From 85bb62ccedf0096efb8a82921daa12747683f20c Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Sun, 21 Mar 2021 22:54:15 +0100 Subject: [PATCH] hw1: done up to 3.2 --- hw1/ex3.m | 11 +- hw1/ex32.tex | 14172 +++++++++++++++++++++++++++++++++++++++++++++++++ hw1/main.pdf | Bin 110017 -> 302456 bytes hw1/main.tex | 26 + 4 files changed, 14206 insertions(+), 3 deletions(-) create mode 100644 hw1/ex32.tex diff --git a/hw1/ex3.m b/hw1/ex3.m index 9d85de0..7d5e4ff 100644 --- a/hw1/ex3.m +++ b/hw1/ex3.m @@ -1,9 +1,12 @@ +% Sources: +% https://www.youtube.com/watch?v=91RZYO1cv_o + %% Exercise 3.1 % f(x1, x2) = x1^2 + u * x2^2; -% [x1 x2] [1 0] [x1] + [0][x1] -% [0 u] [x2] + [0][x2] +% 1/2 * [x1 x2] [2 0] [x1] + [0][x1] +% [0 2u] [x2] + [0][x2] % A = [1 0; 0 u]; b = [0; 0] @@ -40,4 +43,6 @@ for u = 1:10 subplot(4, 5, con); contour(xs, ys, Z, 20); title(sprintf("Contour for u=%d", u)); -end \ No newline at end of file + +end +matlab2tikz('showInfo', false, './ex32.tex') diff --git a/hw1/ex32.tex b/hw1/ex32.tex new file mode 100644 index 0000000..12e0211 --- /dev/null +++ b/hw1/ex32.tex @@ -0,0 +1,14172 @@ +% This file was created by matlab2tikz. +% +\begin{tikzpicture} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(2.65in,8.015in)}, +scale only axis, +xmin=-10, +xmax=10, +tick align=outside, +ymin=-10, +ymax=10, +zmin=0, +zmax=200, +view={-37.5}{30}, +axis background/.style={fill=white}, +title style={font=\bfseries}, +title={Surf for u=1}, +axis x line*=bottom, +axis y line*=left, +axis z line*=left, +xmajorgrids, +ymajorgrids, +zmajorgrids +] + +\addplot3[% +surf, +shader=flat, z buffer=sort, colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); 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rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 300 300\\ +-10 -9 281 281\\ +-10 -8 264 264\\ +-10 -7 249 249\\ +-10 -6 236 236\\ +-10 -5 225 225\\ +-10 -4 216 216\\ +-10 -3 209 209\\ +-10 -2 204 204\\ +-10 -1 201 201\\ +-10 0 200 200\\ +-10 1 201 201\\ +-10 2 204 204\\ +-10 3 209 209\\ +-10 4 216 216\\ +-10 5 225 225\\ +-10 6 236 236\\ +-10 7 249 249\\ +-10 8 264 264\\ +-10 9 281 281\\ +-10 10 300 300\\ +-9 -10 262 262\\ +-9 -9 243 243\\ +-9 -8 226 226\\ +-9 -7 211 211\\ +-9 -6 198 198\\ +-9 -5 187 187\\ +-9 -4 178 178\\ +-9 -3 171 171\\ +-9 -2 166 166\\ +-9 -1 163 163\\ +-9 0 162 162\\ +-9 1 163 163\\ +-9 2 166 166\\ +-9 3 171 171\\ +-9 4 178 178\\ +-9 5 187 187\\ +-9 6 198 198\\ +-9 7 211 211\\ +-9 8 226 226\\ +-9 9 243 243\\ +-9 10 262 262\\ +-8 -10 228 228\\ +-8 -9 209 209\\ +-8 -8 192 192\\ +-8 -7 177 177\\ +-8 -6 164 164\\ +-8 -5 153 153\\ +-8 -4 144 144\\ +-8 -3 137 137\\ +-8 -2 132 132\\ +-8 -1 129 129\\ +-8 0 128 128\\ +-8 1 129 129\\ +-8 2 132 132\\ +-8 3 137 137\\ +-8 4 144 144\\ +-8 5 153 153\\ +-8 6 164 164\\ +-8 7 177 177\\ +-8 8 192 192\\ +-8 9 209 209\\ +-8 10 228 228\\ +-7 -10 198 198\\ +-7 -9 179 179\\ +-7 -8 162 162\\ +-7 -7 147 147\\ +-7 -6 134 134\\ +-7 -5 123 123\\ +-7 -4 114 114\\ +-7 -3 107 107\\ +-7 -2 102 102\\ +-7 -1 99 99\\ +-7 0 98 98\\ +-7 1 99 99\\ +-7 2 102 102\\ +-7 3 107 107\\ +-7 4 114 114\\ +-7 5 123 123\\ +-7 6 134 134\\ +-7 7 147 147\\ +-7 8 162 162\\ +-7 9 179 179\\ +-7 10 198 198\\ +-6 -10 172 172\\ +-6 -9 153 153\\ +-6 -8 136 136\\ +-6 -7 121 121\\ +-6 -6 108 108\\ +-6 -5 97 97\\ +-6 -4 88 88\\ +-6 -3 81 81\\ +-6 -2 76 76\\ +-6 -1 73 73\\ +-6 0 72 72\\ +-6 1 73 73\\ +-6 2 76 76\\ +-6 3 81 81\\ +-6 4 88 88\\ +-6 5 97 97\\ +-6 6 108 108\\ +-6 7 121 121\\ +-6 8 136 136\\ +-6 9 153 153\\ +-6 10 172 172\\ +-5 -10 150 150\\ +-5 -9 131 131\\ +-5 -8 114 114\\ +-5 -7 99 99\\ +-5 -6 86 86\\ +-5 -5 75 75\\ +-5 -4 66 66\\ +-5 -3 59 59\\ +-5 -2 54 54\\ +-5 -1 51 51\\ +-5 0 50 50\\ +-5 1 51 51\\ +-5 2 54 54\\ +-5 3 59 59\\ +-5 4 66 66\\ +-5 5 75 75\\ +-5 6 86 86\\ +-5 7 99 99\\ +-5 8 114 114\\ +-5 9 131 131\\ +-5 10 150 150\\ +-4 -10 132 132\\ +-4 -9 113 113\\ +-4 -8 96 96\\ +-4 -7 81 81\\ +-4 -6 68 68\\ +-4 -5 57 57\\ +-4 -4 48 48\\ +-4 -3 41 41\\ +-4 -2 36 36\\ +-4 -1 33 33\\ +-4 0 32 32\\ +-4 1 33 33\\ +-4 2 36 36\\ +-4 3 41 41\\ +-4 4 48 48\\ +-4 5 57 57\\ +-4 6 68 68\\ +-4 7 81 81\\ +-4 8 96 96\\ +-4 9 113 113\\ +-4 10 132 132\\ +-3 -10 118 118\\ +-3 -9 99 99\\ +-3 -8 82 82\\ +-3 -7 67 67\\ +-3 -6 54 54\\ +-3 -5 43 43\\ +-3 -4 34 34\\ +-3 -3 27 27\\ +-3 -2 22 22\\ +-3 -1 19 19\\ +-3 0 18 18\\ +-3 1 19 19\\ +-3 2 22 22\\ +-3 3 27 27\\ +-3 4 34 34\\ +-3 5 43 43\\ +-3 6 54 54\\ +-3 7 67 67\\ +-3 8 82 82\\ +-3 9 99 99\\ +-3 10 118 118\\ +-2 -10 108 108\\ +-2 -9 89 89\\ +-2 -8 72 72\\ +-2 -7 57 57\\ +-2 -6 44 44\\ +-2 -5 33 33\\ +-2 -4 24 24\\ +-2 -3 17 17\\ +-2 -2 12 12\\ +-2 -1 9 9\\ +-2 0 8 8\\ +-2 1 9 9\\ +-2 2 12 12\\ +-2 3 17 17\\ +-2 4 24 24\\ +-2 5 33 33\\ +-2 6 44 44\\ +-2 7 57 57\\ +-2 8 72 72\\ +-2 9 89 89\\ +-2 10 108 108\\ +-1 -10 102 102\\ +-1 -9 83 83\\ +-1 -8 66 66\\ +-1 -7 51 51\\ +-1 -6 38 38\\ +-1 -5 27 27\\ +-1 -4 18 18\\ +-1 -3 11 11\\ +-1 -2 6 6\\ +-1 -1 3 3\\ +-1 0 2 2\\ +-1 1 3 3\\ +-1 2 6 6\\ +-1 3 11 11\\ +-1 4 18 18\\ +-1 5 27 27\\ +-1 6 38 38\\ +-1 7 51 51\\ +-1 8 66 66\\ +-1 9 83 83\\ +-1 10 102 102\\ +0 -10 100 100\\ +0 -9 81 81\\ +0 -8 64 64\\ +0 -7 49 49\\ +0 -6 36 36\\ +0 -5 25 25\\ +0 -4 16 16\\ +0 -3 9 9\\ +0 -2 4 4\\ +0 -1 1 1\\ +0 0 0 0\\ +0 1 1 1\\ +0 2 4 4\\ +0 3 9 9\\ +0 4 16 16\\ +0 5 25 25\\ +0 6 36 36\\ +0 7 49 49\\ +0 8 64 64\\ +0 9 81 81\\ +0 10 100 100\\ +1 -10 102 102\\ +1 -9 83 83\\ +1 -8 66 66\\ +1 -7 51 51\\ +1 -6 38 38\\ +1 -5 27 27\\ +1 -4 18 18\\ +1 -3 11 11\\ +1 -2 6 6\\ +1 -1 3 3\\ +1 0 2 2\\ +1 1 3 3\\ +1 2 6 6\\ +1 3 11 11\\ +1 4 18 18\\ +1 5 27 27\\ +1 6 38 38\\ +1 7 51 51\\ +1 8 66 66\\ +1 9 83 83\\ +1 10 102 102\\ +2 -10 108 108\\ +2 -9 89 89\\ +2 -8 72 72\\ +2 -7 57 57\\ +2 -6 44 44\\ +2 -5 33 33\\ +2 -4 24 24\\ +2 -3 17 17\\ +2 -2 12 12\\ +2 -1 9 9\\ +2 0 8 8\\ +2 1 9 9\\ +2 2 12 12\\ +2 3 17 17\\ +2 4 24 24\\ +2 5 33 33\\ +2 6 44 44\\ +2 7 57 57\\ +2 8 72 72\\ +2 9 89 89\\ +2 10 108 108\\ +3 -10 118 118\\ +3 -9 99 99\\ +3 -8 82 82\\ +3 -7 67 67\\ +3 -6 54 54\\ +3 -5 43 43\\ +3 -4 34 34\\ +3 -3 27 27\\ +3 -2 22 22\\ +3 -1 19 19\\ +3 0 18 18\\ +3 1 19 19\\ +3 2 22 22\\ +3 3 27 27\\ +3 4 34 34\\ +3 5 43 43\\ +3 6 54 54\\ +3 7 67 67\\ +3 8 82 82\\ +3 9 99 99\\ +3 10 118 118\\ +4 -10 132 132\\ +4 -9 113 113\\ +4 -8 96 96\\ +4 -7 81 81\\ +4 -6 68 68\\ +4 -5 57 57\\ +4 -4 48 48\\ +4 -3 41 41\\ +4 -2 36 36\\ +4 -1 33 33\\ +4 0 32 32\\ +4 1 33 33\\ +4 2 36 36\\ +4 3 41 41\\ +4 4 48 48\\ +4 5 57 57\\ +4 6 68 68\\ +4 7 81 81\\ +4 8 96 96\\ +4 9 113 113\\ +4 10 132 132\\ +5 -10 150 150\\ +5 -9 131 131\\ +5 -8 114 114\\ +5 -7 99 99\\ +5 -6 86 86\\ +5 -5 75 75\\ +5 -4 66 66\\ +5 -3 59 59\\ +5 -2 54 54\\ +5 -1 51 51\\ +5 0 50 50\\ +5 1 51 51\\ +5 2 54 54\\ +5 3 59 59\\ +5 4 66 66\\ +5 5 75 75\\ +5 6 86 86\\ +5 7 99 99\\ +5 8 114 114\\ +5 9 131 131\\ +5 10 150 150\\ +6 -10 172 172\\ +6 -9 153 153\\ +6 -8 136 136\\ +6 -7 121 121\\ +6 -6 108 108\\ +6 -5 97 97\\ +6 -4 88 88\\ +6 -3 81 81\\ +6 -2 76 76\\ +6 -1 73 73\\ +6 0 72 72\\ +6 1 73 73\\ +6 2 76 76\\ +6 3 81 81\\ +6 4 88 88\\ +6 5 97 97\\ +6 6 108 108\\ +6 7 121 121\\ +6 8 136 136\\ +6 9 153 153\\ +6 10 172 172\\ +7 -10 198 198\\ +7 -9 179 179\\ +7 -8 162 162\\ +7 -7 147 147\\ +7 -6 134 134\\ +7 -5 123 123\\ +7 -4 114 114\\ +7 -3 107 107\\ +7 -2 102 102\\ +7 -1 99 99\\ +7 0 98 98\\ +7 1 99 99\\ +7 2 102 102\\ +7 3 107 107\\ +7 4 114 114\\ +7 5 123 123\\ +7 6 134 134\\ +7 7 147 147\\ +7 8 162 162\\ +7 9 179 179\\ +7 10 198 198\\ +8 -10 228 228\\ +8 -9 209 209\\ +8 -8 192 192\\ +8 -7 177 177\\ +8 -6 164 164\\ +8 -5 153 153\\ +8 -4 144 144\\ +8 -3 137 137\\ +8 -2 132 132\\ +8 -1 129 129\\ +8 0 128 128\\ +8 1 129 129\\ +8 2 132 132\\ +8 3 137 137\\ +8 4 144 144\\ +8 5 153 153\\ +8 6 164 164\\ +8 7 177 177\\ +8 8 192 192\\ +8 9 209 209\\ +8 10 228 228\\ +9 -10 262 262\\ +9 -9 243 243\\ +9 -8 226 226\\ +9 -7 211 211\\ +9 -6 198 198\\ +9 -5 187 187\\ +9 -4 178 178\\ +9 -3 171 171\\ +9 -2 166 166\\ +9 -1 163 163\\ +9 0 162 162\\ +9 1 163 163\\ +9 2 166 166\\ +9 3 171 171\\ +9 4 178 178\\ +9 5 187 187\\ +9 6 198 198\\ +9 7 211 211\\ +9 8 226 226\\ +9 9 243 243\\ +9 10 262 262\\ +10 -10 300 300\\ +10 -9 281 281\\ +10 -8 264 264\\ +10 -7 249 249\\ +10 -6 236 236\\ +10 -5 225 225\\ +10 -4 216 216\\ +10 -3 209 209\\ +10 -2 204 204\\ +10 -1 201 201\\ +10 0 200 200\\ +10 1 201 201\\ +10 2 204 204\\ +10 3 209 209\\ +10 4 216 216\\ +10 5 225 225\\ +10 6 236 236\\ +10 7 249 249\\ +10 8 264 264\\ +10 9 281 281\\ +10 10 300 300\\ +}; +\end{axis} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(5.968in,5.727in)}, +scale only axis, +colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); 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rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, +xmin=-10, +xmax=10, +ymin=-10, +ymax=10, +axis background/.style={fill=white}, +title style={font=\bfseries}, +title={Contour for u=2} +] +\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {% +% +14.2857142857143 25\\ +1.54761904761905 -3\\ +1 -3.46938775510204\\ +0 -3.75510204081633\\ +-1 -3.46938775510204\\ +-1.54761904761905 -3\\ +-2 -2.45714285714286\\ +-2.22857142857143 -2\\ +-2.52857142857143 -1\\ +-2.62857142857143 0\\ +-2.52857142857143 1\\ 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rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 400 400\\ +-10 -9 381 381\\ +-10 -8 364 364\\ +-10 -7 349 349\\ +-10 -6 336 336\\ +-10 -5 325 325\\ +-10 -4 316 316\\ +-10 -3 309 309\\ +-10 -2 304 304\\ +-10 -1 301 301\\ +-10 0 300 300\\ +-10 1 301 301\\ +-10 2 304 304\\ +-10 3 309 309\\ +-10 4 316 316\\ +-10 5 325 325\\ +-10 6 336 336\\ +-10 7 349 349\\ +-10 8 364 364\\ +-10 9 381 381\\ +-10 10 400 400\\ +-9 -10 343 343\\ +-9 -9 324 324\\ +-9 -8 307 307\\ +-9 -7 292 292\\ +-9 -6 279 279\\ +-9 -5 268 268\\ +-9 -4 259 259\\ +-9 -3 252 252\\ +-9 -2 247 247\\ +-9 -1 244 244\\ +-9 0 243 243\\ +-9 1 244 244\\ +-9 2 247 247\\ +-9 3 252 252\\ +-9 4 259 259\\ +-9 5 268 268\\ +-9 6 279 279\\ +-9 7 292 292\\ +-9 8 307 307\\ +-9 9 324 324\\ +-9 10 343 343\\ +-8 -10 292 292\\ +-8 -9 273 273\\ +-8 -8 256 256\\ +-8 -7 241 241\\ +-8 -6 228 228\\ +-8 -5 217 217\\ +-8 -4 208 208\\ +-8 -3 201 201\\ +-8 -2 196 196\\ +-8 -1 193 193\\ +-8 0 192 192\\ +-8 1 193 193\\ +-8 2 196 196\\ +-8 3 201 201\\ +-8 4 208 208\\ +-8 5 217 217\\ +-8 6 228 228\\ +-8 7 241 241\\ +-8 8 256 256\\ +-8 9 273 273\\ +-8 10 292 292\\ +-7 -10 247 247\\ +-7 -9 228 228\\ +-7 -8 211 211\\ +-7 -7 196 196\\ +-7 -6 183 183\\ +-7 -5 172 172\\ +-7 -4 163 163\\ +-7 -3 156 156\\ +-7 -2 151 151\\ +-7 -1 148 148\\ +-7 0 147 147\\ +-7 1 148 148\\ +-7 2 151 151\\ +-7 3 156 156\\ +-7 4 163 163\\ +-7 5 172 172\\ +-7 6 183 183\\ +-7 7 196 196\\ +-7 8 211 211\\ +-7 9 228 228\\ +-7 10 247 247\\ +-6 -10 208 208\\ +-6 -9 189 189\\ +-6 -8 172 172\\ +-6 -7 157 157\\ +-6 -6 144 144\\ +-6 -5 133 133\\ +-6 -4 124 124\\ +-6 -3 117 117\\ +-6 -2 112 112\\ +-6 -1 109 109\\ +-6 0 108 108\\ +-6 1 109 109\\ +-6 2 112 112\\ +-6 3 117 117\\ +-6 4 124 124\\ +-6 5 133 133\\ +-6 6 144 144\\ +-6 7 157 157\\ +-6 8 172 172\\ +-6 9 189 189\\ +-6 10 208 208\\ +-5 -10 175 175\\ +-5 -9 156 156\\ +-5 -8 139 139\\ +-5 -7 124 124\\ +-5 -6 111 111\\ +-5 -5 100 100\\ +-5 -4 91 91\\ +-5 -3 84 84\\ +-5 -2 79 79\\ +-5 -1 76 76\\ +-5 0 75 75\\ +-5 1 76 76\\ +-5 2 79 79\\ +-5 3 84 84\\ +-5 4 91 91\\ +-5 5 100 100\\ +-5 6 111 111\\ +-5 7 124 124\\ +-5 8 139 139\\ +-5 9 156 156\\ +-5 10 175 175\\ +-4 -10 148 148\\ +-4 -9 129 129\\ +-4 -8 112 112\\ +-4 -7 97 97\\ +-4 -6 84 84\\ +-4 -5 73 73\\ +-4 -4 64 64\\ +-4 -3 57 57\\ +-4 -2 52 52\\ +-4 -1 49 49\\ +-4 0 48 48\\ +-4 1 49 49\\ +-4 2 52 52\\ +-4 3 57 57\\ +-4 4 64 64\\ +-4 5 73 73\\ +-4 6 84 84\\ +-4 7 97 97\\ +-4 8 112 112\\ +-4 9 129 129\\ +-4 10 148 148\\ +-3 -10 127 127\\ +-3 -9 108 108\\ +-3 -8 91 91\\ +-3 -7 76 76\\ +-3 -6 63 63\\ +-3 -5 52 52\\ +-3 -4 43 43\\ +-3 -3 36 36\\ +-3 -2 31 31\\ +-3 -1 28 28\\ +-3 0 27 27\\ +-3 1 28 28\\ +-3 2 31 31\\ +-3 3 36 36\\ +-3 4 43 43\\ +-3 5 52 52\\ +-3 6 63 63\\ +-3 7 76 76\\ +-3 8 91 91\\ +-3 9 108 108\\ +-3 10 127 127\\ +-2 -10 112 112\\ +-2 -9 93 93\\ +-2 -8 76 76\\ +-2 -7 61 61\\ +-2 -6 48 48\\ +-2 -5 37 37\\ +-2 -4 28 28\\ +-2 -3 21 21\\ +-2 -2 16 16\\ +-2 -1 13 13\\ +-2 0 12 12\\ +-2 1 13 13\\ +-2 2 16 16\\ +-2 3 21 21\\ +-2 4 28 28\\ +-2 5 37 37\\ +-2 6 48 48\\ +-2 7 61 61\\ +-2 8 76 76\\ +-2 9 93 93\\ +-2 10 112 112\\ +-1 -10 103 103\\ +-1 -9 84 84\\ +-1 -8 67 67\\ +-1 -7 52 52\\ +-1 -6 39 39\\ +-1 -5 28 28\\ +-1 -4 19 19\\ +-1 -3 12 12\\ +-1 -2 7 7\\ +-1 -1 4 4\\ +-1 0 3 3\\ +-1 1 4 4\\ +-1 2 7 7\\ +-1 3 12 12\\ +-1 4 19 19\\ +-1 5 28 28\\ +-1 6 39 39\\ +-1 7 52 52\\ +-1 8 67 67\\ +-1 9 84 84\\ +-1 10 103 103\\ +0 -10 100 100\\ +0 -9 81 81\\ +0 -8 64 64\\ +0 -7 49 49\\ +0 -6 36 36\\ +0 -5 25 25\\ +0 -4 16 16\\ +0 -3 9 9\\ +0 -2 4 4\\ +0 -1 1 1\\ +0 0 0 0\\ +0 1 1 1\\ +0 2 4 4\\ +0 3 9 9\\ +0 4 16 16\\ +0 5 25 25\\ +0 6 36 36\\ +0 7 49 49\\ +0 8 64 64\\ +0 9 81 81\\ +0 10 100 100\\ +1 -10 103 103\\ +1 -9 84 84\\ +1 -8 67 67\\ +1 -7 52 52\\ +1 -6 39 39\\ +1 -5 28 28\\ +1 -4 19 19\\ +1 -3 12 12\\ +1 -2 7 7\\ +1 -1 4 4\\ +1 0 3 3\\ +1 1 4 4\\ +1 2 7 7\\ +1 3 12 12\\ +1 4 19 19\\ +1 5 28 28\\ +1 6 39 39\\ +1 7 52 52\\ +1 8 67 67\\ +1 9 84 84\\ +1 10 103 103\\ +2 -10 112 112\\ +2 -9 93 93\\ +2 -8 76 76\\ +2 -7 61 61\\ +2 -6 48 48\\ +2 -5 37 37\\ +2 -4 28 28\\ +2 -3 21 21\\ +2 -2 16 16\\ +2 -1 13 13\\ +2 0 12 12\\ +2 1 13 13\\ +2 2 16 16\\ +2 3 21 21\\ +2 4 28 28\\ +2 5 37 37\\ +2 6 48 48\\ +2 7 61 61\\ +2 8 76 76\\ +2 9 93 93\\ +2 10 112 112\\ +3 -10 127 127\\ +3 -9 108 108\\ +3 -8 91 91\\ +3 -7 76 76\\ +3 -6 63 63\\ +3 -5 52 52\\ +3 -4 43 43\\ +3 -3 36 36\\ +3 -2 31 31\\ +3 -1 28 28\\ +3 0 27 27\\ +3 1 28 28\\ +3 2 31 31\\ +3 3 36 36\\ +3 4 43 43\\ +3 5 52 52\\ +3 6 63 63\\ +3 7 76 76\\ +3 8 91 91\\ +3 9 108 108\\ +3 10 127 127\\ +4 -10 148 148\\ +4 -9 129 129\\ +4 -8 112 112\\ +4 -7 97 97\\ +4 -6 84 84\\ +4 -5 73 73\\ +4 -4 64 64\\ 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147\\ +7 1 148 148\\ +7 2 151 151\\ +7 3 156 156\\ +7 4 163 163\\ +7 5 172 172\\ +7 6 183 183\\ +7 7 196 196\\ +7 8 211 211\\ +7 9 228 228\\ +7 10 247 247\\ +8 -10 292 292\\ +8 -9 273 273\\ +8 -8 256 256\\ +8 -7 241 241\\ +8 -6 228 228\\ +8 -5 217 217\\ +8 -4 208 208\\ +8 -3 201 201\\ +8 -2 196 196\\ +8 -1 193 193\\ +8 0 192 192\\ +8 1 193 193\\ +8 2 196 196\\ +8 3 201 201\\ +8 4 208 208\\ +8 5 217 217\\ +8 6 228 228\\ +8 7 241 241\\ +8 8 256 256\\ +8 9 273 273\\ +8 10 292 292\\ +9 -10 343 343\\ +9 -9 324 324\\ +9 -8 307 307\\ +9 -7 292 292\\ +9 -6 279 279\\ +9 -5 268 268\\ +9 -4 259 259\\ +9 -3 252 252\\ +9 -2 247 247\\ +9 -1 244 244\\ +9 0 243 243\\ +9 1 244 244\\ +9 2 247 247\\ +9 3 252 252\\ +9 4 259 259\\ +9 5 268 268\\ +9 6 279 279\\ +9 7 292 292\\ +9 8 307 307\\ +9 9 324 324\\ +9 10 343 343\\ +10 -10 400 400\\ +10 -9 381 381\\ +10 -8 364 364\\ +10 -7 349 349\\ +10 -6 336 336\\ +10 -5 325 325\\ +10 -4 316 316\\ +10 -3 309 309\\ +10 -2 304 304\\ +10 -1 301 301\\ +10 0 300 300\\ +10 1 301 301\\ +10 2 304 304\\ +10 3 309 309\\ +10 4 316 316\\ +10 5 325 325\\ +10 6 336 336\\ +10 7 349 349\\ +10 8 364 364\\ +10 9 381 381\\ +10 10 400 400\\ +}; +\end{axis} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(9.287in,5.727in)}, +scale only axis, +colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); 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rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, +xmin=-10, +xmax=10, +ymin=-10, +ymax=10, +axis background/.style={fill=white}, +title style={font=\bfseries}, +title={Contour for u=4} +] +\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {% +% +23.8095238095238 29\\ +1.31746031746032 -4\\ +1 -4.42328042328042\\ +0 -4.86772486772487\\ +-1 -4.42328042328042\\ +-1.31746031746032 -4\\ +-1.90079365079365 -3\\ +-2 -2.76190476190476\\ +-2.19047619047619 -2\\ +-2.34047619047619 -1\\ +-2.39047619047619 0\\ +-2.34047619047619 1\\ +-2.19047619047619 2\\ +-2 2.76190476190476\\ +-1.90079365079365 3\\ +-1.31746031746032 4\\ +-1 4.42328042328042\\ +0 4.86772486772487\\ +1 4.42328042328042\\ +1.31746031746032 4\\ +1.90079365079365 3\\ +2 2.76190476190476\\ +2.19047619047619 2\\ +2.34047619047619 1\\ +2.39047619047619 0\\ +2.34047619047619 -1\\ +2.19047619047619 -2\\ +2 -2.76190476190476\\ +1.90079365079365 -3\\ +1.31746031746032 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rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 600 600\\ +-10 -9 581 581\\ +-10 -8 564 564\\ +-10 -7 549 549\\ +-10 -6 536 536\\ +-10 -5 525 525\\ +-10 -4 516 516\\ +-10 -3 509 509\\ +-10 -2 504 504\\ +-10 -1 501 501\\ +-10 0 500 500\\ +-10 1 501 501\\ +-10 2 504 504\\ +-10 3 509 509\\ +-10 4 516 516\\ +-10 5 525 525\\ +-10 6 536 536\\ +-10 7 549 549\\ +-10 8 564 564\\ +-10 9 581 581\\ +-10 10 600 600\\ +-9 -10 505 505\\ +-9 -9 486 486\\ +-9 -8 469 469\\ +-9 -7 454 454\\ +-9 -6 441 441\\ +-9 -5 430 430\\ +-9 -4 421 421\\ +-9 -3 414 414\\ +-9 -2 409 409\\ +-9 -1 406 406\\ +-9 0 405 405\\ +-9 1 406 406\\ +-9 2 409 409\\ +-9 3 414 414\\ +-9 4 421 421\\ +-9 5 430 430\\ +-9 6 441 441\\ +-9 7 454 454\\ +-9 8 469 469\\ +-9 9 486 486\\ +-9 10 505 505\\ +-8 -10 420 420\\ +-8 -9 401 401\\ +-8 -8 384 384\\ +-8 -7 369 369\\ +-8 -6 356 356\\ +-8 -5 345 345\\ +-8 -4 336 336\\ +-8 -3 329 329\\ +-8 -2 324 324\\ +-8 -1 321 321\\ +-8 0 320 320\\ +-8 1 321 321\\ +-8 2 324 324\\ +-8 3 329 329\\ +-8 4 336 336\\ +-8 5 345 345\\ +-8 6 356 356\\ +-8 7 369 369\\ +-8 8 384 384\\ +-8 9 401 401\\ +-8 10 420 420\\ +-7 -10 345 345\\ +-7 -9 326 326\\ +-7 -8 309 309\\ +-7 -7 294 294\\ +-7 -6 281 281\\ +-7 -5 270 270\\ +-7 -4 261 261\\ +-7 -3 254 254\\ +-7 -2 249 249\\ +-7 -1 246 246\\ +-7 0 245 245\\ +-7 1 246 246\\ +-7 2 249 249\\ +-7 3 254 254\\ +-7 4 261 261\\ +-7 5 270 270\\ +-7 6 281 281\\ +-7 7 294 294\\ +-7 8 309 309\\ +-7 9 326 326\\ +-7 10 345 345\\ +-6 -10 280 280\\ +-6 -9 261 261\\ +-6 -8 244 244\\ +-6 -7 229 229\\ +-6 -6 216 216\\ +-6 -5 205 205\\ +-6 -4 196 196\\ +-6 -3 189 189\\ +-6 -2 184 184\\ +-6 -1 181 181\\ +-6 0 180 180\\ +-6 1 181 181\\ +-6 2 184 184\\ +-6 3 189 189\\ +-6 4 196 196\\ +-6 5 205 205\\ +-6 6 216 216\\ +-6 7 229 229\\ +-6 8 244 244\\ +-6 9 261 261\\ +-6 10 280 280\\ +-5 -10 225 225\\ +-5 -9 206 206\\ +-5 -8 189 189\\ +-5 -7 174 174\\ +-5 -6 161 161\\ +-5 -5 150 150\\ +-5 -4 141 141\\ +-5 -3 134 134\\ +-5 -2 129 129\\ +-5 -1 126 126\\ +-5 0 125 125\\ +-5 1 126 126\\ +-5 2 129 129\\ +-5 3 134 134\\ +-5 4 141 141\\ +-5 5 150 150\\ +-5 6 161 161\\ +-5 7 174 174\\ +-5 8 189 189\\ +-5 9 206 206\\ +-5 10 225 225\\ +-4 -10 180 180\\ +-4 -9 161 161\\ +-4 -8 144 144\\ +-4 -7 129 129\\ +-4 -6 116 116\\ +-4 -5 105 105\\ +-4 -4 96 96\\ +-4 -3 89 89\\ +-4 -2 84 84\\ +-4 -1 81 81\\ +-4 0 80 80\\ +-4 1 81 81\\ +-4 2 84 84\\ +-4 3 89 89\\ +-4 4 96 96\\ +-4 5 105 105\\ +-4 6 116 116\\ +-4 7 129 129\\ +-4 8 144 144\\ +-4 9 161 161\\ +-4 10 180 180\\ +-3 -10 145 145\\ +-3 -9 126 126\\ +-3 -8 109 109\\ +-3 -7 94 94\\ +-3 -6 81 81\\ +-3 -5 70 70\\ +-3 -4 61 61\\ +-3 -3 54 54\\ +-3 -2 49 49\\ +-3 -1 46 46\\ +-3 0 45 45\\ +-3 1 46 46\\ +-3 2 49 49\\ +-3 3 54 54\\ +-3 4 61 61\\ +-3 5 70 70\\ +-3 6 81 81\\ +-3 7 94 94\\ +-3 8 109 109\\ +-3 9 126 126\\ +-3 10 145 145\\ +-2 -10 120 120\\ +-2 -9 101 101\\ +-2 -8 84 84\\ +-2 -7 69 69\\ +-2 -6 56 56\\ +-2 -5 45 45\\ +-2 -4 36 36\\ +-2 -3 29 29\\ +-2 -2 24 24\\ +-2 -1 21 21\\ +-2 0 20 20\\ +-2 1 21 21\\ +-2 2 24 24\\ +-2 3 29 29\\ +-2 4 36 36\\ +-2 5 45 45\\ +-2 6 56 56\\ +-2 7 69 69\\ +-2 8 84 84\\ +-2 9 101 101\\ +-2 10 120 120\\ +-1 -10 105 105\\ +-1 -9 86 