16-May-2025 08:49:56 test_interp_nd_test() MATLAB/Octave version 6.4.0 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: 0.920682 2: 0.579318 W parameters: 1: 0.943947 2: 0.0968807 F(X) X(1) X(2) ... 0.664212 0.7986 0.7963 0.999781 0.3977 0.0120 0.892125 0.7797 0.1779 0.899218 0.2952 0.9204 0.914536 0.3580 0.7578 0.998186 0.2359 0.1291 0.993722 0.3455 0.2524 0.976161 0.4386 0.2885 0.961038 0.0283 0.0795 0.853204 0.5556 0.6721 Problem 2 C parameters: 1: 1.13664 2: 0.863359 W parameters: 1: 0.461927 2: 0.238942 F(X) X(1) X(2) ... 0.682074 0.7986 0.7963 0.922479 0.3977 0.0120 0.849482 0.7797 0.1779 0.690579 0.2952 0.9204 0.791001 0.3580 0.7578 0.89531 0.2359 0.1291 0.946291 0.3455 0.2524 0.960575 0.4386 0.2885 0.760384 0.0283 0.0795 0.835387 0.5556 0.6721 Problem 3 C parameters: 1: 0.724409 2: 1.12559 W parameters: 1: 0.24326 2: 0.68038 F(X) X(1) X(2) ... 0.0659748 0.7986 0.7963 0.453517 0.3977 0.0120 0.181842 0.7797 0.1779 0.087808 0.2952 0.9204 0.106097 0.3580 0.7578 0.438586 0.2359 0.1291 0.276811 0.3455 0.2524 0.225682 0.4386 0.2885 0.731149 0.0283 0.0795 0.0993698 0.5556 0.6721 Problem 4 C parameters: 1: 3.97927 2: 3.05073 W parameters: 1: 0.676861 2: 0.734252 F(X) X(1) X(2) ... 0.763051 0.7986 0.7963 0.00226698 0.3977 0.0120 0.0474361 0.7797 0.1779 0.0721573 0.2952 0.9204 0.198857 0.3580 0.7578 0.00152196 0.2359 0.1291 0.02025 0.3455 0.2524 0.0640645 0.4386 0.2885 2.3699e-05 0.0283 0.0795 0.764321 0.5556 0.6721 Problem 5 C parameters: 1: 7.39744 2: 13.0026 W parameters: 1: 0.773604 2: 0.316515 F(X) X(1) X(2) ... 0.00162354 0.7986 0.7963 0.00118197 0.3977 0.0120 0.157583 0.7797 0.1779 1.12965e-05 0.2952 0.9204 0.000148824 0.3580 0.7578 0.00163726 0.2359 0.1291 0.0183106 0.3455 0.2524 0.058298 0.4386 0.2885 0.000185079 0.0283 0.0795 0.00195791 0.5556 0.6721 Problem 6 C parameters: 1: 1.87526 2: 2.42474 W parameters: 1: 0.399033 2: 0.942279 F(X) X(1) X(2) ... 0 0.7986 0.7963 2.17022 0.3977 0.0120 0 0.7797 0.1779 16.2056 0.2952 0.9204 12.2913 0.3580 0.7578 2.12835 0.2359 0.1291 3.52519 0.3455 0.2524 0 0.4386 0.2885 1.27879 0.0283 0.0795 0 0.5556 0.6721 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: 0.379429 2: 0.55145 3: 0.569121 W parameters: 1: 0.334093 2: 0.787778 3: 0.466568 F(X) X(1) X(2) ... -0.911368 0.2548 0.1941 0.7284 -0.9921 0.2652 0.6594 0.7949 -0.933844 0.6593 0.7068 0.0646 -0.968079 0.3998 0.3694 0.7620 -0.795991 0.1000 0.5379 0.1014 -0.783644 0.4769 0.0313 0.3056 -0.898876 0.2280 0.4775 0.4199 -0.95171 0.8665 0.8631 0.9660 -0.934234 0.2864 0.0918 0.9110 -0.959145 0.5273 0.1093 0.8702 Problem 2 C parameters: 1: 1.224 2: 1.28819 3: 0.487813 W parameters: 1: 0.897031 2: 0.458796 3: 0.715988 F(X) X(1) X(2) ... 