16 January 2017 02:55:48 PM

FILON_PRB
  C version
  Test the FILON library.

TEST01
  FILON_TAB_COS estimates the integral of.
  F(X) * COS ( T * X )
  Use integrands F(X)=1, X, X^2.

  A = 0
  B = 6.28319
  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         3.141592653589785         3.141592653589784

                        10    -2.790294798406905e-16    -2.449293598294706e-16
                        10    -1.534662139123798e-15    -1.538769112130467e-15
                        10        0.1256637061435835        0.1256637061435821

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    -3.1823416e-05
      41     -0.008478417820986149     -0.008446594405000001    -3.1823416e-05
      81     -0.008448264693952125     -0.008446594405000001     -1.670289e-06
     161     -0.008446693873063937     -0.008446594405000001    -9.9468064e-08
     321     -0.008446600545717222     -0.008446594405000001    -6.1407172e-09
     641     -0.008446594787479611     -0.008446594405000001    -3.8247961e-10

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    -3.1823416e-05
      41     -0.008478417820986149     -0.008446594405000001    -3.1823416e-05
      81     -0.008448264693952125     -0.008446594405000001     -1.670289e-06
     161     -0.008446693873063937     -0.008446594405000001    -9.9468064e-08
     321     -0.008446600545717222     -0.008446594405000001    -6.1407172e-09
     641     -0.008446594787479611     -0.008446594405000001    -3.8247961e-10

TEST04
  FILON_TAB_SIN estimates the integral of.
  F(X) * SIN ( T * X )
  Use integrands 1, X, X^2.

  A = 0
  B = 6.28319
  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        -3.947841760435743

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    -0.00093002315
      41       -0.1976282136646625         -0.19762680771872    -1.4059459e-06
      81       -0.1976265585745937         -0.19762680771872     2.4914413e-07
     161       -0.1976267885345487         -0.19762680771872     1.9184171e-08
     321       -0.1976268064687492         -0.19762680771872     1.2499708e-09
     641       -0.1976268076398181         -0.19762680771872     7.8901885e-11

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    -0.00093002315
      41       -0.1976282136646625         -0.19762680771872    -1.4059459e-06
      81       -0.1976265585745937         -0.19762680771872     2.4914413e-07
     161       -0.1976267885345487         -0.19762680771872     1.9184171e-08
     321       -0.1976268064687492         -0.19762680771872     1.2499708e-09
     641       -0.1976268076398181         -0.19762680771872     7.8901885e-11

FILON_PRB
  Normal end of execution.

16 January 2017 02:55:48 PM