08-Jan-2022 10:27:26 test_interp_nd_test() MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test test_interp_nd(). TEST_INTERP_ND_TEST01 P00_TITLE returns the problem title. There are a total of 6 problems. 1 "Oscillatory" 2 "Product Peak" 3 "Corner Peak" 4 "Gaussian" 5 "Continuous" 6 "Discontinuous" TEST_INTERP_ND_TEST02 P00_F evaluates the function. Here, we use spatial dimension M = 2 The number of points is N = 10 Problem 1 C parameters: 1: 1.42253 2: 0.077471 W parameters: 1: 0.849129 2: 0.933993 F(X) X(1) X(2) ... 0.960725 0.8147 0.9058 0.767063 0.1270 0.9134 0.999166 0.6324 0.0975 0.873033 0.2785 0.5469 0.882858 0.9575 0.9649 0.796963 0.1576 0.9706 0.899902 0.9572 0.4854 0.979774 0.8003 0.1419 0.96187 0.4218 0.9157 0.968085 0.7922 0.9595 Problem 2 C parameters: 1: 0.945001 2: 1.055 W parameters: 1: 0.743132 2: 0.392227 F(X) X(1) X(2) ... 0.76489 0.8147 0.9058 0.569996 0.1270 0.9134 0.896531 0.6324 0.0975 0.811697 0.2785 0.5469 0.699466 0.9575 0.9649 0.554522 0.1576 0.9706 0.945761 0.9572 0.4854 0.926446 0.8003 0.1419 0.697319 0.4218 0.9157 0.730272 0.7922 0.9595 Problem 3 C parameters: 1: 1.4669 2: 0.3831 W parameters: 1: 0.706046 2: 0.0318328 F(X) X(1) X(2) ... 0.0608707 0.8147 0.9058 0.275844 0.1270 0.9134 0.131804 0.6324 0.0975 0.236066 0.2785 0.5469 0.046836 0.9575 0.9649 0.242756 0.1576 0.9706 0.0575563 0.9572 0.4854 0.0903829 0.8003 0.1419 0.130898 0.4218 0.9157 0.0617743 0.7922 0.9595 Problem 4 C parameters: 1: 6.02539 2: 1.00461 W parameters: 1: 0.0971318 2: 0.823458 F(X) X(1) X(2) ... 7.54925e-09 0.8147 0.9058 0.96029 0.1270 0.9134 1.78743e-05 0.6324 0.0975 0.280433 0.2785 0.5469 2.08761e-12 0.9575 0.9649 0.856712 0.1576 0.9706 1.93882e-12 0.9572 0.4854 1.00186e-08 0.8003 0.1419 0.0216099 0.4218 0.9157 2.36749e-08 0.7922 0.9595 Problem 5 C parameters: 1: 14.0074 2: 6.39258 W parameters: 1: 0.950222 2: 0.0344461 F(X) X(1) X(2) ... 0.000570996 0.8147 0.9058 3.56317e-08 0.1270 0.9134 0.00778331 0.6324 0.0975 3.09754e-06 0.2785 0.5469 0.00235794 0.9575 0.9649 3.79575e-08 0.1576 0.9706 0.0507988 0.9572 0.4854 0.0615987 0.8003 0.1419 2.18022e-06 0.4218 0.9157 0.000295509 0.7922 0.9595 Problem 6 C parameters: 1: 2.29988 2: 2.00012 W parameters: 1: 0.765517 2: 0.7952 F(X) X(1) X(2) ... 0 0.8147 0.9058 0 0.1270 0.9134 5.20409 0.6324 0.0975 5.66519 0.2785 0.5469 0 0.9575 0.9649 0 0.1576 0.9706 0 0.9572 0.4854 0 0.8003 0.1419 0 0.4218 0.9157 0 0.7922 0.9595 TEST_INTERP_ND_TEST02 P00_F evaluates the function. Here, we use spatial dimension M = 3 The number of points is N = 10 Problem 1 C parameters: 1: 0.944474 2: 0.355712 3: 0.199813 W parameters: 1: 0.251084 2: 0.616045 3: 0.473289 F(X) X(1) X(2) ... -0.431862 0.1869 0.4898 0.4456 -0.852298 0.6463 0.7094 0.7547 -0.597344 0.2760 0.6797 0.6551 -0.297718 0.1626 0.1190 0.4984 -0.913289 0.9597 0.3404 0.5853 -0.511046 0.2238 0.7513 0.2551 -0.790337 0.5060 0.6991 0.8909 -0.906613 0.9593 0.5472 0.1386 -0.396223 0.1493 0.2575 0.8407 -0.552436 0.2543 0.8143 0.2435 Problem 2 C parameters: 1: 0.596791 2: 1.40997 3: 0.993234 W parameters: 1: 0.549724 2: 0.917194 3: 0.285839 F(X) X(1) X(2) ... 