July 29 2007 4:37:50.452 PM TEST_INT_LAGUERRE_PRB FORTRAN90 version Test the routines in the TEST_INT_LAGUERRE tests. TEST01 P00_PROBLEM_NUM returns the number of problems. P00_TITLE returns the title of a problem. P00_PROBLEM_NUM: number of problems is 14 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) )" TEST02 P00_ALPHA returns the lower limit of integration. P00_EXACT returns the "exact" integral. Problem ALPHA EXACT 1 2.00000 .1952475419827644 2 2.00000 .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 .1626689100000000 8 2.00000 0.5833485249773468E-01 9 .000000 24.00000000000000 10 .000000 1.570796326794897 11 .000000 3.141592653589793 12 .000000 .5000000000000000 13 .000000 1.570796326794897 14 .000000 1.063461810172240 TEST03 P00_GAUSS_LAGUERRE applies a Gauss-Laguerre rule to estimate an integral on [ALPHA,+Infinity). Problem Order Estimate Exact Error 1 1 .101600 .195248 0.936472E-01 1 2 .127915 .195248 0.673326E-01 1 4 .145108 .195248 0.501400E-01 1 8 .155432 .195248 0.398156E-01 1 16 .162236 .195248 0.330112E-01 1 32 .167086 .195248 0.281618E-01 1 64 .170693 .195248 0.245547E-01 2 1 .106492 .325108 .218616 2 2 .137350 .325108 .187758 2 4 .161013 .325108 .164095 2 8 .178329 .325108 .146780 2 16 .191424 .325108 .133684 2 32 .201636 .325108 .123473 2 64 .209815 .325108 .115293 3 1 .121287 13.6280 13.5067 3 2 .188887 13.6280 13.4391 3 4 .270119 13.6280 13.3579 3 8 .358719 13.6280 13.2693 3 16 .449969 13.6280 13.1780 3 32 .541454 13.6280 13.0865 3 64 .632226 13.6280 12.9958 4 1 0.173050E-01 -0.468485E-02 0.219899E-01 4 2 -0.426205E-01 -0.468485E-02 0.379357E-01 4 4 -0.587194E-01 -0.468485E-02 0.540345E-01 4 8 -0.407974E-01 -0.468485E-02 0.361125E-01 4 16 -0.392587E-01 -0.468485E-02 0.345739E-01 4 32 -0.239952E-03 -0.468485E-02 0.444490E-02 4 64 -0.253828E-01 -0.468485E-02 0.206979E-01 5 1 0.202735E-15 0.158973E-02 0.158973E-02 5 2 -.383132 0.158973E-02 .384722 5 4 -1.39924 0.158973E-02 1.40083 5 8 -2.05291 0.158973E-02 2.05450 5 16 -0.675426E-01 0.158973E-02 0.691323E-01 5 32 1.12513 0.158973E-02 1.12354 5 64 -4.59048 0.158973E-02 4.59207 6 1 0.453999E-04 0.561037E-03 0.515637E-03 6 2 0.258956E-03 0.561037E-03 0.302081E-03 6 4 0.512184E-03 0.561037E-03 0.488529E-04 6 8 0.563868E-03 0.561037E-03 0.283132E-05 6 16 0.561008E-03 0.561037E-03 0.293541E-07 6 32 0.561037E-03 0.561037E-03 0.210696E-11 6 64 0.561037E-03 0.561037E-03 0.379362E-15 7 1 .193130 .162669 0.304616E-01 7 2 0.346675E-01 .162669 .128001 7 4 0.367188E-01 .162669 .125950 7 8 0.395037E-01 .162669 .123165 7 16 0.970831E-01 .162669 0.655858E-01 7 32 .100708 .162669 0.619605E-01 7 64 .107105 .162669 0.555637E-01 8 1 0.578259E-01 0.583349E-01 0.508954E-03 8 2 0.583055E-01 0.583349E-01 0.293945E-04 8 4 0.583352E-01 0.583349E-01 0.330047E-06 8 8 0.583349E-01 0.583349E-01 0.116389E-09 8 16 0.583349E-01 0.583349E-01 0.412170E-14 8 32 