07-Mar-2024 09:43:43 atkinson_test(): MATLAB/Octave version 5.2.0 Test atkinson() bisect_test(): Test bisect(): iteration = 1.0000e+00 0.0000e+00 2.0000e+00 1.0000e+00 -1.0000e+00 1.0000e+00 iteration = 2.0000e+00 1.0000e+00 2.0000e+00 1.5000e+00 8.8906e+00 5.0000e-01 iteration = 3.0000e+00 1.0000e+00 1.5000e+00 1.2500e+00 1.5647e+00 2.5000e-01 iteration = 4.0000e+00 1.0000e+00 1.2500e+00 1.1250e+00 -9.7713e-02 1.2500e-01 iteration = 5.0000e+00 1.1250e+00 1.2500e+00 1.1875e+00 6.1665e-01 6.2500e-02 iteration = 6.0000e+00 1.1250e+00 1.1875e+00 1.1562e+00 2.3327e-01 3.1250e-02 iteration = 7.0000e+00 1.1250e+00 1.1562e+00 1.1406e+00 6.1578e-02 1.5625e-02 iteration = 8.0000e+00 1.1250e+00 1.1406e+00 1.1328e+00 -1.9576e-02 7.8125e-03 iteration = 9.0000e+00 1.1328e+00 1.1406e+00 1.1367e+00 2.0619e-02 3.9062e-03 iteration = 1.0000e+01 1.1328e+00 1.1367e+00 1.1348e+00 4.2684e-04 1.9531e-03 iteration = 1.1000e+01 1.1328e+00 1.1348e+00 1.1338e+00 -9.5980e-03 9.7656e-04 iteration = 1.2000e+01 1.1338e+00 1.1348e+00 1.1343e+00 -4.5915e-03 4.8828e-04 iteration = 1.3000e+01 1.1343e+00 1.1348e+00 1.1345e+00 -2.0838e-03 2.4414e-04 iteration = 1.4000e+01 1.1345e+00 1.1348e+00 1.1346e+00 -8.2885e-04 1.2207e-04 iteration = 1.5000e+01 1.1346e+00 1.1348e+00 1.1347e+00 -2.0110e-04 6.1035e-05 iteration = 1.6000e+01 1.1347e+00 1.1348e+00 1.1347e+00 1.1285e-04 3.0518e-05 iteration = 1.7000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -4.4131e-05 1.5259e-05 iteration = 1.8000e+01 1.1347e+00 1.1347e+00 1.1347e+00 3.4357e-05 7.6294e-06 iteration = 1.9000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -4.8874e-06 3.8147e-06 iteration = 2.0000e+01 1.1347e+00 1.1347e+00 1.1347e+00 1.4735e-05 1.9073e-06 iteration = 2.1000e+01 1.1347e+00 1.1347e+00 1.1347e+00 4.9237e-06 9.5367e-07 iteration = 2.2000e+01 1.1347e+00 1.1347e+00 1.1347e+00 1.8165e-08 4.7684e-07 iteration = 2.3000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -2.4346e-06 2.3842e-07 iteration = 2.4000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -1.2082e-06 1.1921e-07 iteration = 2.5000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -5.9503e-07 5.9605e-08 iteration = 2.6000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -2.8843e-07 2.9802e-08 iteration = 2.7000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -1.3513e-07 1.4901e-08 iteration = 2.8000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -5.8484e-08 7.4506e-09 iteration = 2.9000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -2.0159e-08 3.7253e-09 iteration = 3.0000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -9.9716e-10 1.8626e-09 iteration = 3.1000e+01 1.1347e+00 1.1347e+00 1.1347e+00 8.5839e-09 9.3132e-10 iteration = 3.2000e+01 1.1347e+00 1.1347e+00 1.1347e+00 3.7934e-09 4.6566e-10 iteration = 3.3000e+01 1.1347e+00 1.1347e+00 1.1347e+00 1.3981e-09 2.3283e-10 iteration = 3.4000e+01 1.1347e+00 1.1347e+00 1.1347e+00 2.0048e-10 1.1642e-10 iteration = 3.5000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -3.9834e-10 5.8208e-11 iteration = 3.6000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -9.8934e-11 2.9104e-11 iteration = 3.7000e+01 1.1347e+00 1.1347e+00 1.1347e+00 5.0770e-11 1.4552e-11 iteration = 3.8000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -2.4082e-11 7.2760e-12 iteration = 3.9000e+01 1.1347e+00 1.1347e+00 1.1347e+00 1.3344e-11 3.6380e-12 iteration = 4.0000e+01 1.1347e+00 1.1347e+00 1.1347e+00 -5.3690e-12 1.8190e-12 root = 1.134724138401907 error_bound = 9.0949e-13 it_count = 40 Estimated root is x = 1.13472 f(x) = 3.98748e-12 iteration = 1.0000e+00 0.0000e+00 5.0000e+00 2.5000e+00 2.4179e+00 2.5000e+00 iteration = 2.0000e+00 0.0000e+00 2.5000e+00 1.2500e+00 9.6350e-01 1.2500e+00 iteration = 3.0000e+00 0.0000e+00 1.2500e+00 6.2500e-01 8.9739e-02 6.2500e-01 iteration = 4.0000e+00 0.0000e+00 6.2500e-01 3.1250e-01 -4.1912e-01 3.1250e-01 iteration = 5.0000e+00 3.1250e-01 6.2500e-01 4.6875e-01 -1.5703e-01 1.5625e-01 iteration = 6.0000e+00 4.6875e-01 6.2500e-01 5.4688e-01 -3.1881e-02 7.8125e-02 iteration = 7.0000e+00 5.4688e-01 6.2500e-01 