17-Aug-2022 20:20:51 atkinson_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test atkinson() bisect_test: MATLAB version Test bisect(): iteration = 1 0 2 1 -1 1 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 5.0000e+00 2.5000e+00 2.4179e+00 2.5000e+00 iteration = 2.0000e+00 0 2.5000e+00 1.2500e+00 9.6350e-01 1.2500e+00 iteration = 3.0000e+00 0 1.2500e+00 6.2500e-01 8.9739e-02 6.2500e-01 iteration = 4.0000e+00 0 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 = 0.567143290409717 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 = 2.7141e-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. eval_exp_simple(): Taylor series for exp(x) over [-2,2,] x exp(x) err1 err2 err3 err4 ans = -2.0000 0.1353 1.1353 -0.8647 0.4687 -0.1980 -1.8000 0.1653 0.9653 -0.6547 0.3173 -0.1201 -1.6000 0.2019 0.8019 -0.4781 0.2046 -0.0685 -1.4000 0.2466 0.6466 -0.3334 0.1239 -0.0361 -1.2000 0.3012 0.5012 -0.2188 0.0692 -0.0172 -1.0000 0.3679 0.3679 -0.1321 0.0345 -0.0071 -0.8000 0.4493 0.2493 -0.0707 0.0147 -0.0024 -0.6000 0.5488 0.1488 -0.0312 0.0048 -0.0006 -0.4000 0.6703 0.0703 -0.0097 0.0010 -0.0001 -0.2000 0.8187 0.0187 -0.0013 0.0001 -0.0000 0 1.0000 0 0 0 0 0.2000 1.2214 0.0214 0.0014 0.0001 0.0000 0.4000 1.4918 0.0918 0.0118 0.0012 0.0001 0.6000 1.8221 0.2221 0.0421 0.0061 0.0007 0.8000 2.2255 0.4255 0.1055 0.0202 0.0031 1.0000 2.7183 0.7183 0.2183 0.0516 0.0099 1.2000 3.3201 1.1201 0.4001 0.1121 0.0257 1.4000 4.0552 1.6552 0.6752 0.2179 0.0578 1.6000 4.9530 2.3530 1.0730 0.3904 0.1173 1.8000 6.0496 3.2496 1.6296 0.6576 0.2202 2.0000 7.3891 4.3891 2.3891 1.0557 0.3891 gaussint_test: MATLAB version Test gaussint(): Estimate integral of exp(-x^2) over [0,2] 1 0.7357588823428847 2 0.9194861166409162 4 0.8822290959326038 8 0.8820813904198997 16 0.8820813907624221 Estimate integral of 1/(1+x^2) over [0,4] 1 0.8 2 1.349112426035503 4 1.327713222795399 8 1.325838869084081 16 1.325817663720426 32 1.325817663668032 Estimate integral of 1/(2+sin(x)) over [0,pi] 1 1.047197551196598 2 1.200827173482707 4 1.209224894232256 8 1.209199575798513 16 1.209199576156147 Estimate integral of exp(cos(x)) over [0,pi] 1 3.141592653589793 2 4.167393283551555 4 3.976316211656984 8 3.977463340835657 16 3.977463260506426 32 3.977463260506421 gaussint_test: Normal end of execution. gs_test() Test gs() x0 = 0 0 0 0 0 0 0 0 0 5.5000 x0 = 0 0 0 0 0 0 0 0 2.7500 6.8750 x0 = 0 0 0 0 0 0 0 1.3750 4.1250 7.5625 x0 = 0 