Wed Mar 18 09:40:26 2026

filon_rule_test():
  numpy version:  1.26.4
  python version: 3.10.12
  Test filon_rule():

filon_test01
  FILON_TAB_COS estimates the integral of.
  F(X) * COS ( T * X )
  Use integrands F(X)=1, X, X**2.

  A =  0.0
  B =  6.283185307179586
  N =  11

       T        Approximate             Exact

           1    -1.905476522093207e-16    -2.449293598294706e-16
           1    -1.322518650155724e-15    -1.554312234475219e-15
           1         12.56637061435916         12.56637061435916

           2    -2.590075573475023e-16    -2.449293598294706e-16
           2    -1.465504961912174e-15     -1.52655665885959e-15
           2         3.141592653589786         3.141592653589784

          10    -2.790294798406905e-16    -2.449293598294706e-16
          10    -1.534662139123798e-15    -1.538769112130467e-15
          10        0.1256637061435835         0.125663706143582

filon_test02():
  Integrate F(X) = log(1+X)*cos(T*X):
  Supply integrand as a table.
  T = 10, and N increases

       N    Approximate             Exact                   Error

      21   -0.008478417820979797   -0.008446594405000001  -3.1823e-05
      41   -0.008478417820986177   -0.008446594405000001  -3.1823e-05
      81   -0.008448264693958464   -0.008446594405000001  -1.6703e-06
     161   -0.008446693873057905   -0.008446594405000001  -9.9468e-08
     321   -0.008446600545718301   -0.008446594405000001  -6.1407e-09
     641   -0.008446594787480999   -0.008446594405000001  -3.8248e-10

filon_test03():
  Integrate F(X)=log(1+X)*cos(T*X):
  Supply integrand as a function.
  T = 10, and N increases

       N    Approximate             Exact                   Error

      21   -0.008478417820979797   -0.008446594405000001  -3.1823e-05
      41   -0.008478417820986177   -0.008446594405000001  -3.1823e-05
      81   -0.008448264693958464   -0.008446594405000001  -1.6703e-06
     161   -0.008446693873057905   -0.008446594405000001  -9.9468e-08
     321   -0.008446600545718301   -0.008446594405000001  -6.1407e-09
     641   -0.008446594787480999   -0.008446594405000001  -3.8248e-10

filon_test04
  FILON_TAB_SIN estimates the integral of.
  F(X) * SIN ( T * X )
  Use integrands 1, X, X**2.

  A =  0.0
  B =  6.283185307179586
  N =  11

           T        Approximate             Exact


           1     8.425908742155465e-17                         0
           1        -6.283185307179585        -6.283185307179586
           1        -39.47841760435743        -39.47841760435743

           2    -3.509817438266788e-17                         0
           2        -3.141592653589794        -3.141592653589793
           2        -19.73920880217872        -19.73920880217872

          10     6.195699061366312e-32                         0
          10       -0.6283185307179586       -0.6283185307179586
          10        -3.947841760435743        -3.947841760435744

filon_test05():
  Integrate F(X)=log(1+X)*sin(T*X):
  Supply integrand as a table.
  T = 10, and N increases

       N    Approximate             Exact                   Error

      21     -0.1985568308709911       -0.19762680771872  -9.3002e-04
      41     -0.1976282136646625       -0.19762680771872  -1.4059e-06
      81     -0.1976265585745947       -0.19762680771872  2.4914e-07
     161     -0.1976267885345484       -0.19762680771872  1.9184e-08
     321     -0.1976268064687507       -0.19762680771872  1.2500e-09
     641     -0.1976268076398179       -0.19762680771872  7.8902e-11

filon_test06():
  Integrate F(X)=log(1+X)*sin(T*X):
  Supply integrand as a function.
  T = 10, and N increases

       N    Approximate             Exact                   Error

      21     -0.1985568308709911       -0.19762680771872  -9.3002e-04
      41     -0.1976282136646625       -0.19762680771872  -1.4059e-06
      81     -0.1976265585745947       -0.19762680771872  2.4914e-07
     161     -0.1976267885345484       -0.19762680771872  1.9184e-08
     321     -0.1976268064687507       -0.19762680771872  1.2500e-09
     641     -0.1976268076398179       -0.19762680771872  7.8902e-11

filon_rule_test():
  Normal end of execution.
Wed Mar 18 09:40:26 2026