0.583349E-01 0.583349E-01 0.756339E-15 8 64 0.583349E-01 0.583349E-01 0.700134E-14 9 1 1.00000 24.0000 23.0000 9 2 20.0000 24.0000 4.00000 9 4 24.0000 24.0000 .000000 9 8 24.0000 24.0000 .000000 9 16 24.0000 24.0000 0.213163E-13 9 32 24.0000 24.0000 0.390799E-13 9 64 24.0000 24.0000 0.177636E-12 10 1 1.35914 1.57080 .211655 10 2 1.49326 1.57080 0.775394E-01 10 4 1.50119 1.57080 0.696068E-01 10 8 1.53376 1.57080 0.370363E-01 10 16 1.55374 1.57080 0.170586E-01 10 32 1.56248 1.57080 0.831362E-02 10 64 1.56672 1.57080 0.407150E-02 11 1 1.35914 3.14159 1.78245 11 2 1.80904 3.14159 1.33255 11 4 2.18472 3.14159 .956869 11 8 2.46506 3.14159 .676529 11 16 2.66527 3.14159 .476324 11 32 2.80639 3.14159 .335205 11 64 2.90552 3.14159 .236072 12 1 .540302 .500000 0.403023E-01 12 2 .570209 .500000 0.702088E-01 12 4 .502494 .500000 0.249371E-02 12 8 .500001 .500000 0.120627E-05 12 16 .500000 .500000 0.418814E-10 12 32 .500000 .500000 0.162093E-13 12 64 .500000 .500000 0.127176E-12 13 1 2.28736 1.57080 .716559 13 2 1.09611 1.57080 .474688 13 4 1.20608 1.57080 .364713 13 8 1.02696 1.57080 .543832 13 16 1.43995 1.57080 .130844 13 32 1.13614 1.57080 .434661 13 64 1.34907 1.57080 .221727 14 1 1.02389 1.06346 0.395762E-01 14 2 1.07766 1.06346 0.141955E-01 14 4 1.09741 1.06346 0.339522E-01 14 8 1.07181 1.06346 0.834701E-02 14 16 1.06347 1.06346 0.953238E-05 14 32 1.06345 1.06346 0.914272E-05 14 64 1.06346 1.06346 0.121845E-07 TEST04 P00_EXP_TRANSFORM applies an exponential transform to estimate an integral on [ALPHA,+Infinity) as a transformed integral on (0,exp(-ALPHA)], and applying a Gauss-Legendre rule. Problem Order Estimate Exact Error 1 1 .102397 .195248 0.928505E-01 1 2 .115146 .195248 0.801017E-01 1 4 .122829 .195248 0.724187E-01 1 8 .128835 .195248 0.664122E-01 1 16 .133495 .195248 0.617524E-01 1 32 .137146 .195248 0.581017E-01 1 64 .140064 .195248 0.551833E-01 2 1 .101920 .325108 .223188 2 2 .116144 .325108 .208964 2 4 .126716 .325108 .198393 2 8 .135293 .325108 .189816 2 16 .142154 .325108 .182954 2 32 .147686 .325108 .177423 2 64 .152222 .325108 .172886 3 1 0.995127E-01 13.6280 13.5285 3 2 .126993 13.6280 13.5010 3 4 .153374 13.6280 13.4746 3 8 .177288 13.6280 13.4507 3 16 .198463 13.6280 13.4295 3 32 .217138 13.6280 13.4109 3 64 .233692 13.6280 13.3943 4 1 0.435748E-01 -0.468485E-02 0.482597E-01 4 2 -0.600007E-02 -0.468485E-02 0.131522E-02 4 4 -0.419134E-01 -0.468485E-02 0.372285E-01 4 8 -0.259274E-01 -0.468485E-02 0.212425E-01 4 16 0.117997E-01 -0.468485E-02 0.164846E-01 4 32 0.174096E-01 -0.468485E-02 0.220945E-01 4 64 -0.911287E-02 -0.468485E-02 0.442802E-02 5 1 .104775 0.158973E-02 .103185 5 2 .173538 0.158973E-02 .171948 5 4 -.473965 0.158973E-02 .475555 5 8 0.110092E-01 0.158973E-02 0.941949E-02 5 16 .216734 0.158973E-02 .215144 5 32 -.144816 0.158973E-02 .146406 5 64 .184938 0.158973E-02 .183348 6 1 0.191639E-03 