06-Jun-2023 15:47:06 test_interp_nd_test() MATLAB/Octave version 5.2.0 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: 1.43743 2: 0.0625681 W parameters: 1: 0.0675185 2: 0.115773 F(X) X(1) X(2) ... -0.232801 0.9312 0.6872 -0.330542 0.9942 0.8694 -0.0821942 0.8479 0.1612 0.229458 0.6006 0.8258 0.231202 0.5944 0.9394 0.166049 0.6639 0.4060 -0.146482 0.8922 0.1764 0.296284 0.5754 0.2991 0.574196 0.3452 0.6189 0.603984 0.3293 0.3947 Problem 2 C parameters: 1: 0.461142 2: 1.53886 W parameters: 1: 0.507167 2: 0.281167 F(X) X(1) X(2) ... 0.348831 0.9312 0.6872 0.263489 0.9942 0.8694 0.475238 0.8479 0.1612 0.295237 0.6006 0.8258 0.248152 0.5944 0.9394 0.483129 0.6639 0.4060 0.475828 0.8922 0.1764 0.502699 0.5754 0.2991 0.394303 0.3452 0.6189 0.485404 0.3293 0.3947 Problem 3 C parameters: 1: 0.314254 2: 1.53575 W parameters: 1: 0.690969 2: 0.41401 F(X) X(1) X(2) ... 0.0772484 0.9312 0.6872 0.0538811 0.9942 0.8694 0.288185 0.8479 0.1612 0.0674179 0.6006 0.8258 0.0550027 0.5944 0.9394 0.162595 0.6639 0.4060 0.267828 0.8922 0.1764 0.226658 0.5754 0.2991 0.114576 0.3452 0.6189 0.200127 0.3293 0.3947 Problem 4 C parameters: 1: 4.22977 2: 2.80023 W parameters: 1: 0.570454 2: 0.307703 F(X) X(1) X(2) ... 0.0315057 0.9312 0.6872 0.00339302 0.9942 0.8694 0.213233 0.8479 0.1612 0.119871 0.6006 0.8258 0.0433111 0.5944 0.9394 0.79289 0.6639 0.4060 0.137018 0.8922 0.1764 0.998985 0.5754 0.2991 0.188841 0.3452 0.6189 0.333017 0.3293 0.3947 Problem 5 C parameters: 1: 10.3344 2: 10.0656 W parameters: 1: 0.287934 2: 0.396461 F(X) X(1) X(2) ... 6.94873e-05 0.9312 0.6872 5.79219e-06 0.9942 0.8694 0.000287241 0.8479 0.1612 0.000524302 0.6006 0.8258 0.00017819 0.5944 0.9394 0.018654 0.6639 0.4060 0.00021183 0.8922 0.1764 0.019242 0.5754 0.2991 0.0589802 0.3452 0.6189 0.640375 0.3293 0.3947 Problem 6 C parameters: 1: 3.7678 2: 0.532199 W parameters: 1: 0.868071 2: 0.659047 F(X) X(1) X(2) ... 0 0.9312 0.6872 0 0.9942 0.8694 26.5866 0.8479 0.1612 0 0.6006 0.8258 0 0.5944 0.9394 15.1439 0.6639 0.4060 0 0.8922 0.1764 10.2476 0.5754 0.2991 5.10418 0.3452 0.6189 4.26684 0.3293 0.3947 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: 0.958985 2: 0.0197365 3: 0.521279 W parameters: 1: 0.107271 2: 0.135913 3: 0.101668 F(X) X(1) X(2) ... 0.22376 0.3570 0.9332 0.5954 -0.293017 0.9249 0.9143 0.5548 -0.26526 0.9014 0.9213 0.5422 0.403815 0.0016 0.7025 0.8934 0.251431 0.4680 0.1416 0.3665 -0.329893 0.7798 0.8566 0.8983 -0.0660658 0.9445 0.8540 0.0773 0.221195 0.6205 0.0354 0.1496 0.141948 0.2300 0.8114 0.9933 0.203062 0.3664 0.5880 0.6318 Problem 2 C parameters: 1: 0.588935 2: 1.05667 3: 1.35439 W parameters: 1: 0.97402 2: 0.957158 3: 0.710414 F(X) X(1) X(2) ... 