07-Jan-2022 18:13:24 continuation_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2. Test continuation(). newton_test Demonstrate the newton() function for continuation. Starting X0: 1: 0.5 2: -2 ||F(X0)|| = 3.25 Solution X: 1: 0.5 2: -0.866026 ||F(X)|| = 1.08217e-06 tangent_test Demonstrate the tangent() function. At a point X, using continuation parameter P, compute the tangent vector of unit norm. Index of current continuation parameter P = 1 Current point X: 1: 0.5 2: -0.866025 Unit tangent vector T2: 1: 0.866025 2: 0.5 Index of next continuation parameter P2 = 1 step_test Test step(). Starting X0: 1: 0.5 2: -0.866025 ||F(X0)|| = 1.11022e-16 Suggested stepsize H = 0.1 Solution X2: 1: 0.586603 2: -0.809875 ||F(X)|| = 5.3721e-10 circle_test Trace points on a circle. 0 0.5 -2 3.25e+00 1 0.5 -0.866026 1.08e-06 2 0.629904 -0.776673 1.70e-08 3 0.746405 -0.665492 4.17e-08 4 0.846229 -0.53282 1.50e-07 Switching parameters from 1 to 2 5 0.913924 -0.405886 6.52e-09 6 0.963197 -0.268797 4.78e-09 7 0.992242 -0.124318 4.01e-09 8 0.999699 0.0245187 3.84e-09 9 0.984662 0.174474 4.20e-09 10 0.946681 0.322173 5.29e-09 11 0.885744 0.464175 7.84e-09 12 0.802214 0.597037 1.40e-08 13 0.696694 0.717369 3.20e-08 14 0.569671 0.821873 1.02e-07 Switching parameters from 2 to 1 15 0.44639 0.894838 7.38e-09 16 0.312165 0.950028 5.18e-09 17 0.16966 0.985503 4.17e-09 18 0.0218351 0.999762 3.84e-09 19 -0.128129 0.991757 4.02e-09 20 -0.276893 0.960901 4.85e-09 21 -0.421028 0.907048 6.81e-09 22 -0.557085 0.830455 1.14e-08 23 -0.681653 0.731675 2.40e-08 24 -0.791405 0.611293 6.82e-08 25 -0.883099 0.469188 3.08e-07 Switching parameters from 1 to 2 26 -0.941604 0.336723 5.46e-09 27 -0.980707 0.195483 4.30e-09 28 -0.998829 0.0483764 3.86e-09 29 -0.994841 -0.101448 3.95e-09 30 -0.968072 -0.250674 4.64e-09 31 -0.9183 -0.395885 6.33e-09 32 -0.845718 -0.53363 1.03e-08 33 -0.750837 -0.660488 2.07e-08 34 -0.634268 -0.773113 5.51e-08 35 -0.496121 -0.868253 2.25e-07 Switching parameters from 2 to 1 Plot file saved as "circle_test.png" lotka_test Trace points on the Hamiltonian curve associated with a Lotka problem. 0 4 2 4.44e-16 1 4 2 4.44e-16 2 3.99286 2.15 1.60e-06 3 3.97278 2.29935 1.20e-06 4 3.94173 2.44713 9.15e-07 5 3.90142 2.59283 7.06e-07 6 3.85327 2.73621 5.57e-07 7 3.79844 2.87719 4.50e-07 8 3.73786 3.01579 3.72e-07 9 3.67227 3.15207 3.16e-07 10 3.60227 3.28611 2.74e-07 11 3.52835 3.418 2.44e-07 12 3.45089 3.54782 2.23e-07 13 3.37021 3.67563 2.08e-07 14 3.28654 3.8015 1.99e-07 15 3.20009 3.92547 1.96e-07 16 3.11102 4.04758 1.97e-07 17 3.01944 4.16784 2.03e-07 18 2.92543 4.28624 2.16e-07 19 2.82904 4.40278 2.36e-07 20 2.73029 4.5174 2.67e-07 21 2.62916 4.63005 3.11e-07 22 2.52561 4.74062 3.76e-07 23 2.41954 4.84899 4.73e-07 24 2.31083 4.95498 