>> test_tri_int_test 10-Apr-2007 12:05:41 TEST_TRI_INT_PRB MATLAB version Run the TEST_TRI_INT tests. 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 0.742890 0.257110 2 0.460129 0.539871 4 1.032671 0.032671 8 0.941403 0.058597 16 1.097198 0.097198 32 0.945269 0.054731 64 0.920776 0.079224 128 0.940040 0.059960 256 0.994328 0.005672 512 1.078333 0.078333 1024 0.984721 0.015279 2048 1.006852 0.006852 4096 0.999650 0.000350 8192 1.006302 0.006302 16384 0.996580 0.003420 32768 1.000822 0.000822 f(x,y) = 6 * y 3 1.000000 123456789 1 0.739686 0.260314 2 1.103856 0.103856 4 0.816994 0.183006 8 0.944790 0.055210 16 1.011933 0.011933 32 0.864928 0.135072 64 1.017774 0.017774 128 1.039110 0.039110 256 1.024345 0.024345 512 1.040805 0.040805 1024 1.001933 0.001933 2048 0.999277 0.000723 4096 0.988180 0.011820 8192 0.995404 0.004596 16384 1.000664 0.000664 32768 0.997771 0.002229 f(x,y) = 12 * x^2 4 1.000000 123456789 1 0.014547 0.985453 2 0.606008 0.393992 4 0.031455 0.968545 8 0.817032 0.182968 16 1.092927 0.092927 32 1.378398 0.378398 64 0.909440 0.090560 128 1.132143 0.132143 256 0.961365 0.038635 512 1.026152 0.026152 1024 1.075422 0.075422 2048 0.954595 0.045405 4096 0.957924 0.042076 8192 0.978828 0.021172 16384 1.008271 0.008271 32768 1.003339 0.003339 f(x,y) = 24 * x*y 5 1.000000 123456789 1 2.395881 1.395881 2 1.201422 0.201422 4 0.751352 0.248648 8 1.705098 0.705098 16 0.931668 0.068332 32 0.823031 0.176969 64 0.893799 0.106201 128 1.025891 0.025891 256 1.022856 0.022856 512 1.001222 0.001222 1024 1.008295 0.008295 2048 0.994993 0.005007 4096 1.004360 0.004360 8192 1.004640 0.004640 16384 1.003142 0.003142 32768 0.999456 0.000544 f(x,y) = 12 * y^2 6 1.000000 123456789 1 1.005722 0.005722 2 1.751607 0.751607 4 2.223460 1.223460 8 0.418805 0.581195 16 0.900189 0.099811 32 1.180306 0.180306 64 1.286675 0.286675 128 1.130653 0.130653 256 1.055366 0.055366 512 0.953226 0.046774 1024 1.061680 0.061680 2048 1.022797 0.022797 4096 1.001708 0.001708 8192 1.001441 0.001441 16384 1.002119 0.002119 32768 1.005131 0.005131 f(x,y) = 20 * x^3 7 1.000000 123456789 1 0.001950 0.998050 2 0.916330 0.083670 4 0.931978 0.068022 8 1.135858 0.135858 16 1.521994 0.521994 32 1.047851 0.047851 64 0.902339 0.097661 128 0.954944 0.045056 256 0.945779 0.054221 512 0.867784 0.132216 1024 0.977150 0.022850 2048 0.958830 0.041170 4096 1.027655 0.027655 8192 0.990189 0.009811 16384 1.005418 0.005418 32768 1.003934 0.003934 f(x,y) = 30 * x^4 8 1.000000 123456789 1 0.193336 0.806664 2 0.264825 0.735175 4 0.578442 0.421558 8 0.452759 0.547241 16 0.745335 0.254665 32 0.904663 0.095337 64 1.195984 0.195984 128 0.931159 0.068841 256 0.903288 0.096712 512 1.090622 0.090622 1024 0.939251 0.060749 2048 0.971590 0.028410 4096 1.018960 0.018960 8192 0.946319 0.053681 16384 0.994736 0.005264 32768 0.988318 0.011682 f(x,y) = 42 * x^5 9 1.000000 123456789 1 0.000001 