0.612266 0.3570 0.9332 0.5954 0.678224 0.9249 0.9143 0.5548 0.673164 0.9014 0.9213 0.5422 0.469982 0.0016 0.7025 0.8934 0.307627 0.4680 0.1416 0.3665 0.651213 0.7798 0.8566 0.8983 0.40447 0.9445 0.8540 0.0773 0.22157 0.6205 0.0354 0.1496 0.507654 0.2300 0.8114 0.9933 0.540443 0.3664 0.5880 0.6318 Problem 3 C parameters: 1: 1.63696 2: 0.0280013 3: 0.185037 W parameters: 1: 0.495549 2: 0.201568 3: 0.0327625 F(X) X(1) X(2) ... 0.114074 0.3570 0.9332 0.5954 0.0205176 0.9249 0.9143 0.5548 0.0218265 0.9014 0.9213 0.5422 0.50265 0.0016 0.7025 0.8934 0.0876441 0.4680 0.1416 0.3665 0.0270118 0.7798 0.8566 0.8983 0.0224195 0.9445 0.8540 0.0773 0.0572388 0.6205 0.0354 0.1496 0.159235 0.2300 0.8114 0.9933 0.11083 0.3664 0.5880 0.6318 Problem 4 C parameters: 1: 1.54704 2: 3.5726 3: 1.91036 W parameters: 1: 0.738717 2: 0.55294 3: 0.100435 F(X) X(1) X(2) ... 0.0455821 0.3570 0.9332 0.5954 0.0818743 0.9249 0.9143 0.5548 0.0815039 0.9014 0.9213 0.5422 0.0206461 0.0016 0.7025 0.8934 0.0747497 0.4680 0.1416 0.3665 0.0300613 0.7798 0.8566 0.8983 0.283628 0.9445 0.8540 0.0773 0.0313951 0.6205 0.0354 0.1496 0.0125147 0.2300 0.8114 0.9933 0.252143 0.3664 0.5880 0.6318 Problem 5 C parameters: 1: 12.6412 2: 5.78816 3: 1.97062 W parameters: 1: 0.244683 2: 0.677163 3: 0.752897 F(X) X(1) X(2) ... 0.0402632 0.3570 0.9332 0.5954 3.16454e-05 0.9249 0.9143 0.5548 3.98829e-05 0.9014 0.9213 0.5422 0.0303224 0.0016 0.7025 0.8934 0.00124973 0.4680 0.1416 0.3665 0.000306734 0.7798 0.8566 0.8983 1.36584e-05 0.9445 0.8540 0.0773 6.41187e-05 0.6205 0.0354 0.1496 0.237919 0.2300 0.8114 0.9933 0.100898 0.3664 0.5880 0.6318 Problem 6 C parameters: 1: 0.444283 2: 2.54393 3: 1.31179 W parameters: 1: 0.502071 2: 0.0798042 3: 0.260839 F(X) X(1) X(2) ... 0 0.3570 0.9332 0.5954 0 0.9249 0.9143 0.5548 0 0.9014 0.9213 0.5422 0 0.0016 0.7025 0.8934 0 0.4680 0.1416 0.3665 0 0.7798 0.8566 0.8983 0 0.9445 0.8540 0.0773 0 0.6205 0.0354 0.1496 0 0.2300 0.8114 0.9933 0 0.3664 0.5880 0.6318 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: 0.615037 2: 0.122848 3: 0.529379 4: 0.232736 W parameters: 1: 0.130268 2: 0.0477222 3: 0.974673 4: 0.506468 F(X) X(1) X(2) ... -0.48177 0.9888 0.3373 0.8570 0.6517 0.0424305 0.1546 0.6769 0.6825 0.7318 -0.449244 0.8385 0.4647 0.9028 0.7198 -0.109907 0.3606 0.9185 0.6633 0.7592 -0.0428288 0.6276 0.0693 0.5255 0.5261 -0.0170831 0.8500 0.1053 0.3807 0.1380 -0.0864018 0.8111 0.9523 0.1389 0.6422 -0.15601 0.3932 0.2667 0.9771 0.5032 0.113643 0.1054 0.9294 0.8154 0.1192 -0.193835 0.4346 0.6132 0.8210 0.7309 Problem 2 C parameters: 1: 0.468217 2: 0.244509 3: 1.61343 4: 1.67384 W parameters: 1: 0.281944 2: 0.506556 3: 0.939921 4: 0.743822 F(X) X(1) X(2) ... 