0.47743 0.1869 0.4898 0.4456 0.526883 0.6463 0.7094 0.7547 0.539226 0.2760 0.6797 0.6551 0.280079 0.1626 0.1190 0.4984 0.364439 0.9597 0.3404 0.5853 0.637524 0.2238 0.7513 0.2551 0.468507 0.5060 0.6991 0.8909 0.507284 0.9593 0.5472 0.1386 0.271735 0.1493 0.2575 0.8407 0.662308 0.2543 0.8143 0.2435 Problem 3 C parameters: 1: 0.740636 2: 0.737241 3: 0.372123 W parameters: 1: 0.567822 2: 0.0758543 3: 0.0539501 F(X) X(1) X(2) ... 0.130029 0.1869 0.4898 0.4456 0.0368437 0.6463 0.7094 0.7547 0.0692582 0.2760 0.6797 0.6551 0.265109 0.1626 0.1190 0.4984 0.0443124 0.9597 0.3404 0.5853 0.0922401 0.2238 0.7513 0.2551 0.041049 0.5060 0.6991 0.8909 0.0454744 0.9593 0.5472 0.1386 0.14763 0.1493 0.2575 0.8407 0.0801748 0.2543 0.8143 0.2435 Problem 4 C parameters: 1: 1.6629 2: 2.441 3: 2.9261 W parameters: 1: 0.129906 2: 0.568824 3: 0.469391 F(X) X(1) X(2) ... 0.950214 0.1869 0.4898 0.4456 0.211821 0.6463 0.7094 0.7547 0.652088 0.2760 0.6797 0.6551 0.296471 0.1626 0.1190 0.4984 0.097283 0.9597 0.3404 0.5853 0.54015 0.2238 0.7513 0.2551 0.133537 0.5060 0.6991 0.8909 0.0583279 0.9593 0.5472 0.1386 0.172202 0.1493 0.2575 0.8407 0.432325 0.2543 0.8143 0.2435 Problem 5 C parameters: 1: 0.474959 2: 13.4531 3: 6.47198 W parameters: 1: 0.794285 2: 0.311215 3: 0.528533 F(X) X(1) X(2) ... 0.039662 0.1869 0.4898 0.4456 0.00101763 0.6463 0.7094 0.7547 0.00242345 0.2760 0.6797 0.6551 0.0459048 0.1626 0.1190 0.4984 0.432485 0.9597 0.3404 0.5853 0.000348914 0.2238 0.7513 0.2551 0.000452772 0.5060 0.6991 0.8909 0.00309867 0.9593 0.5472 0.1386 0.0473915 0.1493 0.2575 0.8407 0.000140701 0.2543 0.8143 0.2435 Problem 6 C parameters: 1: 0.691139 2: 2.51166 3: 1.0972 W parameters: 1: 0.654079 2: 0.689215 3: 0.748152 F(X) X(1) X(2) ... 6.34822 0.1869 0.4898 0.4456 0 0.6463 0.7094 0.7547 13.6909 0.2760 0.6797 0.6551 2.60667 0.1626 0.1190 0.4984 0 0.9597 0.3404 0.5853 0 0.2238 0.7513 0.2551 0 0.5060 0.6991 0.8909 0 0.9593 0.5472 0.1386 5.32489 0.1493 0.2575 0.8407 0 0.2543 0.8143 0.2435 TEST_INTERP_ND_TEST02 P00_F evaluates the function. Here, we use spatial dimension M = 4 The number of points is N = 10 Problem 1 C parameters: 1: 0.270435 2: 0.0321815 3: 0.585059 4: 0.612325 W parameters: 1: 0.490864 2: 0.489253 3: 0.337719 4: 0.900054 F(X) X(1) X(2) ... -0.724587 0.4505 0.0838 0.2290 0.9133 -0.593575 0.1524 0.8258 0.5383 0.9961 -0.808394 0.0782 0.4427 0.1067 0.9619 -0.55795 0.0046 0.7749 0.8173 0.8687 -0.81374 0.0844 0.3998 0.2599 0.8001 -0.937125 0.4314 0.9106 0.1818 0.2638 -0.660066 0.1455 0.1361 0.8693 0.5797 -0.560392 0.5499 0.1450 0.8530 0.6221 -0.944206 0.3510 0.5132 0.4018 0.0760 -0.964837 0.2399 0.1233 0.1839 0.2400 Problem 2 C parameters: 1: 0.894905 2: 0.26951 3: 1.89102 4: 0.944569 W parameters: 1: 0.241691 2: 0.403912 3: 0.0964545 4: 0.131973 F(X) X(1) X(2) ... 