0 0 0 0 0 0.6875 2.4062 4.9844 7.9922 x0 = 0 0 0 0 0 0.3438 1.3750 3.1797 5.5859 8.2930 x0 = 0 0 0 0 0.1719 0.7734 1.9766 3.7812 6.0371 8.5186 x0 = 0 0 0 0.0859 0.4297 1.2031 2.4922 4.2646 6.3916 8.6958 x0 = 0 0 0.0430 0.2363 0.7197 1.6060 2.9353 4.6635 6.6796 8.8398 x0 = 0 0.0215 0.1289 0.4243 1.0151 1.9752 3.3193 4.9995 6.9196 8.9598 x0 = 0.0107 0.0698 0.2471 0.6311 1.3032 2.3112 3.6554 5.2875 7.1237 9.0618 x0 = 0.0349 0.1410 0.3860 0.8446 1.5779 2.6166 3.9521 5.5379 7.2999 9.1499 x0 = 0.0705 0.2283 0.5364 1.0572 1.8369 2.8945 4.2162 5.7580 7.4540 9.2270 x0 = 0.1141 0.3253 0.6912 1.2641 2.0793 3.1477 4.4529 5.9534 7.5902 9.2951 x0 = 0.1626 0.4269 0.8455 1.4624 2.3051 3.3790 4.6662 6.1282 7.7117 9.3558 x0 = 0.2135 0.5295 0.9959 1.6505 2.5147 3.5905 4.8593 6.2855 7.8207 9.4103 x0 = 0.2647 0.6303 1.1404 1.8276 2.7090 3.7842 5.0348 6.4277 7.9190 9.4595 x0 = 0.3152 0.7278 1.2777 1.9934 2.8888 3.9618 5.1948 6.5569 8.0082 9.5041 x0 = 0.3639 0.8208 1.4071 2.1479 3.0549 4.1248 5.3409 6.6745 8.0893 9.5447 x0 = 0.4104 0.9087 1.5283 2.2916 3.2082 4.2745 5.4745 6.7819 8.1633 9.5816 x0 = 0.4544 0.9913 1.6415 2.4248 3.3497 4.4121 5.5970 6.8802 8.2309 9.6155 x0 = 0.4957 1.0686 1.7467 2.5482 3.4802 4.5386 5.7094 6.9701 8.2928 9.6464 x0 = 0.5343 1.1405 1.8443 2.6622 3.6004 4.6549 5.8125 7.0527 8.3495 9.6748 x0 = 0.5702 1.2073 1.9348 2.7676 3.7112 4.7619 5.9073 7.1284 8.4016 9.7008 x0 = 0.6036 1.2692 2.0184 2.8648 3.8134 4.8603 5.9944 7.1980 8.4494 9.7247 x0 = 0.6346 1.3265 2.0957 2.9545 3.9074 4.9509 6.0744 7.2619 8.4933 9.7466 x0 = 0.6633 1.3795 2.1670 3.0372 3.9940 5.0342 6.1481 7.3207 8.5337 9.7668 x0 = 0.6897 1.4284 2.2328 3.1134 4.0738 5.1109 6.2158 7.3747 8.5708 9.7854 x0 = 0.7142 1.4735 2.2934 3.1836 4.1473 5.1815 6.2781 7.4245 8.6049 9.8025 x0 = 0.7367 1.5151 2.3494 3.2483 4.2149 5.2465 6.3355 7.4702 8.6363 9.8182 x0 = 0.7575 1.5535 2.4009 3.3079 4.2772 5.3064 6.3883 7.5123 8.6652 9.8326 x0 = 0.7767 1.5888 2.4484 3.3628 4.3346 5.3614 6.4369 7.5511 8.6918 9.8459 x0 = 0.7944 1.6214 2.4921 3.4133 4.3874 5.4121 6.4816 7.5867 8.7163 9.8582 x0 = 0.8107 1.6514 2.5324 3.4599 4.4360 5.4588 6.5228 7.6195 8.7388 9.8694 x0 = 0.8257 1.6790 2.5695 3.5027 4.4808 5.5018 6.5606 7.6497 8.7596 9.8798 x0 = 0.8395 1.7045 2.6036 3.5422 4.5220 5.5413 6.5955 7.6776 8.7787 9.8893 x0 = 0.8522 1.7279 2.6351 3.5785 4.5599 5.5777 6.6276 7.7032 8.7962 9.8981 x0 = 0.8640 1.7495 2.6640 3.6120 4.5948 5.6112 6.6572 7.7267 8.8124 