6.21e-07 Switching parameters from 2 to 1 25 2.20214 5.05576 2.64e-07 26 2.09082 5.1535 2.95e-07 27 1.97668 5.24775 3.41e-07 28 1.85946 5.33791 4.13e-07 29 1.73883 5.42315 5.22e-07 30 1.6144 5.50231 6.97e-07 31 1.48565 5.57375 9.87e-07 32 1.35202 5.63498 1.50e-06 33 1.21292 5.6822 2.46e-06 34 1.06814 5.70943 4.40e-06 35 0.918859 5.7075 8.42e-06 36 0.770226 5.66458 1.90e-11 37 0.634011 5.5739 4.80e-11 38 0.522534 5.44533 5.95e-11 39 0.437142 5.29708 4.43e-11 Switching parameters from 1 to 2 40 0.379722 5.16204 5.91e-08 41 0.332649 5.02159 2.23e-08 42 0.293684 4.87791 9.76e-09 43 0.261092 4.73223 4.82e-09 44 0.233569 4.58526 2.63e-09 45 0.210136 4.43742 1.54e-09 46 0.19005 4.289 9.67e-10 47 0.172738 4.14016 6.36e-10 48 0.157752 3.99103 4.36e-10 49 0.144741 3.84168 3.09e-10 50 0.133421 3.69217 2.26e-10 51 0.123564 3.54254 1.70e-10 52 0.114988 3.39282 1.31e-10 53 0.107545 3.24304 1.04e-10 54 0.101114 3.0932 8.54e-11 55 0.0956014 2.94332 7.28e-11 56 0.0909366 2.7934 6.51e-11 57 0.0870685 2.64346 6.18e-11 58 0.0839682 2.4935 6.33e-11 59 0.0816291 2.34353 7.11e-11 60 0.0800717 2.19354 8.93e-11 61 0.0793499 2.04354 1.28e-10 62 0.0795631 1.89354 2.11e-10 63 0.0808766 1.74355 4.05e-10 64 0.0835562 1.59356 9.11e-10 65 0.0880316 1.4436 2.40e-09 66 0.095016 1.2937 7.40e-09 67 0.105749 1.14395 2.69e-08 68 0.122532 0.994533 1.17e-07 69 0.15003 0.846006 6.30e-07 70 0.198767 0.700173 4.36e-06 71 0.294146 0.563928 1.41e-09 72 0.47641 0.461057 8.37e-08 Switching parameters from 2 to 1 73 0.618886 0.427068 3.40e-07 74 0.766832 0.409512 3.75e-08 75 0.916375 0.402226 5.74e-09 76 1.06634 0.401825 1.29e-09 77 1.21632 0.40648 4.11e-10 78 1.36616 0.415183 1.77e-10 79 1.51579 0.427376 9.82e-11 80 1.66516 0.442772 6.74e-11 81 1.8142 0.461257 5.49e-11 82 1.96286 0.482848 5.13e-11 83 2.11106 0.507663 5.34e-11 84 2.25872 0.535909 6.08e-11 85 2.40569 0.567885 7.44e-11 86 2.55182 0.603984 9.71e-11 87 2.69688 0.644707 1.34e-10 88 2.84058 0.69068 1.97e-10 89 2.98252 0.74268 3.06e-10 90 3.12214 0.801669 5.07e-10 91 3.25869 0.868829 9.02e-10 92 3.3911 0.945602 1.74e-09 93 3.51787 1.03372 3.70e-09 94 3.63697 1.13519 8.83e-09 95 3.74563 1.25224 2.45e-08 96 3.84037 1.38723 8.34e-08 Switching parameters from 1 to 2 97 3.90611 1.51601 4.07e-06 98 3.95468 1.65385 3.57e-06 99 3.98545 1.79829 2.95e-06 100 3.99904 1.94664 2.32e-06 101 3.99699 2.09654 1.77e-06 102 3.98129 2.24626 1.33e-06 103 3.95395 2.39467 1.01e-06 104 3.91676 2.54115 7.73e-07 105 3.87126 2.68537 6.05e-07 106 3.81869 2.82721 4.84e-07 107 3.76006 2.96665 3.97e-07 108 3.69618 3.10375 3.34e-07 109 3.6277 3.23858 2.88e-07 110 3.55513 3.37123 2.54e-07 111 3.47889 3.50177 2.30e-07 112 3.39932 3.63029 2.13e-07 113 3.31669 3.75685 2.02e-07 114 3.23122 3.88149 1.96e-07 115 3.14307 4.00426 1.96e-07 