86\\ +-1 -8 69 69\\ +-1 -7 54 54\\ +-1 -6 41 41\\ +-1 -5 30 30\\ +-1 -4 21 21\\ +-1 -3 14 14\\ +-1 -2 9 9\\ +-1 -1 6 6\\ +-1 0 5 5\\ +-1 1 6 6\\ +-1 2 9 9\\ +-1 3 14 14\\ +-1 4 21 21\\ +-1 5 30 30\\ +-1 6 41 41\\ +-1 7 54 54\\ +-1 8 69 69\\ +-1 9 86 86\\ +-1 10 105 105\\ +0 -10 100 100\\ +0 -9 81 81\\ +0 -8 64 64\\ +0 -7 49 49\\ +0 -6 36 36\\ +0 -5 25 25\\ +0 -4 16 16\\ +0 -3 9 9\\ +0 -2 4 4\\ +0 -1 1 1\\ +0 0 0 0\\ +0 1 1 1\\ +0 2 4 4\\ +0 3 9 9\\ +0 4 16 16\\ +0 5 25 25\\ +0 6 36 36\\ +0 7 49 49\\ +0 8 64 64\\ +0 9 81 81\\ +0 10 100 100\\ +1 -10 105 105\\ +1 -9 86 86\\ +1 -8 69 69\\ +1 -7 54 54\\ +1 -6 41 41\\ +1 -5 30 30\\ +1 -4 21 21\\ +1 -3 14 14\\ +1 -2 9 9\\ +1 -1 6 6\\ +1 0 5 5\\ +1 1 6 6\\ +1 2 9 9\\ +1 3 14 14\\ +1 4 21 21\\ +1 5 30 30\\ +1 6 41 41\\ +1 7 54 54\\ +1 8 69 69\\ +1 9 86 86\\ +1 10 105 105\\ +2 -10 120 120\\ +2 -9 101 101\\ +2 -8 84 84\\ +2 -7 69 69\\ +2 -6 56 56\\ +2 -5 45 45\\ +2 -4 36 36\\ +2 -3 29 29\\ +2 -2 24 24\\ +2 -1 21 21\\ +2 0 20 20\\ +2 1 21 21\\ +2 2 24 24\\ +2 3 29 29\\ +2 4 36 36\\ +2 5 45 45\\ +2 6 56 56\\ +2 7 69 69\\ +2 8 84 84\\ +2 9 101 101\\ +2 10 120 120\\ +3 -10 145 145\\ +3 -9 126 126\\ +3 -8 109 109\\ +3 -7 94 94\\ +3 -6 81 81\\ +3 -5 70 70\\ +3 -4 61 61\\ +3 -3 54 54\\ +3 -2 49 49\\ +3 -1 46 46\\ +3 0 45 45\\ +3 1 46 46\\ +3 2 49 49\\ +3 3 54 54\\ +3 4 61 61\\ +3 5 70 70\\ +3 6 81 81\\ +3 7 94 94\\ +3 8 109 109\\ +3 9 126 126\\ +3 10 145 145\\ +4 -10 180 180\\ +4 -9 161 161\\ +4 -8 144 144\\ +4 -7 129 129\\ +4 -6 116 116\\ +4 -5 105 105\\ +4 -4 96 96\\ +4 -3 89 89\\ +4 -2 84 84\\ +4 -1 81 81\\ +4 0 80 80\\ +4 1 81 81\\ +4 2 84 84\\ +4 3 89 89\\ +4 4 96 96\\ +4 5 105 105\\ +4 6 116 116\\ +4 7 129 129\\ +4 8 144 144\\ +4 9 161 161\\ +4 10 180 180\\ +5 -10 225 225\\ +5 -9 206 206\\ +5 -8 189 189\\ +5 -7 174 174\\ +5 -6 161 161\\ +5 -5 150 150\\ +5 -4 141 141\\ +5 -3 134 134\\ +5 -2 129 129\\ +5 -1 126 126\\ +5 0 125 125\\ +5 1 126 126\\ +5 2 129 129\\ +5 3 134 134\\ +5 4 141 141\\ +5 5 150 150\\ +5 6 161 161\\ +5 7 174 174\\ +5 8 189 189\\ +5 9 206 206\\ +5 10 225 225\\ +6 -10 280 280\\ +6 -9 261 261\\ +6 -8 244 244\\ +6 -7 229 229\\ +6 -6 216 216\\ +6 -5 205 205\\ +6 -4 196 196\\ +6 -3 189 189\\ +6 -2 184 184\\ +6 -1 181 181\\ +6 0 180 180\\ +6 1 181 181\\ +6 2 184 184\\ +6 3 189 189\\ +6 4 196 196\\ +6 5 205 205\\ +6 6 216 216\\ +6 7 229 229\\ +6 8 244 244\\ +6 9 261 261\\ +6 10 280 280\\ +7 -10 345 345\\ +7 -9 326 326\\ +7 -8 309 309\\ +7 -7 294 294\\ +7 -6 281 281\\ +7 -5 270 270\\ +7 -4 261 261\\ +7 -3 254 254\\ +7 -2 249 249\\ +7 -1 246 246\\ +7 0 245 245\\ +7 1 246 246\\ +7 2 249 249\\ +7 3 254 254\\ +7 4 261 261\\ +7 5 270 270\\ +7 6 281 281\\ +7 7 294 294\\ +7 8 309 309\\ +7 9 326 326\\ +7 10 345 345\\ +8 -10 420 420\\ +8 -9 401 401\\ +8 -8 384 384\\ +8 -7 369 369\\ +8 -6 356 356\\ +8 -5 345 345\\ +8 -4 336 336\\ +8 -3 329 329\\ +8 -2 324 324\\ +8 -1 321 321\\ +8 0 320 320\\ +8 1 321 321\\ +8 2 324 324\\ +8 3 329 329\\ +8 4 336 336\\ +8 5 345 345\\ +8 6 356 356\\ +8 7 369 369\\ +8 8 384 384\\ +8 9 401 401\\ +8 10 420 420\\ +9 -10 505 505\\ +9 -9 486 486\\ +9 -8 469 469\\ +9 -7 454 454\\ +9 -6 441 441\\ +9 -5 430 430\\ +9 -4 421 421\\ +9 -3 414 414\\ +9 -2 409 409\\ +9 -1 406 406\\ +9 0 405 405\\ +9 1 406 406\\ +9 2 409 409\\ +9 3 414 414\\ +9 4 421 421\\ +9 5 430 430\\ +9 6 441 441\\ +9 7 454 454\\ +9 8 469 469\\ +9 9 486 486\\ +9 10 505 505\\ +10 -10 600 600\\ +10 -9 581 581\\ +10 -8 564 564\\ +10 -7 549 549\\ +10 -6 536 536\\ +10 -5 525 525\\ +10 -4 516 516\\ +10 -3 509 509\\ +10 -2 504 504\\ +10 -1 501 501\\ +10 0 500 500\\ +10 1 501 501\\ +10 2 504 504\\ +10 3 509 509\\ +10 4 516 516\\ +10 5 525 525\\ +10 6 536 536\\ +10 7 549 549\\ +10 8 564 564\\ +10 9 581 581\\ +10 10 600 600\\ +}; +\end{axis} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(15.924in,5.727in)}, +scale only axis, +colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); 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rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, +xmin=-10, +xmax=10, +ymin=-10, +ymax=10, +axis background/.style={fill=white}, +title style={font=\bfseries}, +title={Contour for u=5} +] +\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {% +% +28.5714285714286 33\\ +0.714285714285715 -5\\ +0 -5.32467532467532\\ +-0.714285714285715 -5\\ +-1 -4.84126984126984\\ +-1.5047619047619 -4\\ +-1.97142857142857 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rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); 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rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); 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rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 800 800\\ +-10 -9 781 781\\ +-10 -8 764 764\\ +-10 -7 749 749\\ +-10 -6 736 736\\ +-10 -5 725 725\\ +-10 -4 716 716\\ +-10 -3 709 709\\ +-10 -2 704 704\\ +-10 -1 701 701\\ +-10 0 700 700\\ +-10 1 701 701\\ +-10 2 704 704\\ +-10 3 709 709\\ +-10 4 716 716\\ +-10 5 725 725\\ +-10 6 736 736\\ +-10 7 749 749\\ +-10 8 764 764\\ +-10 9 781 781\\ +-10 10 800 800\\ +-9 -10 667 667\\ +-9 -9 648 648\\ +-9 -8 631 631\\ +-9 -7 616 616\\ +-9 -6 603 603\\ +-9 -5 592 592\\ +-9 -4 583 583\\ +-9 -3 576 576\\ +-9 -2 571 571\\ +-9 -1 568 568\\ +-9 0 567 567\\ +-9 1 568 568\\ +-9 2 571 571\\ +-9 3 576 576\\ +-9 4 583 583\\ +-9 5 592 592\\ +-9 6 603 603\\ +-9 7 616 616\\ +-9 8 631 631\\ +-9 9 648 648\\ +-9 10 667 667\\ +-8 -10 548 548\\ +-8 -9 529 529\\ +-8 -8 512 512\\ +-8 -7 497 497\\ +-8 -6 484 484\\ +-8 -5 473 473\\ +-8 -4 464 464\\ +-8 -3 457 457\\ +-8 -2 452 452\\ +-8 -1 449 449\\ +-8 0 448 448\\ +-8 1 449 449\\ +-8 2 452 452\\ +-8 3 457 457\\ +-8 4 464 464\\ +-8 5 473 473\\ +-8 6 484 484\\ +-8 7 497 497\\ +-8 8 512 512\\ +-8 9 529 529\\ +-8 10 548 548\\ +-7 -10 443 443\\ +-7 -9 424 424\\ +-7 -8 407 407\\ +-7 -7 392 392\\ +-7 -6 379 379\\ +-7 -5 368 368\\ +-7 -4 359 359\\ +-7 -3 352 352\\ +-7 -2 347 347\\ +-7 -1 344 344\\ +-7 0 343 343\\ +-7 1 344 344\\ +-7 2 347 347\\ +-7 3 352 352\\ +-7 4 359 359\\ +-7 5 368 368\\ +-7 6 379 379\\ +-7 7 392 392\\ +-7 8 407 407\\ +-7 9 424 424\\ +-7 10 443 443\\ +-6 -10 352 352\\ +-6 -9 333 333\\ +-6 -8 316 316\\ +-6 -7 301 301\\ +-6 -6 288 288\\ +-6 -5 277 277\\ +-6 -4 268 268\\ +-6 -3 261 261\\ +-6 -2 256 256\\ +-6 -1 253 253\\ +-6 0 252 252\\ +-6 1 253 253\\ +-6 2 256 256\\ +-6 3 261 261\\ +-6 4 268 268\\ +-6 5 277 277\\ +-6 6 288 288\\ +-6 7 301 301\\ +-6 8 316 316\\ +-6 9 333 333\\ +-6 10 352 352\\ +-5 -10 275 275\\ +-5 -9 256 256\\ +-5 -8 239 239\\ +-5 -7 224 224\\ +-5 -6 211 211\\ +-5 -5 200 200\\ +-5 -4 191 191\\ +-5 -3 184 184\\ +-5 -2 179 179\\ +-5 -1 176 176\\ +-5 0 175 175\\ +-5 1 176 176\\ +-5 2 179 179\\ +-5 3 184 184\\ +-5 4 191 191\\ +-5 5 200 200\\ +-5 6 211 211\\ +-5 7 224 224\\ +-5 8 239 239\\ +-5 9 256 256\\ +-5 10 275 275\\ +-4 -10 212 212\\ +-4 -9 193 193\\ +-4 -8 176 176\\ +-4 -7 161 161\\ +-4 -6 148 148\\ +-4 -5 137 137\\ +-4 -4 128 128\\ +-4 -3 121 121\\ +-4 -2 116 116\\ +-4 -1 113 113\\ +-4 0 112 112\\ +-4 1 113 113\\ +-4 2 116 116\\ +-4 3 121 121\\ +-4 4 128 128\\ +-4 5 137 137\\ +-4 6 148 148\\ +-4 7 161 161\\ +-4 8 176 176\\ +-4 9 193 193\\ +-4 10 212 212\\ +-3 -10 163 163\\ +-3 -9 144 144\\ +-3 -8 127 127\\ +-3 -7 112 112\\ +-3 -6 99 99\\ +-3 -5 88 88\\ +-3 -4 79 79\\ +-3 -3 72 72\\ +-3 -2 67 67\\ +-3 -1 64 64\\ +-3 0 63 63\\ +-3 1 64 64\\ +-3 2 67 67\\ +-3 3 72 72\\ +-3 4 79 79\\ +-3 5 88 88\\ +-3 6 99 99\\ +-3 7 112 112\\ +-3 8 127 127\\ +-3 9 144 144\\ +-3 10 163 163\\ +-2 -10 128 128\\ +-2 -9 109 109\\ +-2 -8 92 92\\ +-2 -7 77 77\\ +-2 -6 64 64\\ +-2 -5 53 53\\ +-2 -4 44 44\\ +-2 -3 37 37\\ +-2 -2 32 32\\ +-2 -1 29 29\\ +-2 0 28 28\\ +-2 1 29 29\\ +-2 2 32 32\\ +-2 3 37 37\\ +-2 4 44 44\\ +-2 5 53 53\\ +-2 6 64 64\\ +-2 7 77 77\\ +-2 8 92 92\\ +-2 9 109 109\\ +-2 10 128 128\\ +-1 -10 107 107\\ +-1 -9 88 88\\ +-1 -8 71 71\\ +-1 -7 56 56\\ +-1 -6 43 43\\ +-1 -5 32 32\\ +-1 -4 23 23\\ +-1 -3 16 16\\ +-1 -2 11 11\\ +-1 -1 8 8\\ +-1 0 7 7\\ +-1 1 8 8\\ +-1 2 11 11\\ +-1 3 16 16\\ +-1 4 23 23\\ +-1 5 32 32\\ +-1 6 43 43\\ +-1 7 56 56\\ +-1 8 71 71\\ +-1 9 88 88\\ +-1 10 107 107\\ +0 -10 100 100\\ +0 -9 81 81\\ +0 -8 64 64\\ +0 -7 49 49\\ +0 -6 36 36\\ +0 -5 25 25\\ +0 -4 16 16\\ +0 -3 9 9\\ +0 -2 4 4\\ +0 -1 1 1\\ +0 0 0 0\\ +0 1 1 1\\ +0 2 4 4\\ +0 3 9 9\\ +0 4 16 16\\ +0 5 25 25\\ +0 6 36 36\\ +0 7 49 49\\ +0 8 64 64\\ +0 9 81 81\\ +0 10 100 100\\ +1 -10 107 107\\ +1 -9 88 88\\ +1 -8 71 71\\ +1 -7 56 56\\ +1 -6 43 43\\ +1 -5 32 32\\ +1 -4 23 23\\ +1 -3 16 16\\ +1 -2 11 11\\ +1 -1 8 8\\ +1 0 7 7\\ +1 1 8 8\\ +1 2 11 11\\ +1 3 16 16\\ +1 4 23 23\\ +1 5 32 32\\ +1 6 43 43\\ +1 7 56 56\\ +1 8 71 71\\ +1 9 88 88\\ +1 10 107 107\\ +2 -10 128 128\\ +2 -9 109 109\\ +2 -8 92 92\\ +2 -7 77 77\\ +2 -6 64 64\\ +2 -5 53 53\\ +2 -4 44 44\\ +2 -3 37 37\\ +2 -2 32 32\\ +2 -1 29 29\\ +2 0 28 28\\ +2 1 29 29\\ +2 2 32 32\\ +2 3 37 37\\ +2 4 44 44\\ +2 5 53 53\\ +2 6 64 64\\ +2 7 77 77\\ +2 8 92 92\\ +2 9 109 109\\ +2 10 128 128\\ +3 -10 163 163\\ +3 -9 144 144\\ +3 -8 127 127\\ +3 -7 112 112\\ +3 -6 99 99\\ +3 -5 88 88\\ +3 -4 79 79\\ +3 -3 72 72\\ +3 -2 67 67\\ +3 -1 64 64\\ +3 0 63 63\\ +3 1 64 64\\ +3 2 67 67\\ +3 3 72 72\\ +3 4 79 79\\ +3 5 88 88\\ +3 6 99 99\\ +3 7 112 112\\ +3 8 127 127\\ +3 9 144 144\\ +3 10 163 163\\ +4 -10 212 212\\ +4 -9 193 193\\ +4 -8 176 176\\ +4 -7 161 161\\ +4 -6 148 148\\ +4 -5 137 137\\ +4 -4 128 128\\ +4 -3 121 121\\ +4 -2 116 116\\ +4 -1 113 113\\ +4 0 112 112\\ +4 1 113 113\\ +4 2 116 116\\ +4 3 121 121\\ +4 4 128 128\\ +4 5 137 137\\ +4 6 148 148\\ +4 7 161 161\\ +4 8 176 176\\ +4 9 193 193\\ +4 10 212 212\\ +5 -10 275 275\\ +5 -9 256 256\\ +5 -8 239 239\\ +5 -7 224 224\\ +5 -6 211 211\\ +5 -5 200 200\\ +5 -4 191 191\\ +5 -3 184 184\\ +5 -2 179 179\\ +5 -1 176 176\\ +5 0 175 175\\ +5 1 176 176\\ +5 2 179 179\\ +5 3 184 184\\ +5 4 191 191\\ +5 5 200 200\\ +5 6 211 211\\ +5 7 224 224\\ +5 8 239 239\\ +5 9 256 256\\ +5 10 275 275\\ +6 -10 352 352\\ +6 -9 333 333\\ +6 -8 316 316\\ +6 -7 301 301\\ +6 -6 288 288\\ +6 -5 277 277\\ +6 -4 268 268\\ +6 -3 261 261\\ +6 -2 256 256\\ +6 -1 253 253\\ +6 0 252 252\\ +6 1 253 253\\ +6 2 256 256\\ +6 3 261 261\\ +6 4 268 268\\ +6 5 277 277\\ +6 6 288 288\\ +6 7 301 301\\ +6 8 316 316\\ +6 9 333 333\\ +6 10 352 352\\ +7 -10 443 443\\ +7 -9 424 424\\ +7 -8 407 407\\ +7 -7 392 392\\ +7 -6 379 379\\ +7 -5 368 368\\ +7 -4 359 359\\ +7 -3 352 352\\ +7 -2 347 347\\ +7 -1 344 344\\ +7 0 343 343\\ +7 1 344 344\\ +7 2 347 347\\ +7 3 352 352\\ +7 4 359 359\\ +7 5 368 368\\ +7 6 379 379\\ +7 7 392 392\\ +7 8 407 407\\ +7 9 424 424\\ +7 10 443 443\\ +8 -10 548 548\\ +8 -9 529 529\\ +8 -8 512 512\\ +8 -7 497 497\\ +8 -6 484 484\\ +8 -5 473 473\\ +8 -4 464 464\\ +8 -3 457 457\\ +8 -2 452 452\\ +8 -1 449 449\\ +8 0 448 448\\ +8 1 449 449\\ +8 2 452 452\\ +8 3 457 457\\ +8 4 464 464\\ +8 5 473 473\\ +8 6 484 484\\ +8 7 497 497\\ +8 8 512 512\\ +8 9 529 529\\ +8 10 548 548\\ +9 -10 667 667\\ +9 -9 648 648\\ +9 -8 631 631\\ +9 -7 616 616\\ +9 -6 603 603\\ +9 -5 592 592\\ +9 -4 583 583\\ +9 -3 576 576\\ +9 -2 571 571\\ +9 -1 568 568\\ +9 0 567 567\\ +9 1 568 568\\ +9 2 571 571\\ +9 3 576 576\\ +9 4 583 583\\ +9 5 592 592\\ +9 6 603 603\\ +9 7 616 616\\ +9 8 631 631\\ +9 9 648 648\\ +9 10 667 667\\ +10 -10 800 800\\ +10 -9 781 781\\ +10 -8 764 764\\ +10 -7 749 749\\ +10 -6 736 736\\ +10 -5 725 725\\ +10 -4 716 716\\ +10 -3 709 709\\ +10 -2 704 704\\ +10 -1 701 701\\ +10 0 700 700\\ +10 1 701 701\\ +10 2 704 704\\ +10 3 709 709\\ +10 4 716 716\\ +10 5 725 725\\ +10 6 736 736\\ +10 7 749 749\\ +10 8 764 764\\ +10 9 781 781\\ +10 10 800 800\\ +}; +\end{axis} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(5.968in,1.149in)}, +scale only axis, +colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); 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rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, +xmin=-10, +xmax=10, +ymin=-10, +ymax=10, +axis background/.style={fill=white}, +title style={font=\bfseries}, +title={Contour for u=7} +] +\addplot[contour prepared, contour prepared format=matlab, contour/labels=false] table[row sep=crcr] {% +% +38.0952380952381 37\\ +0.299319727891156 -6\\ +0 -6.16117216117216\\ +-0.299319727891156 -6\\ +-1 -5.55411255411255\\ +-1.29024943310658 -5\\ +-1.718820861678 -4\\ +-2 -3.15646258503401\\ +-2.0312925170068 -3\\ +-2.17414965986395 