15 September 2021 8:27:06.823 AM laguerre_integrands_test FORTRAN90 version Test laguerre_integrands. TEST01 P00_PROBLEM_NUM returns the number of problems. P00_TITLE returns the title of a problem. P00_PROBLEM_NUM: number of problems is 20 Problem Title 1 "1 / ( x * log(x)^2 )" 2 "1 / ( x * log(x)^(3/2) )" 3 "1 / ( x^1.01 )" 4 "Sine integral" 5 "Fresnel integral" 6 "Complementary error function" 7 "Bessel function" 8 "Debye function" 9 "Gamma(Z=5) function" 10 "1/(1+x*x)" 11 "1 / ( (1+x) * sqrt(x) )" 12 "exp ( - x ) * cos ( x )" 13 "sin(x) / x" 14 "sin ( exp(-x) + exp(-4x) )" 15 "log(x) / ( 1 + 100 x^2 )" 16 "cos(pi x / 2 ) / sqrt(x)" 17 "exp ( - x / 2^beta ) * cos ( x ) / sqrt ( x )" 18 "x^2 * exp ( - x / 2^beta )" 19 "x^(beta-1) / ( 1 + 10 x )^2" 20 "1 / ( 2^beta * ( ( x - 1 )^2 + (1/4)^beta ) * ( x - 2 ) )" TEST02 P00_ALPHA returns the lower limit of integration. P00_EXACT returns the "exact" integral. Problem ALPHA EXACT 1 2.00000 0.1952475419827644 2 2.00000 0.3251084827899133 3 2.00000 13.62800000000000 4 2.00000 -0.4684854133508064E-02 5 2.00000 0.1589728615859233E-02 6 2.00000 0.5610371114838712E-03 7 2.00000 0.1626689100000000 8 0.00000 1.644934066848226 9 0.00000 24.00000000000000 10 0.00000 1.570796326794897 11 0.00000 3.141592653589793 12 0.00000 0.5000000000000000 13 0.00000 1.570796326794897 14 0.00000 1.063461810172240 15 0.00000 -0.3616892206207732 16 0.00000 1.000000000000000 17 0.00000 1.376043390090716 18 0.00000 16.00000000000000 19 0.00000 0.4967294132898050 20 0.00000 -2.393675868282822 TEST03 P00_GAUSS_LAGUERRE applies a Gauss-Laguerre rule to estimate an integral on [ALPHA,+oo). Exact/ Problem Order Estimate Error 1 0.195248 1 0.101600 0.936472E-01 2 0.127915 0.673326E-01 4 0.145108 0.501400E-01 8 0.155432 0.398156E-01 16 0.162236 0.330112E-01 32 0.167086 0.281618E-01 64 0.170693 0.245547E-01 2 0.325108 1 0.106492 0.218616 2 0.137350 0.187758 4 0.161013 0.164095 8 0.178329 0.146780 16 0.191424 0.133684 32 0.201636 0.123473 64 0.209815 0.115293 3 13.6280 1 0.121287 13.5067 2 0.188887 13.4391 4 0.270119 13.3579 8 0.358719 13.2693 16 0.449969 13.1780 32 0.541454 13.0865 64 0.632226 12.9958 4 -0.468485E-02 1 0.173050E-01 0.219899E-01 2 -0.426205E-01 0.379357E-01 4 -0.587194E-01 0.540345E-01 8 -0.407974E-01 0.361125E-01 16 -0.392587E-01 0.345739E-01 32 -0.239952E-03 0.444490E-02 64 -0.253828E-01 0.206979E-01 5 0.158973E-02 1 0.202735E-15 0.158973E-02 2 -0.383132 0.384722 4 -1.39924 1.40083 8 -2.05291 2.05450 16 -0.675426E-01 0.691323E-01 32 1.12513 1.12354 64 -4.59048 4.59207 6 0.561037E-03 1 0.453999E-04 0.515637E-03 2 0.258956E-03 0.302081E-03 4 0.512184E-03 0.488529E-04 8 0.563868E-03 0.283132E-05 16 0.561008E-03 0.293541E-07 32 0.561037E-03 0.210696E-11 64 0.561037E-03 0.379362E-15 7 0.162669 1 0.193130 0.304616E-01 2 0.346675E-01 0.128001 4 0.367188E-01 0.125950 8 0.395037E-01 0.123165 16 0.970831E-01 0.655858E-01 32 0.100708 0.619605E-01 64 0.107105 0.555637E-01 8 1.64493 1 1.58198 0.629574E-01 2 1.64483 0.100537E-03 4 1.64492 0.127760E-04 8 1.64493 0.947983E-07 16 1.64493 