.220446E-16 15
dqag f4-1 5.140419E-01 0.000000E+00 15
dqag i2-1 8.435118E-01 1.110223E-16 15
dqag i3-1 2.467401E+00 4.440892E-16 105
dqag C(1)-2 5.904893E-01 5.551115E-16 21
dqag f1-2 2.500000E-01 0.000000E+00 21
dqag f2-2 2.106573E-01 2.775558E-17 21
dqag f3-2 1.905239E+00 0.000000E+00 21
dqag f4-2 5.140419E-01 0.000000E+00 21
dqag i2-2 8.435118E-01 1.110223E-16 21
dqag i3-2 2.467401E+00 0.000000E+00 63
dqag C(1)-3 5.904893E-01 5.551115E-16 31
dqag f1-3 2.500000E-01 0.000000E+00 31
dqag f2-3 2.106573E-01 2.775558E-17 31
dqag f3-3 1.905239E+00 0.000000E+00 31
dqag f4-3 5.140419E-01 0.000000E+00 31
dqag i2-3 8.435118E-01 1.110223E-16 31
dqag i3-3 2.467401E+00 0.000000E+00 93
dqag C(1)-4 5.904893E-01 6.661338E-16 41
dqag f1-4 2.500000E-01 5.551115E-17 41
dqag f2-4 2.106573E-01 2.775558E-17 41
dqag f3-4 1.905239E+00 6.661338E-16 41
dqag f4-4 5.140419E-01 0.000000E+00 41
dqag i2-4 8.435118E-01 1.110223E-16 41
dqag i3-4 2.467401E+00 0.000000E+00 41
dqag C(1)-5 5.904893E-01 5.551115E-16 51
dqag f1-5 2.500000E-01 5.551115E-17 51
dqag f2-5 2.106573E-01 5.551115E-17 51
dqag f3-5 1.905239E+00 2.220446E-16 51
dqag f4-5 5.140419E-01 0.000000E+00 51
dqag i2-5 8.435118E-01 1.110223E-16 51
dqag i3-5 2.467401E+00 4.440892E-16 51
dqng C(1)-6 5.904893E-01 5.551115E-16 21
dquad C(1)-6 5.904893E-01 5.551115E-16 15
dgauss8 C(1)-6 5.904893E-01 2.220446E-16 15
simpson C(1)-6 5.904893E-01 2.923517E-11 15
lobatto C(1)-6 5.904893E-01 1.311865E-08 15
dqng f1-6 2.500000E-01 0.000000E+00 21
dquad f1-6 2.500000E-01 0.000000E+00 15
dgauss8 f1-6 2.500000E-01 2.775558E-17 15
simpson f1-6 2.500000E-01 5.609141E-11 15
lobatto f1-6 2.500000E-01 8.951853E-10 15
dqng f2-6 2.106573E-01 2.775558E-17 21
dquad f2-6 2.106573E-01 2.775558E-17 15
dgauss8 f2-6 2.106573E-01 8.326673E-17 15
simpson f2-6 2.106573E-01 9.364062E-11 15
lobatto f2-6 2.106572E-01 6.346478E-09 15
dqng f3-6 1.905239E+00 0.000000E+00 21
dquad f3-6 1.905239E+00 2.220446E-16 15
dgauss8 f3-6 1.905239E+00 0.000000E+00 15
simpson f3-6 1.905239E+00 6.870144E-10 15
lobatto f3-6 1.905239E+00 6.133078E-10 15
dqng f4-6 5.140419E-01 0.000000E+00 21
dquad f4-6 5.140419E-01 0.000000E+00 15
dgauss8 f4-6 5.140419E-01 6.661338E-16 15
simpson f4-6 5.140419E-01 2.331491E-11 15
lobatto f4-6 5.140419E-01 1.047380E-08 15
dqng i2-6 8.435118E-01 1.110223E-16 21
dquad i2-6 8.435118E-01 1.110223E-16 15
dgauss8 i2-6 8.435118E-01 0.000000E+00 15
dqng i3-6 2.467401E+00 4.440892E-16 43
dquad i3-6 2.467401E+00 4.440892E-16 63
dgauss8 i3-6 2.467401E+00 1.966738E-11 63
simpson i3-6 2.467401E+00 1.319596E-07 63
lobatto i3-6 2.467401E+00 1.015241E-10 63