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rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); rgb(164pt)=(0.4184,0.803,0.4122); rgb(165pt)=(0.4322,0.8028,0.4013); rgb(166pt)=(0.4463,0.8024,0.3904); rgb(167pt)=(0.4608,0.8018,0.3797); rgb(168pt)=(0.4753,0.8011,0.3691); rgb(169pt)=(0.4899,0.8002,0.3586); rgb(170pt)=(0.5044,0.7993,0.348); rgb(171pt)=(0.5187,0.7982,0.3374); rgb(172pt)=(0.5329,0.797,0.3267); rgb(173pt)=(0.547,0.7957,0.3159); rgb(175pt)=(0.5748,0.7929,0.2941); rgb(176pt)=(0.5886,0.7913,0.2833); rgb(177pt)=(0.6024,0.7896,0.2726); rgb(178pt)=(0.6161,0.7878,0.2622); rgb(179pt)=(0.6297,0.7859,0.2521); rgb(180pt)=(0.6433,0.7839,0.2423); rgb(181pt)=(0.6567,0.7818,0.2329); rgb(182pt)=(0.6701,0.7796,0.2239); rgb(183pt)=(0.6833,0.7773,0.2155); rgb(184pt)=(0.6963,0.775,0.2075); rgb(185pt)=(0.7091,0.7727,0.1998); rgb(186pt)=(0.7218,0.7703,0.1924); rgb(187pt)=(0.7344,0.7679,0.1852); rgb(188pt)=(0.7468,0.7654,0.1782); rgb(189pt)=(0.759,0.7629,0.1717); rgb(190pt)=(0.771,0.7604,0.1658); rgb(191pt)=(0.7829,0.7579,0.1608); rgb(192pt)=(0.7945,0.7554,0.157); rgb(193pt)=(0.806,0.7529,0.1546); rgb(194pt)=(0.8172,0.7505,0.1535); rgb(195pt)=(0.8281,0.7481,0.1536); rgb(196pt)=(0.8389,0.7457,0.1546); rgb(197pt)=(0.8495,0.7435,0.1564); rgb(198pt)=(0.86,0.7413,0.1587); rgb(199pt)=(0.8703,0.7392,0.1615); rgb(200pt)=(0.8804,0.7372,0.165); rgb(201pt)=(0.8903,0.7353,0.1695); rgb(202pt)=(0.9,0.7336,0.1749); rgb(203pt)=(0.9093,0.7321,0.1815); rgb(204pt)=(0.9184,0.7308,0.189); rgb(205pt)=(0.9272,0.7298,0.1973); rgb(206pt)=(0.9357,0.729,0.2061); rgb(207pt)=(0.944,0.7285,0.2151); rgb(208pt)=(0.9523,0.7284,0.2237); rgb(209pt)=(0.9606,0.7285,0.2312); rgb(210pt)=(0.9689,0.7292,0.2373); rgb(211pt)=(0.977,0.7304,0.2418); rgb(212pt)=(0.9842,0.733,0.2446); rgb(213pt)=(0.99,0.7365,0.2429); rgb(214pt)=(0.9946,0.7407,0.2394); rgb(215pt)=(0.9966,0.7458,0.2351); rgb(216pt)=(0.9971,0.7513,0.2309); rgb(217pt)=(0.9972,0.7569,0.2267); rgb(218pt)=(0.9971,0.7626,0.2224); rgb(219pt)=(0.9969,0.7683,0.2181); rgb(220pt)=(0.9966,0.774,0.2138); rgb(221pt)=(0.9962,0.7798,0.2095); rgb(222pt)=(0.9957,0.7856,0.2053); rgb(223pt)=(0.9949,0.7915,0.2012); rgb(224pt)=(0.9938,0.7974,0.1974); rgb(225pt)=(0.9923,0.8034,0.1939); rgb(226pt)=(0.9906,0.8095,0.1906); rgb(227pt)=(0.9885,0.8156,0.1875); rgb(228pt)=(0.9861,0.8218,0.1846); rgb(229pt)=(0.9835,0.828,0.1817); rgb(230pt)=(0.9807,0.8342,0.1787); rgb(231pt)=(0.9778,0.8404,0.1757); rgb(232pt)=(0.9748,0.8467,0.1726); rgb(233pt)=(0.972,0.8529,0.1695); rgb(234pt)=(0.9694,0.8591,0.1665); rgb(235pt)=(0.9671,0.8654,0.1636); rgb(236pt)=(0.9651,0.8716,0.1608); rgb(237pt)=(0.9634,0.8778,0.1582); rgb(238pt)=(0.9619,0.884,0.1557); rgb(239pt)=(0.9608,0.8902,0.1532); rgb(240pt)=(0.9601,0.8963,0.1507); rgb(241pt)=(0.9596,0.9023,0.148); rgb(242pt)=(0.9595,0.9084,0.145); rgb(243pt)=(0.9597,0.9143,0.1418); rgb(244pt)=(0.9601,0.9203,0.1382); rgb(245pt)=(0.9608,0.9262,0.1344); rgb(246pt)=(0.9618,0.932,0.1304); rgb(247pt)=(0.9629,0.9379,0.1261); rgb(248pt)=(0.9642,0.9437,0.1216); rgb(249pt)=(0.9657,0.9494,0.1168); rgb(250pt)=(0.9674,0.9552,0.1116); rgb(251pt)=(0.9692,0.9609,0.1061); rgb(252pt)=(0.9711,0.9667,0.1001); rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 1000 1000\\ +-10 -9 981 981\\ +-10 -8 964 964\\ +-10 -7 949 949\\ +-10 -6 936 936\\ +-10 -5 925 925\\ +-10 -4 916 916\\ +-10 -3 909 909\\ +-10 -2 904 904\\ +-10 -1 901 901\\ +-10 0 900 900\\ +-10 1 901 901\\ +-10 2 904 904\\ +-10 3 909 909\\ +-10 4 916 916\\ +-10 5 925 925\\ +-10 6 936 936\\ +-10 7 949 949\\ +-10 8 964 964\\ +-10 9 981 981\\ +-10 10 1000 1000\\ +-9 -10 829 829\\ +-9 -9 810 810\\ +-9 -8 793 793\\ +-9 -7 778 778\\ +-9 -6 765 765\\ +-9 -5 754 754\\ +-9 -4 745 745\\ +-9 -3 738 738\\ +-9 -2 733 733\\ +-9 -1 730 730\\ +-9 0 729 729\\ +-9 1 730 730\\ +-9 2 733 733\\ +-9 3 738 738\\ +-9 4 745 745\\ +-9 5 754 754\\ +-9 6 765 765\\ +-9 7 778 778\\ +-9 8 793 793\\ +-9 9 810 810\\ +-9 10 829 829\\ +-8 -10 676 676\\ +-8 -9 657 657\\ +-8 -8 640 640\\ +-8 -7 625 625\\ +-8 -6 612 612\\ +-8 -5 601 601\\ +-8 -4 592 592\\ +-8 -3 585 585\\ +-8 -2 580 580\\ +-8 -1 577 577\\ +-8 0 576 576\\ +-8 1 577 577\\ +-8 2 580 580\\ +-8 3 585 585\\ +-8 4 592 592\\ +-8 5 601 601\\ +-8 6 612 612\\ +-8 7 625 625\\ +-8 8 640 640\\ +-8 9 657 657\\ +-8 10 676 676\\ +-7 -10 541 541\\ +-7 -9 522 522\\ +-7 -8 505 505\\ +-7 -7 490 490\\ +-7 -6 477 477\\ +-7 -5 466 466\\ +-7 -4 457 457\\ +-7 -3 450 450\\ +-7 -2 445 445\\ +-7 -1 442 442\\ +-7 0 441 441\\ +-7 1 442 442\\ +-7 2 445 445\\ +-7 3 450 450\\ +-7 4 457 457\\ +-7 5 466 466\\ +-7 6 477 477\\ +-7 7 490 490\\ +-7 8 505 505\\ +-7 9 522 522\\ +-7 10 541 541\\ +-6 -10 424 424\\ +-6 -9 405 405\\ +-6 -8 388 388\\ 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181 181\\ +-3 -9 162 162\\ +-3 -8 145 145\\ +-3 -7 130 130\\ +-3 -6 117 117\\ +-3 -5 106 106\\ +-3 -4 97 97\\ +-3 -3 90 90\\ +-3 -2 85 85\\ +-3 -1 82 82\\ +-3 0 81 81\\ +-3 1 82 82\\ +-3 2 85 85\\ +-3 3 90 90\\ +-3 4 97 97\\ +-3 5 106 106\\ +-3 6 117 117\\ +-3 7 130 130\\ +-3 8 145 145\\ +-3 9 162 162\\ +-3 10 181 181\\ +-2 -10 136 136\\ +-2 -9 117 117\\ +-2 -8 100 100\\ +-2 -7 85 85\\ +-2 -6 72 72\\ +-2 -5 61 61\\ +-2 -4 52 52\\ +-2 -3 45 45\\ +-2 -2 40 40\\ +-2 -1 37 37\\ +-2 0 36 36\\ +-2 1 37 37\\ +-2 2 40 40\\ +-2 3 45 45\\ +-2 4 52 52\\ +-2 5 61 61\\ +-2 6 72 72\\ +-2 7 85 85\\ +-2 8 100 100\\ +-2 9 117 117\\ +-2 10 136 136\\ +-1 -10 109 109\\ +-1 -9 90 90\\ +-1 -8 73 73\\ +-1 -7 58 58\\ +-1 -6 45 45\\ +-1 -5 34 34\\ +-1 -4 25 25\\ +-1 -3 18 18\\ +-1 -2 13 13\\ +-1 -1 10 10\\ +-1 0 9 9\\ +-1 1 10 10\\ +-1 2 13 13\\ +-1 3 18 18\\ +-1 4 25 25\\ +-1 5 34 34\\ +-1 6 45 45\\ +-1 7 58 58\\ +-1 8 73 73\\ +-1 9 90 90\\ +-1 10 109 109\\ +0 -10 100 100\\ +0 -9 81 81\\ +0 -8 64 64\\ +0 -7 49 49\\ +0 -6 36 36\\ +0 -5 25 25\\ +0 -4 16 16\\ +0 -3 9 9\\ +0 -2 4 4\\ +0 -1 1 1\\ +0 0 0 0\\ +0 1 1 1\\ +0 2 4 4\\ +0 3 9 9\\ +0 4 16 16\\ +0 5 25 25\\ +0 6 36 36\\ +0 7 49 49\\ +0 8 64 64\\ +0 9 81 81\\ +0 10 100 100\\ +1 -10 109 109\\ +1 -9 90 90\\ +1 -8 73 73\\ +1 -7 58 58\\ +1 -6 45 45\\ +1 -5 34 34\\ +1 -4 25 25\\ +1 -3 18 18\\ +1 -2 13 13\\ +1 -1 10 10\\ +1 0 9 9\\ +1 1 10 10\\ +1 2 13 13\\ +1 3 18 18\\ +1 4 25 25\\ +1 5 34 34\\ +1 6 45 45\\ +1 7 58 58\\ +1 8 73 73\\ +1 9 90 90\\ +1 10 109 109\\ +2 -10 136 136\\ +2 -9 117 117\\ +2 -8 100 100\\ +2 -7 85 85\\ +2 -6 72 72\\ +2 -5 61 61\\ +2 -4 52 52\\ +2 -3 45 45\\ +2 -2 40 40\\ +2 -1 37 37\\ +2 0 36 36\\ +2 1 37 37\\ +2 2 40 40\\ +2 3 45 45\\ +2 4 52 52\\ +2 5 61 61\\ +2 6 72 72\\ +2 7 85 85\\ +2 8 100 100\\ +2 9 117 117\\ +2 10 136 136\\ +3 -10 181 181\\ +3 -9 162 162\\ +3 -8 145 145\\ +3 -7 130 130\\ +3 -6 117 117\\ +3 -5 106 106\\ +3 -4 97 97\\ +3 -3 90 90\\ +3 -2 85 85\\ +3 -1 82 82\\ +3 0 81 81\\ +3 1 82 82\\ +3 2 85 85\\ 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rgb(253pt)=(0.973,0.9724,0.0938); rgb(254pt)=(0.9749,0.9782,0.0872); rgb(255pt)=(0.9769,0.9839,0.0805)}, mesh/rows=21] +table[row sep=crcr, point meta=\thisrow{c}] {% +% +x y z c\\ +-10 -10 1100 1100\\ +-10 -9 1081 1081\\ +-10 -8 1064 1064\\ +-10 -7 1049 1049\\ +-10 -6 1036 1036\\ +-10 -5 1025 1025\\ +-10 -4 1016 1016\\ +-10 -3 1009 1009\\ +-10 -2 1004 1004\\ +-10 -1 1001 1001\\ +-10 0 1000 1000\\ +-10 1 1001 1001\\ +-10 2 1004 1004\\ +-10 3 1009 1009\\ +-10 4 1016 1016\\ +-10 5 1025 1025\\ +-10 6 1036 1036\\ +-10 7 1049 1049\\ +-10 8 1064 1064\\ +-10 9 1081 1081\\ +-10 10 1100 1100\\ +-9 -10 910 910\\ +-9 -9 891 891\\ +-9 -8 874 874\\ +-9 -7 859 859\\ +-9 -6 846 846\\ +-9 -5 835 835\\ +-9 -4 826 826\\ +-9 -3 819 819\\ +-9 -2 814 814\\ +-9 -1 811 811\\ +-9 0 810 810\\ +-9 1 811 811\\ +-9 2 814 814\\ +-9 3 819 819\\ +-9 4 826 826\\ +-9 5 835 835\\ +-9 6 846 846\\ +-9 7 859 859\\ +-9 8 874 874\\ +-9 9 891 891\\ +-9 10 910 910\\ +-8 -10 740 740\\ +-8 -9 721 721\\ +-8 -8 704 704\\ +-8 -7 689 689\\ +-8 -6 676 676\\ +-8 -5 665 665\\ +-8 -4 656 656\\ +-8 -3 649 649\\ +-8 -2 644 644\\ +-8 -1 641 641\\ +-8 0 640 640\\ +-8 1 641 641\\ +-8 2 644 644\\ +-8 3 649 649\\ +-8 4 656 656\\ +-8 5 665 665\\ +-8 6 676 676\\ +-8 7 689 689\\ +-8 8 704 704\\ +-8 9 721 721\\ +-8 10 740 740\\ +-7 -10 590 590\\ +-7 -9 571 571\\ +-7 -8 554 554\\ +-7 -7 539 539\\ +-7 -6 526 526\\ +-7 -5 515 515\\ +-7 -4 506 506\\ +-7 -3 499 499\\ +-7 -2 494 494\\ +-7 -1 491 491\\ +-7 0 490 490\\ +-7 1 491 491\\ +-7 2 494 494\\ +-7 3 499 499\\ +-7 4 506 506\\ +-7 5 515 515\\ +-7 6 526 526\\ +-7 7 539 539\\ +-7 8 554 554\\ +-7 9 571 571\\ +-7 10 590 590\\ +-6 -10 460 460\\ +-6 -9 441 441\\ +-6 -8 424 424\\ +-6 -7 409 409\\ +-6 -6 396 396\\ +-6 -5 385 385\\ +-6 -4 376 376\\ +-6 -3 369 369\\ +-6 -2 364 364\\ +-6 -1 361 361\\ +-6 0 360 360\\ +-6 1 361 361\\ +-6 2 364 364\\ +-6 3 369 369\\ +-6 4 376 376\\ +-6 5 385 385\\ +-6 6 396 396\\ +-6 7 409 409\\ +-6 8 424 424\\ +-6 9 441 441\\ +-6 10 460 460\\ +-5 -10 350 350\\ +-5 -9 331 331\\ +-5 -8 314 314\\ +-5 -7 299 299\\ +-5 -6 286 286\\ +-5 -5 275 275\\ +-5 -4 266 266\\ +-5 -3 259 259\\ +-5 -2 254 254\\ +-5 -1 251 251\\ +-5 0 250 250\\ +-5 1 251 251\\ +-5 2 254 254\\ +-5 3 259 259\\ +-5 4 266 266\\ +-5 5 275 275\\ +-5 6 286 286\\ +-5 7 299 299\\ +-5 8 314 314\\ +-5 9 331 331\\ +-5 10 350 350\\ +-4 -10 260 260\\ +-4 -9 241 241\\ +-4 -8 224 224\\ +-4 -7 209 209\\ +-4 -6 196 196\\ +-4 -5 185 185\\ +-4 -4 176 176\\ +-4 -3 169 169\\ +-4 -2 164 164\\ +-4 -1 161 161\\ +-4 0 160 160\\ +-4 1 161 161\\ +-4 2 164 164\\ +-4 3 169 169\\ +-4 4 176 176\\ +-4 5 185 185\\ +-4 6 196 196\\ +-4 7 209 209\\ +-4 8 224 224\\ +-4 9 241 241\\ +-4 10 260 260\\ +-3 -10 190 190\\ +-3 -9 171 171\\ +-3 -8 154 154\\ +-3 -7 139 139\\ +-3 -6 126 126\\ +-3 -5 115 115\\ +-3 -4 106 106\\ +-3 -3 99 99\\ +-3 -2 94 94\\ +-3 -1 91 91\\ +-3 0 90 90\\ +-3 1 91 91\\ +-3 2 94 94\\ +-3 3 99 99\\ +-3 4 106 106\\ +-3 5 115 115\\ +-3 6 126 126\\ +-3 7 139 139\\ +-3 8 154 154\\ +-3 9 171 171\\ 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35 35\\ +1 -4 26 26\\ +1 -3 19 19\\ +1 -2 14 14\\ +1 -1 11 11\\ +1 0 10 10\\ +1 1 11 11\\ +1 2 14 14\\ +1 3 19 19\\ +1 4 26 26\\ +1 5 35 35\\ +1 6 46 46\\ +1 7 59 59\\ +1 8 74 74\\ +1 9 91 91\\ +1 10 110 110\\ +2 -10 140 140\\ +2 -9 121 121\\ +2 -8 104 104\\ +2 -7 89 89\\ +2 -6 76 76\\ +2 -5 65 65\\ +2 -4 56 56\\ +2 -3 49 49\\ +2 -2 44 44\\ +2 -1 41 41\\ +2 0 40 40\\ +2 1 41 41\\ +2 2 44 44\\ +2 3 49 49\\ +2 4 56 56\\ +2 5 65 65\\ +2 6 76 76\\ +2 7 89 89\\ +2 8 104 104\\ +2 9 121 121\\ +2 10 140 140\\ +3 -10 190 190\\ +3 -9 171 171\\ +3 -8 154 154\\ +3 -7 139 139\\ +3 -6 126 126\\ +3 -5 115 115\\ +3 -4 106 106\\ +3 -3 99 99\\ +3 -2 94 94\\ +3 -1 91 91\\ +3 0 90 90\\ +3 1 91 91\\ +3 2 94 94\\ +3 3 99 99\\ +3 4 106 106\\ +3 5 115 115\\ +3 6 126 126\\ +3 7 139 139\\ +3 8 154 154\\ +3 9 171 171\\ +3 10 190 190\\ +4 -10 260 260\\ +4 -9 241 241\\ +4 -8 224 224\\ +4 -7 209 209\\ +4 -6 196 196\\ +4 -5 185 185\\ +4 -4 176 176\\ +4 -3 169 169\\ +4 -2 164 164\\ +4 -1 161 161\\ +4 0 160 160\\ +4 1 161 161\\ +4 2 164 164\\ +4 3 169 169\\ +4 4 176 176\\ +4 5 185 185\\ +4 6 196 196\\ +4 7 209 209\\ +4 8 224 224\\ +4 9 241 241\\ +4 10 260 260\\ +5 -10 350 350\\ +5 -9 331 331\\ +5 -8 314 314\\ +5 -7 299 299\\ +5 -6 286 286\\ +5 -5 275 275\\ +5 -4 266 266\\ +5 -3 259 259\\ +5 -2 254 254\\ +5 -1 251 251\\ +5 0 250 250\\ +5 1 251 251\\ +5 2 254 254\\ +5 3 259 259\\ +5 4 266 266\\ +5 5 275 275\\ +5 6 286 286\\ +5 7 299 299\\ +5 8 314 314\\ +5 9 331 331\\ +5 10 350 350\\ +6 -10 460 460\\ +6 -9 441 441\\ +6 -8 424 424\\ +6 -7 409 409\\ +6 -6 396 396\\ +6 -5 385 385\\ +6 -4 376 376\\ +6 -3 369 369\\ +6 -2 364 364\\ +6 -1 361 361\\ +6 0 360 360\\ +6 1 361 361\\ +6 2 364 364\\ +6 3 369 369\\ +6 4 376 376\\ +6 5 385 385\\ +6 6 396 396\\ +6 7 409 409\\ +6 8 424 424\\ +6 9 441 441\\ +6 10 460 460\\ +7 -10 590 590\\ +7 -9 571 571\\ +7 -8 554 554\\ +7 -7 539 539\\ +7 -6 526 526\\ +7 -5 515 515\\ +7 -4 506 506\\ +7 -3 499 499\\ +7 -2 494 494\\ +7 -1 491 491\\ +7 0 490 490\\ +7 1 491 491\\ +7 2 494 494\\ +7 3 499 499\\ +7 4 506 506\\ +7 5 515 515\\ +7 6 526 526\\ +7 7 539 539\\ +7 8 554 554\\ +7 9 571 571\\ +7 10 590 590\\ +8 -10 740 740\\ +8 -9 721 721\\ +8 -8 704 704\\ +8 -7 689 689\\ +8 -6 676 676\\ +8 -5 665 665\\ +8 -4 656 656\\ +8 -3 649 649\\ +8 -2 644 644\\ +8 -1 641 641\\ +8 0 640 640\\ +8 1 641 641\\ +8 2 644 644\\ +8 3 649 649\\ +8 4 656 656\\ +8 5 665 665\\ +8 6 676 676\\ +8 7 689 689\\ +8 8 704 704\\ +8 9 721 721\\ +8 10 740 740\\ +9 -10 910 910\\ +9 -9 891 891\\ +9 -8 874 874\\ +9 -7 859 859\\ +9 -6 846 846\\ +9 -5 835 835\\ +9 -4 826 826\\ +9 -3 819 819\\ +9 -2 814 814\\ +9 -1 811 811\\ +9 0 810 810\\ +9 1 811 811\\ +9 2 814 814\\ +9 3 819 819\\ +9 4 826 826\\ +9 5 835 835\\ +9 6 846 846\\ +9 7 859 859\\ +9 8 874 874\\ +9 9 891 891\\ +9 10 910 910\\ +10 -10 1100 1100\\ +10 -9 1081 1081\\ +10 -8 1064 1064\\ +10 -7 1049 1049\\ +10 -6 1036 1036\\ +10 -5 1025 1025\\ +10 -4 1016 1016\\ +10 -3 1009 1009\\ +10 -2 1004 1004\\ +10 -1 1001 1001\\ +10 0 1000 1000\\ +10 1 1001 1001\\ +10 2 1004 1004\\ +10 3 1009 1009\\ +10 4 1016 1016\\ +10 5 1025 1025\\ +10 6 1036 1036\\ +10 7 1049 1049\\ +10 8 1064 1064\\ +10 9 1081 1081\\ +10 10 1100 1100\\ +}; +\end{axis} + +\begin{axis}[% +width=2.408in, +height=1.648in, +at={(15.924in,1.149in)}, +scale only