0.999999 2 0.452296 0.547704 4 0.722608 0.277392 8 1.239001 0.239001 16 0.568640 0.431360 32 1.002692 0.002692 64 0.445324 0.554676 128 0.985542 0.014458 256 0.770794 0.229206 512 0.941247 0.058753 1024 1.046713 0.046713 2048 1.071224 0.071224 4096 1.024997 0.024997 8192 0.944270 0.055730 16384 1.001361 0.001361 32768 0.974173 0.025827 f(x,y) = x^(-0.2) on ((1,0),(5,0),(5,1)) 10 1.000000 123456789 1 1.202447 0.202447 2 0.160403 0.839597 4 0.846167 0.153833 8 2.124266 1.124266 16 1.768938 0.768938 32 0.775700 0.224300 64 0.968692 0.031308 128 0.668234 0.331766 256 1.210465 0.210465 512 1.199794 0.199794 1024 0.899493 0.100507 2048 0.955602 0.044398 4096 0.962069 0.037931 8192 0.944115 0.055885 16384 0.994402 0.005598 32768 0.951278 0.048722 f(x,y) = (x+y)^(-0.2) 11 1.000000 123456789 1 0.929170 0.070830 2 1.023240 0.023240 4 0.975257 0.024743 8 1.035648 0.035648 16 1.005286 0.005286 32 0.983258 0.016742 64 0.996967 0.003033 128 0.998372 0.001628 256 1.004672 0.004672 512 0.998651 0.001349 1024 1.000724 0.000724 2048 0.996991 0.003009 4096 1.003916 0.003916 8192 1.000222 0.000222 16384 1.001849 0.001849 32768 1.000870 0.000870 f(x,y) = (1-x-y)^(-0.2) on ((-1,-3),(3,-2),(-1,2)) 12 1.000000 123456789 1 1.020437 0.020437 2 1.014283 0.014283 4 0.974595 0.025405 8 0.816572 0.183428 16 1.013399 0.013399 32 0.917013 0.082987 64 0.966753 0.033247 128 1.008927 0.008927 256 0.996299 0.003701 512 1.021827 0.021827 1024 0.997453 0.002547 2048 1.000371 0.000371 4096 1.002801 0.002801 8192 1.002622 0.002622 16384 0.997861 0.002139 32768 0.998826 0.001174 f(x,y) = (x*y)^(-0.2) on ((0,0),(-7,0),(0,-3)) 13 1.000000 123456789 1 1.001904 0.001904 2 0.981916 0.018084 4 0.944576 0.055424 8 0.978519 0.021481 16 1.030219 0.030219 32 0.941309 0.058691 64 1.032452 0.032452 128 0.966889 0.033111 256 0.994287 0.005713 512 1.005439 0.005439 1024 1.004228 0.004228 2048 1.000607 0.000607 4096 1.007542 0.007542 8192 0.995585 0.004415 16384 1.000095 0.000095 32768 1.001164 0.001164 f(x,y) = 1/sqrt(x) + 1/sqrt(y) + 1/sqrt(x+y) 14 1.000000 123456789 1 0.597051 0.402949 2 1.706181 0.706181 4 0.677438 0.322562 8 1.006032 0.006032 16 1.009615 0.009615 32 1.018752 0.018752 64 0.923619 0.076381 128 0.944977 0.055023 256 0.957240 0.042760 512 0.999502 0.000498 1024 0.975719 0.024281 2048 0.973943 0.026057 4096 0.968856 0.031144 8192 1.002365 0.002365 16384 0.995047 0.004953 32768 0.998962 0.001038 f(x,y) = 1/sqrt(1-x-y) 15 1.000000 123456789 1 0.718485 0.281515 2 1.716721 0.716721 4 0.647895 0.352105 8 0.766683 0.233317 16 1.086557 0.086557 32 0.855326 0.144674 64 1.063848 0.063848 128 1.107787 0.107787 256 1.072413 0.072413 512 1.434064 0.434064 1024 0.983082 0.016918 2048 0.981877 0.018123 4096 0.985225 0.014775 8192 1.011570 0.011570 16384 0.985077 0.014923 32768 1.015563 0.015563 f(x,y) = log(x*y) 16 1.000000 123456789 1 2.134539 1.134539 2 1.175170 0.175170 4 