26 March 2023 10:11:43.063 AM intlib_test(): FORTRAN90 version Test INTLIB(). TEST1D Test 1D quadrature codes for integral of F(X) on [A,B]. A = 0.000000000000000 B = 1.000000000000000 F(X)=1 PLINT 1.000000000000000 AVINT 1.000000000000000 CUBINT 1.000000000000000 WEDINT 1.000000000000000 CSPINT 1.000000000000000 GAUS8 1.000000000000000 QNC79 1.000000000000000 QUAD 1.000000000000000 RMINSP 1.000000000000000 RMINSP 1.000000008144895 IRATEX 1.000000000000000 CADRE 1.000000000000000 CHINSP 1.000000000000000 SIMP 1.000000000000000 HIORDQ 1.000000000000000 SIMPSN 1.000000000000000 SIMPNE 0.9999999999999994 MONTE 1.000000000000000 F(X)=X PLINT 0.5000000000000000 AVINT 0.4999999999999981 CUBINT 0.5000000000000000 WEDINT 0.5000000000000000 CSPINT 0.5000000000000000 GAUS8 0.5000000000000000 QNC79 0.5000000000000000 QUAD 0.5000000000000000 RMINSP 0.5000000000000000 RMINSP 0.5000000040724475 IRATEX 0.5000000000000000 CADRE 0.5000000000000000 CHINSP 0.5000000000000000 SIMP 0.4999999999999999 HIORDQ 0.5000000000000000 SIMPSN 0.5000000000000000 SIMPNE 0.4999999999999994 MONTE 0.5131066699439216 F(X)=X*2 PLINT 0.3350000000000000 AVINT 0.3333333333333307 CUBINT 0.3333333333333333 WEDINT 0.3333333333333333 CSPINT 0.3333075499629904 GAUS8 0.3333333333333334 QNC79 0.3333333333333333 QUAD 0.3333333333333333 RMINSP 0.3333333333333333 RMINSP 0.3333334314792369 IRATEX 0.3333333333333333 CADRE 0.3333333333333333 CHINSP 0.3333333333333333 SIMP 0.3333333333333333 HIORDQ 0.3333333333333333 SIMPSN 0.3333333333333333 SIMPNE 0.3333333333333328 MONTE 0.3221254018948529 F(X)=X*3 PLINT 0.2525000000000000 AVINT 0.2499999999999967 CUBINT 0.2500000000000000 WEDINT 0.2500000000000000 CSPINT 0.2499613249444856 GAUS8 0.2500000000000000 QNC79 0.2500000000000000 QUAD 0.2500000000000000 RMINSP 0.2500000000000000 RMINSP 0.2500001456953123 IRATEX 0.2500000000000000 CADRE 0.2500000000000000 CHINSP 0.2500000000000000 SIMP 0.2499999999999999 HIORDQ 0.2500000000000001 SIMPSN 0.2500000000000001 SIMPNE 0.2499999999999994 MONTE 0.2593311938732388 F(X)=EXP(X) PLINT 1.719713491389315 AVINT 1.718285603659730 CUBINT 1.718280689969431 WEDINT 1.718281829142442 CSPINT 1.718256414829643 GAUS8 1.718281828459045 QNC79 1.718281828459062 QUAD 1.718281828794530 RMINSP 1.718282687924757 RMINSP 1.718289053009826 IRATEX 1.718281828748127 CADRE 1.718281842218440 CHINSP 1.718281485923365 SIMP 1.718281919360811 HIORDQ 1.718281828596558 SIMPSN 1.718282781924824 SIMPNE 1.718282781924822 MONTE 1.716552697962859 F(X)=SQRT(X) PLINT 0.6605093417068174 AVINT 0.6635010228308571 CUBINT 0.6641434954006141 WEDINT 0.6650535616890338 CSPINT 0.6604963313545729 GAUS8 0.6667263865838025 QNC79 0.6665983750085234 QUAD 0.6662876990338410 RMINSP 0.6665327411998945 RMINSP 0.6666674396445580 IRATEX 1.446000892918399 CADRE 0.6666667581306702 CHINSP 0.6666397894393591 SIMP 0.6656036087477379 HIORDQ 0.6643813438980771 SIMPSN 0.6640995897574211 SIMPNE 0.6640995897574204 MONTE 0.6752001201977343 F(X)=1/(1+X*X) PLINT 0.7849814972267898 AVINT 0.7853941898596490 CUBINT 0.7854043733938071 WEDINT 0.7853981693615854 CSPINT 0.7854072690402837 GAUS8 0.7853981633974492 QNC79 0.7853981633976420 QUAD 0.7853964459404684 RMINSP 0.7853981256146767 RMINSP 0.7853983319700113 IRATEX 0.7854051174482681 CADRE 0.7853985235314721 CHINSP 0.7853981625692409 SIMP 0.7853981631057922 HIORDQ 0.7853974673628619 SIMPSN 0.7853981534848038 SIMPNE 0.7853981534848036 