October 9 2008 3:29:04.920 PM TEST_TRI_INT_PRB FORTRAN90 version Test the routines in the TEST_TRI_INT library. TEST01 GET_PROB_NUM reports the number of problems. P00_TITLE returns a title for each problem. The number of problems available is 22 The problem titles: 1 f(x,y) = 2 2 f(x,y) = 6 * x 3 f(x,y) = 6 * y 4 f(x,y) = 12 * x^2 5 f(x,y) = 24 * x*y 6 f(x,y) = 12 * y^2 7 f(x,y) = 20 * x^3 8 f(x,y) = 30 * x^4 9 f(x,y) = 42 * x^5 10 f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 11 f(x,y) = (x+y)^(-0.2) 12 f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 13 f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 14 f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 15 f(x,y) = 1/sqrt(1-x-y) 16 f(x,y) = log(x*y) 17 f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 18 f(x,y) = log ( x + y ) 19 f(x,y) = sin ( x ) cos ( 5 y ) 20 f(x,y) = sin ( 11 x ) cos ( y ) 21 f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 22 f(x,y) = log ( r ) / r TEST02 P00_MONTE_CARLO applies a Monte Carlo rule. Problem Exact Seed Pts Approx Error f(x,y) = 2 1 1.000000 123456789 1 1.000000 0.000000 2 1.000000 0.000000 4 1.000000 0.000000 8 1.000000 0.000000 16 1.000000 0.000000 32 1.000000 0.000000 64 1.000000 0.000000 128 1.000000 0.000000 256 1.000000 0.000000 512 1.000000 0.000000 1024 1.000000 0.000000 2048 1.000000 0.000000 4096 1.000000 0.000000 8192 1.000000 0.000000 16384 1.000000 0.000000 32768 1.000000 0.000000 f(x,y) = 6 * x 2 1.000000 123456789 1 0.072346 0.927654 2 1.209931 0.209931 4 0.625099 0.374901 8 1.067347 0.067347 16 1.244131 0.244131 32 1.093796 0.093796 64 1.097989 0.097989 128 1.060303 0.060303 256 0.942353 0.057647 512 1.008032 0.008032 1024 1.059003 0.059003 2048 1.015973 0.015973 4096 1.020350 0.020350 8192 1.003196 0.003196 16384 1.012552 0.012552 32768 0.995040 0.004960 f(x,y) = 6 * y 3 1.000000 123456789 1 0.308437 0.691563 2 0.630121 0.369879 4 0.993224 0.006776 8 0.799986 0.200014 16 0.683970 0.316030 32 1.114462 0.114462 64 0.861939 0.138061 128 0.964636 0.035364 256 1.024191 0.024191 512 1.032365 0.032365 1024 0.943665 0.056335 2048 0.984313 0.015687 4096 0.984507 0.015493 8192 0.980449 0.019551 16384 0.995022 0.004978 32768 1.002763 0.002763 f(x,y) = 12 * x^2 4 1.000000 123456789 1 0.003489 0.996511 2 1.017891 0.017891 4 0.714883 0.285117 8 1.018921 0.018921 16 1.270778 0.270778 32 1.082003 0.082003 64 1.114608 0.114608 128 1.081890 0.081890 256 0.921397 0.078603 512 0.983440 0.016560 1024 1.100865 0.100865 2048 1.015238 0.015238 4096 1.028768 0.028768 8192 1.004063 0.004063 16384 1.021751 0.021751 32768 0.995324 0.004676 f(x,y) = 24 * x*y 5 1.000000 123456789 1 0.029752 0.970248 2 0.899543 0.100457 4 0.432535 0.567465 8 0.804738 0.195262 16 1.037171 0.037171 32 1.364863 0.364863 64 0.957261 0.042739 128 1.095750 0.095750 256 0.958958 0.041042 512 1.036673 0.036673 1024 0.995095 0.004905 2048 1.006466 0.006466 4096 1.008881 0.008881 8192 0.991920 0.008080 16384 1.004033 0.004033 32768 0.993150 0.006850 f(x,y) = 12 * y^2 6 1.000000 123456789 1 0.063422 0.936578 2 0.346303 0.653697 4 1.039338 0.039338 8 0.737597 0.262403 16 0.509046 