0.327535 0.2548 0.1941 0.7284 0.346491 0.2652 0.6594 0.7949 0.449512 0.6593 0.7068 0.0646 0.425828 0.3998 0.3694 0.7620 0.275262 0.1000 0.5379 0.1014 0.345161 0.4769 0.0313 0.3056 0.346701 0.2280 0.4775 0.4199 0.457914 0.8665 0.8631 0.9660 0.307424 0.2864 0.0918 0.9110 0.405977 0.5273 0.1093 0.8702 Problem 3 C parameters: 1: 0.148516 2: 0.905211 3: 0.796273 W parameters: 1: 0.67482 2: 0.505087 3: 0.907466 F(X) X(1) X(2) ... 0.0966467 0.2548 0.1941 0.7284 0.037711 0.2652 0.6594 0.7949 0.0976019 0.6593 0.7068 0.0646 0.0624334 0.3998 0.3694 0.7620 0.15945 0.1000 0.5379 0.1014 0.307842 0.4769 0.0313 0.3056 0.0951575 0.2280 0.4775 0.4199 0.0194101 0.8665 0.8631 0.9660 0.0851846 0.2864 0.0918 0.9110 0.0817497 0.5273 0.1093 0.8702 Problem 4 C parameters: 1: 0.394441 2: 2.43986 3: 4.1957 W parameters: 1: 0.760291 2: 0.70175 3: 0.96119 F(X) X(1) X(2) ... 0.079807 0.2548 0.1941 0.7284 0.585216 0.2652 0.6594 0.7949 7.12446e-07 0.6593 0.7068 0.0646 0.252567 0.3998 0.3694 0.7620 1.77672e-06 0.1000 0.5379 0.1014 3.52206e-05 0.4769 0.0313 0.3056 0.00408245 0.2280 0.4775 0.4199 0.854611 0.8665 0.8631 0.9660 0.100844 0.2864 0.0918 0.9110 0.106059 0.5273 0.1093 0.8702 Problem 5 C parameters: 1: 4.80186 2: 6.68045 3: 8.91768 W parameters: 1: 0.712724 2: 0.146279 3: 0.771961 F(X) X(1) X(2) ... 0.054642 0.2548 0.1941 0.7284 0.00308419 0.2652 0.6594 0.7949 3.33156e-05 0.6593 0.7068 0.0646 0.0458803 0.3998 0.3694 0.7620 9.75245e-06 0.1000 0.5379 0.1014 0.00233623 0.4769 0.0313 0.3056 0.000462093 0.2280 0.4775 0.4199 0.00070527 0.8665 0.8631 0.9660 0.0259544 0.2864 0.0918 0.9110 0.133502 0.5273 0.1093 0.8702 Problem 6 C parameters: 1: 1.244 2: 2.76046 3: 0.295548 W parameters: 1: 0.989754 2: 0.932225 3: 0.989275 F(X) X(1) X(2) ... 2.90938 0.2548 0.1941 0.7284 10.8611 0.2652 0.6594 0.7949 16.2853 0.6593 0.7068 0.0646 5.71015 0.3998 0.3694 0.7620 5.15086 0.1000 0.5379 0.1014 2.15964 0.4769 0.0313 0.3056 5.61779 0.2280 0.4775 0.4199 42.3478 0.8665 0.8631 0.9660 2.40805 0.2864 0.0918 0.9110 3.3697 0.5273 0.1093 0.8702 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: 0.626592 2: 0.357988 3: 0.490106 4: 0.0253141 W parameters: 1: 0.950707 2: 0.503327 3: 0.225444 4: 0.579537 F(X) X(1) X(2) ... 0.878466 0.6920 0.8118 0.1614 0.1789 0.97456 0.0588 0.5699 0.5840 0.3440 0.807254 0.6462 0.2032 0.9303 0.2940 0.99617 0.0914 0.7676 0.1240 0.1756 0.977068 0.6781 0.0700 0.1237 0.5411 0.645807 0.9792 0.7577 0.5911 0.1553 0.690626 0.7894 0.4546 0.9381 0.0400 0.983695 0.2066 0.1359 0.6127 0.4794 0.839531 0.1608 0.9742 0.8679 0.3639 0.997237 0.0908 0.8963 0.0018 0.2131 Problem 2 C parameters: 1: 0.884471 2: 1.51868 3: 0.0830444 4: 1.5138 W parameters: 1: 0.714776 2: 0.164018 3: 0.0225926 4: 0.495105 F(X) X(1) X(2) ... 