July 5 2007 11:04:17.946 AM 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 0.201182 0.798818 2 0.930572 0.069428 4 0.841437 0.158563 8 0.682820 0.317180 16 1.053414 0.053414 32 0.855727 0.144273 64 1.029275 0.029275 128 0.995366 0.004634 256 0.986829 0.013171 512 1.007178 0.007178 1024 1.028439 0.028439 2048 1.015979 0.015979 4096 0.971915 0.028085 8192 0.984897 0.015103 16384 1.001590 0.001590 32768 0.997974 0.002026 f(x,y) = 6 * y 3 1.000000 123456789 1 1.218362 0.218362 2 1.114804 0.114804 4 1.853611 0.853611 8 1.100635 0.100635 16 0.856965 0.143035 32 1.135162 0.135162 64 0.923314 0.076686 128 1.003151 0.003151 256 0.977933 0.022067 512 0.981206 0.018794 1024 0.995136 0.004864 2048 1.012884 0.012884 4096 0.990927 0.009073 8192 0.993535 0.006465 16384 1.001732 0.001732 32768 1.000187 0.000187 f(x,y) = 12 * x^2 4 1.000000 123456789 1 0.026983 0.973017 2 0.604725 0.395275 4 0.776302 0.223698 8 0.431821 0.568179 16 1.141373 0.141373 32 0.702988 0.297012 64 0.979177 0.020823 128 1.025838 0.025838 256 0.974229 0.025771 512 1.010971 0.010971 1024 1.040846 0.040846 2048 1.023060 0.023060 4096 0.958632 0.041368 8192 0.984583 0.015417 16384 1.004377 0.004377 32768 0.997722 0.002278 f(x,y) = 24 * x*y 5 1.000000 123456789 1 0.326817 0.673183 2 1.310604 0.310604 4 1.332660 0.332660 8 0.971511 0.028489 16 0.909611 0.090389 32 0.979732 0.020268 64 0.924211 0.075789 128 0.953120 0.046880 256 1.009313 0.009313 512 0.977853 0.022147 1024 1.024598 0.024598 2048 1.027198 0.027198 4096 0.971674 0.028326 8192 0.980299 0.019701 16384 0.999179 0.000821 32768 0.997977 0.002023 f(x,y) = 12 * y^2 6 1.000000 123456789 1 0.989603 0.010397 2 0.876594 0.123406 4 2.751058 1.751058 8 1.041565 0.041565 16 0.690665 0.309335 32 1.277480 0.277480 64 0.909614 0.090386 128 0.999380 0.000620 256 0.943359 0.056641 512 0.982467 0.017533 1024 0.990358 0.009642 2048 1.014857 0.014857 4096 0.985797 0.014203 8192 0.992392 0.007608 16384 1.006366 0.006366 32768 1.002787 0.002787 f(x,y) = 20 * x^3 7 1.000000 123456789 1 0.003016 0.996984 2 0.340980 0.659020 4 0.702203 0.297797 8 0.268411 0.731589 16 1.196483 0.196483 32 0.565772 0.434228 64 0.932034 0.067966 128 1.055348 0.055348 256 0.946937 0.053063 512 1.018679 0.018679 1024 1.052855 0.052855 2048 1.028636 0.028636 4096 0.951449 0.048551 8192 0.987359 0.012641 16384 1.007138 0.007138 32768 0.998214 0.001786 f(x,y) = 30 * x^4 8 1.000000 123456789 1 0.000303 0.999697 2 0.178750 0.821250 4 0.606534 0.393466 8 0.164496 0.835504 16 1.207317 0.207317 32 0.452962 0.547038 64 0.893722 0.106278 128 1.078232 0.078232 256 0.907686 0.092314 512 1.031620 0.031620 1024 1.068754 0.068754 2048 1.033235 0.033235 4096 0.947709 0.052291 8192 0.991187 0.008813 16384 1.009092 0.009092 32768 0.998526 0.001474 f(x,y) = 42 * x^5 9 1.000000 123456789 1 0.000028 0.999972 2 0.089624 0.910376 4 0.503943 0.496057 