0.0825355 0.9888 0.3373 0.8570 0.6517 0.0810607 0.1546 0.6769 0.6825 0.7318 0.0890394 0.8385 0.4647 0.9028 0.7198 0.0787525 0.3606 0.9185 0.6633 0.7592 0.0561776 0.6276 0.0693 0.5255 0.5261 0.0240319 0.8500 0.1053 0.3807 0.1380 0.0323944 0.8111 0.9523 0.1389 0.6422 0.0814528 0.3932 0.2667 0.9771 0.5032 0.0431372 0.1054 0.9294 0.8154 0.1192 0.0916222 0.4346 0.6132 0.8210 0.7309 Problem 3 C parameters: 1: 0.330657 2: 0.587026 3: 0.443047 4: 0.489271 W parameters: 1: 0.296709 2: 0.91996 3: 0.848739 4: 0.962731 F(X) X(1) X(2) ... 0.018397 0.9888 0.3373 0.8570 0.6517 0.023974 0.1546 0.6769 0.6825 0.7318 0.0154634 0.8385 0.4647 0.9028 0.7198 0.0147599 0.3606 0.9185 0.6633 0.7592 0.0629858 0.6276 0.0693 0.5255 0.5261 0.101866 0.8500 0.1053 0.3807 0.1380 0.0192745 0.8111 0.9523 0.1389 0.6422 0.0340771 0.3932 0.2667 0.9771 0.5032 0.0312479 0.1054 0.9294 0.8154 0.1192 0.0183372 0.4346 0.6132 0.8210 0.7309 Problem 4 C parameters: 1: 1.72576 2: 3.18425 3: 0.0831732 4: 2.03681 W parameters: 1: 0.32851 2: 0.842507 3: 0.497141 4: 0.0528144 F(X) X(1) X(2) ... 0.00463063 0.9888 0.3373 0.8570 0.6517 0.102199 0.1546 0.6769 0.6825 0.7318 0.0171056 0.8385 0.4647 0.9028 0.7198 0.118632 0.3606 0.9185 0.6633 0.7592 0.000704855 0.6276 0.0693 0.5255 0.5261 0.00174413 0.8500 0.1053 0.3807 0.1380 0.104586 0.8111 0.9523 0.1389 0.6422 0.0147342 0.3932 0.2667 0.9771 0.5032 0.78366 0.1054 0.9294 0.8154 0.1192 0.0841325 0.4346 0.6132 0.8210 0.7309 Problem 5 C parameters: 1: 10.1473 2: 1.93905 3: 2.01076 4: 6.30286 W parameters: 1: 0.56615 2: 0.27585 3: 0.369558 4: 0.196447 F(X) X(1) X(2) ... 0.000259219 0.9888 0.3373 0.8570 0.6517 0.000128895 0.1546 0.6769 0.6825 0.7318 0.000553039 0.8385 0.4647 0.9028 0.7198 0.000570222 0.3606 0.9185 0.6633 0.7592 0.0328617 0.6276 0.0693 0.5255 0.5261 0.0272663 0.8500 0.1053 0.3807 0.1380 0.000850044 0.8111 0.9523 0.1389 0.6422 0.00724316 0.3932 0.2667 0.9771 0.5032 0.000658383 0.1054 0.9294 0.8154 0.1192 0.0019013 0.4346 0.6132 0.8210 0.7309 Problem 6 C parameters: 1: 1.54679 2: 1.44418 3: 0.135149 4: 1.17388 W parameters: 1: 0.8791 2: 0.859192 3: 0.712264 4: 0.48301 F(X) X(1) X(2) ... 0 0.9888 0.3373 0.8570 0.6517 8.74078 0.1546 0.6769 0.6825 0.7318 18.8208 0.8385 0.4647 0.9028 0.7198 0 0.3606 0.9185 0.6633 0.7592 5.80924 0.6276 0.0693 0.5255 0.5261 5.36702 0.8500 0.1053 0.3807 0.1380 0 0.8111 0.9523 0.1389 0.6422 5.5628 0.3932 0.2667 0.9771 0.5032 0 0.1054 0.9294 0.8154 0.1192 12.5132 0.4346 0.6132 0.8210 0.7309 test_interp_nd_test03(): p00_d() evaluates derivative components. Here, we use spatial dimension M = 2 The number of points is N = 2 Problem 1 C parameters: 1: 0.612138 2: 0.887862 W parameters: 1: 0.600442 2: 0.58188 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 -0.229624 0.5958 0.8641 0.8209 0.1445 -0.304023 0.5832 0.8458 Problem 2 C parameters: 1: 1.30735 2: 0.692649 W parameters: 1: 0.147717 2: 0.102039 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 