0.0117825 0.6920 0.8118 0.1614 0.1789 0.0146589 0.0588 0.5699 0.5840 0.3440 0.0257618 0.6462 0.2032 0.9303 0.2940 0.00962811 0.0914 0.7676 0.1240 0.1756 0.0277784 0.6781 0.0700 0.1237 0.5411 0.0117667 0.9792 0.7577 0.5911 0.1553 0.0160225 0.7894 0.4546 0.9381 0.0400 0.0236086 0.2066 0.1359 0.6127 0.4794 0.00875636 0.1608 0.9742 0.8679 0.3639 0.00826491 0.0908 0.8963 0.0018 0.2131 Problem 3 C parameters: 1: 0.526957 2: 0.278813 3: 0.48715 4: 0.557079 W parameters: 1: 0.695784 2: 0.164343 3: 0.451668 4: 0.263922 F(X) X(1) X(2) ... 0.0576721 0.6920 0.8118 0.1614 0.1789 0.077921 0.0588 0.5699 0.5840 0.3440 0.0301684 0.6462 0.2032 0.9303 0.2940 0.172969 0.0914 0.7676 0.1240 0.1756 0.0629621 0.6781 0.0700 0.1237 0.5411 0.024384 0.9792 0.7577 0.5911 0.1553 0.0295839 0.7894 0.4546 0.9381 0.0400 0.0679337 0.2066 0.1359 0.6127 0.4794 0.0327022 0.1608 0.9742 0.8679 0.3639 0.174826 0.0908 0.8963 0.0018 0.2131 Problem 4 C parameters: 1: 1.04198 2: 1.72192 3: 1.31498 4: 2.95112 W parameters: 1: 0.174578 2: 0.18925 3: 0.418759 4: 0.263129 F(X) X(1) X(2) ... 0.198641 0.6920 0.8118 0.1614 0.1789 0.577964 0.0588 0.5699 0.5840 0.3440 0.495196 0.6462 0.2032 0.9303 0.2940 0.296278 0.0914 0.7676 0.1240 0.1756 0.319585 0.6781 0.0700 0.1237 0.5411 0.163074 0.9792 0.7577 0.5911 0.1553 0.218938 0.7894 0.4546 0.9381 0.0400 0.617606 0.2066 0.1359 0.6127 0.4794 0.103878 0.1608 0.9742 0.8679 0.3639 0.163259 0.0908 0.8963 0.0018 0.2131 Problem 5 C parameters: 1: 7.4396 2: 3.99909 3: 4.21961 4: 4.7417 W parameters: 1: 0.528431 2: 0.33024 3: 0.547491 4: 0.684559 F(X) X(1) X(2) ... 0.000769567 0.6920 0.8118 0.1614 0.1789 0.00198739 0.0588 0.5699 0.5840 0.3440 0.00781619 0.6462 0.2032 0.9303 0.2940 0.000100915 0.0914 0.7676 0.1240 0.1756 0.00982357 0.6781 0.0700 0.1237 0.5411 0.000428017 0.9792 0.7577 0.5911 0.1553 0.000790178 0.7894 0.4546 0.9381 0.0400 0.0120389 0.2066 0.1359 0.6127 0.4794 0.000279405 0.1608 0.9742 0.8679 0.3639 4.28592e-05 0.0908 0.8963 0.0018 0.2131 Problem 6 C parameters: 1: 0.691646 2: 2.02278 3: 0.867186 4: 0.718391 W parameters: 1: 0.784208 2: 0.667213 3: 0.518564 4: 0.316587 F(X) X(1) X(2) ... 0 0.6920 0.8118 0.1614 0.1789 7.00714 0.0588 0.5699 0.5840 0.3440 6.52657 0.6462 0.2032 0.9303 0.2940 0 0.0914 0.7676 0.1240 0.1756 3.02392 0.6781 0.0700 0.1237 0.5411 0 0.9792 0.7577 0.5911 0.1553 0 0.7894 0.4546 0.9381 0.0400 3.64566 0.2066 0.1359 0.6127 0.4794 0 0.1608 0.9742 0.8679 0.3639 0 0.0908 0.8963 0.0018 0.2131 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: 0.898601 2: 0.601399 W parameters: 1: 0.674348 2: 0.0169413 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 -0.226918 0.8752 0.5857 0.0473 0.2047 -0.304779 0.8558 0.5728 Problem 2 C parameters: 1: 1.27888 2: 0.721116 W parameters: 1: 0.927884 2: 0.546968 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 0.429821 0.5430 0.2052 0.0473 0.2047 0.353437 0.4488 0.1186 Problem 3 C parameters: 1: 1.229 2: 0.621002 W parameters: 1: 0.471273 2: 0.800683 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 0.422593 -1.1692 -0.5908 0.0473 0.2047 0.600541 -1.8681 -0.9439 Problem 4 C parameters: 1: 6.0043 2: 1.0257 W parameters: 1: 0.865079 2: 0.706334 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 1.10493e-06 0.0000 0.0000 0.0473 0.2047 2.59854e-11 0.0000 0.0000 Problem 5 C parameters: 1: 14.6689 2: 5.73114 W parameters: 1: 0.288155 2: 0.248072 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 0.179741 2.6366 1.0301 0.0473 0.2047 0.0227919 0.3343 0.1306 Problem 6 C parameters: 1: 1.94326 2: 2.35674 W parameters: 1: 0.455618 2: 0.493603 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.2595 0.0221 1.74407 3.3892 4.1103 0.0473 0.2047 1.77603 3.4513 4.1856 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: 0.208615 2: 0.948518 3: 0.342867 W parameters: 1: 0.749932 2: 0.927014 3: 0.246181 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 0.386196 0.1924 0.8749 0.3163 0.9998 0.6932 0.1988 0.803889 0.1241 0.5642 0.2039 Problem 2 C parameters: 1: 1.79824 2: 0.848387 3: 0.353368 W parameters: 1: 0.33501 2: 0.386585 3: 0.691821 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 0.117419 -0.2094 0.0438 0.0125 0.9998 0.6932 0.1988 0.108764 -0.1925 -0.0450 0.0130 Problem 3 C parameters: 1: 0.32752 2: 0.681508 3: 0.840972 W parameters: 1: 0.45265 2: 0.12385 3: 0.862212 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 0.149433 -0.1217 -0.2533 -0.3125 0.9998 0.6932 0.1988 0.0667903 -0.0445 -0.0926 -0.1142 Problem 4 C parameters: 1: 1.10886 2: 2.49945 3: 3.4217 W parameters: 1: 0.28215 2: 0.430544 3: 0.80945 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 0.00813414 -0.0137 0.0322 0.1057 0.9998 0.6932 0.1988 0.00438634 -0.0077 -0.0144 0.0627 Problem 5 C parameters: 1: 12.693 2: 5.88675 3: 1.8202 W parameters: 1: 0.184968 2: 0.900712 3: 0.969868 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 1.2809e-07 -0.0000 0.0000 0.0000 0.9998 0.6932 0.1988 2.3343e-06 -0.0000 0.0000 0.0000 Problem 6 C parameters: 1: 1.14832 2: 1.68777 3: 1.46391 W parameters: 1: 0.918486 2: 0.0752764 3: 0.430454 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.9677 0.1137 0.2544 0 0.0000 0.0000 0.0000 0.9998 0.6932 0.1988 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: 0.379731 2: 0.247766 3: 0.388543 4: 0.483959 W parameters: 1: 0.745795 2: 0.0399364 3: 0.373203 4: 0.696723 