9.9062 x0 = 0.8748 1.7694 2.6907 3.6428 4.6270 5.6421 6.6844 7.7484 8.8273 9.9137 x0 = 0.8847 1.7877 2.7152 3.6711 4.6566 5.6705 6.7095 7.7684 8.8410 9.9205 x0 = 0.8938 1.8045 2.7378 3.6972 4.6839 5.6967 6.7325 7.7868 8.8536 9.9268 x0 = 0.9023 1.8200 2.7586 3.7212 4.7090 5.7207 6.7538 7.8037 8.8653 9.9326 x0 = 0.9100 1.8343 2.7778 3.7434 4.7321 5.7429 6.7733 7.8193 8.8760 9.9380 x0 = 0.9172 1.8475 2.7954 3.7637 4.7533 5.7633 6.7913 7.8336 8.8858 9.9429 x0 = 0.9237 1.8596 2.8117 3.7825 4.7729 5.7821 6.8079 7.8468 8.8949 9.9474 x0 = 0.9298 1.8707 2.8266 3.7998 4.7909 5.7994 6.8231 7.8590 8.9032 9.9516 x0 = 0.9354 1.8810 2.8404 3.8156 4.8075 5.8153 6.8372 7.8702 8.9109 9.9554 x0 = 0.9405 1.8904 2.8530 3.8303 4.8228 5.8300 6.8501 7.8805 8.9180 9.9590 x0 = 0.9452 1.8991 2.8647 3.8438 4.8369 5.8435 6.8620 7.8900 8.9245 9.9622 x0 = 0.9496 1.9071 2.8754 3.8562 4.8498 5.8559 6.8729 7.8987 8.9305 9.9652 x0 = 0.9536 1.9145 2.8853 3.8676 4.8617 5.8673 6.8830 7.9067 8.9360 9.9680 x0 = 0.9573 1.9213 2.8944 3.8781 4.8727 5.8779 6.8923 7.9141 8.9411 9.9705 x0 = 0.9606 1.9275 2.9028 3.8878 4.8828 5.8876 6.9009 7.9210 8.9457 9.9729 x0 = 0.9638 1.9333 2.9105 3.8967 4.8921 5.8965 6.9087 7.9272 8.9501 9.9750 x0 = 0.9666 1.9386 2.9176 3.9049 4.9007 5.9047 6.9160 7.9330 8.9540 9.9770 x0 = 0.9693 1.9435 2.9242 3.9124 4.9086 5.9123 6.9226 7.9383 8.9577 9.9788 x0 = 0.9717 1.9479 2.9302 3.9194 4.9158 5.9192 6.9288 7.9432 8.9610 9.9805 x0 = 0.9740 1.9521 2.9357 3.9258 4.9225 5.9256 6.9344 7.9477 8.9641 9.9821 x0 = 0.9760 1.9559 2.9408 3.9317 4.9287 5.9315 6.9396 7.9519 8.9670 9.9835 x0 = 0.9779 1.9594 2.9455 3.9371 4.9343 5.9370 6.9444 7.9557 8.9696 9.9848 x0 = 0.9797 1.9626 2.9498 3.9421 4.9395 5.9420 6.9488 7.9592 8.9720 9.9860 x0 = 0.9813 1.9656 2.9538 3.9467 4.9443 5.9466 6.9529 7.9625 8.9742 9.9871 x0 = 0.9828 1.9683 2.9575 3.9509 4.9487 5.9508 6.9566 7.9654 8.9763 9.9881 x0 = 0.9842 1.9708 2.9609 3.9548 4.9528 5.9547 6.9601 7.9682 8.9782 9.9891 x0 = 0.9854 1.9731 2.9640 3.9584 4.9566 5.9583 6.9632 7.9707 8.9799 9.9899 x0 = 0.9866 1.9753 2.9668 3.9617 4.9600 5.9616 6.9662 7.9730 8.9815 9.9907 x0 = 0.9876 1.9772 2.9695 3.9647 4.9632 5.9647 6.9689 7.9752 8.9830 9.9915 x0 = 0.9886 1.9790 2.9719 3.9675 4.9661 5.9675 6.9713 7.9771 8.9843 9.9922 x0 = 0.9895 1.9807 2.9741 3.9701 4.9688 5.9701 6.9736 7.9790 8.9856 9.9928 x0 = 0.9904 1.9822 2.9762 3.9725 4.9713 5.9724 6.9757 7.9806 8.9867 9.9934 x0 = 0.9911 1.9836 2.9781 