davint square 1.600000E+01 0.000000E+00 0
quadpack_tests : quad. tol = 1.5700924586837750593933823719638E-0015
1 abnormal return from dqag
dqag-1 1.154701E+00 5.227969E-17 5985
1 abnormal return from dqag
dqag-2 1.154701E+00 9.018180E-17 8379
1 abnormal return from dqag
dqag-3 1.154701E+00 1.771697E-17 12369
1 abnormal return from dqag
dqag-4 1.154701E+00 5.278726E-17 16359
1 abnormal return from dqag
dqag-5 1.154701E+00 3.806301E-18 20349
1 abnormal return from dqagi
dqagi 3.079571E+00 3.434551E-07 2985 FAILED
dqagp 1.000000E+00 3.253688E+00 63 FAILED
dqags 2.000000E+00 5.779070E-18 1323
1 abnormal return from dqawc
dqawc -6.284617E+02 1.939811E-05 6015 FAILED
7 abnormal return from dqawf
dqawf 1.422564E+00 1.201838E-05 48850 FAILED
1 abnormal return from dqawo
dqawo -1.616467E-01 1.599254E-02 3015 FAILED
1 abnormal return from dqaws
dqaws 1.184967E+00 6.499482E-01 3000 FAILED
1 abnormal return from dqng
dqng 1.270724E+00 1.830308E-18 87
1 abnormal return from dqag
dqag C(1)-1 5.904893E-01 3.888394E-21 29985
1 abnormal return from dqag
dqag f1-1 2.500000E-01 7.537140E-20 29985
1 abnormal return from dqag
dqag f2-1 2.106573E-01 6.413316E-19 29985
1 abnormal return from dqag
dqag f3-1 1.905239E+00 2.503727E-17 29985
1 abnormal return from dqag
dqag f4-1 5.140419E-01 1.308953E-18 29985
1 abnormal return from dqag
dqag i2-1 8.435118E-01 6.104299E-18 29985
1 abnormal return from dqag
dqag i3-1 2.467401E+00 1.145248E-19 29985
1 abnormal return from dqag
dqag C(1)-2 5.904893E-01 1.717091E-18 41979
1 abnormal return from dqag
dqag f1-2 2.500000E-01 3.142121E-19 41979
1 abnormal return from dqag
dqag f2-2 2.106573E-01 7.630082E-19 41979
1 abnormal return from dqag
dqag f3-2 1.905239E+00 2.146826E-17 41979
1 abnormal return from dqag
dqag f4-2 5.140419E-01 1.933207E-18 41979
1 abnormal return from dqag
dqag i2-2 8.435118E-01 5.953484E-18 41979
1 abnormal return from dqag
dqag i3-2 2.467401E+00 7.829301E-19 41979
1 abnormal return from dqag
dqag C(1)-3 5.904893E-01 5.833722E-19 61969
1 abnormal return from dqag
dqag f1-3 2.500000E-01 1.501668E-19 61969
1 abnormal return from dqag
dqag f2-3 2.106573E-01 3.572056E-19 61969
1 abnormal return from dqag
dqag f3-3 1.905239E+00 2.612518E-17 61969
1 abnormal return from dqag
dqag f4-3 5.140419E-01 3.368674E-18 61969
1 abnormal return from dqag
dqag i2-3 8.435118E-01 6.433859E-18 61969
1 abnormal return from dqag
dqag i3-3 2.467401E+00 5.731918E-19 61969
1 abnormal return from dqag
dqag C(1)-4 5.904893E-01 1.204052E-18 81959
1 abnormal return from dqag
dqag f1-4 2.500000E-01 1.637829E-20 81959
1 abnormal return from dqag