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0.69987 0.2712 0.1770 0.2775 0.3457 0.6628 0.3841 0.7370 0.6176 0.786835 0.2344 0.1529 0.2398 0.2987 Problem 2 C parameters: 1: 1.11767 2: 0.9083 3: 0.582666 4: 1.39136 W parameters: 1: 0.050081 2: 0.433441 3: 0.76475 4: 0.643226 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0.21635 -0.2351 -0.1229 0.0006 0.2970 0.6628 0.3841 0.7370 0.6176 0.459456 -0.4788 0.0373 0.0087 0.0456 Problem 3 C parameters: 1: 0.588791 2: 0.372244 3: 0.255272 4: 0.633692 W parameters: 1: 0.885024 2: 0.32711 3: 0.6939 4: 0.295717 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0.0341249 -0.0511 -0.0323 -0.0222 -0.0550 0.6628 0.3841 0.7370 0.6176 0.0237565 -0.0331 -0.0209 -0.0144 -0.0356 Problem 4 C parameters: 1: 0.0446546 2: 2.96054 3: 1.50618 4: 2.51863 W parameters: 1: 0.661177 2: 0.430788 3: 0.792454 4: 0.293854 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0.171562 -0.0001 -1.1716 0.0245 0.5670 0.6628 0.3841 0.7370 0.6176 0.501155 -0.0000 0.4100 0.1262 -2.0583 Problem 5 C parameters: 1: 7.546 2: 7.10301 3: 3.56409 4: 2.1869 W parameters: 1: 0.693802 2: 0.246881 3: 0.487751 4: 0.839294 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0.000696999 -0.0053 -0.0050 -0.0025 0.0015 0.6628 0.3841 0.7370 0.6176 0.0756512 0.5709 -0.5374 -0.2696 0.1654 Problem 6 C parameters: 1: 1.59541 2: 0.285824 3: 1.94387 4: 0.474889 W parameters: 1: 0.382625 2: 0.661727 3: 0.827397 4: 0.241203 X(1) X(2) ... F(X) dFdX(1) dFdX(2) ... 0.7546 0.8204 0.7610 0.0334 0 0.0000 0.0000 0.0000 0.0000 0.6628 0.3841 0.7370 0.6176 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: 0.281829 2: 0.519608 3: 0.58236 4: 0.116203 W parameters: 1: 0.230204 2: 0.412485 3: 0.429015 4: 0.367373 Exact Integral Q -0.568679 -0.568486 Problem 2 C parameters: 1: 0.634588 2: 0.035433 3: 2.14979 4: 1.18019 W parameters: 1: 0.32842 2: 0.555927 3: 0.576564 4: 0.258809 Exact Integral Q 0.00203503 0.00203052 Problem 3 C parameters: 1: 0.469439 2: 0.42853 3: 0.616338 4: 0.335694 W parameters: 1: 0.836733 2: 0.0810409 3: 0.0867426 4: 0.652945 Exact Integral Q 0.0529946 0.0528669 Problem 4 C parameters: 1: 4.80793 2: 2.02385 3: 0.0241344 4: 0.174084 W parameters: 1: 0.491472 2: 0.0120406 3: 0.71078 4: 0.642913 Exact Integral Q 0.164468 0.167124 Problem 5 C parameters: 1: 4.10743 2: 7.57584 3: 8.02956 4: 0.687174 W parameters: 1: 0.989244 2: 0.384473 3: 0.0251053 4: 0.17986 Exact Integral Q 0.00748337 0.00726657 Problem 6 C parameters: 1: 1.10451 2: 1.46889 3: 0.859891 4: 0.866711 W parameters: 1: 0.0190493 2: 0.518216 3: 0.556929 4: 0.0339413 Exact Integral Q 0.0377075 0.0404566 test_interp_nd_test(): Normal end of execution. 16-May-2025 08:49:57