3.9747 4.9736 5.9746 6.9776 7.9822 8.9878 9.9939 x0 = 0.9918 1.9849 2.9798 3.9767 4.9757 5.9766 6.9794 7.9836 8.9887 9.9944 x0 = 0.9925 1.9861 2.9814 3.9785 4.9776 5.9785 6.9810 7.9849 8.9896 9.9948 x0 = 0.9931 1.9872 2.9829 3.9802 4.9794 5.9802 6.9825 7.9861 8.9904 9.9952 x0 = 0.9936 1.9883 2.9842 3.9818 4.9810 5.9818 6.9839 7.9872 8.9912 9.9956 x0 = 0.9941 1.9892 2.9855 3.9832 4.9825 5.9832 6.9852 7.9882 8.9919 9.9960 x0 = 0.9946 1.9900 2.9866 3.9846 4.9839 5.9845 6.9864 7.9891 8.9925 9.9963 x0 = 0.9950 1.9908 2.9877 3.9858 4.9852 5.9858 6.9875 7.9900 8.9931 9.9966 x0 = 0.9954 1.9916 2.9887 3.9869 4.9864 5.9869 6.9885 7.9908 8.9937 9.9968 x0 = 0.9958 1.9922 2.9896 3.9880 4.9874 5.9879 6.9894 7.9915 8.9942 9.9971 x0 = 0.9961 1.9928 2.9904 3.9889 4.9884 5.9889 6.9902 7.9922 8.9946 9.9973 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 0 0 0 0 0 0 0 0 5.5000 x = 0 0 0 0 0 0 0 0 2.7500 5.5000 x = 0 0 0 0 0 0 0 1.3750 2.7500 6.8750 x = 0 0 0 0 0 0 0.6875 1.3750 4.1250 6.8750 x = 0 0 0 0 0 0.3438 0.6875 2.4062 4.1250 7.5625 x = 0 0 0 0 0.1719 0.3438 1.3750 2.4062 4.9844 7.5625 x = 0 0 0 0.0859 0.1719 0.7734 1.3750 3.1797 4.9844 7.9922 x = 0 0 0.0430 0.0859 0.4297 0.7734 1.9766 3.1797 5.5859 7.9922 x = 0 0.0215 0.0430 0.2363 0.4297 1.2031 1.9766 3.7812 5.5859 8.2930 x = 0.0107 0.0215 0.1289 0.2363 0.7197 1.2031 2.4922 3.7812 6.0371 8.2930 x = 0.0107 0.0698 0.1289 0.4243 0.7197 1.6060 2.4922 4.2646 6.0371 8.5186 x = 0.0349 0.0698 0.2471 0.4243 1.0151 1.6060 2.9353 4.2646 6.3916 8.5186 x = 0.0349 0.1410 0.2471 0.6311 1.0151 1.9752 2.9353 4.6635 6.3916 8.6958 x = 0.0705 0.1410 0.3860 0.6311 1.3032 1.9752 3.3193 4.6635 6.6796 8.6958 x = 0.0705 0.2283 0.3860 0.8446 1.3032 2.3112 3.3193 4.9995 6.6796 8.8398 x = 0.1141 0.2283 0.5364 0.8446 1.5779 2.3112 3.6554 4.9995 6.9196 8.8398 x = 0.1141 0.3253 0.5364 1.0572 1.5779 2.6166 3.6554 5.2875 6.9196 8.9598 x = 0.1626 0.3253 0.6912 1.0572 1.8369 2.6166 3.9521 5.2875 7.1237 8.9598 x = 0.1626 0.4269 0.6912 1.2641 1.8369 2.8945 3.9521 5.5379 7.1237 9.0618 x = 0.2135 0.4269 0.8455 1.2641 2.0793 2.8945 4.2162 5.5379 7.2999 9.0618 x = 0.2135 0.5295 0.8455 1.4624 2.0793 3.1477 4.2162 5.7580 7.2999 9.1499 x = 0.2647 0.5295 0.9959 1.4624 2.3051 3.1477 4.4529 5.7580 7.4540 9.1499 x = 0.2647 0.6303 0.9959 1.6505 2.3051 3.3790 4.4529 5.9534 7.4540 9.2270 x = 0.3152 0.6303 1.1404 1.6505 2.5147 3.3790 4.6662 5.9534 7.5902 9.2270 x = 0.3152 0.7278 1.1404 1.8276 