5.8594e-01 2.9354e-02 3.9062e-02 iteration = 8.0000e+00 5.4688e-01 5.8594e-01 5.6641e-01 -1.1552e-03 1.9531e-02 iteration = 9.0000e+00 5.6641e-01 5.8594e-01 5.7617e-01 1.4126e-02 9.7656e-03 iteration = 1.0000e+01 5.6641e-01 5.7617e-01 5.7129e-01 6.4922e-03 4.8828e-03 iteration = 1.1000e+01 5.6641e-01 5.7129e-01 5.6885e-01 2.6702e-03 2.4414e-03 iteration = 1.2000e+01 5.6641e-01 5.6885e-01 5.6763e-01 7.5790e-04 1.2207e-03 iteration = 1.3000e+01 5.6641e-01 5.6763e-01 5.6702e-01 -1.9854e-04 6.1035e-04 iteration = 1.4000e+01 5.6702e-01 5.6763e-01 5.6732e-01 2.7971e-04 3.0518e-04 iteration = 1.5000e+01 5.6702e-01 5.6732e-01 5.6717e-01 4.0587e-05 1.5259e-04 iteration = 1.6000e+01 5.6702e-01 5.6717e-01 5.6709e-01 -7.8977e-05 7.6294e-05 iteration = 1.7000e+01 5.6709e-01 5.6717e-01 5.6713e-01 -1.9194e-05 3.8147e-05 iteration = 1.8000e+01 5.6713e-01 5.6717e-01 5.6715e-01 1.0697e-05 1.9073e-05 iteration = 1.9000e+01 5.6713e-01 5.6715e-01 5.6714e-01 -4.2488e-06 9.5367e-06 iteration = 2.0000e+01 5.6714e-01 5.6715e-01 5.6715e-01 3.2239e-06 4.7684e-06 iteration = 2.1000e+01 5.6714e-01 5.6715e-01 5.6714e-01 -5.1246e-07 2.3842e-06 iteration = 2.2000e+01 5.6714e-01 5.6715e-01 5.6714e-01 1.3557e-06 1.1921e-06 iteration = 2.3000e+01 5.6714e-01 5.6714e-01 5.6714e-01 4.2163e-07 5.9605e-07 iteration = 2.4000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -4.5411e-08 2.9802e-07 iteration = 2.5000e+01 5.6714e-01 5.6714e-01 5.6714e-01 1.8811e-07 1.4901e-07 iteration = 2.6000e+01 5.6714e-01 5.6714e-01 5.6714e-01 7.1350e-08 7.4506e-08 iteration = 2.7000e+01 5.6714e-01 5.6714e-01 5.6714e-01 1.2969e-08 3.7253e-08 iteration = 2.8000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -1.6221e-08 1.8626e-08 iteration = 2.9000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -1.6258e-09 9.3132e-09 iteration = 3.0000e+01 5.6714e-01 5.6714e-01 5.6714e-01 5.6717e-09 4.6566e-09 iteration = 3.1000e+01 5.6714e-01 5.6714e-01 5.6714e-01 2.0229e-09 2.3283e-09 iteration = 3.2000e+01 5.6714e-01 5.6714e-01 5.6714e-01 1.9855e-10 1.1642e-09 iteration = 3.3000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -7.1365e-10 5.8208e-10 iteration = 3.4000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -2.5755e-10 2.9104e-10 iteration = 3.5000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -2.9501e-11 1.4552e-10 iteration = 3.6000e+01 5.6714e-01 5.6714e-01 5.6714e-01 8.4523e-11 7.2760e-11 iteration = 3.7000e+01 5.6714e-01 5.6714e-01 5.6714e-01 2.7511e-11 3.6380e-11 iteration = 3.8000e+01 5.6714e-01 5.6714e-01 5.6714e-01 -9.9509e-13 1.8190e-11 iteration = 3.9000e+01 5.6714e-01 5.6714e-01 5.6714e-01 1.3258e-11 9.0949e-12 iteration = 4.0000e+01 5.6714e-01 5.6714e-01 5.6714e-01 6.1314e-12 4.5475e-12 iteration = 4.1000e+01 5.6714e-01 5.6714e-01 5.6714e-01 2.5682e-12 2.2737e-12 iteration = 4.2000e+01 5.6714e-01 5.6714e-01 5.6714e-01 7.8659e-13 1.1369e-12 root = 5.671432904097173e-01 error_bound = 5.6843e-13 it_count = 42 Estimated root is x = 0.567143 f(x) = -1.0425e-13 bisect_test: Normal end of execution. chebyshev_interp_test maximum error = 2.714e-11 divdif_test: MATLAB version Test divdif(): i x(i) cos(x(i)) divdif(i) 1 0.00 1.000000 1 2 0.20 0.980067 -0.0996671 3 0.40 0.921061 -0.488402 4 0.60 0.825336 0.0490076 5 0.80 0.696707 0.0381225 6 1.00 0.540302 -0.00396205 7 1.20 0.362358 -0.00113489 divdif_test: Normal end of execution. Graphics saved as "eval_exp_simple.png" eval_exp_simple(): Taylor series for exp(x) over [-2,2,] x exp(x) err1 err2 err3 err4 ans = -2.00000 0.13534 1.13534 -0.86466 0.46867 -0.19800 -1.80000 0.16530 0.96530 -0.65470 0.31730 -0.12010 -1.60000 0.20190 0.80190 -0.47810 0.20456 -0.06850 -1.40000 0.24660 0.64660 -0.33340 0.12393 -0.03614 -1.20000 0.30119 0.50119 -0.21881 0.06919 -0.01721 -1.00000 0.36788 0.36788 -0.13212 0.03455 -0.00712 -0.80000 0.44933 0.24933 -0.07067 0.01466 -0.00240 -0.60000 0.54881 0.14881 -0.03119 0.00481 -0.00059 -0.40000 0.67032 0.07032 -0.00968 0.00099 -0.00008 -0.20000 0.81873 0.01873 -0.00127 0.00006 -0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.20000 1.22140 0.02140 