0.108425 0.4505 0.0838 0.2290 0.9133 0.0643379 0.1524 0.8258 0.5383 0.9961 0.112488 0.0782 0.4427 0.1067 0.9619 0.0414507 0.0046 0.7749 0.8173 0.8687 0.11881 0.0844 0.3998 0.2599 0.8001 0.169955 0.4314 0.9106 0.1818 0.2638 0.049578 0.1455 0.1361 0.8693 0.5797 0.0463914 0.5499 0.1450 0.8530 0.6221 0.137364 0.3510 0.5132 0.4018 0.0760 0.177776 0.2399 0.1233 0.1839 0.2400 Problem 3 C parameters: 1: 0.687988 2: 0.698274 3: 0.42008 4: 0.0436576 W parameters: 1: 0.23478 2: 0.353159 3: 0.821194 4: 0.0154034 F(X) X(1) X(2) ... 0.129704 0.4505 0.0838 0.2290 0.9133 0.0353658 0.1524 0.8258 0.5383 0.9961 0.156179 0.0782 0.4427 0.1067 0.9619 0.0377773 0.0046 0.7749 0.8173 0.8687 0.140191 0.0844 0.3998 0.2599 0.8001 0.0296894 0.4314 0.9106 0.1818 0.2638 0.09977 0.1455 0.1361 0.8693 0.5797 0.0443189 0.5499 0.1450 0.8530 0.6221 0.057246 0.3510 0.5132 0.4018 0.0760 0.232411 0.2399 0.1233 0.1839 0.2400 Problem 4 C parameters: 1: 0.189884 2: 0.745832 3: 2.86485 4: 3.22943 W parameters: 1: 0.647746 2: 0.450924 3: 0.547009 4: 0.296321 F(X) X(1) X(2) ... 0.0076198 0.4505 0.0838 0.2290 0.9133 0.0055428 0.1524 0.8258 0.5383 0.9961 0.00198262 0.0782 0.4427 0.1067 0.9619 0.0167448 0.0046 0.7749 0.8173 0.8687 0.0355746 0.0844 0.3998 0.2599 0.8001 0.293853 0.4314 0.9106 0.1818 0.2638 0.173038 0.1455 0.1361 0.8693 0.5797 0.145495 0.5499 0.1450 0.8530 0.6221 0.504203 0.3510 0.5132 0.4018 0.0760 0.306998 0.2399 0.1233 0.1839 0.2400 Problem 5 C parameters: 1: 8.42144 2: 2.13682 3: 7.76648 4: 2.07526 W parameters: 1: 0.368485 2: 0.625619 3: 0.780227 4: 0.0811258 F(X) X(1) X(2) ... 0.000386999 0.4505 0.0838 0.2290 0.9133 0.00241709 0.1524 0.8258 0.5383 0.9961 5.0433e-05 0.0782 0.4427 0.1067 0.9619 0.00496416 0.0046 0.7749 0.8173 0.8687 0.000223075 0.0844 0.3998 0.2599 0.8001 0.00210083 0.4314 0.9106 0.1818 0.2638 0.00956157 0.1455 0.1361 0.8693 0.5797 0.0143712 0.5499 0.1450 0.8530 0.6221 0.0355274 0.3510 0.5132 0.4018 0.0760 0.000811224 0.2399 0.1233 0.1839 0.2400 Problem 6 C parameters: 1: 1.52083 2: 1.26936 3: 0.796577 4: 0.713231 W parameters: 1: 0.446784 2: 0.306349 3: 0.508509 4: 0.510772 F(X) X(1) X(2) ... 0 0.4505 0.0838 0.2290 0.9133 0 0.1524 0.8258 0.5383 0.9961 0 0.0782 0.4427 0.1067 0.9619 0 0.0046 0.7749 0.8173 0.8687 0 0.0844 0.3998 0.2599 0.8001 0 0.4314 0.9106 0.1818 0.2638 4.48161 0.1455 0.1361 0.8693 0.5797 0 0.5499 0.1450 0.8530 0.6221 0 0.3510 0.5132 0.4018 0.0760 2.31416 0.2399 0.1233 0.1839 0.2400 TEST_INTERP_ND_TEST03 P00_F evaluates derivative components. Here, we use spatial dimension M = 2 The number of points is N = 2 Problem 1 C parameters: 1: 0.905508 2: 0.594492 W parameters: 1: 0.350727 2: 0.939002 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 -0.962431 0.2459 0.1614 0.6443 0.3786 -0.99164 -0.1168 -0.0767 