116 3.05237 4.12518 2.00e-07 117 2.95922 4.24425 2.11e-07 118 2.86367 4.36145 2.28e-07 119 2.76577 4.47677 2.55e-07 120 2.66549 4.59012 2.93e-07 121 2.56281 4.70145 3.50e-07 122 2.45765 4.81062 4.34e-07 123 2.3499 4.91748 5.60e-07 124 2.23937 5.02182 7.59e-07 Switching parameters from 2 to 1 125 2.12897 5.12064 2.83e-07 126 2.01581 5.21614 3.23e-07 127 1.89967 5.30776 3.85e-07 128 1.78024 5.39479 4.79e-07 129 1.65715 5.47617 6.28e-07 130 1.52994 5.55047 8.70e-07 131 1.39803 5.61551 1.29e-06 132 1.26085 5.66804 2.06e-06 133 1.11797 5.70291 3.58e-06 134 0.969913 5.71215 6.72e-06 135 0.820083 5.68445 1.24e-11 136 0.678002 5.60985 3.75e-11 137 0.557313 5.49209 5.99e-11 138 0.463574 5.34879 5.03e-11 Switching parameters from 1 to 2 139 0.401303 5.21686 9.12e-08 140 0.350387 5.07824 3.24e-08 141 0.308416 4.93566 1.34e-08 142 0.273453 4.79068 6.31e-09 143 0.244036 4.64416 3.31e-09 144 0.219069 4.49663 1.89e-09 145 0.197721 4.34841 1.16e-09 146 0.179359 4.19973 7.48e-10 147 0.16349 4.0507 5.05e-10 148 0.149727 3.90143 3.53e-10 149 0.13776 3.75198 2.55e-10 150 0.127343 3.60239 1.90e-10 151 0.118275 3.45271 1.45e-10 152 0.110394 3.30295 1.14e-10 153 0.10357 3.15313 9.21e-11 154 0.0977006 3.00326 7.72e-11 155 0.0927041 2.85336 6.77e-11 156 0.0885221 2.70343 6.26e-11 157 0.0851169 2.55348 6.21e-11 158 0.0824725 2.40351 6.70e-11 159 0.0805981 2.25352 8.03e-11 160 0.0795331 2.10353 1.09e-10 161 0.0793569 1.95353 1.69e-10 162 0.0802051 1.80353 3.06e-10 163 0.0822979 1.65354 6.47e-10 164 0.0859891 1.50356 1.60e-09 165 0.0918585 1.35364 4.63e-09 166 0.100893 1.20381 1.57e-08 167 0.114874 1.05422 6.35e-08 168 0.137274 0.90523 3.12e-07 169 0.175597 0.757932 1.95e-06 170 0.247747 0.616312 2.17e-10 171 0.392224 0.495701 2.06e-08 172 0.616397 0.427487 2.64e-07 Switching parameters from 2 to 1 173 0.764295 0.409712 3.88e-08 174 0.913824 0.402286 5.90e-09 175 1.06378 0.401785 1.32e-09 176 1.21376 0.406365 4.18e-10 177 1.36361 0.415005 1.79e-10 178 1.51325 0.427142 9.90e-11 179 1.66262 0.442484 6.77e-11 180 1.81166 0.460917 5.50e-11 181 1.96033 0.482454 5.13e-11 182 2.10855 0.507212 5.34e-11 183 2.25621 0.535398 6.06e-11 184 2.40319 0.567307 7.41e-11 185 2.54934 0.603332 9.66e-11 186 2.69442 0.643972 1.34e-10 187 2.83815 0.689849 1.96e-10 188 2.98012 0.74174 3.04e-10 189 3.11979 0.800601 5.02e-10 190 3.2564 0.86761 8.92e-10 191 3.38888 0.944206 1.72e-09 192 3.51577 1.03211 3.65e-09 193 3.63502 1.13334 8.69e-09 194 3.74388 1.2501 2.40e-08 195 3.83889 1.38477 8.15e-08 Switching parameters from 1 to 2 196 3.90496 1.51334 4.08e-06 197 3.95388 1.65103 3.58e-06 198 3.985 1.79537 2.96e-06 199 3.99892 1.94366 2.33e-06 200 3.99717 2.09355 1.78e-06 Graphics saved as "lotka_test.png" continuation_test(): Normal end of execution. 07-Jan-2022 18:13:28