0.316740E-10 32 1.64493 0.177636E-13 64 1.64493 0.176081E-12 9 24.0000 1 1.00000 23.0000 2 20.0000 4.00000 4 24.0000 0.00000 8 24.0000 0.00000 16 24.0000 0.213163E-13 32 24.0000 0.390799E-13 64 24.0000 0.177636E-12 10 1.57080 1 1.35914 0.211655 2 1.49326 0.775394E-01 4 1.50119 0.696068E-01 8 1.53376 0.370363E-01 16 1.55374 0.170586E-01 32 1.56248 0.831362E-02 64 1.56672 0.407150E-02 11 3.14159 1 1.35914 1.78245 2 1.80904 1.33255 4 2.18472 0.956869 8 2.46506 0.676529 16 2.66527 0.476324 32 2.80639 0.335205 64 2.90552 0.236072 12 0.500000 1 0.540302 0.403023E-01 2 0.570209 0.702088E-01 4 0.502494 0.249371E-02 8 0.500001 0.120627E-05 16 0.500000 0.418814E-10 32 0.500000 0.162093E-13 64 0.500000 0.127176E-12 13 1.57080 1 2.28736 0.716559 2 1.09611 0.474688 4 1.20608 0.364713 8 1.02696 0.543832 16 1.43995 0.130844 32 1.13614 0.434661 64 1.34907 0.221727 14 1.06346 1 1.02389 0.395762E-01 2 1.07766 0.141955E-01 4 1.09741 0.339522E-01 8 1.07181 0.834701E-02 16 1.06347 0.953238E-05 32 1.06345 0.914272E-05 64 1.06346 0.121845E-07 15 -0.361689 1 0.00000 0.361689 2 -0.185358E-01 0.343153 4 -0.745814E-01 0.287108 8 -0.192106 0.169584 16 -0.318721 0.429683E-01 32 -0.353294 0.839552E-02 64 -0.351930 0.975936E-02 16 1.00000 1 0.166447E-15 1.00000 2 2.67249 1.67249 4 -0.242586 1.24259 8 1.76499 0.764991 16 2.82550 1.82550 32 4.56271 3.56271 64 -2.86491 3.86491 17 1.37604 1 1.14382 0.232223 2 0.453928 0.922116 4 0.810611 0.565433 8 1.06598 0.310066 16 1.16154 0.214505 32 1.22319 0.152856 64 1.26758 0.108461 18 16.0000 1 1.64872 14.3513 2 9.80382 6.19618 4 15.6359 0.364054 8 15.9997 0.289382E-03 16 16.0000 0.365485E-10 32 16.0000 0.142109E-13 64 16.0000 0.147438E-12 19 0.496729 1 0.224651E-01 0.474264 2 0.445483E-01 0.452181 4 0.876999E-01 0.409029 8 0.159062 0.337668 16 0.248273 0.248456 32 0.328154 0.168576 64 0.383161 0.113569 20 -2.39368 1 -5.43656 3.04289 2 -1.02704 1.36664 4 -5.28423 2.89056 8 -0.537746E-01 2.33990 16 0.850874 3.24455 32 -2.95414 0.560466 64 -2.49357 0.998919E-01 TEST04 P00_EXP_TRANSFORM applies an exponential transform to estimate an integral on [ALPHA,+oo) as a transformed integral on (0,exp(-ALPHA)], and applying a Gauss-Legendre rule. Exact/ Problem Order Estimate Error 1 0.195248 1 0.102397 0.928505E-01 2 0.115146 0.801017E-01 4 0.122829 0.724187E-01 8 0.128835 0.664122E-01 16 0.133495 0.617524E-01 32 0.137146 0.581017E-01 64 0.140064 0.551833E-01 2 0.325108 1 0.101920 0.223188 2 0.116144 0.208964 4 0.126716 0.198393 8 0.135293 0.189816 16 0.142154 0.182954 32 0.147686 0.177423 64 0.152222 0.172886 3 13.6280 1 0.995127E-01 13.5285 2 0.126993 13.5010 4 0.153374 13.4746 8 0.177288 13.4507 16 0.198463 13.4295 32 0.217138 13.4109 64 0.233692 13.3943 4 -0.468485E-02 1 0.435748E-01 0.482597E-01 2 -0.600007E-02 0.131522E-02 4 -0.419134E-01 0.372285E-01 8 -0.259274E-01 0.212425E-01 16 0.117997E-01 0.164846E-01 32 0.174096E-01 0.220945E-01 64 -0.911287E-02 0.442802E-02 5 0.158973E-02 1 0.104775 0.103185 2 0.173538 0.171948 4 -0.473965 0.475555 8 0.110092E-01 0.941949E-02 16 0.216734 0.215144 32 -0.144816 0.146406 64 0.184938 0.183348 6 0.561037E-03 1 0.191639E-03 0.369398E-03 2 0.575718E-03 0.146805E-04 4 0.561177E-03 0.139594E-06 8 0.561037E-03 0.164560E-10 16 0.561037E-03 0.181062E-15 32 0.561037E-03 0.433681E-18 64 0.561037E-03 0.216840E-18 7 0.162669 1 0.196625 0.339564E-01 2 0.186723 0.240540E-01 4 0.137365 0.253035E-01 8 0.115478 0.471910E-01 16 0.146863 0.158063E-01 32 0.183056 0.203868E-01 64 0.178131 0.154619E-01 8 1.64493 1 1.38629 0.258640 2 1.54712 0.978139E-01 4 1.61408 0.308561E-01 8 1.63622 0.871295E-02 16 1.64262 0.231729E-02 32 1.64434 0.597636E-03 64 1.64478 0.151758E-03 9 24.0000 1 0.230835 23.7692 2 2.92019 21.0798 4 9.30591 14.6941 8 15.7830 8.21704 16 20.0896 3.91037 32 22.3400 1.66002 64 23.3506 0.649369 10 1.57080 1 1.35094 0.219858 2 1.29277 0.278022 4 1.35731 0.213491 8 1.39914 0.171655 16 1.42930 0.141492 32 1.45127 0.119524 64 1.46768 0.103120 11 3.14159 1 1.41880 1.72279 2 1.79448 1.34711 4 2.06235 1.07924 8 2.24277 0.898827 16 2.36290 0.778689 32 2.44506 0.696537 64 2.50394 0.637657 12 0.500000 1 0.769239 0.269239 2 0.494195 0.580528E-02 4 0.464401 0.355990E-01 8 0.494232 0.576837E-02 16 0.501907 0.190658E-02 32 0.500620 0.619801E-03 64 0.499939 0.605169E-04 13 1.57080 1 1.84365 0.272856 2 2.15002 0.579222 4 1.88708 0.316285 8 1.41836 0.152440 16 1.30452 0.266278 32 1.56761 0.318175E-02 64 1.75694 0.186140 14 1.06346 1 1.06661 0.314354E-02 2 1.08600 0.225388E-01 4 1.06333 0.131201E-03 8 1.06346 0.169167E-08 16 1.06346 0.222045E-15 32 1.06346 0.444089E-15 64 1.06346 0.222045E-15 15 -0.361689 1 -0.149459E-01 0.346743 2 -0.133081 0.228608 4 -0.345925 0.157643E-01 8 -0.357263 0.442669E-02 16 -0.363602 0.191283E-02 32 -0.364854 0.316517E-02 64 -0.364930 0.324060E-02 16 1.00000 1 1.11357 0.113573 2 -0.239747 1.23975 4 0.389418 0.610582 8 1.73613 0.736133 16 0.623858 0.376142 32 0.613312 0.386688 64 1.59929 0.599290 17 1.37604 1 1.55389 0.177849 2 1.21294 0.163102 4 0.939947 0.436096 8 1.07844 0.297607 16 1.35380 0.222480E-01 32 1.44072 0.646723E-01 64 1.37484 0.120703E-02 18 16.0000 1 0.679463 15.3205 2 2.65956 13.3404 4 5.45890 10.5411 8 8.31384 7.68616 16 10.7285 5.27147 32 12.5458 3.45421 64 13.8127 2.18726 19 0.496729 1 0.381865E-01 0.458543 2 0.121232 0.375497 4 0.274752 0.221977 8 0.389742 0.106988 16 0.443148 0.535816E-01 32 0.469610 0.271197E-01 64 0.483005 0.137240E-01 20 -2.39368 1 -2.22338 0.170291 2 -4.97953 2.58585 4 -1.79100 0.602681 8 -1.35869 1.03498 16 -0.704593 1.68908 32 6.81347 9.20714 64 -3.40821 1.01454 TEST05 P00_RAT_TRANSFORM applies a rational transform to estimate an integral on [ALPHA,+oo) as a transformed integral on (0,1/(1+ALPHA)], and applying a Gauss-Legendre rule. Exact/ Problem Order Estimate Error 1 0.195248 1 0.125393 0.698544E-01 2 0.161260 0.339874E-01 4 0.171148 0.240999E-01 8 0.175379 0.198685E-01 16 0.178502 0.167453E-01 32 0.180849 0.143983E-01 64 0.182650 0.125978E-01 2 0.325108 1 0.159078 0.166030 2 0.194318 0.130791 4 0.209901 0.115207 8 0.220796 0.104313 16 0.229533 0.955756E-01 32 0.236585 0.885234E-01 64 0.242364 