Problem 2 C parameters: 1: 1.22845 2: 0.771554 W parameters: 1: 0.622475 2: 0.587045 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 0.828237 -0.4613 -0.1998 0.6443 0.3786 0.87507 -0.0576 0.2117 Problem 3 C parameters: 1: 0.755072 2: 1.09493 W parameters: 1: 0.470923 2: 0.230488 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 0.0649579 -0.0591 -0.0858 0.6443 0.3786 0.145551 -0.1734 -0.2515 Problem 4 C parameters: 1: 5.71229 2: 1.31771 W parameters: 1: 0.225922 2: 0.170708 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 5.55536e-06 -0.0002 -0.0000 0.6443 0.3786 0.00306667 -0.0837 -0.0022 Problem 5 C parameters: 1: 7.00122 2: 13.3988 W parameters: 1: 0.311102 2: 0.92338 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 0.00515037 -0.0361 0.0690 0.6443 0.3786 6.55843e-05 -0.0005 0.0009 Problem 6 C parameters: 1: 3.00784 2: 1.29216 W parameters: 1: 0.904881 2: 0.979748 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8176 0.7948 32.6663 98.2548 42.2101 0.6443 0.3786 11.3275 34.0711 14.6369 TEST_INTERP_ND_TEST03 P00_F evaluates derivative components. Here, we use spatial dimension M = 3 The number of points is N = 2 Problem 1 C parameters: 1: 0.588788 2: 0.694635 3: 0.216577 W parameters: 1: 0.117418 2: 0.296676 3: 0.318778 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0.42735 -0.5323 -0.6280 -0.1958 0.4087 0.5949 0.2622 0.12206 -0.5844 -0.6894 -0.2150 Problem 2 C parameters: 1: 1.25056 2: 1.49731 3: 0.252125 W parameters: 1: 0.262482 2: 0.801015 3: 0.0292203 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0.102479 -0.0539 0.1534 -0.0030 0.4087 0.5949 0.2622 0.196233 -0.0869 0.1656 -0.0058 Problem 3 C parameters: 1: 0.800068 2: 0.62907 3: 0.420863 W parameters: 1: 0.578525 2: 0.237284 3: 0.458849 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0.182661 -0.3822 -0.3005 -0.2010 0.4087 0.5949 0.2622 0.0928454 -0.1640 -0.1290 -0.0863 Problem 4 C parameters: 1: 3.33354 2: 1.89266 3: 1.80381 W parameters: 1: 0.231594 2: 0.488898 3: 0.62406 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0.240628 -1.1085 0.6513 0.5731 0.4087 0.5949 0.2622 0.442681 -1.7427 -0.3362 1.0424 Problem 5 C parameters: 1: 9.60716 2: 5.59502 3: 5.19782 W parameters: 1: 0.987982 2: 0.0377389 3: 0.885168 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0.000130317 0.0013 -0.0007 0.0007 0.4087 0.5949 0.2622 6.65339e-06 0.0001 -0.0000 0.0000 Problem 6 C parameters: 1: 2.17187 2: 1.89339 3: 0.234745 W parameters: 1: 0.261871 2: 0.335357 3: 0.679728 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.4389 0.1111 0.2581 0 0.0000 0.0000 0.0000 0.4087 0.5949 0.2622 0 0.0000 0.0000 0.0000 TEST_INTERP_ND_TEST03 P00_F evaluates derivative components. Here, we use spatial dimension M = 4 The number of points is N = 2 Problem 1 C parameters: 1: 0.629882 2: 0.236253 3: 0.494013 4: 0.139852 W parameters: 1: 0.0305409 2: 0.744074 3: 