0.490954 32 1.046736 0.046736 64 0.788071 0.211929 128 0.925559 0.074441 256 1.022653 0.022653 512 1.033515 0.033515 1024 0.917825 0.082175 2048 0.974661 0.025339 4096 0.969537 0.030463 8192 0.970918 0.029082 16384 0.992624 0.007376 32768 1.005688 0.005688 f(x,y) = 20 * x^3 7 1.000000 123456789 1 0.000140 0.999860 2 0.740587 0.259413 4 0.795254 0.204746 8 1.034890 0.034890 16 1.200229 0.200229 32 1.027815 0.027815 64 1.081018 0.081018 128 1.110010 0.110010 256 0.914747 0.085253 512 0.960754 0.039246 1024 1.128600 0.128600 2048 1.009711 0.009711 4096 1.031989 0.031989 8192 1.003438 0.003438 16384 1.030308 0.030308 32768 0.997654 0.002346 f(x,y) = 30 * x^4 8 1.000000 123456789 1 0.000005 0.999995 2 0.499921 0.500079 4 0.811445 0.188555 8 1.114979 0.114979 16 1.079974 0.079974 32 0.960092 0.039908 64 1.025994 0.025994 128 1.151713 0.151713 256 0.916263 0.083737 512 0.946431 0.053569 1024 1.148790 0.148790 2048 1.005546 0.005546 4096 1.031960 0.031960 8192 1.002340 0.002340 16384 1.038543 0.038543 32768 1.000459 0.000459 f(x,y) = 42 * x^5 9 1.000000 123456789 1 0.000000 1.000000 2 0.322442 0.677558 4 0.774501 0.225499 8 1.226402 0.226402 16 0.942781 0.057219 32 0.887871 0.112129 64 0.964571 0.035429 128 1.204327 0.204327 256 0.921885 0.078115 512 0.939717 0.060283 1024 1.164807 0.164807 2048 1.004154 0.004154 4096 1.029676 0.029676 8192 1.000966 0.000966 16384 1.046156 0.046156 32768 1.003271 0.003271 f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 10 1.000000 123456789 1 7.483685 6.483685 2 0.505185 0.494815 4 1.691831 0.691831 8 0.678398 0.321602 16 0.924809 0.075191 32 0.403052 0.596948 64 1.543233 0.543233 128 0.854046 0.145954 256 1.003479 0.003479 512 0.670111 0.329889 1024 0.997108 0.002892 2048 1.072268 0.072268 4096 0.957551 0.042449 8192 1.183583 0.183583 16384 0.991592 0.008408 32768 1.057896 0.057896 f(x,y) = (x+y)^(-0.2) 11 1.000000 123456789 1 1.359976 0.359976 2 0.992778 0.007222 4 1.062966 0.062966 8 1.002944 0.002944 16 1.008682 0.008682 32 0.967000 0.033000 64 1.010012 0.010012 128 0.998210 0.001790 256 1.004338 0.004338 512 0.989147 0.010853 1024 1.000471 0.000471 2048 1.000326 0.000326 4096 0.998710 0.001290 8192 1.003427 0.003427 16384 0.999095 0.000905 32768 1.000323 0.000323 f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 12 1.000000 123456789 1 0.739814 0.260186 2 0.871466 0.128534 4 0.884838 0.115162 8 0.912624 0.087376 16 0.964978 0.035022 32 1.086412 0.086412 64 0.988772 0.011228 128 1.031247 0.031247 256 0.980486 0.019514 512 0.994743 0.005257 1024 1.003840 0.003840 2048 1.001083 0.001083 4096 1.002324 0.002324 8192 0.996739 0.003261 16384 1.001129 0.001129 32768 0.999513 0.000487 f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 13 1.000000 123456789 1 1.750844 0.750844 2 0.903521 0.096479 4 1.295122 0.295122 8 1.089339 0.089339 16 0.964293 0.035707 32 0.902520 0.097480 64 1.077367 0.077367 128 0.989133 0.010867 256 1.009672 0.009672 512 0.980025 0.019975 1024 1.002254 0.002254 2048 0.999962 0.000038 4096 0.999709 0.000291 8192 1.007851 0.007851 16384 0.998046 0.001954 32768 1.001778 0.001778 f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 