0.00140 0.00007 0.00000 0.40000 1.49182 0.09182 0.01182 0.00116 0.00009 0.60000 1.82212 0.22212 0.04212 0.00612 0.00072 0.80000 2.22554 0.42554 0.10554 0.02021 0.00314 1.00000 2.71828 0.71828 0.21828 0.05162 0.00995 1.20000 3.32012 1.12012 0.40012 0.11212 0.02572 1.40000 4.05520 1.65520 0.67520 0.21787 0.05780 1.60000 4.95303 2.35303 1.07303 0.39037 0.11730 1.80000 6.04965 3.24965 1.62965 0.65765 0.22025 2.00000 7.38906 4.38906 2.38906 1.05572 0.38906 gaussint_test: MATLAB version Test gaussint(): Estimate integral of exp(-x^2) over [0,2] 1 0.7357588823428847 2 0.9194861166409162 4 0.8822290959326042 8 0.8820813904199003 16 0.8820813907624223 Estimate integral of 1/(1+x^2) over [0,4] 1 0.8 2 1.349112426035503 4 1.327713222795399 8 1.325838869084083 16 1.325817663720426 32 1.325817663668031 Estimate integral of 1/(2+sin(x)) over [0,pi] 1 1.047197551196598 2 1.200827173482707 4 1.209224894232257 8 1.209199575798514 16 1.209199576156147 Estimate integral of exp(cos(x)) over [0,pi] 1 3.141592653589793 2 4.167393283551555 4 3.976316211656985 8 3.977463340835659 16 3.977463260506426 32 3.977463260506419 gaussint_test: Normal end of execution. gs_test() Test gs() x0 = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 5.50000 x0 = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.75000 6.87500 x0 = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.37500 4.12500 7.56250 x0 = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.68750 2.40625 4.98438 7.99219 x0 = 0.00000 0.00000 0.00000 0.00000 0.00000 0.34375 1.37500 3.17969 5.58594 8.29297 x0 = 0.00000 0.00000 0.00000 0.00000 0.17188 0.77344 1.97656 3.78125 6.03711 8.51855 x0 = 0.00000 0.00000 0.00000 0.08594 0.42969 1.20312 2.49219 4.26465 6.39160 8.69580 x0 = 0.00000 0.00000 0.04297 0.23633 0.71973 1.60596 2.93530 4.66345 6.67963 8.83981 x0 = 0.00000 0.02148 0.12891 0.42432 1.01514 1.97522 3.31934 4.99948 6.91965 8.95982 x0 = 0.010742 0.069824 0.247070 0.631104 1.303162 2.311249 3.655365 5.287506 7.123665 9.061832 x0 = 0.034912 0.140991 0.386047 0.844604 1.577927 2.616646 3.952076 5.537870 7.299851 9.149926 x0 = 0.070496 0.228271 0.536438 1.057182 1.836914 2.894495 4.216183 5.758017 7.453971 9.226986 x0 = 0.11414 0.32529 0.69123 1.26407 2.07928 3.14773 4.45288 5.95342 7.59020 9.29510 x0 = 0.16264 0.42694 0.84551 1.46240 2.30506 3.37897 4.66620 6.12820 7.71165 9.35583 x0 = 0.21347 0.52949 0.99594 1.65050 2.51474 3.59047 4.85933 6.28549 7.82066 9.41033 x0 = 0.26474 0.63034 1.14042 1.82758 2.70902 3.78418 5.03484 6.42775 7.91904 9.45952 x0 = 0.31517 0.72780 1.27769 1.99336 2.88877 3.96180 5.19477 6.55691 8.00821 9.50411 x0 = 0.36390 0.82079 1.40707 2.14792 3.05486 4.12482 5.34086 6.67454 8.08932 9.54466 x0 = 0.41040 0.90874 1.52833 2.29159 3.20821 4.27453 5.47454 6.78193 8.16329 9.58165 x0 = 0.45437 0.99135 1.64147 2.42484 3.34969 4.41211 5.59702 6.88016 8.23090 9.61545 x0 = 0.49567 1.06857 1.74671 2.54820 3.48015 4.53859 5.70937 6.97014 8.29279 9.64640 x0 = 0.53429 1.14050 1.84435 2.66225 3.60042 4.65490 5.81252 7.05266 8.34953 9.67476 x0 = 0.57025 1.20730 1.93477 2.76760 3.71125 4.76188 5.90727 7.12840 8.40158 9.70079 x0 = 0.60365 1.26921 2.01840 2.86482 3.81335 4.86031 5.99435 7.19797 8.44938 9.72469 x0 = 0.63461 1.32650 2.09566 2.95451 3.90741 4.95088 6.07442 7.26190 8.49330 9.74665 x0 = 0.66325 1.37946 2.16698 3.03720 3.99404 5.03423 6.14807 7.32068 8.53366 9.76683 x0 = 0.68973 1.42836 2.23278 3.11341 4.07382 5.11094 6.21581 7.37474 8.57079 9.78539 x0 = 0.71418 1.47348 2.29344 3.18363 4.14729 5.18155 6.27814 7.42446 8.60493 9.80246 x0 = 0.73674 1.51509 2.34936 3.24832 4.21494 5.24654 6.33550 7.47022 8.63634 9.81817 x0 = 0.75755 1.55345 2.40089 3.30791 4.27723 5.30636 6.38829 7.51231 8.66524 9.83262 x0 = 0.77673 1.58881 2.44836 3.36279 4.33458 5.36143 6.43687 7.55106 8.69184 9.84592 x0 = 0.79440 1.62138 2.49209 3.41333 4.38738 5.41213 6.48159 7.58672 8.71632 9.85816 x0 = 0.81069 1.65139 2.53236 3.45987 4.43600 5.45880 6.52276 7.61954 8.73885 9.86942 x0 = 0.82569 1.67903 2.56945 3.50273 4.48076 5.50176 6.56065 7.64975 8.75959 9.87979 x0 = 0.83951 