dqag f2-4 2.106573E-01 4.474537E-19 81959
1 abnormal return from dqag
dqag f3-4 1.905239E+00 2.804307E-17 81959
1 abnormal return from dqag
dqag f4-4 5.140419E-01 1.598495E-18 81959
1 abnormal return from dqag
dqag i2-4 8.435118E-01 5.283390E-18 81959
1 abnormal return from dqag
dqag i3-4 2.467401E+00 5.742480E-19 81959
1 abnormal return from dqag
dqag C(1)-5 5.904893E-01 1.242315E-18 101949
1 abnormal return from dqag
dqag f1-5 2.500000E-01 6.336580E-20 101949
1 abnormal return from dqag
dqag f2-5 2.106573E-01 4.832431E-19 101949
1 abnormal return from dqag
dqag f3-5 1.905239E+00 2.317711E-17 101949
1 abnormal return from dqag
dqag f4-5 5.140419E-01 2.357995E-18 101949
1 abnormal return from dqag
dqag i2-5 8.435118E-01 5.587286E-18 101949
1 abnormal return from dqag
dqag i3-5 2.467401E+00 7.423489E-19 101949
1 abnormal return from dqng
dqng C(1)-6 5.904893E-01 1.146231E-17 87
dquad C(1)-6 5.904893E-01 1.417488E-17 31
dgauss8 C(1)-6 5.904893E-01 1.030343E-17 31
simpson C(1)-6 5.904893E-01 3.117412E-17 31
lobatto C(1)-6 5.904893E-01 1.045952E-17 31
1 abnormal return from dqng
dqng f1-6 2.500000E-01 7.197586E-20 87
dquad f1-6 2.500000E-01 9.199595E-18 31
dgauss8 f1-6 2.500000E-01 2.412610E-18 31
simpson f1-6 2.500000E-01 1.605058E-17 31
lobatto f1-6 2.500000E-01 1.929508E-18 31
1 abnormal return from dqng
dqng f2-6 2.106573E-01 3.437434E-18 87
dquad f2-6 2.106573E-01 7.876112E-18 31
dgauss8 f2-6 2.106573E-01 6.626995E-19 31
simpson f2-6 2.106573E-01 9.742583E-18 31
lobatto f2-6 2.106573E-01 6.533981E-18 31
1 abnormal return from dqng
dqng f3-6 1.905239E+00 4.730162E-17 87
dquad f3-6 1.905239E+00 4.706427E-17 31
dgauss8 f3-6 1.905239E+00 1.929328E-16 31
simpson f3-6 1.905239E+00 1.063923E-16 31
lobatto f3-6 1.905239E+00 2.708267E-17 31
1 abnormal return from dqng
dqng f4-6 5.140419E-01 6.822315E-18 87
dquad f4-6 5.140419E-01 6.122437E-18 31
dgauss8 f4-6 5.140419E-01 1.397192E-18 31
simpson f4-6 5.140419E-01 2.591403E-17 31
lobatto f4-6 5.140419E-01 8.518830E-18 31
1 abnormal return from dqng
dqng i2-6 8.435118E-01 3.276626E-17 87
dquad i2-6 8.435118E-01 5.113956E-17 31
dgauss8 i2-6 8.435118E-01 5.129981E-17 31
1 abnormal return from dqng
dqng i3-6 2.467401E+00 6.532903E-17 87
dquad i3-6 2.467401E+00 4.128064E-17 3
dgauss8 i3-6 2.467401E+00 2.769334E-17 3
simpson i3-6 2.467401E+00 1.236958E-18 3
lobatto i3-6 2.467401E+00 8.233701E-17 3
davint square 1.600000E+01 0.000000E+00 0
Patterson method from NSCW library
See the quad routine, which looks to be a different formulation of what is being done in dqng. Add it for testing.
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