8 0.099523 0.900477 16 1.179604 0.179604 32 0.364025 0.635975 64 0.860961 0.139039 128 1.092966 0.092966 256 0.861305 0.138695 512 1.047966 0.047966 1024 1.089280 0.089280 2048 1.036754 0.036754 4096 0.945983 0.054017 8192 0.995399 0.004601 16384 1.009920 0.009920 32768 0.998173 0.001827 f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 10 1.000000 123456789 1 0.931023 0.068977 2 0.364255 0.635745 4 0.087081 0.912919 8 0.969042 0.030958 16 1.019834 0.019834 32 0.657100 0.342900 64 0.633048 0.366952 128 0.767018 0.232982 256 1.101158 0.101158 512 0.931618 0.068382 1024 0.987546 0.012454 2048 0.936090 0.063910 4096 1.261560 0.261560 8192 1.120762 0.120762 16384 0.985434 0.014566 32768 0.994407 0.005593 f(x,y) = (x+y)^(-0.2) 11 1.000000 123456789 1 1.045290 0.045290 2 0.971776 0.028224 4 0.919923 0.080077 8 1.022492 0.022492 16 1.010791 0.010791 32 0.994197 0.005803 64 0.995177 0.004823 128 0.996636 0.003364 256 1.007578 0.007578 512 1.001352 0.001352 1024 0.996366 0.003634 2048 0.995532 0.004468 4096 1.006232 0.006232 8192 1.004689 0.004689 16384 0.999683 0.000317 32768 1.000665 0.000665 f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 12 1.000000 123456789 1 0.818465 0.181535 2 0.905812 0.094188 4 1.178810 0.178810 8 0.917146 0.082854 16 0.942351 0.057649 32 1.024388 0.024388 64 0.994428 0.005572 128 1.009225 0.009225 256 0.993796 0.006204 512 0.997612 0.002388 1024 1.010753 0.010753 2048 1.009768 0.009768 4096 0.989800 0.010200 8192 0.996417 0.003583 16384 1.004213 0.004213 32768 1.000008 0.000008 f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 13 1.000000 123456789 1 1.084151 0.084151 2 0.821272 0.178728 4 0.839996 0.160004 8 0.970856 0.029144 16 0.978196 0.021804 32 1.004551 0.004551 64 0.986559 0.013441 128 1.033426 0.033426 256 1.003581 0.003581 512 1.008447 0.008447 1024 0.988917 0.011083 2048 0.992875 0.007125 4096 1.013116 0.013116 8192 1.015009 0.015009 16384 0.999709 0.000291 32768 1.000835 0.000835 f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 14 1.000000 123456789 1 1.032675 0.032675 2 0.707685 0.292315 4 0.759166 0.240834 8 0.893228 0.106772 16 0.912566 0.087434 32 1.029317 0.029317 64 1.015289 0.015289 128 1.106897 0.106897 256 0.992107 0.007893 512 1.000156 0.000156 1024 0.977508 0.022492 2048 0.989360 0.010640 4096 1.010331 0.010331 8192 1.022639 0.022639 16384 1.000619 0.000619 32768 0.997521 0.002479 f(x,y) = 1/sqrt(1-x-y) 15 1.000000 123456789 1 0.516655 0.483345 2 0.665963 0.334037 4 1.315956 0.315956 8 0.726652 0.273348 16 0.781896 0.218104 32 1.075830 0.075830 64 1.090439 0.090439 128 1.066006 0.066006 256 0.970782 0.029218 512 0.972485 0.027515 1024 1.042474 0.042474 2048 1.029813 0.029813 4096 0.955114 0.044886 8192 1.014854 0.014854 16384 1.029546 0.029546 32768 1.009573 0.009573 f(x,y) = log(x*y) 16 1.000000 123456789 1 1.201087 0.201087 2 0.738237 