1.70448 2.60360 3.54218 4.52197 5.54131 6.59553 7.67756 8.77868 9.88934 x0 = 0.85224 1.72792 2.63505 3.57851 4.55991 5.57772 6.62764 7.70316 8.79625 9.89812 x0 = 0.86396 1.74951 2.66401 3.61196 4.59484 5.61124 6.65720 7.72672 8.81242 9.90621 x0 = 0.87475 1.76938 2.69067 3.64276 4.62700 5.64210 6.68441 7.74842 8.82731 9.91366 x0 = 0.88469 1.78768 2.71522 3.67111 4.65660 5.67051 6.70946 7.76839 8.84102 9.92051 x0 = 0.89384 1.80453 2.73782 3.69721 4.68386 5.69666 6.73252 7.78677 8.85364 9.92682 x0 = 0.90226 1.82004 2.75863 3.72124 4.70895 5.72074 6.75376 7.80370 8.86526 9.93263 x0 = 0.91002 1.83432 2.77778 3.74337 4.73205 5.74290 6.77330 7.81928 8.87596 9.93798 x0 = 0.91716 1.84747 2.79542 3.76374 4.75332 5.76331 6.79130 7.83363 8.88580 9.94290 x0 = 0.92374 1.85958 2.81166 3.78249 4.77290 5.78210 6.80786 7.84683 8.89487 9.94743 x0 = 0.92979 1.87072 2.82661 3.79975 4.79093 5.79939 6.82311 7.85899 8.90321 9.95161 x0 = 0.93536 1.88098 2.84037 3.81565 4.80752 5.81532 6.83715 7.87018 8.91089 9.95545 x0 = 0.94049 1.89043 2.85304 3.83028 4.82280 5.82998 6.85008 7.88049 8.91797 9.95898 x0 = 0.94521 1.89913 2.86470 3.84375 4.83686 5.84347 6.86198 7.88997 8.92448 9.96224 x0 = 0.94956 1.90713 2.87544 3.85615 4.84981 5.85589 6.87293 7.89871 8.93047 9.96524 x0 = 0.95357 1.91450 2.88533 3.86757 4.86173 5.86733 6.88302 7.90675 8.93599 9.96800 x0 = 0.95725 1.92129 2.89443 3.87808 4.87271 5.87786 6.89230 7.91415 8.94107 9.97054 x0 = 0.96065 1.92754 2.90281 3.88776 4.88281 5.88756 6.90085 7.92096 8.94575 9.97287 x0 = 0.96377 1.93329 2.91052 3.89667 4.89211 5.89648 6.90872 7.92724 8.95006 9.97503 x0 = 0.96664 1.93858 2.91763 3.90487 4.90068 5.90470 6.91597 7.93301 8.95402 9.97701 x0 = 0.96929 1.94346 2.92416 3.91242 4.90856 5.91226 6.92264 7.93833 8.95767 9.97883 x0 = 0.97173 1.94795 2.93018 3.91937 4.91582 5.91923 6.92878 7.94322 8.96103 9.98051 x0 = 0.97397 1.95208 2.93572 3.92577 4.92250 5.92564 6.93443 7.94773 8.96412 9.98206 x0 = 0.97604 1.95588 2.94083 3.93166 4.92865 5.93154 6.93964 7.95188 8.96697 9.98348 x0 = 0.97794 1.95938 2.94552 3.93709 4.93431 5.93697 6.94443 7.95570 8.96959 9.98480 x0 = 0.97969 1.96261 2.94985 3.94208 4.93953 5.94198 6.94884 7.95921 8.97201 9.98600 x0 = 0.98130 1.96558 2.95383 3.94668 4.94433 5.94658 6.95290 7.96245 8.97423 9.98711 x0 = 0.98279 1.96831 2.95749 3.95091 4.94875 5.95082 6.95664 7.96543 8.97627 9.98814 x0 = 0.98415 1.97082 2.96087 3.95481 4.95281 5.95473 6.96008 7.96818 8.97816 9.98908 x0 = 0.98541 1.97314 2.96397 3.95839 4.95656 5.95832 6.96325 7.97070 8.97989 9.98995 x0 = 0.98657 1.97527 2.96683 3.96170 4.96001 5.96163 6.96616 7.97303 8.98149 9.99074 x0 = 0.98764 1.97723 2.96947 3.96474 4.96318 5.96467 6.96885 7.97517 8.98296 9.99148 x0 = 0.98862 1.97904 2.97189 3.96754 4.96610 5.96748 6.97132 7.97714 8.98431 9.99215 x0 = 0.98952 1.98070 2.97412 3.97011 4.96879 5.97006 6.97360 7.97895 8.98555 9.99278 x0 = 0.99035 1.98224 2.97617 3.97248 4.97127 5.97244 6.97569 7.98062 8.98670 9.99335 x0 = 0.99112 1.98365 2.97807 3.97467 4.97355 5.97462 6.97762 7.98216 8.98776 9.99388 x0 = 0.99182 1.98494 2.97981 3.97668 4.97565 5.97664 6.97940 7.98358 8.98873 9.99436 x0 = 0.99247 1.98614 2.98141 3.97853 4.97758 5.97849 6.98104 7.98488 8.98962 9.99481 x0 = 0.99307 1.98724 2.98288 3.98023 4.97936 5.98020 6.98254 7.98608 8.99045 9.99522 x0 = 0.99362 1.98825 2.98424 3.98180 4.98100 5.98177 6.98393 7.98719 8.99120 9.99560 x0 = 0.99413 1.98918 2.98549 3.98325 4.98251 5.98322 6.98520 7.98820 8.99190 9.99595 x0 = 0.99459 1.99004 2.98665 3.98458 4.98390 5.98455 6.98638 7.98914 8.99255 9.99627 x0 = 0.99502 1.99083 2.98771 3.98580 4.98518 5.98578 6.98746 7.99000 8.99314 9.99657 x0 = 0.99542 1.99156 2.98868 3.98693 4.98635 5.98691 6.98845 7.99080 8.99368 9.99684 x0 = 0.99578 1.99223 2.98958 3.98797 4.98744 5.98794 6.98937 7.99153 8.99418 9.99709 x0 = 0.99612 1.99285 2.99041 3.98892 4.98843 5.98890 6.99021 7.99220 8.99465 9.99732 gs() returned iflag = 1 gs() took 80 iterations i x(i) x_true(i) A*x-b(i) 1 0.9961 1.0000 -6.166598e-04 2 1.9928 2.0000 -8.270972e-04 3 2.9904 3.0000 -9.551821e-04 4 3.9889 4.0000 -9.972846e-04 5 4.9884 5.0000 -9.568875e-04 6 5.9889 6.0000 -8.437457e-04 7 6.9902 7.0000 -6.726135e-04 8 7.9922 8.0000 -4.616770e-04 9 8.9946 9.0000 -2.308385e-04 10 9.9973 10.0000 0.000000e+00 humps_fun_test: Test humps_fun() Graphics saved as "humps_fun_test.png" interp_test: Test interp(): Graphics saved as "interp_test.png" jacobi_test() Test jacobi() x = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 5.50000 x = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.75000 5.50000 x = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.37500 2.75000 6.87500 x = 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.68750 1.37500 4.12500 6.87500 x = 0.00000 0.00000 0.00000 0.00000 0.00000 0.34375 0.68750 2.40625 4.12500 7.56250 x = 0.00000 0.00000 0.00000 0.00000 0.17188 0.34375 1.37500 2.40625 4.98438 7.56250 x = 0.00000 0.00000 0.00000 0.08594 0.17188 0.77344 1.37500 3.17969 4.98438 7.99219 x = 0.00000 0.00000 0.04297 0.08594 0.42969 0.77344 1.97656 3.17969 5.58594 7.99219 x = 0.00000 0.02148 0.04297 0.23633 0.42969 1.20312 1.97656 3.78125 5.58594 8.29297 x = 0.010742 0.021484 0.128906 0.236328 0.719727 1.203125 2.492188 3.781250 6.037109 8.292969 x = 0.010742 0.069824 0.128906 0.424316 0.719727 1.605957 2.492188 4.264648 6.037109 8.518555 x = 0.034912 0.069824 0.247070 0.424316 1.015137 1.605957 2.935303 4.264648 6.391602 8.518555 x = 0.034912 0.140991 0.247070 0.631104 1.015137 1.975220 2.935303 4.663452 6.391602 8.695801 x = 0.070496 0.140991 0.386047 0.631104 1.303162 1.975220 3.319336 4.663452 6.679626 8.695801 x = 0.070496 0.228271 0.386047 0.844604 1.303162 2.311249 3.319336 4.999481 6.679626 8.839813 x = 0.11414 0.22827 0.53644 0.84460 1.57793 2.31125 3.65536 4.99948 6.91965 8.83981 x = 0.11414 0.32529 0.53644 1.05718 1.57793 2.61665 3.65536 5.28751 6.91965 8.95982 x = 0.16264 0.32529 0.69123 1.05718 1.83691 2.61665 3.95208 5.28751 7.12366 8.95982 x = 0.16264 0.42694 0.69123 1.26407 1.83691 2.89450 3.95208 5.53787 7.12366 9.06183 x = 0.21347 0.42694 0.84551 1.26407 2.07928 2.89450 4.21618 5.53787 7.29985 9.06183 x = 0.21347 0.52949 0.84551 1.46240 2.07928 3.14773 4.21618 5.75802 7.29985 9.14993 x = 0.26474 0.52949 0.99594 1.46240 2.30506 3.14773 4.45288 5.75802 7.45397 9.14993 x = 0.26474 0.63034 0.99594 1.65050 2.30506 3.37897 4.45288 5.95342 7.45397 9.22699 x = 0.31517 0.63034 1.14042 1.65050 2.51474 3.37897 4.66620 5.95342 7.59020 9.22699 x = 0.31517 0.72780 1.14042 1.82758 2.51474 3.59047 4.66620 6.12820 7.59020 9.29510 x = 0.36390 0.72780 1.27769 1.82758 2.70902 3.59047 4.85933 6.12820 7.71165 9.29510 x = 0.36390 0.82079 1.27769 1.99336 2.70902 3.78418 4.85933 6.28549 7.71165 9.35583 x = 0.41040 0.82079 1.40707 1.99336 2.88877 3.78418 5.03484 6.28549 7.82066 9.35583 x = 0.41040 0.90874 1.40707 2.14792 2.88877 3.96180 5.03484 6.42775 7.82066 9.41033 x = 0.45437 0.90874 1.52833 2.14792 3.05486 3.96180 5.19477 6.42775 7.91904 9.41033 x = 0.45437 0.99135 1.52833 2.29159 3.05486 4.12482 5.19477 6.55691 7.91904 9.45952 x = 0.49567 0.99135 1.64147 2.29159 3.20821 4.12482 5.34086 6.55691 8.00821 9.45952 x = 0.49567 1.06857 1.64147 2.42484 3.20821 4.27453 5.34086 6.67454 8.00821 9.50411 x = 0.53429 1.06857 1.74671 2.42484 3.34969 4.27453 5.47454 6.67454 8.08932 9.50411 x = 0.53429 1.14050 1.74671 2.54820 3.34969 4.41211 5.47454 6.78193 8.08932 9.54466 x = 0.57025 1.14050 1.84435 2.54820 3.48015 4.41211 5.59702 6.78193 8.16329 9.54466 x = 0.57025 1.20730 1.84435 2.66225 3.48015 4.53859 5.59702 6.88016 8.16329 9.58165 x = 0.60365 1.20730 1.93477 2.66225 3.60042 4.53859 5.70937 6.88016 8.23090 9.58165 x = 0.60365 1.26921 1.93477 2.76760 3.60042 4.65490 5.70937 6.97014 8.23090 9.61545 x = 0.63461 1.26921 2.01840 2.76760 3.71125 4.65490 5.81252 6.97014 8.29279 9.61545 x = 0.63461 1.32650 2.01840 2.86482 3.71125 4.76188 5.81252 7.05266 8.29279 9.64640 x = 0.66325 1.32650 2.09566 2.86482 3.81335 4.76188 5.90727 7.05266 8.34953 9.64640 x = 0.66325 1.37946 2.09566 2.95451 3.81335 4.86031 5.90727 7.12840 8.34953 9.67476 x = 0.68973 1.37946 2.16698 2.95451 3.90741 4.86031 5.99435 7.12840 8.40158 