0.500022 4: 0.479922 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 0.829564 -0.3517 -0.1319 -0.2759 -0.0781 0.4942 0.7791 0.7150 0.9037 0.393056 -0.5792 -0.2172 -0.4543 -0.1286 Problem 2 C parameters: 1: 1.20964 2: 0.815412 3: 0.825841 4: 1.1491 W parameters: 1: 0.805489 2: 0.576722 3: 0.182922 4: 0.239932 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 0.424234 0.5019 -0.0804 0.0439 -0.3781 0.4942 0.7791 0.7150 0.9037 0.395812 0.3158 -0.1037 -0.2408 -0.4386 Problem 3 C parameters: 1: 1.04261 2: 0.0337233 3: 0.576166 4: 0.197497 W parameters: 1: 0.978681 2: 0.712694 3: 0.500472 4: 0.471088 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 0.217063 -0.8337 -0.0270 -0.4607 -0.1579 0.4942 0.7791 0.7150 0.9037 0.0227038 -0.0555 -0.0018 -0.0307 -0.0105 Problem 4 C parameters: 1: 0.489932 2: 5.60426 3: 0.348688 4: 0.58712 W parameters: 1: 0.52165 2: 0.09673 3: 0.818149 4: 0.817547 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 4.30686e-06 0.0000 -0.0002 0.0000 0.0000 0.4942 0.7791 0.7150 0.9037 4.44501e-07 0.0000 -0.0000 0.0000 -0.0000 Problem 5 C parameters: 1: 7.18738 2: 1.49098 3: 6.56226 4: 5.15938 W parameters: 1: 0.972975 2: 0.648991 3: 0.800331 4: 0.453798 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 8.27369e-06 0.0001 -0.0000 0.0001 -0.0000 0.4942 0.7791 0.7150 0.9037 0.00147916 0.0106 -0.0022 0.0097 -0.0076 Problem 6 C parameters: 1: 1.26109 2: 2.40707 3: 0.243444 4: 0.3884 W parameters: 1: 0.173389 2: 0.390938 3: 0.83138 4: 0.803364 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.1366 0.7212 0.1068 0.6538 0 0.0000 0.0000 0.0000 0.0000 0.4942 0.7791 0.7150 0.9037 0 0.0000 0.0000 0.0000 0.0000 test_interp_nd_test04(): P00_Q returns the integral of F over [0,1]^m. Here, we use spatial dimension M = 4 The number of sample points is N = 10000 Problem 1 C parameters: 1: 0.575845 2: 0.167653 3: 0.226795 4: 0.529707 W parameters: 1: 0.666451 2: 0.542481 3: 0.392035 4: 0.914552 Exact Integral Q 0.216794 0.214441 Problem 2 C parameters: 1: 1.97992 2: 0.614389 3: 1.16644 4: 0.239248 W parameters: 1: 0.762395 2: 0.658191 3: 0.0621667 4: 0.117271 Exact Integral Q 0.0609936 0.0607107 Problem 3 C parameters: 1: 0.62107 2: 0.333057 3: 0.289255 4: 0.606619 W parameters: 1: 0.800498 2: 0.403401 3: 0.384311 4: 0.238203 Exact Integral Q 0.054045 0.0540671 Problem 4 C parameters: 1: 1.09147 2: 1.68991 3: 3.08908 4: 1.15954 W parameters: 1: 0.956506 2: 0.363871 3: 0.50477 4: 0.234084 Exact Integral Q 0.268487 0.266316 Problem 5 C parameters: 1: 6.03405 2: 6.33029 3: 0.621065 4: 7.4146 W parameters: 1: 0.795778 2: 0.581647 3: 0.0696146 4: 0.646938 Exact Integral Q 0.0169927 0.0172896 Problem 6 C parameters: 1: 0.759802 2: 0.754689 3: 1.8965 4: 0.889011 W parameters: 1: 0.819915 2: 0.775007 3: 0.461763 4: 0.918841 Exact Integral Q 5.7656 5.81255 test_interp_nd_test(): Normal end of execution. 08-Jan-2022 10:27:27