2.5147 3.5905 4.6662 6.1282 7.5902 9.2951 x = 0.3639 0.7278 1.2777 1.8276 2.7090 3.5905 4.8593 6.1282 7.7117 9.2951 x = 0.3639 0.8208 1.2777 1.9934 2.7090 3.7842 4.8593 6.2855 7.7117 9.3558 x = 0.4104 0.8208 1.4071 1.9934 2.8888 3.7842 5.0348 6.2855 7.8207 9.3558 x = 0.4104 0.9087 1.4071 2.1479 2.8888 3.9618 5.0348 6.4277 7.8207 9.4103 x = 0.4544 0.9087 1.5283 2.1479 3.0549 3.9618 5.1948 6.4277 7.9190 9.4103 x = 0.4544 0.9913 1.5283 2.2916 3.0549 4.1248 5.1948 6.5569 7.9190 9.4595 x = 0.4957 0.9913 1.6415 2.2916 3.2082 4.1248 5.3409 6.5569 8.0082 9.4595 x = 0.4957 1.0686 1.6415 2.4248 3.2082 4.2745 5.3409 6.6745 8.0082 9.5041 x = 0.5343 1.0686 1.7467 2.4248 3.3497 4.2745 5.4745 6.6745 8.0893 9.5041 x = 0.5343 1.1405 1.7467 2.5482 3.3497 4.4121 5.4745 6.7819 8.0893 9.5447 x = 0.5702 1.1405 1.8443 2.5482 3.4802 4.4121 5.5970 6.7819 8.1633 9.5447 x = 0.5702 1.2073 1.8443 2.6622 3.4802 4.5386 5.5970 6.8802 8.1633 9.5816 x = 0.6036 1.2073 1.9348 2.6622 3.6004 4.5386 5.7094 6.8802 8.2309 9.5816 x = 0.6036 1.2692 1.9348 2.7676 3.6004 4.6549 5.7094 6.9701 8.2309 9.6155 x = 0.6346 1.2692 2.0184 2.7676 3.7112 4.6549 5.8125 6.9701 8.2928 9.6155 x = 0.6346 1.3265 2.0184 2.8648 3.7112 4.7619 5.8125 7.0527 8.2928 9.6464 x = 0.6633 1.3265 2.0957 2.8648 3.8134 4.7619 5.9073 7.0527 8.3495 9.6464 x = 0.6633 1.3795 2.0957 2.9545 3.8134 4.8603 5.9073 7.1284 8.3495 9.6748 x = 0.6897 1.3795 2.1670 2.9545 3.9074 4.8603 5.9944 7.1284 8.4016 9.6748 x = 0.6897 1.4284 2.1670 3.0372 3.9074 4.9509 5.9944 7.1980 8.4016 9.7008 x = 0.7142 1.4284 2.2328 3.0372 3.9940 4.9509 6.0744 7.1980 8.4494 9.7008 x = 0.7142 1.4735 2.2328 3.1134 3.9940 5.0342 6.0744 7.2619 8.4494 9.7247 x = 0.7367 1.4735 2.2934 3.1134 4.0738 5.0342 6.1481 7.2619 8.4933 9.7247 x = 0.7367 1.5151 2.2934 3.1836 4.0738 5.1109 6.1481 7.3207 8.4933 9.7466 x = 0.7575 1.5151 2.3494 3.1836 4.1473 5.1109 6.2158 7.3207 8.5337 9.7466 x = 0.7575 1.5535 2.3494 3.2483 4.1473 5.1815 6.2158 7.3747 8.5337 9.7668 x = 0.7767 1.5535 2.4009 3.2483 4.2149 5.1815 6.2781 7.3747 8.5708 9.7668 x = 0.7767 1.5888 2.4009 3.3079 4.2149 5.2465 6.2781 7.4245 8.5708 9.7854 x = 0.7944 1.5888 2.4484 3.3079 4.2772 5.2465 6.3355 7.4245 8.6049 9.7854 x = 0.7944 1.6214 2.4484 3.3628 4.2772 5.3064 6.3355 7.4702 8.6049 9.8025 x = 0.8107 1.6214 2.4921 3.3628 4.3346 5.3064 6.3883 7.4702 8.6363 9.8025 x = 0.8107 1.6514 2.4921 3.4133 4.3346 5.3614 6.3883 7.5123 8.6363 9.8182 x = 0.8257 1.6514 2.5324 