9.67476 x = 0.68973 1.42836 2.16698 3.03720 3.90741 4.95088 5.99435 7.19797 8.40158 9.70079 x = 0.71418 1.42836 2.23278 3.03720 3.99404 4.95088 6.07442 7.19797 8.44938 9.70079 x = 0.71418 1.47348 2.23278 3.11341 3.99404 5.03423 6.07442 7.26190 8.44938 9.72469 x = 0.73674 1.47348 2.29344 3.11341 4.07382 5.03423 6.14807 7.26190 8.49330 9.72469 x = 0.73674 1.51509 2.29344 3.18363 4.07382 5.11094 6.14807 7.32068 8.49330 9.74665 x = 0.75755 1.51509 2.34936 3.18363 4.14729 5.11094 6.21581 7.32068 8.53366 9.74665 x = 0.75755 1.55345 2.34936 3.24832 4.14729 5.18155 6.21581 7.37474 8.53366 9.76683 x = 0.77673 1.55345 2.40089 3.24832 4.21494 5.18155 6.27814 7.37474 8.57079 9.76683 x = 0.77673 1.58881 2.40089 3.30791 4.21494 5.24654 6.27814 7.42446 8.57079 9.78539 x = 0.79440 1.58881 2.44836 3.30791 4.27723 5.24654 6.33550 7.42446 8.60493 9.78539 x = 0.79440 1.62138 2.44836 3.36279 4.27723 5.30636 6.33550 7.47022 8.60493 9.80246 x = 0.81069 1.62138 2.49209 3.36279 4.33458 5.30636 6.38829 7.47022 8.63634 9.80246 x = 0.81069 1.65139 2.49209 3.41333 4.33458 5.36143 6.38829 7.51231 8.63634 9.81817 x = 0.82569 1.65139 2.53236 3.41333 4.38738 5.36143 6.43687 7.51231 8.66524 9.81817 x = 0.82569 1.67903 2.53236 3.45987 4.38738 5.41213 6.43687 7.55106 8.66524 9.83262 x = 0.83951 1.67903 2.56945 3.45987 4.43600 5.41213 6.48159 7.55106 8.69184 9.83262 x = 0.83951 1.70448 2.56945 3.50273 4.43600 5.45880 6.48159 7.58672 8.69184 9.84592 x = 0.85224 1.70448 2.60360 3.50273 4.48076 5.45880 6.52276 7.58672 8.71632 9.84592 x = 0.85224 1.72792 2.60360 3.54218 4.48076 5.50176 6.52276 7.61954 8.71632 9.85816 x = 0.86396 1.72792 2.63505 3.54218 4.52197 5.50176 6.56065 7.61954 8.73885 9.85816 x = 0.86396 1.74951 2.63505 3.57851 4.52197 5.54131 6.56065 7.64975 8.73885 9.86942 x = 0.87475 1.74951 2.66401 3.57851 4.55991 5.54131 6.59553 7.64975 8.75959 9.86942 x = 0.87475 1.76938 2.66401 3.61196 4.55991 5.57772 6.59553 7.67756 8.75959 9.87979 x = 0.88469 1.76938 2.69067 3.61196 4.59484 5.57772 6.62764 7.67756 8.77868 9.87979 x = 0.88469 1.78768 2.69067 3.64276 4.59484 5.61124 6.62764 7.70316 8.77868 9.88934 x = 0.89384 1.78768 2.71522 3.64276 4.62700 5.61124 6.65720 7.70316 8.79625 9.88934 x = 0.89384 1.80453 2.71522 3.67111 4.62700 5.64210 6.65720 7.72672 8.79625 9.89812 x = 0.90226 1.80453 2.73782 3.67111 4.65660 5.64210 6.68441 7.72672 8.81242 9.89812 x = 0.90226 1.82004 2.73782 3.69721 4.65660 5.67051 6.68441 7.74842 8.81242 9.90621 x = 0.91002 1.82004 2.75863 3.69721 4.68386 5.67051 6.70946 7.74842 8.82731 9.90621 x = 0.91002 1.83432 2.75863 3.72124 4.68386 5.69666 6.70946 7.76839 8.82731 9.91366 x = 0.91716 1.83432 2.77778 3.72124 4.70895 5.69666 6.73252 7.76839 8.84102 9.91366 x = 0.91716 1.84747 2.77778 3.74337 4.70895 5.72074 6.73252 7.78677 8.84102 9.92051 x = 0.92374 1.84747 2.79542 3.74337 4.73205 5.72074 6.75376 7.78677 8.85364 9.92051 x = 0.92374 1.85958 2.79542 3.76374 4.73205 5.74290 6.75376 7.80370 8.85364 9.92682 x = 0.92979 1.85958 2.81166 3.76374 4.75332 5.74290 6.77330 7.80370 8.86526 9.92682 x = 0.92979 1.87072 2.81166 3.78249 4.75332 5.76331 6.77330 7.81928 8.86526 9.93263 x = 0.93536 1.87072 2.82661 3.78249 4.77290 5.76331 6.79130 7.81928 8.87596 9.93263 x = 0.93536 1.88098 2.82661 3.79975 4.77290 5.78210 6.79130 7.83363 8.87596 9.93798 x = 0.94049 1.88098 2.84037 3.79975 4.79093 5.78210 6.80786 7.83363 8.88580 9.93798 x = 0.94049 1.89043 2.84037 3.81565 4.79093 5.79939 6.80786 7.84683 8.88580 9.94290 x = 0.94521 1.89043 2.85304 3.81565 4.80752 5.79939 6.82311 7.84683 8.89487 9.94290 x = 0.94521 1.89913 2.85304 3.83028 4.80752 5.81532 6.82311 7.85899 8.89487 9.94743 x = 0.94956 1.89913 2.86470 3.83028 4.82280 5.81532 6.83715 7.85899 8.90321 9.94743 x = 0.94956 1.90713 2.86470 3.84375 4.82280 5.82998 6.83715 7.87018 8.90321 9.95161 x = 0.95357 1.90713 2.87544 3.84375 4.83686 5.82998 6.85008 7.87018 8.91089 9.95161 x = 0.95357 1.91450 2.87544 3.85615 4.83686 5.84347 6.85008 7.88049 8.91089 9.95545 x = 0.95725 1.91450 2.88533 3.85615 4.84981 5.84347 6.86198 7.88049 8.91797 9.95545 x = 0.95725 1.92129 2.88533 