0.889508 0.110492 8 1.047593 0.047593 16 1.010857 0.010857 32 0.986835 0.013165 64 1.011159 0.011159 128 0.976424 0.023576 256 1.026294 0.026294 512 1.003531 0.003531 1024 0.996439 0.003561 2048 0.983666 0.016334 4096 1.004473 0.004473 8192 0.994812 0.005188 16384 0.999030 0.000970 32768 1.001606 0.001606 f(x,y) = 1/sqrt(|x-1/4|) + 1/sqrt(|y-1/2|) 17 1.000000 123456789 1 0.746981 0.253019 2 0.777955 0.222045 4 0.993702 0.006298 8 0.938435 0.061565 16 1.050542 0.050542 32 0.990613 0.009387 64 1.050649 0.050649 128 0.968112 0.031888 256 1.028278 0.028278 512 1.004132 0.004132 1024 0.984752 0.015248 2048 0.968360 0.031640 4096 0.983123 0.016877 8192 0.990804 0.009196 16384 0.997447 0.002553 32768 1.006216 0.006216 f(x,y) = log ( x + y ) 18 1.000000 123456789 1 0.031436 0.968564 2 2.183567 1.183567 4 0.770745 0.229255 8 1.446697 0.446697 16 1.147982 0.147982 32 0.928731 0.071269 64 1.054218 0.054218 128 1.021577 0.021577 256 0.871613 0.128387 512 0.982577 0.017423 1024 0.958002 0.041998 2048 1.045676 0.045676 4096 0.989365 0.010635 8192 0.983996 0.016004 16384 1.024185 0.024185 32768 1.004804 0.004804 f(x,y) = sin ( x ) cos ( 5 y ) 19 1.000000 123456789 1 -0.048128 1.048128 2 2.849761 1.849761 4 -1.173883 2.173883 8 0.462049 0.537951 16 1.874773 0.874773 32 0.780182 0.219818 64 0.824021 0.175979 128 0.945844 0.054156 256 0.960492 0.039508 512 1.269284 0.269284 1024 0.857541 0.142459 2048 1.108910 0.108910 4096 1.066183 0.066183 8192 0.967743 0.032257 16384 0.991463 0.008537 32768 1.007899 0.007899 f(x,y) = sin ( 11 x ) cos ( y ) 20 1.000000 123456789 1 4.658040 3.658040 2 1.382946 0.382946 4 0.915558 0.084442 8 0.382773 0.617227 16 0.584272 0.415728 32 1.706468 0.706468 64 0.227830 0.772170 128 0.770576 0.229424 256 0.651032 0.348968 512 0.866184 0.133816 1024 0.962526 0.037474 2048 0.906251 0.093749 4096 0.989991 0.010009 8192 0.982379 0.017621 16384 1.009794 0.009794 32768 1.012067 0.012067 f(x,y) = 1 / r = 1 / sqrt ( x^2 + y^2 ) 21 1.000000 123456789 1 0.913409 0.086591 2 0.647872 0.352128 4 0.907339 0.092661 8 0.775492 0.224508 16 1.186800 0.186800 32 0.854237 0.145763 64 0.940803 0.059197 128 1.035965 0.035965 256 1.031071 0.031071 512 0.893831 0.106169 1024 0.955303 0.044697 2048 0.965393 0.034607 4096 0.991869 0.008131 8192 0.996640 0.003360 16384 0.989355 0.010645 32768 0.981356 0.018644 f(x,y) = log ( r ) / r 22 1.000000 123456789 1 0.267672 0.732328 2 0.130913 0.869087 4 0.425360 0.574640 8 0.944437 0.055563 16 0.547686 0.452314 32 0.874373 0.125627 64 0.727530 0.272470 128 0.803291 0.196709 256 1.222943 0.222943 512 0.805481 0.194519 1024 0.900515 0.099485 2048 0.955590 0.044410 4096 0.912837 0.087163 8192 0.995753 0.004247 16384 1.008404 0.008404 32768 1.004105 0.004105 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. singularity = 3 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. 10-Apr-2007 12:05:54 >>