14 1.000000 123456789 1 1.854769 0.854769 2 0.808467 0.191533 4 1.581776 0.581776 8 1.220984 0.220984 16 0.891742 0.108258 32 0.858851 0.141149 64 1.176460 0.176460 128 0.969857 0.030143 256 0.996146 0.003854 512 0.985466 0.014534 1024 0.983037 0.016963 2048 0.995108 0.004892 4096 1.011287 0.011287 8192 1.003836 0.003836 16384 0.992092 0.007908 32768 1.002937 0.002937 f(x,y) = 1/sqrt(1-x-y) 15 1.000000 123456789 1 0.401334 0.598666 2 0.604735 0.395265 4 0.649809 0.350191 8 0.698817 0.301183 16 0.861417 0.138583 32 1.281058 0.281058 64 1.074851 0.074851 128 1.169144 0.169144 256 0.932088 0.067912 512 0.958144 0.041856 1024 0.995636 0.004364 2048 1.009452 0.009452 4096 1.019291 0.019291 8192 0.986408 0.013592 16384 0.997672 0.002328 32768 1.012227 0.012227 f(x,y) = log(x*y) 16 1.000000 123456789 1 1.999921 0.999921 2 0.891582 0.108418 4 1.429056 0.429056 8 1.132435 0.132435 16 0.955996 0.044004 32 0.847754 0.152246 64 1.057450 0.057450 128 0.983742 0.016258 256 1.017050 0.017050 512 0.972770 0.027230 1024 1.006809 0.006809 2048 0.996976 0.003024 4096 0.996298 0.003702 8192 1.009334 0.009334 16384 0.996940 0.003060 32768 1.002258 0.002258 f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 17 1.000000 123456789 1 0.592692 0.407308 2 0.787858 0.212142 4 0.648431 0.351569 8 0.918015 0.081985 16 0.843230 0.156770 32 1.065248 0.065248 64 0.857236 0.142764 128 1.135014 0.135014 256 0.976963 0.023037 512 0.984207 0.015793 1024 1.035634 0.035634 2048 0.972240 0.027760 4096 1.001336 0.001336 8192 1.003065 0.003065 16384 0.985593 0.014407 32768 0.993616 0.006384 f(x,y) = log ( x + y ) 18 1.000000 123456789 1 4.128277 3.128277 2 0.980539 0.019461 4 1.580936 0.580936 8 1.059567 0.059567 16 1.087332 0.087332 32 0.699160 0.300840 64 1.074592 0.074592 128 0.983555 0.016445 256 1.040736 0.040736 512 0.909155 0.090845 1024 1.002629 0.002629 2048 1.000724 0.000724 4096 0.989153 0.010847 8192 1.029104 0.029104 16384 0.990904 0.009096 32768 1.002703 0.002703 f(x,y) = sin ( x ) cos ( 5 y ) 19 1.000000 123456789 1 0.243847 0.756153 2 2.311979 1.311979 4 1.428853 0.428853 8 1.680147 0.680147 16 2.124440 1.124440 32 0.219637 0.780363 64 1.470655 0.470655 128 0.868461 0.131539 256 0.917466 0.082534 512 0.879316 0.120684 1024 1.233247 0.233247 2048 1.046926 0.046926 4096 1.043020 0.043020 8192 1.044174 0.044174 16384 1.043448 0.043448 32768 1.003203 0.003203 f(x,y) = sin ( 11 x ) cos ( y ) 20 1.000000 123456789 1 1.525615 0.525615 2 -3.344840 4.344840 4 3.437050 2.437050 8 -0.610219 1.610219 16 1.018507 0.018507 32 0.419679 0.580321 64 0.576754 0.423246 128 0.739467 0.260533 256 0.986506 0.013494 512 0.706230 0.293770 1024 0.870872 0.129128 2048 0.737684 0.262316 4096 1.010210 0.010210 8192 0.978769 0.021231 16384 0.975318 0.024682 32768 1.039971 0.039971 f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 21 1.000000 123456789 1 3.798568 2.798568 2 0.843351 0.156649 4 1.408670 0.408670 8 0.898932 0.101068 16 0.997130 0.002870 32 0.757396 0.242604 64 1.140584 0.140584 128 0.954702 0.045298 256 1.020180 0.020180 512 0.881146 0.118854 1024 1.002980 0.002980 2048 