3.86757 4.84981 5.85589 6.86198 7.88997 8.91797 9.95898 x = 0.96065 1.92129 2.89443 3.86757 4.86173 5.85589 6.87293 7.88997 8.92448 9.95898 x = 0.96065 1.92754 2.89443 3.87808 4.86173 5.86733 6.87293 7.89871 8.92448 9.96224 x = 0.96377 1.92754 2.90281 3.87808 4.87271 5.86733 6.88302 7.89871 8.93047 9.96224 x = 0.96377 1.93329 2.90281 3.88776 4.87271 5.87786 6.88302 7.90675 8.93047 9.96524 x = 0.96664 1.93329 2.91052 3.88776 4.88281 5.87786 6.89230 7.90675 8.93599 9.96524 x = 0.96664 1.93858 2.91052 3.89667 4.88281 5.88756 6.89230 7.91415 8.93599 9.96800 x = 0.96929 1.93858 2.91763 3.89667 4.89211 5.88756 6.90085 7.91415 8.94107 9.96800 iflag = -1 jacobi() returned iflag = -1 jacobi() took 100 iterations i x(i) x_true(i) A*x-b(i) 1 0.9693 1.0000 0.000000e+00 2 1.9386 2.0000 -9.749515e-03 3 2.9176 3.0000 0.000000e+00 4 3.8967 4.0000 -1.640368e-02 5 4.8921 5.0000 -8.881784e-16 6 5.8876 6.0000 -1.784984e-02 7 6.9009 7.0000 8.881784e-16 8 7.9141 8.0000 -1.362878e-02 9 8.9411 9.0000 0.000000e+00 10 9.9680 10.0000 -5.080624e-03 ncs_test: Test ncs() Graphics saved as "ncs_test.png" newton_test: MATLAB version Test newton(): iteration = 0.0000e+00 0.0000e+00 -1.0000e+00 -1.0000e+00 -1.0000e+00 iteration = 1.0000e+00 -1.0000e+00 1.0000e+00 -7.0000e+00 1.4286e-01 iteration = 2.0000e+00 -8.5714e-01 2.5371e-01 -3.7760e+00 6.7191e-02 iteration = 3.0000e+00 -7.8995e-01 3.2950e-02 -2.8457e+00 1.1579e-02 iteration = 4.0000e+00 -7.7837e-01 7.6801e-04 -2.7143e+00 2.8295e-04 iteration = 5.0000e+00 -7.7809e-01 4.4061e-07 -2.7112e+00 1.6251e-07 iteration = 6.0000e+00 -7.7809e-01 1.4522e-13 -2.7112e+00 5.3513e-14 root = -7.780895986786012e-01 error = 5.3513e-14 it_count = 7 Estimated root is x = -0.77809 f(x) = 2.22045e-16 iteration = 0.0000e+00 0.0000e+00 -1.0000e+00 2.0000e+00 5.0000e-01 iteration = 1.0000e+00 5.0000e-01 -1.0653e-01 1.6065e+00 6.6311e-02 iteration = 2.0000e+00 5.6631e-01 -1.3045e-03 1.5676e+00 8.3216e-04 iteration = 3.0000e+00 5.6714e-01 -1.9648e-07 1.5671e+00 1.2537e-07 iteration = 4.0000e+00 5.6714e-01 -4.4409e-15 1.5671e+00 2.8866e-15 root = 5.671432904097840e-01 error = 2.8866e-15 it_count = 5 Estimated root is x = 0.567143 f(x) = 1.11022e-16 newton_test: Normal end of execution. secant_test: MATLAB version Test secant(): iteration = 0.0000e+00 5.0000e-01 -1.4844e+00 iteration = 1.0000e+00 1.0000e+00 -1.0000e+00 1.0323e+00 iteration = 2.0000e+00 2.0323e+00 6.7416e+01 -1.0172e+00 iteration = 3.0000e+00 1.0151e+00 -9.2108e-01 1.3710e-02 iteration = 4.0000e+00 1.0288e+00 -8.4308e-01 1.4820e-01 iteration = 5.0000e+00 1.1770e+00 4.8161e-01 -5.3880e-02 iteration = 6.0000e+00 1.1231e+00 -1.1610e-01 1.0466e-02 iteration = 7.0000e+00 1.1336e+00 -1.1704e-02 1.1733e-03 iteration = 8.0000e+00 1.1348e+00 3.3457e-04 -3.2609e-05 iteration = 9.0000e+00 1.1347e+00 -9.2384e-07 8.9794e-08 iteration = 1.0000e+01 1.1347e+00 -7.2619e-11 7.0588e-12 iteration = 1.1000e+01 1.1347e+00 -8.8818e-16 0.0000e+00 root = 1.134724138401519 error = 0.0000e+00 it_count = 11 Estimated root is x = 1.13472 f(x) = -8.88178e-16 iteration = 0.0000e+00 0.0000e+00 -1.0000e+00 iteration = 1.0000e+00 1.0000e+00 6.3212e-01 -3.8730e-01 iteration = 2.0000e+00 6.1270e-01 7.0814e-02 -4.8861e-02 iteration = 3.0000e+00 5.6384e-01 -5.1824e-03 3.3320e-03 iteration = 4.0000e+00 5.6717e-01 4.2419e-05 -2.7052e-05 iteration = 5.0000e+00 5.6714e-01 2.5380e-08 -1.6195e-08 iteration = 6.0000e+00 5.6714e-01 -1.2423e-13 7.9270e-14 root = 5.671432904097838e-01 error = 7.9270e-14 it_count = 6 Estimated root is x = 0.567143 f(x) = 0 secant_test: Normal end of execution. simpson_test: MATLAB version Test simpson(): #1 Exact = 0.746824, Estimate = 0.746824, Difference = 1.18905e-13 #2 Exact = 1.32582, Estimate = 1.32582, Difference = 3.54827e-13 #3 Exact = 3.6276, Estimate = 3.6276, Difference = 6.66134e-15 #4 Exact = 7.95493, Estimate = 7.95493, Difference = 7.10543e-15 simpson_test: Normal end of execution. trapezoidal_test: MATLAB version Test trapezoidal(): #1 Exact = 0.746824, Estimate = 0.746824, Difference = 2.33891e-07 #2 Exact = 1.32582, Estimate = 1.32582, Difference = 1.40796e-07 #3 Exact = 3.6276, Estimate = 3.6276, Difference = 1.77636e-15 #4 Exact = 7.95493, Estimate = 7.95493, Difference = 1.24345e-14 trapezoidal_test: Normal end of execution. tridiag_test tridiag factors and solves a tridiagonal linear system. The matrix size is N = 100 Factor the matrix and solve the system. x = Columns 1 through 7: 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000 7.00000 Columns 8 through 14: 8.00000 9.00000 10.00000 11.00000 12.00000 13.00000 14.00000 Columns 15 through 21: 15.00000 16.00000 17.00000 18.00000 19.00000 20.00000 21.00000 Columns 22 through 28: 22.00000 23.00000 24.00000 25.00000 26.00000 27.00000 28.00000 Columns 29 through 35: 29.00000 30.00000 31.00000 32.00000 33.00000 34.00000 35.00000 Columns 36 through 42: 36.00000 37.00000 38.00000 39.00000 40.00000 41.00000 42.00000 Columns 43 through 49: 43.00000 44.00000 45.00000 46.00000 47.00000 48.00000 49.00000 Columns 50 through 56: 50.00000 51.00000 52.00000 53.00000 54.00000 55.00000 56.00000 Columns 57 through 63: 57.00000 58.00000 59.00000 60.00000 61.00000 62.00000 63.00000 Columns 64 through 70: 64.00000 65.00000 66.00000 67.00000 68.00000 69.00000 70.00000 Columns 71 through 77: 71.00000 72.00000 73.00000 74.00000 75.00000 76.00000 77.00000 Columns 78 through 84: 78.00000 79.00000 80.00000 81.00000 82.00000 83.00000 84.00000 Columns 85 through 91: 85.00000 86.00000 87.00000 88.00000 89.00000 90.00000 91.00000 Columns 92 through 98: 92.00000 93.00000 94.00000 95.00000 96.00000 97.00000 98.00000 Columns 99 and 100: 99.00000 100.00000 alpha = Columns 1 through 8: 0.00000 -0.50000 -0.66667 -0.75000 -0.80000 -0.83333 -0.85714 -0.87500 Columns 9 through 16: -0.88889 -0.90000 -0.90909 -0.91667 -0.92308 -0.92857 -0.93333 -0.93750 Columns 17 through 24: -0.94118 -0.94444 -0.94737 -0.95000 -0.95238 -0.95455 -0.95652 -0.95833 Columns 25 through 32: -0.96000 -0.96154 -0.96296 -0.96429 -0.96552 -0.96667 -0.96774 -0.96875 Columns 33 through 40: -0.96970 -0.97059 -0.97143 -0.97222 -0.97297 -0.97368 -0.97436 -0.97500 Columns 41 through 48: -0.97561 -0.97619 -0.97674 -0.97727 -0.97778 -0.97826 -0.97872 -0.97917 Columns 49 through 56: -0.97959 -0.98000 -0.98039 -0.98077 -0.98113 -0.98148 -0.98182 -0.98214 Columns 57 through 64: -0.98246 -0.98276 -0.98305 -0.98333 -0.98361 -0.98387 -0.98413 -0.98438 Columns 65 through 72: -0.98462 -0.98485 -0.98507 -0.98529 -0.98551 -0.98571 -0.98592 -0.98611 Columns 73 through 80: -0.98630 -0.98649 -0.98667 -0.98684 -0.98701 -0.98718 -0.98734 -0.98750 Columns 81 through 88: -0.98765 -0.98780 -0.98795 -0.98810 -0.98824 -0.98837 -0.98851 -0.98864 Columns 89 through 96: -0.98876 -0.98889 -0.98901 -0.98913 -0.98925 -0.98936 -0.98947 -0.98958 Columns 97 through 100: -0.98969 -0.98980 -0.98990 -0.99000 beta = Columns 1 through 8: 2.0000 1.5000 1.3333 1.2500 1.2000 1.1667 1.1429 1.1250 Columns 9 through 16: 1.1111 1.1000 1.0909 1.0833 1.0769 1.0714 1.0667 1.0625 Columns 17 through 24: 1.0588 1.0556 1.0526 1.0500 1.0476 1.0455 1.0435 1.0417 Columns 25 through 32: 1.0400 1.0385 1.0370 1.0357 1.0345 1.0333 1.0323 1.0313 Columns 33 through 40: 1.0303 1.0294 1.0286 1.0278 1.0270 1.0263 1.0256 1.0250 Columns 41 through 48: 1.0244 1.0238 1.0233 1.0227 1.0222 1.0217 1.0213 1.0208 Columns 49 through 56: 1.0204 1.0200 1.0196 1.0192 1.0189 1.0185 1.0182 1.0179 Columns 57 through 64: 1.0175 1.0172 1.0169 1.0167 1.0164 1.0161 1.0159 1.0156 Columns 65 through 72: 1.0154 1.0152 1.0149 1.0147 1.0145 1.0143 1.0141 1.0139 Columns 73 through 80: 1.0137 1.0135 1.0133 1.0132 1.0130 1.0128 1.0127 1.0125 Columns 81 through 88: 1.0123 1.0122 1.0120 1.0119 1.0118 1.0116 1.0115 1.0114 Columns 89 through 96: 1.0112 1.0111 1.0110 1.0109 1.0108 1.0106 1.0105 1.0104 Columns 97 through 100: 1.0103 1.0102 1.0101 1.0100 ier = 0 The first and last 5 entries of the solution: (Should be 1,2,3,4,5,...,n,n-1): 1 1.000000 2 2.000000 3 3.000000 4 4.000000 5 5.000000 ...... .............. 96 96.000000 97 97.000000 98 98.000000 99 99.000000 100 100.000000 atkinson_test(): Normal end of execution. 07-Mar-2024 09:44:05