0.561037E-03 0.369398E-03 6 2 0.575718E-03 0.561037E-03 0.146805E-04 6 4 0.561177E-03 0.561037E-03 0.139594E-06 6 8 0.561037E-03 0.561037E-03 0.164560E-10 6 16 0.561037E-03 0.561037E-03 0.181062E-15 6 32 0.561037E-03 0.561037E-03 0.433681E-18 6 64 0.561037E-03 0.561037E-03 0.216840E-18 7 1 .196625 .162669 0.339564E-01 7 2 .186723 .162669 0.240540E-01 7 4 .137365 .162669 0.253035E-01 7 8 .115478 .162669 0.471910E-01 7 16 .146863 .162669 0.158063E-01 7 32 .183056 .162669 0.203868E-01 7 64 .178131 .162669 0.154619E-01 8 1 0.529068E-01 0.583349E-01 0.542806E-02 8 2 0.564465E-01 0.583349E-01 0.188833E-02 8 4 0.577602E-01 0.583349E-01 0.574690E-03 8 8 0.581745E-01 0.583349E-01 0.160342E-03 8 16 0.582924E-01 0.583349E-01 0.424963E-04 8 32 0.583239E-01 0.583349E-01 0.109497E-04 8 64 0.583321E-01 0.583349E-01 0.277977E-05 9 1 .230835 24.0000 23.7692 9 2 2.92019 24.0000 21.0798 9 4 9.30591 24.0000 14.6941 9 8 15.7830 24.0000 8.21704 9 16 20.0896 24.0000 3.91037 9 32 22.3400 24.0000 1.66002 9 64 23.3506 24.0000 .649369 10 1 1.35094 1.57080 .219858 10 2 1.29277 1.57080 .278022 10 4 1.35731 1.57080 .213491 10 8 1.39914 1.57080 .171655 10 16 1.42930 1.57080 .141492 10 32 1.45127 1.57080 .119524 10 64 1.46768 1.57080 .103120 11 1 1.41880 3.14159 1.72279 11 2 1.79448 3.14159 1.34711 11 4 2.06235 3.14159 1.07924 11 8 2.24277 3.14159 .898827 11 16 2.36290 3.14159 .778689 11 32 2.44506 3.14159 .696537 11 64 2.50394 3.14159 .637657 12 1 .769239 .500000 .269239 12 2 .494195 .500000 0.580528E-02 12 4 .464401 .500000 0.355990E-01 12 8 .494232 .500000 0.576837E-02 12 16 .501907 .500000 0.190658E-02 12 32 .500620 .500000 0.619801E-03 12 64 .499939 .500000 0.605169E-04 13 1 1.84365 1.57080 .272856 13 2 2.15002 1.57080 .579222 13 4 1.88708 1.57080 .316285 13 8 1.41836 1.57080 .152440 13 16 1.30452 1.57080 .266278 13 32 1.56761 1.57080 0.318175E-02 13 64 1.75694 1.57080 .186140 14 1 1.06661 1.06346 0.314354E-02 14 2 1.08600 1.06346 0.225388E-01 14 4 1.06333 1.06346 0.131201E-03 14 8 1.06346 1.06346 0.169167E-08 14 16 1.06346 1.06346 0.222045E-15 14 32 1.06346 1.06346 0.444089E-15 14 64 1.06346 1.06346 0.222045E-15 TEST05 P00_RAT_TRANSFORM applies a rational transform to estimate an integral on [ALPHA,+Infinity) as a transformed integral on (0,1/(1+ALPHA)], and applying a Gauss-Legendre rule. Problem Order Estimate Exact Error 1 1 .125393 .195248 0.698544E-01 1 2 .161260 .195248 0.339874E-01 1 4 .171148 .195248 0.240999E-01 1 8 .175379 .195248 0.198685E-01 1 16 .178502 .195248 0.167453E-01 1 32 .180849 .195248 0.143983E-01 1 64 .182650 .195248 0.125978E-01 2 1 .159078 .325108 .166030 2 2 .194318 .325108 .130791 2 4 .209901 .325108 .115207 2 8 .220796 .325108 .104313 2 16 .229533 .325108 0.955756E-01 2 32 .236585 .325108 0.885234E-01 2 64 .242364 .325108 0.827449E-01 3 1 .319619 13.6280 13.3084 3 2 .450904 13.6280 13.1771 3 4 .601571 