3.4133 4.3874 5.3614 6.4369 7.5123 8.6652 9.8182 x = 0.8257 1.6790 2.5324 3.4599 4.3874 5.4121 6.4369 7.5511 8.6652 9.8326 x = 0.8395 1.6790 2.5695 3.4599 4.4360 5.4121 6.4816 7.5511 8.6918 9.8326 x = 0.8395 1.7045 2.5695 3.5027 4.4360 5.4588 6.4816 7.5867 8.6918 9.8459 x = 0.8522 1.7045 2.6036 3.5027 4.4808 5.4588 6.5228 7.5867 8.7163 9.8459 x = 0.8522 1.7279 2.6036 3.5422 4.4808 5.5018 6.5228 7.6195 8.7163 9.8582 x = 0.8640 1.7279 2.6351 3.5422 4.5220 5.5018 6.5606 7.6195 8.7388 9.8582 x = 0.8640 1.7495 2.6351 3.5785 4.5220 5.5413 6.5606 7.6497 8.7388 9.8694 x = 0.8748 1.7495 2.6640 3.5785 4.5599 5.5413 6.5955 7.6497 8.7596 9.8694 x = 0.8748 1.7694 2.6640 3.6120 4.5599 5.5777 6.5955 7.6776 8.7596 9.8798 x = 0.8847 1.7694 2.6907 3.6120 4.5948 5.5777 6.6276 7.6776 8.7787 9.8798 x = 0.8847 1.7877 2.6907 3.6428 4.5948 5.6112 6.6276 7.7032 8.7787 9.8893 x = 0.8938 1.7877 2.7152 3.6428 4.6270 5.6112 6.6572 7.7032 8.7962 9.8893 x = 0.8938 1.8045 2.7152 3.6711 4.6270 5.6421 6.6572 7.7267 8.7962 9.8981 x = 0.9023 1.8045 2.7378 3.6711 4.6566 5.6421 6.6844 7.7267 8.8124 9.8981 x = 0.9023 1.8200 2.7378 3.6972 4.6566 5.6705 6.6844 7.7484 8.8124 9.9062 x = 0.9100 1.8200 2.7586 3.6972 4.6839 5.6705 6.7095 7.7484 8.8273 9.9062 x = 0.9100 1.8343 2.7586 3.7212 4.6839 5.6967 6.7095 7.7684 8.8273 9.9137 x = 0.9172 1.8343 2.7778 3.7212 4.7090 5.6967 6.7325 7.7684 8.8410 9.9137 x = 0.9172 1.8475 2.7778 3.7434 4.7090 5.7207 6.7325 7.7868 8.8410 9.9205 x = 0.9237 1.8475 2.7954 3.7434 4.7321 5.7207 6.7538 7.7868 8.8536 9.9205 x = 0.9237 1.8596 2.7954 3.7637 4.7321 5.7429 6.7538 7.8037 8.8536 9.9268 x = 0.9298 1.8596 2.8117 3.7637 4.7533 5.7429 6.7733 7.8037 8.8653 9.9268 x = 0.9298 1.8707 2.8117 3.7825 4.7533 5.7633 6.7733 7.8193 8.8653 9.9326 x = 0.9354 1.8707 2.8266 3.7825 4.7729 5.7633 6.7913 7.8193 8.8760 9.9326 x = 0.9354 1.8810 2.8266 3.7998 4.7729 5.7821 6.7913 7.8336 8.8760 9.9380 x = 0.9405 1.8810 2.8404 3.7998 4.7909 5.7821 6.8079 7.8336 8.8858 9.9380 x = 0.9405 1.8904 2.8404 3.8156 4.7909 5.7994 6.8079 7.8468 8.8858 9.9429 x = 0.9452 1.8904 2.8530 3.8156 4.8075 5.7994 6.8231 7.8468 8.8949 9.9429 x = 0.9452 1.8991 2.8530 3.8303 4.8075 5.8153 6.8231 7.8590 8.8949 9.9474 x = 0.9496 1.8991 2.8647 3.8303 4.8228 5.8153 6.8372 7.8590 8.9032 9.9474 x = 0.9496 1.9071 2.8647 3.8438 4.8228 5.8300 6.8372 7.8702 8.9032 9.9516 x = 0.9536 1.9071 2.8754 3.8438 4.8369 5.8300 6.8501 7.8702 8.9109 9.9516 x = 0.9536 