MONTE 0.7925374982569892 TEST27 FILON_COS estimates the integral of. F(X) * COS ( T * X ) Integrate F(X)*COS(T*X): with F(X)=1, X, X**2. A = 0.000000000000000 B = 6.283185307179586 NTAB = 11 H = 0.6283185307179586 T Approximate Exact 1.000000000000000 -0.1905476522093207E-15 -0.2449293598294706E-15 1.000000000000000 -0.1322518650155724E-14 -0.1554312234475219E-14 1.000000000000000 12.56637061435916 12.56637061435916 2.000000000000000 -0.2590075573475023E-15 -0.2449293598294706E-15 2.000000000000000 -0.1465504961912174E-14 -0.1526556658859590E-14 2.000000000000000 3.141592653589786 3.141592653589784 10.00000000000000 -0.2790294798406905E-15 -0.2449293598294706E-15 10.00000000000000 -0.1534662139123798E-14 -0.1538769112130467E-14 10.00000000000000 0.1256637061435835 0.1256637061435820 Integrate log(1+X)*cos(T*X): T = 10, and NTAB increases NTAB H Approximate Exact Error 21 0.3142 -0.8478417820979797E-02 -0.8446594405000001E-02 -0.31823416E-04 41 0.1571 -0.8478417820986149E-02 -0.8446594405000001E-02 -0.31823416E-04 81 0.0785 -0.8448264693952125E-02 -0.8446594405000001E-02 -0.16702890E-05 161 0.0393 -0.8446693873063937E-02 -0.8446594405000001E-02 -0.99468064E-07 321 0.0196 -0.8446600545717286E-02 -0.8446594405000001E-02 -0.61407173E-08 641 0.0098 -0.8446594787479611E-02 -0.8446594405000001E-02 -0.38247961E-09 TEST28 FILON_SIN estimates the integral of. F(X) * SIN ( T * X ) A = 0.000000000000000 B = 6.283185307179586 NTAB = 11 H = 0.6283185307179586 Integrate F(X)*SIN(T*X) with F(X)=1, X, X**2. T Approximate Exact 1.000000000000000 0.8425908742155465E-16 0.000000000000000 1.000000000000000 -6.283185307179585 -6.283185307179586 1.000000000000000 -39.47841760435743 -39.47841760435743 2.000000000000000 -0.3509817438266788E-16 0.000000000000000 2.000000000000000 -3.141592653589794 -3.141592653589793 2.000000000000000 -19.73920880217872 -19.73920880217872 10.00000000000000 0.6195699061366312E-31 0.000000000000000 10.00000000000000 -0.6283185307179586 -0.6283185307179586 10.00000000000000 -3.947841760435743 -3.947841760435744 Integrate log(1+X)*sin(T*X): T = 10, and NTAB increases NTAB H Approximate Exact Error 21 0.3142 -0.1985568308709911 -0.1976268077187200 -0.93002315E-03 41 0.1571 -0.1976282136646625 -0.1976268077187200 -0.14059459E-05 81 0.0785 -0.1976265585745937 -0.1976268077187200 0.24914413E-06 161 0.0393 -0.1976267885345487 -0.1976268077187200 0.19184171E-07 321 0.0196 -0.1976268064687506 -0.1976268077187200 0.12499694E-08 641 0.0098 -0.1976268076398181 -0.1976268077187200 0.78901857E-10 TEST29 Compare PLINT and AVINT on badly scaled data. The Y values are all POSITIVE, so we expect every partial integral to be positive as well. B PLINT AVINT 216.583 0.151840 0.147341 730.615 0.383411 0.358760 1638.55 0.638995 0.599415 5870.48 1.35419 1.18517 16380.7 2.24388 1.92731 52411.8 3.66351 2.94414 117519. 4.76382 3.85544 255870. 5.93496 4.87188 705121. 7.70501 6.17503 0.152517E+07 9.09090 7.31959 0.333982E+07 10.6270 8.64091 0.976600E+07 13.1589 10.4258 0.230000E+08 15.3955 12.2015 0.584000E+08 18.3921 14.6653 0.521000E+09 35.6008 6.06565 0.778000E+09 39.3787 9.72465 0.102000E+10 41.4272 11.7415 0.128000E+10 42.4516 12.7145 0.144000E+10 42.7220 12.9767 0.158000E+10 42.8405 13.0914 0.175000E+10 42.9075 13.1542 0.187000E+10 42.9278 13.1737 0.198000E+10 42.9371 13.1826 intlib_test(): Normal end of execution. 26 March 2023 10:11:43.064 AM