0.261763 4 0.768746 0.231254 8 0.982459 0.017541 16 0.989162 0.010838 32 1.003856 0.003856 64 0.995230 0.004770 128 1.036172 0.036172 256 1.001226 0.001226 512 1.011823 0.011823 1024 0.986374 0.013626 2048 0.988331 0.011669 4096 1.018028 0.018028 8192 1.018146 0.018146 16384 0.999452 0.000548 32768 1.001110 0.001110 f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 17 1.000000 123456789 1 0.899569 0.100431 2 1.736851 0.736851 4 0.769869 0.230131 8 0.968165 0.031835 16 0.891380 0.108620 32 1.168255 0.168255 64 0.913338 0.086662 128 1.064927 0.064927 256 1.036016 0.036016 512 0.963787 0.036213 1024 1.413346 0.413346 2048 1.020322 0.020322 4096 0.999652 0.000348 8192 0.974370 0.025630 16384 1.028681 0.028681 32768 1.006876 0.006876 f(x,y) = log ( x + y ) 18 1.000000 123456789 1 1.496553 0.496553 2 0.767095 0.232905 4 0.218185 0.781815 8 1.231851 0.231851 16 1.104322 0.104322 32 0.963239 0.036761 64 0.979186 0.020814 128 0.977597 0.022403 256 1.065501 0.065501 512 1.013890 0.013890 1024 0.966204 0.033796 2048 0.958252 0.041748 4096 1.055469 0.055469 8192 1.040013 0.040013 16384 0.996705 0.003295 32768 1.005449 0.005449 f(x,y) = sin ( x ) cos ( 5 y ) 19 1.000000 123456789 1 -0.345366 1.345366 2 -0.593229 1.593229 4 -0.126801 1.126801 8 -0.289104 1.289104 16 1.598301 0.598301 32 0.584504 0.415496 64 1.390243 0.390243 128 1.152387 0.152387 256 0.958294 0.041706 512 1.109313 0.109313 1024 1.018957 0.018957 2048 0.967903 0.032097 4096 0.980095 0.019905 8192 0.991073 0.008927 16384 1.020345 0.020345 32768 1.002913 0.002913 f(x,y) = sin ( 11 x ) cos ( y ) 20 1.000000 123456789 1 3.614557 2.614557 2 -1.191697 2.191697 4 1.305295 0.305295 8 1.296701 0.296701 16 2.056657 1.056657 32 0.359421 0.640579 64 0.823015 0.176985 128 1.289799 0.289799 256 1.202845 0.202845 512 0.805074 0.194926 1024 0.787917 0.212083 2048 1.046896 0.046896 4096 1.032947 0.032947 8192 0.996647 0.003353 16384 1.025860 0.025860 32768 1.021462 0.021462 f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 21 1.000000 123456789 1 0.974537 0.025463 2 0.810346 0.189654 4 0.539637 0.460363 8 1.085033 0.085033 16 1.058609 0.058609 32 0.873807 0.126193 64 0.873953 0.126047 128 0.913120 0.086880 256 1.067490 0.067490 512 0.984951 0.015049 1024 0.995583 0.004417 2048 0.974011 0.025989 4096 1.076832 0.076832 8192 1.046919 0.046919 16384 0.995307 0.004693 32768 1.003271 0.003271 f(x,y) = log ( r ) / r 22 1.000000 123456789 1 0.705647 0.294353 2 0.465623 0.534377 4 0.135097 0.864903 8 1.000287 0.000287 16 1.048001 0.048001 32 0.618273 0.381727 64 0.610480 0.389520 128 0.728679 0.271321 256 1.119508 0.119508 512 0.912654 0.087346 1024 1.034404 0.034404 2048 0.948862 0.051138 4096 1.252280 0.252280 8192 1.121639 0.121639 16384 0.979199 0.020801 32768 0.993664 0.006336 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. July 5 2007 11:04:19.611 AM