0.530866 -0.6566 -0.1080 0.8209 0.1445 0.461691 -0.5987 -0.0188 Problem 3 C parameters: 1: 0.92093 2: 0.92907 W parameters: 1: 0.220821 2: 0.920726 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 0.137911 -0.1969 -0.1986 0.8209 0.1445 0.148068 -0.2164 -0.2183 Problem 4 C parameters: 1: 4.15957 2: 2.87043 W parameters: 1: 0.221245 2: 0.81842 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 0.00266167 -0.0436 0.0219 0.8209 0.1445 4.70852e-05 -0.0010 0.0005 Problem 5 C parameters: 1: 11.7711 2: 8.62886 W parameters: 1: 0.57409 2: 0.171348 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 0.0680991 -0.8016 -0.5876 0.8209 0.1445 0.0434176 -0.5111 0.3746 Problem 6 C parameters: 1: 1.71004 2: 2.58996 W parameters: 1: 0.140524 2: 0.361861 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.6943 0.3188 0 0.0000 0.0000 0.8209 0.1445 0 0.0000 0.0000 test_interp_nd_test03(): p00_d() evaluates derivative components. Here, we use spatial dimension M = 3 The number of points is N = 2 Problem 1 C parameters: 1: 0.645909 2: 0.292273 3: 0.561819 W parameters: 1: 0.309195 2: 0.214519 3: 0.138261 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 -0.906159 -0.2732 -0.1236 -0.2376 0.9595 0.8433 0.3240 -0.988674 -0.0969 -0.0439 -0.0843 Problem 2 C parameters: 1: 0.285685 2: 1.3222 3: 1.39212 W parameters: 1: 0.59547 2: 0.541218 3: 0.0243391 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 0.271925 -0.0111 -0.0643 -0.0449 0.9595 0.8433 0.3240 0.200961 -0.0118 -0.1830 -0.1988 Problem 3 C parameters: 1: 0.325073 2: 1.20467 3: 0.320261 W parameters: 1: 0.991258 2: 0.833904 3: 0.406973 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 0.0588145 -0.0377 -0.1396 -0.0371 0.9595 0.8433 0.3240 0.028608 -0.0153 -0.0567 -0.0151 Problem 4 C parameters: 1: 6.3058 2: 0.0720876 3: 0.652117 W parameters: 1: 0.873522 2: 0.467553 3: 0.21522 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 0.961048 2.1095 -0.0014 0.1211 0.9595 0.8433 0.3240 0.7411 -5.0666 -0.0029 -0.0685 Problem 5 C parameters: 1: 5.20826 2: 8.44341 3: 6.74832 W parameters: 1: 0.853548 2: 0.413787 3: 0.04239 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 0.155975 0.8124 -1.3170 -1.0526 0.9595 0.8433 0.3240 0.00229213 -0.0119 -0.0194 -0.0155 Problem 6 C parameters: 1: 1.67302 2: 0.596209 3: 2.03077 W parameters: 1: 0.590921 2: 0.134283 3: 0.45502 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.8459 0.6094 0.0671 0 0.0000 0.0000 0.0000 0.9595 0.8433 0.3240 0 0.0000 0.0000 0.0000 test_interp_nd_test03(): p00_d() evaluates derivative components. Here, we use spatial dimension M = 4 The number of points is N = 2 Problem 1 C parameters: 1: 0.342411 2: 0.441467 3: 0.527944 4: 0.188179 W parameters: 1: 0.449647 2: 0.597161 3: 0.284377 