1.020028 0.020028 4096 0.986014 0.013986 8192 1.051116 0.051116 16384 0.997427 0.002573 32768 1.013169 0.013169 f(x,y) = log ( r ) / r 22 1.000000 123456789 1 6.965864 5.965864 2 0.511762 0.488238 4 1.781510 0.781510 8 0.639733 0.360267 16 0.871994 0.128006 32 0.421792 0.578208 64 1.392268 0.392268 128 0.828967 0.171033 256 1.013503 0.013503 512 0.665986 0.334014 1024 0.997980 0.002020 2048 1.062398 0.062398 4096 0.961309 0.038691 8192 1.183936 0.183936 16384 0.997033 0.002967 32768 1.062884 0.062884 TEST03 P00_VERTEX_SUB applies a vertex rule with subdivision. Problem Exact Pts Approx Error f(x,y) = 2 1 1.000000 3 1.000000 0.000000 6 1.000000 0.000000 15 1.000000 0.000000 45 1.000000 0.000000 153 1.000000 0.000000 f(x,y) = 6 * x 2 1.000000 3 1.000000 0.000000 6 1.000000 0.000000 15 1.000000 0.000000 45 1.000000 0.000000 153 1.000000 0.000000 f(x,y) = 6 * y 3 1.000000 3 1.000000 0.000000 6 1.000000 0.000000 15 1.000000 0.000000 45 1.000000 0.000000 153 1.000000 0.000000 f(x,y) = 12 * x^2 4 1.000000 3 2.000000 1.000000 6 1.250000 0.250000 15 1.125000 0.125000 45 1.078125 0.078125 153 1.046875 0.046875 f(x,y) = 24 * x*y 5 1.000000 3 0.000000 1.000000 6 0.750000 0.250000 15 0.875000 0.125000 45 0.921875 0.078125 153 0.953125 0.046875 f(x,y) = 12 * y^2 6 1.000000 3 2.000000 1.000000 6 1.250000 0.250000 15 1.125000 0.125000 45 1.078125 0.078125 153 1.046875 0.046875 f(x,y) = 20 * x^3 7 1.000000 3 3.333333 2.333333 6 1.458333 0.458333 15 1.223958 0.223958 45 1.147786 0.147786 153 1.091390 0.091390 f(x,y) = 30 * x^4 8 1.000000 3 5.000000 4.000000 6 1.718750 0.718750 15 1.318359 0.318359 45 1.213257 0.213257 153 1.134422 0.134422 f(x,y) = 42 * x^5 9 1.000000 3 7.000000 6.000000 6 2.078125 1.078125 15 1.411621 0.411621 45 1.274155 0.274155 153 1.175731 0.175731 f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 10 1.000000 Skip this problem, it has edge singularities. f(x,y) = (x+y)^(-0.2) 11 1.000000 Skip this problem, it has vertex singularities. f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 12 1.000000 Skip this problem, it has edge singularities. f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 13 1.000000 Skip this problem, it has edge singularities. f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 14 1.000000 Skip this problem, it has edge singularities. f(x,y) = 1/sqrt(1-x-y) 15 1.000000 Skip this problem, it has edge singularities. f(x,y) = log(x*y) 16 1.000000 Skip this problem, it has edge singularities. f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 17 1.000000 Skip this problem, it has internal singularities. f(x,y) = log ( x + y ) 18 1.000000 Skip this problem, it has vertex singularities. f(x,y) = sin ( x ) cos ( 5 y ) 19 1.000000 3 3.257551 2.257551 6 1.091193 0.091193 15 1.213464 0.213464 45 1.175858 0.175858 153 1.112362 0.112362 f(x,y) = sin ( 11 x ) cos ( y ) 20 1.000000 3 -1.950026 2.950026 6 -2.424940 3.424940 15 0.611848 0.388152 45 0.818723 0.181277 153 0.896438 0.103562 f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 21 1.000000 Skip this problem, it has vertex singularities. f(x,y) = log ( r ) / r 22 1.000000 Skip