1.9145 2.8754 3.8562 4.8369 5.8435 6.8501 7.8805 8.9109 9.9554 x = 0.9573 1.9145 2.8853 3.8562 4.8498 5.8435 6.8620 7.8805 8.9180 9.9554 x = 0.9573 1.9213 2.8853 3.8676 4.8498 5.8559 6.8620 7.8900 8.9180 9.9590 x = 0.9606 1.9213 2.8944 3.8676 4.8617 5.8559 6.8729 7.8900 8.9245 9.9590 x = 0.9606 1.9275 2.8944 3.8781 4.8617 5.8673 6.8729 7.8987 8.9245 9.9622 x = 0.9638 1.9275 2.9028 3.8781 4.8727 5.8673 6.8830 7.8987 8.9305 9.9622 x = 0.9638 1.9333 2.9028 3.8878 4.8727 5.8779 6.8830 7.9067 8.9305 9.9652 x = 0.9666 1.9333 2.9105 3.8878 4.8828 5.8779 6.8923 7.9067 8.9360 9.9652 x = 0.9666 1.9386 2.9105 3.8967 4.8828 5.8876 6.8923 7.9141 8.9360 9.9680 x = 0.9693 1.9386 2.9176 3.8967 4.8921 5.8876 6.9009 7.9141 8.9411 9.9680 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 0 -1 -1 -1 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 = -0.778089598678601 error = 5.3513e-14 it_count = 7 Estimated root is x = -0.77809 f(x) = 2.22045e-16 iteration = 0 0 -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 -4.5519e-15 1.5671e+00 2.8866e-15 root = 0.567143290409784 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 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 root = 1.134724138401519 error = 0 it_count = 11 Estimated root is x = 1.13472 f(x) = -8.88178e-16 iteration = 0 0 -1 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 = 0.567143290409784 error = 7.9270e-14 it_count = 6 Estimated root is x = 0.567143 f(x) = -1.11022e-16 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 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 Columns 8 through 14 8.0000 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000 Columns 15 through 21 15.0000 16.0000 17.0000 18.0000 19.0000 20.0000 21.0000 Columns 22 through 28 22.0000 23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 Columns 29 through 35 29.0000 30.0000 31.0000 32.0000 33.0000 34.0000 35.0000 Columns 36 through 42 36.0000 37.0000 38.0000 39.0000 40.0000 41.0000 42.0000 Columns 43 through 49 43.0000 44.0000 45.0000 46.0000 47.0000 48.0000 49.0000 Columns 50 through 56 50.0000 51.0000 52.0000 53.0000 54.0000 55.0000 56.0000 Columns 57 through 63 57.0000 58.0000 59.0000 60.0000 61.0000 62.0000 63.0000 Columns 64 through 70 64.0000 65.0000 66.0000 67.0000 68.0000 69.0000 70.0000 Columns 71 through 77 71.0000 72.0000 73.0000 74.0000 75.0000 76.0000 77.0000 Columns 78 through 84 78.0000 79.0000 80.0000 81.0000 82.0000 83.0000 