4: 0.977175 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 -0.897762 0.1508 0.1945 0.2325 0.0829 0.1681 0.0435 0.2091 0.5363 -0.999599 -0.0097 -0.0125 -0.0149 -0.0053 Problem 2 C parameters: 1: 0.655848 2: 2.00542 3: 0.0615981 4: 1.27713 W parameters: 1: 0.541489 2: 0.644778 3: 0.848636 4: 0.951095 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 0.00293261 -0.0010 0.0056 0.0000 0.0037 0.1681 0.0435 0.2091 0.5363 0.00320878 0.0010 0.0063 0.0000 0.0034 Problem 3 C parameters: 1: 0.689386 2: 0.43269 3: 0.0433906 4: 0.684533 W parameters: 1: 0.8696 2: 0.913685 3: 0.679412 4: 0.079159 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 0.0436009 -0.0803 -0.0504 -0.0051 -0.0798 0.1681 0.0435 0.2091 0.5363 0.126999 -0.2897 -0.1818 -0.0182 -0.2877 Problem 4 C parameters: 1: 0.633775 2: 0.151803 3: 3.67236 4: 2.57207 W parameters: 1: 0.811011 2: 0.859439 3: 0.595415 4: 0.220394 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 0.878823 -0.1056 0.0236 0.4855 1.4769 0.1681 0.0435 0.2091 0.5363 0.0575775 0.0297 0.0022 0.6000 -0.2407 Problem 5 C parameters: 1: 5.12399 2: 3.94745 3: 5.92991 4: 5.39865 W parameters: 1: 0.164282 2: 0.817322 3: 0.206625 4: 0.520032 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 2.25852e-05 -0.0001 0.0001 -0.0001 0.0001 0.1681 0.0435 0.2091 0.5363 0.0417129 -0.2137 0.1647 -0.2474 -0.2252 Problem 6 C parameters: 1: 0.903558 2: 1.24552 3: 1.41455 4: 0.736381 W parameters: 1: 0.202943 2: 0.375784 3: 0.919384 4: 0.872546 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9605 0.2775 0.5749 0.0934 0 0.0000 0.0000 0.0000 0.0000 0.1681 0.0435 0.2091 0.5363 2.45156 2.2151 3.0535 3.4678 1.8053 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: 0.359719 2: 0.306028 3: 0.365838 4: 0.468415 W parameters: 1: 0.855967 2: 0.254656 3: 0.273244 4: 0.388141 Exact Integral Q 0.96454 0.964692 Problem 2 C parameters: 1: 1.48855 2: 1.09641 3: 0.913037 4: 0.502001 W parameters: 1: 0.358804 2: 0.904641 3: 0.70568 4: 0.842993 Exact Integral Q 0.331813 0.332248 Problem 3 C parameters: 1: 0.0399835 2: 0.267955 3: 0.210119 4: 1.33194 W parameters: 1: 0.486362 2: 0.383197 3: 0.238553 4: 0.762214 Exact Integral Q 0.075338 0.0764523 Problem 4 C parameters: 1: 1.05934 2: 2.61584 3: 2.40747 4: 0.947348 W parameters: 1: 0.32986 2: 0.269941 3: 0.706281 4: 0.881251 Exact Integral Q 0.257486 0.259095 Problem 5 C parameters: 1: 2.70837 2: 6.46145 3: 3.75709 4: 7.47309 W parameters: 1: 0.267163 2: 0.417978 3: 0.399381 4: 0.00258548 Exact Integral Q 0.00911919 0.00941679 Problem 6 C parameters: 1: 0.0343049 2: 1.29674 3: 1.5385 4: 1.43046 W parameters: 1: 0.148171 2: 0.0231705 3: 0.957515 4: 0.335125 Exact Integral Q 0.0184705 0.0170405 test_interp_nd_test(): Normal end of execution. 06-Jun-2023 15:47:06