13.6280 13.0264 3 8 .763468 13.6280 12.8645 3 16 .930418 13.6280 12.6976 3 32 1.09885 13.6280 12.5292 3 64 1.26686 13.6280 12.3611 4 1 -.311463 -0.468485E-02 .306778 4 2 .241453 -0.468485E-02 .246138 4 4 -.192659 -0.468485E-02 .187974 4 8 -.339783 -0.468485E-02 .335098 4 16 -.146902 -0.468485E-02 .142217 4 32 -.115974 -0.468485E-02 .111289 4 64 -.237789 -0.468485E-02 .233104 5 1 -0.234775E-13 0.158973E-02 0.158973E-02 5 2 -4.11997 0.158973E-02 4.12156 5 4 -10.8893 0.158973E-02 10.8908 5 8 41.5222 0.158973E-02 41.5206 5 16 202.350 0.158973E-02 202.349 5 32 -603.212 0.158973E-02 603.213 5 64 -2630.29 0.158973E-02 2630.30 6 1 0.225543E-10 0.561037E-03 0.561037E-03 6 2 0.125740E-03 0.561037E-03 0.435297E-03 6 4 0.581908E-03 0.561037E-03 0.208712E-04 6 8 0.561006E-03 0.561037E-03 0.315466E-07 6 16 0.561037E-03 0.561037E-03 0.246977E-11 6 32 0.561037E-03 0.561037E-03 0.325261E-18 6 64 0.561037E-03 0.561037E-03 0.542101E-18 7 1 -.317343 .162669 .480012 7 2 0.762029E-01 .162669 0.864660E-01 7 4 .186351 .162669 0.236826E-01 7 8 -.223540 .162669 .386209 7 16 -.343201 .162669 .505870 7 32 -.117109 .162669 .279778 7 64 -.237837 .162669 .400506 8 1 0.550841E-01 0.583349E-01 0.325078E-02 8 2 0.591184E-01 0.583349E-01 0.783576E-03 8 4 0.576952E-01 0.583349E-01 0.639645E-03 8 8 0.583444E-01 0.583349E-01 0.953429E-05 8 16 0.583349E-01 0.583349E-01 0.445532E-08 8 32 0.583349E-01 0.583349E-01 0.254102E-13 8 64 0.583349E-01 0.583349E-01 0.138778E-16 9 1 1.47152 24.0000 22.5285 9 2 52.0087 24.0000 28.0087 9 4 8.46450 24.0000 15.5355 9 8 22.6791 24.0000 1.32091 9 16 24.0287 24.0000 0.286696E-01 9 32 24.0000 24.0000 0.120629E-04 9 64 24.0000 24.0000 0.380236E-09 10 1 2.00000 1.57080 .429204 10 2 1.50000 1.57080 0.707963E-01 10 4 1.56863 1.57080 0.216888E-02 10 8 1.57079 1.57080 0.191425E-05 10 16 1.57080 1.57080 0.145262E-11 10 32 1.57080 1.57080 0.444089E-15 10 64 1.57080 1.57080 0.133227E-14 11 1 2.00000 3.14159 1.14159 11 2 2.44949 3.14159 .692103 11 4 2.75540 3.14159 .386188 11 8 2.93684 3.14159 .204751 11 16 3.03607 3.14159 .105522 11 32 3.08801 3.14159 0.535788E-01 11 64 3.11459 3.14159 0.269979E-01 12 1 .795064 .500000 .295064 12 2 .370271 .500000 .129729 12 4 .402708 .500000 0.972924E-01 12 8 .480352 .500000 0.196480E-01 12 16 .498803 .500000 0.119723E-02 12 32 .499991 .500000 0.885320E-05 12 64 .500000 .500000 0.238633E-08 13 1 3.36588 1.57080 1.79509 13 2 -.875962 1.57080 2.44676 13 4 4.21763 1.57080 2.64684 13 8 .252453 1.57080 1.31834 13 16 .204644 1.57080 1.36615 13 32 2.33642 1.57080 .765622 13 64 -1.30872 1.57080 2.87951 14 1 1.50667 1.06346 .443204 14 2 .987107 1.06346 0.763550E-01 14 4 1.08821 1.06346 0.247513E-01 14 8 1.06425 1.06346 0.785980E-03 14 16 1.06346 1.06346 0.438520E-05 14 32 1.06346 1.06346 0.550759E-09 14 64 1.06346 1.06346 .000000 TEST_INT_LAGUERRE_PRB Normal end of execution. July 29 2007 4:37:50.517 PM