84.0000 Columns 85 through 91 85.0000 86.0000 87.0000 88.0000 89.0000 90.0000 91.0000 Columns 92 through 98 92.0000 93.0000 94.0000 95.0000 96.0000 97.0000 98.0000 Columns 99 through 100 99.0000 100.0000 alpha = Columns 1 through 7 0 -0.5000 -0.6667 -0.7500 -0.8000 -0.8333 -0.8571 Columns 8 through 14 -0.8750 -0.8889 -0.9000 -0.9091 -0.9167 -0.9231 -0.9286 Columns 15 through 21 -0.9333 -0.9375 -0.9412 -0.9444 -0.9474 -0.9500 -0.9524 Columns 22 through 28 -0.9545 -0.9565 -0.9583 -0.9600 -0.9615 -0.9630 -0.9643 Columns 29 through 35 -0.9655 -0.9667 -0.9677 -0.9687 -0.9697 -0.9706 -0.9714 Columns 36 through 42 -0.9722 -0.9730 -0.9737 -0.9744 -0.9750 -0.9756 -0.9762 Columns 43 through 49 -0.9767 -0.9773 -0.9778 -0.9783 -0.9787 -0.9792 -0.9796 Columns 50 through 56 -0.9800 -0.9804 -0.9808 -0.9811 -0.9815 -0.9818 -0.9821 Columns 57 through 63 -0.9825 -0.9828 -0.9831 -0.9833 -0.9836 -0.9839 -0.9841 Columns 64 through 70 -0.9844 -0.9846 -0.9848 -0.9851 -0.9853 -0.9855 -0.9857 Columns 71 through 77 -0.9859 -0.9861 -0.9863 -0.9865 -0.9867 -0.9868 -0.9870 Columns 78 through 84 -0.9872 -0.9873 -0.9875 -0.9877 -0.9878 -0.9880 -0.9881 Columns 85 through 91 -0.9882 -0.9884 -0.9885 -0.9886 -0.9888 -0.9889 -0.9890 Columns 92 through 98 -0.9891 -0.9892 -0.9894 -0.9895 -0.9896 -0.9897 -0.9898 Columns 99 through 100 -0.9899 -0.9900 beta = Columns 1 through 7 2.0000 1.5000 1.3333 1.2500 1.2000 1.1667 1.1429 Columns 8 through 14 1.1250 1.1111 1.1000 1.0909 1.0833 1.0769 1.0714 Columns 15 through 21 1.0667 1.0625 1.0588 1.0556 1.0526 1.0500 1.0476 Columns 22 through 28 1.0455 1.0435 1.0417 1.0400 1.0385 1.0370 1.0357 Columns 29 through 35 1.0345 1.0333 1.0323 1.0313 1.0303 1.0294 1.0286 Columns 36 through 42 1.0278 1.0270 1.0263 1.0256 1.0250 1.0244 1.0238 Columns 43 through 49 1.0233 1.0227 1.0222 1.0217 1.0213 1.0208 1.0204 Columns 50 through 56 1.0200 1.0196 1.0192 1.0189 1.0185 1.0182 1.0179 Columns 57 through 63 1.0175 1.0172 1.0169 1.0167 1.0164 1.0161 1.0159 Columns 64 through 70 1.0156 1.0154 1.0152 1.0149 1.0147 1.0145 1.0143 Columns 71 through 77 1.0141 1.0139 1.0137 1.0135 1.0133 1.0132 1.0130 Columns 78 through 84 1.0128 1.0127 1.0125 1.0123 1.0122 1.0120 1.0119 Columns 85 through 91 1.0118 1.0116 1.0115 1.0114 1.0112 1.0111 1.0110 Columns 92 through 98 1.0109 1.0108 1.0106 1.0105 1.0104 1.0103 1.0102 Columns 99 through 100 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. 17-Aug-2022 20:21:17