0.827449E-01 3 13.6280 1 0.319619 13.3084 2 0.450904 13.1771 4 0.601571 13.0264 8 0.763468 12.8645 16 0.930418 12.6976 32 1.09885 12.5292 64 1.26686 12.3611 4 -0.468485E-02 1 -0.311463 0.306778 2 0.241453 0.246138 4 -0.192659 0.187974 8 -0.339783 0.335098 16 -0.146902 0.142217 32 -0.115974 0.111289 64 -0.237789 0.233104 5 0.158973E-02 1 -0.234775E-13 0.158973E-02 2 -4.11997 4.12156 4 -10.8893 10.8908 8 41.5222 41.5206 16 202.350 202.349 32 -603.212 603.213 64 -2630.29 2630.30 6 0.561037E-03 1 0.225543E-10 0.561037E-03 2 0.125740E-03 0.435297E-03 4 0.581908E-03 0.208712E-04 8 0.561006E-03 0.315466E-07 16 0.561037E-03 0.246977E-11 32 0.561037E-03 0.325261E-18 64 0.561037E-03 0.433681E-18 7 0.162669 1 -0.317343 0.480012 2 0.762029E-01 0.864660E-01 4 0.186351 0.236826E-01 8 -0.223540 0.386209 16 -0.343201 0.505870 32 -0.117109 0.279778 64 -0.237837 0.400506 8 1.64493 1 2.32791 0.682973 2 1.72598 0.810422E-01 4 1.67512 0.301885E-01 8 1.64399 0.947990E-03 16 1.64493 0.174589E-05 32 1.64493 0.609277E-08 64 1.64493 0.222045E-13 9 24.0000 1 1.47152 22.5285 2 52.0087 28.0087 4 8.46450 15.5355 8 22.6791 1.32091 16 24.0287 0.286696E-01 32 24.0000 0.120629E-04 64 24.0000 0.380236E-09 10 1.57080 1 2.00000 0.429204 2 1.50000 0.707963E-01 4 1.56863 0.216888E-02 8 1.57079 0.191425E-05 16 1.57080 0.145262E-11 32 1.57080 0.444089E-15 64 1.57080 0.133227E-14 11 3.14159 1 2.00000 1.14159 2 2.44949 0.692103 4 2.75540 0.386188 8 2.93684 0.204751 16 3.03607 0.105522 32 3.08801 0.535788E-01 64 3.11459 0.269979E-01 12 0.500000 1 0.795064 0.295064 2 0.370271 0.129729 4 0.402708 0.972924E-01 8 0.480352 0.196480E-01 16 0.498803 0.119723E-02 32 0.499991 0.885320E-05 64 0.500000 0.238633E-08 13 1.57080 1 3.36588 1.79509 2 -0.875962 2.44676 4 4.21763 2.64684 8 0.252453 1.31834 16 0.204644 1.36615 32 2.33642 0.765622 64 -1.30872 2.87951 14 1.06346 1 1.50667 0.443204 2 0.987107 0.763550E-01 4 1.08821 0.247513E-01 8 1.06425 0.785980E-03 16 1.06346 0.438520E-05 32 1.06346 0.550759E-09 64 1.06346 0.00000 15 -0.361689 1 0.00000 0.361689 2 -0.118844 0.242846 4 -0.344891 0.167980E-01 8 -0.352298 0.939102E-02 16 -0.359399 0.229021E-02 32 -0.361098 0.591410E-03 64 -0.361539 0.150225E-03 16 1.00000 1 0.244929E-15 1.00000 2 6.70713 5.70713 4 -6.45361 7.45361 8 -7.56856 8.56856 16 31.3685 30.3685 32 -79.7133 80.7133 64 -1.62490 2.62490 17 1.37604 1 1.68315 0.307108 2 -0.493307 1.86935 4 1.19672 0.179324 8 0.646258 0.729786 16 1.37496 0.108488E-02 32 1.39595 0.199039E-01 64 1.35831 0.177285E-01 18 16.0000 1 2.42612 13.5739 2 24.1806 8.18059 4 12.5776 3.42238 8 17.2060 1.20602 16 16.0042 0.415399E-02 32 16.0001 0.703207E-04 64 16.0000 0.946375E-09 19 0.496729 1 0.330579E-01 0.463672 2 0.118649 0.378081 4 0.275815 0.220915 8 0.390405 0.106325 16 0.443513 0.532160E-01 32 0.469882 0.268470E-01 64 0.483223 0.135062E-01 20 -2.39368 1 -8.00000 5.60632 2 0.123711 2.51739 4 37.2697 39.6634 8 -2.67768 0.284002 16 -3.37891 0.985234 32 -27.2455 24.8518 64 -2.46434 0.706601E-01 laguerre_integrands_test Normal end of execution. 15 September 2021 8:27:06.831 AM