axis, +colormap={mymap}{[1pt] rgb(0pt)=(0.2422,0.1504,0.6603); rgb(1pt)=(0.2444,0.1534,0.6728); rgb(2pt)=(0.2464,0.1569,0.6847); rgb(3pt)=(0.2484,0.1607,0.6961); rgb(4pt)=(0.2503,0.1648,0.7071); rgb(5pt)=(0.2522,0.1689,0.7179); rgb(6pt)=(0.254,0.1732,0.7286); rgb(7pt)=(0.2558,0.1773,0.7393); rgb(8pt)=(0.2576,0.1814,0.7501); rgb(9pt)=(0.2594,0.1854,0.761); rgb(11pt)=(0.2628,0.1932,0.7828); rgb(12pt)=(0.2645,0.1972,0.7937); rgb(13pt)=(0.2661,0.2011,0.8043); rgb(14pt)=(0.2676,0.2052,0.8148); rgb(15pt)=(0.2691,0.2094,0.8249); rgb(16pt)=(0.2704,0.2138,0.8346); rgb(17pt)=(0.2717,0.2184,0.8439); rgb(18pt)=(0.2729,0.2231,0.8528); rgb(19pt)=(0.274,0.228,0.8612); rgb(20pt)=(0.2749,0.233,0.8692); rgb(21pt)=(0.2758,0.2382,0.8767); rgb(22pt)=(0.2766,0.2435,0.884); rgb(23pt)=(0.2774,0.2489,0.8908); rgb(24pt)=(0.2781,0.2543,0.8973); rgb(25pt)=(0.2788,0.2598,0.9035); rgb(26pt)=(0.2794,0.2653,0.9094); rgb(27pt)=(0.2798,0.2708,0.915); rgb(28pt)=(0.2802,0.2764,0.9204); rgb(29pt)=(0.2806,0.2819,0.9255); rgb(30pt)=(0.2809,0.2875,0.9305); rgb(31pt)=(0.2811,0.293,0.9352); rgb(32pt)=(0.2813,0.2985,0.9397); rgb(33pt)=(0.2814,0.304,0.9441); rgb(34pt)=(0.2814,0.3095,0.9483); rgb(35pt)=(0.2813,0.315,0.9524); rgb(36pt)=(0.2811,0.3204,0.9563); rgb(37pt)=(0.2809,0.3259,0.96); rgb(38pt)=(0.2807,0.3313,0.9636); rgb(39pt)=(0.2803,0.3367,0.967); rgb(40pt)=(0.2798,0.3421,0.9702); rgb(41pt)=(0.2791,0.3475,0.9733); rgb(42pt)=(0.2784,0.3529,0.9763); rgb(43pt)=(0.2776,0.3583,0.9791); rgb(44pt)=(0.2766,0.3638,0.9817); rgb(45pt)=(0.2754,0.3693,0.984); rgb(46pt)=(0.2741,0.3748,0.9862); rgb(47pt)=(0.2726,0.3804,0.9881); rgb(48pt)=(0.271,0.386,0.9898); rgb(49pt)=(0.2691,0.3916,0.9912); rgb(50pt)=(0.267,0.3973,0.9924); rgb(51pt)=(0.2647,0.403,0.9935); rgb(52pt)=(0.2621,0.4088,0.9946); rgb(53pt)=(0.2591,0.4145,0.9955); rgb(54pt)=(0.2556,0.4203,0.9965); rgb(55pt)=(0.2517,0.4261,0.9974); rgb(56pt)=(0.2473,0.4319,0.9983); rgb(57pt)=(0.2424,0.4378,0.9991); rgb(58pt)=(0.2369,0.4437,0.9996); rgb(59pt)=(0.2311,0.4497,0.9995); rgb(60pt)=(0.225,0.4559,0.9985); rgb(61pt)=(0.2189,0.462,0.9968); rgb(62pt)=(0.2128,0.4682,0.9948); rgb(63pt)=(0.2066,0.4743,0.9926); rgb(64pt)=(0.2006,0.4803,0.9906); rgb(65pt)=(0.195,0.4861,0.9887); rgb(66pt)=(0.1903,0.4919,0.9867); rgb(67pt)=(0.1869,0.4975,0.9844); rgb(68pt)=(0.1847,0.503,0.9819); rgb(69pt)=(0.1831,0.5084,0.9793); rgb(70pt)=(0.1818,0.5138,0.9766); rgb(71pt)=(0.1806,0.5191,0.9738); rgb(72pt)=(0.1795,0.5244,0.9709); rgb(73pt)=(0.1785,0.5296,0.9677); rgb(74pt)=(0.1778,0.5349,0.9641); rgb(75pt)=(0.1773,0.5401,0.9602); rgb(76pt)=(0.1768,0.5452,0.956); rgb(77pt)=(0.1764,0.5504,0.9516); rgb(78pt)=(0.1755,0.5554,0.9473); rgb(79pt)=(0.174,0.5605,0.9432); rgb(80pt)=(0.1716,0.5655,0.9393); rgb(81pt)=(0.1686,0.5705,0.9357); rgb(82pt)=(0.1649,0.5755,0.9323); rgb(83pt)=(0.161,0.5805,0.9289); rgb(84pt)=(0.1573,0.5854,0.9254); rgb(85pt)=(0.154,0.5902,0.9218); rgb(86pt)=(0.1513,0.595,0.9182); rgb(87pt)=(0.1492,0.5997,0.9147); rgb(88pt)=(0.1475,0.6043,0.9113); rgb(89pt)=(0.1461,0.6089,0.908); rgb(90pt)=(0.1446,0.6135,0.905); rgb(91pt)=(0.1429,0.618,0.9022); rgb(92pt)=(0.1408,0.6226,0.8998); rgb(93pt)=(0.1383,0.6272,0.8975); rgb(94pt)=(0.1354,0.6317,0.8953); rgb(95pt)=(0.1321,0.6363,0.8932); rgb(96pt)=(0.1288,0.6408,0.891); rgb(97pt)=(0.1253,0.6453,0.8887); rgb(98pt)=(0.1219,0.6497,0.8862); rgb(99pt)=(0.1185,0.6541,0.8834); rgb(100pt)=(0.1152,0.6584,0.8804); rgb(101pt)=(0.1119,0.6627,0.877); rgb(102pt)=(0.1085,0.6669,0.8734); rgb(103pt)=(0.1048,0.671,0.8695); rgb(104pt)=(0.1009,0.675,0.8653); rgb(105pt)=(0.0964,0.6789,0.8609); rgb(106pt)=(0.0914,0.6828,0.8562); rgb(107pt)=(0.0855,0.6865,0.8513); rgb(108pt)=(0.0789,0.6902,0.8462); rgb(109pt)=(0.0713,0.6938,0.8409); rgb(110pt)=(0.0628,0.6972,0.8355); rgb(111pt)=(0.0535,0.7006,0.8299); rgb(112pt)=(0.0433,0.7039,0.8242); rgb(113pt)=(0.0328,0.7071,0.8183); rgb(114pt)=(0.0234,0.7103,0.8124); rgb(115pt)=(0.0155,0.7133,0.8064); rgb(116pt)=(0.0091,0.7163,0.8003); rgb(117pt)=(0.0046,0.7192,0.7941); rgb(118pt)=(0.0019,0.722,0.7878); rgb(119pt)=(0.0009,0.7248,0.7815); rgb(120pt)=(0.0018,0.7275,0.7752); rgb(121pt)=(0.0046,0.7301,0.7688); rgb(122pt)=(0.0094,0.7327,0.7623); rgb(123pt)=(0.0162,0.7352,0.7558); rgb(124pt)=(0.0253,0.7376,0.7492); rgb(125pt)=(0.0369,0.74,0.7426); rgb(126pt)=(0.0504,0.7423,0.7359); rgb(127pt)=(0.0638,0.7446,0.7292); rgb(128pt)=(0.077,0.7468,0.7224); rgb(129pt)=(0.0899,0.7489,0.7156); rgb(130pt)=(0.1023,0.751,0.7088); rgb(131pt)=(0.1141,0.7531,0.7019); rgb(132pt)=(0.1252,0.7552,0.695); rgb(133pt)=(0.1354,0.7572,0.6881); rgb(134pt)=(0.1448,0.7593,0.6812); rgb(135pt)=(0.1532,0.7614,0.6741); rgb(136pt)=(0.1609,0.7635,0.6671); rgb(137pt)=(0.1678,0.7656,0.6599); rgb(138pt)=(0.1741,0.7678,0.6527); rgb(139pt)=(0.1799,0.7699,0.6454); rgb(140pt)=(0.1853,0.7721,0.6379); rgb(141pt)=(0.1905,0.7743,0.6303); rgb(142pt)=(0.1954,0.7765,0.6225); rgb(143pt)=(0.2003,0.7787,0.6146); rgb(144pt)=(0.2061,0.7808,0.6065); rgb(145pt)=(0.2118,0.7828,0.5983); rgb(146pt)=(0.2178,0.7849,0.5899); rgb(147pt)=(0.2244,0.7869,0.5813); rgb(148pt)=(0.2318,0.7887,0.5725); rgb(149pt)=(0.2401,0.7905,0.5636); rgb(150pt)=(0.2491,0.7922,0.5546); rgb(151pt)=(0.2589,0.7937,0.5454); rgb(152pt)=(0.2695,0.7951,0.536); rgb(153pt)=(0.2809,0.7964,0.5266); rgb(154pt)=(0.2929,0.7975,0.517); rgb(155pt)=(0.3052,0.7985,0.5074); rgb(156pt)=(0.3176,0.7994,0.4975); rgb(157pt)=(0.3301,0.8002,0.4876); rgb(158pt)=(0.3424,0.8009,0.4774); rgb(159pt)=(0.3548,0.8016,0.4669); rgb(160pt)=(0.3671,0.8021,0.4563); rgb(161pt)=(0.3795,0.8026,0.4454); rgb(162pt)=(0.3921,0.8029,0.4344); rgb(163pt)=(0.405,0.8031,0.4233); 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+\usepackage{hyperref} +\usetikzlibrary{arrows} \setlength{\parindent}{0cm} \setlength{\parskip}{0.5\baselineskip} @@ -67,4 +72,25 @@ Not in general. If for example we consider A and b to be only zeros, then $J(x) However, for if $A$ would be guaranteed to have full rank, the minimizer would be unique because the first order necessary condition would hold only for one value $x^*$. This is because the linear system $Ax^* = b$ would have one and only one solution (due to $A$ being full rank). +\section{Exercise 3} + +\subsection{Quadratic form} + +$f(x,y)$ can be written in quadratic form in the following way: + +\[f(v) = \frac12 \langle\begin{bmatrix}2 & 0\\0 & 2\mu\end{bmatrix}v, v\rangle + \langle\begin{bmatrix}0\\0\end{bmatrix}, x\rangle\] + +where: + +\[v = \begin{bmatrix}x\\y\end{bmatrix}\] + +\subsection{Matlab implementation with \texttt{surf} and \texttt{contour}} + +The graphs generated by MATLAB are shown below: + +\resizebox{\textwidth}{!}{\input{ex32.tex}} + +Isolines get stretched along the y axis as $\mu$ increases. For a large $\mu$, points well far away from the axes could be a +problem since picking search directions and steps using a naive gradient based method iterations will zig-zag to the minimizer reaching it slowly. + \end{document}