this problem, it has vertex singularities. TEST04 P00_WANDZURA05_SUB applies a Wandzura rule with subdivision. Problem Exact Pts Approx Error f(x,y) = 2 1 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 6 * x 2 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 6 * y 3 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 12 * x^2 4 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 24 * x*y 5 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 12 * y^2 6 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 20 * x^3 7 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 30 * x^4 8 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = 42 * x^5 9 1.000000 7 1.000000 0.000000 Accuracy acceptable f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 10 1.000000 7 0.798157 0.201843 28 0.883684 0.116316 112 0.933087 0.066913 448 0.961538 0.038462 1792 0.977901 0.022099 7168 0.987305 0.012695 f(x,y) = (x+y)^(-0.2) 11 1.000000 7 0.998396 0.001604 28 0.999539 0.000461 112 0.999868 0.000132 448 0.999962 0.000038 1792 0.999989 0.000011 7168 0.999997 0.000003 f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 12 1.000000 7 0.972572 0.027428 28 0.983878 0.016122 112 0.990635 0.009365 448 0.994591 0.005409 1792 0.996884 0.003116 7168 0.998208 0.001792 f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 13 1.000000 7 0.949590 0.050410 28 0.970474 0.029526 112 0.982868 0.017132 448 0.990106 0.009894 1792 0.994300 0.005700 7168 0.996721 0.003279 f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 14 1.000000 7 0.873246 0.126754 28 0.909736 0.090264 112 0.935949 0.064051 448 0.954630 0.045370 1792 0.967890 0.032110 7168 0.977285 0.022715 f(x,y) = 1/sqrt(1-x-y) 15 1.000000 7 0.843800 0.156200 28 0.887964 0.112036 112 0.920217 0.079783 448 0.943387 0.056613 1792 0.959898 0.040102 7168 0.971619 0.028381 f(x,y) = log(x*y) 16 1.000000 7 0.950264 0.049736 28 0.974388 0.025612 112 0.987008 0.012992 448 0.993457 0.006543 1792 0.996717 0.003283 7168 0.998356 0.001644 f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 17 1.000000 7 0.864525 0.135475 28 0.965722 0.034278 112 0.913986 0.086014 448 0.939178 0.060822 1792 0.956993 0.043007 7168 0.969589 0.030411 f(x,y) = log ( x + y ) 18 1.000000 7 0.991081 0.008919 28 0.997766 0.002234 112 0.999442 0.000558 448 0.999860 0.000140 1792 0.999965 0.000035 7168 0.999991 0.000009 f(x,y) = sin ( x ) cos ( 5 y ) 19 1.000000 7 0.975991 0.024009 28 0.999840 0.000160 112 0.999998 0.000002 448 1.000000 0.000000 Accuracy acceptable f(x,y) = sin ( 11 x ) cos ( y ) 20 1.000000 7 0.051313 0.948687 28 1.019286 0.019286 112 1.000129 0.000129 448 1.000002 0.000002 1792 1.000000 0.000000 Accuracy acceptable f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 21 1.000000 7 0.973846 0.026154 28 0.987025 0.012975 112 0.993511 0.006489 448 0.996756 0.003244 1792 0.998378 0.001622 7168 0.999189 0.000811 f(x,y) = log ( r ) / r 22 1.000000 7 0.862016 0.137984 28 0.923815 0.076185 112 0.958237 0.041763 448 0.977284 0.022716 1792 0.987725 0.012275 7168 0.993404 0.006596 TEST_TRI_INT_PRB Normal end of execution. October 9 2008 3:29:05.817 PM