* AMPL Model by Hande Y. Benson * * Copyright (C) 2001 Princeton University * All Rights Reserved * * Permission to use, copy, modify, and distribute this software and * its documentation for any purpose and without fee is hereby * granted, provided that the above copyright notice appear in all * copies and that the copyright notice and this * permission notice appear in all supporting documentation. * Source: * Francois Grondin (francois.grondin@qc.forintek.ca) * Forintek Canada Corp, 319, rue Franquet, Quebec, G1P 4R4, CANADA * SIF input: Nick Gould, Dec 1997. * classification QOR2-AN-583-774 $Set n 195 $Set m 4 Set I /i0*i%n%/; Set j /j0*j%m%/; Set left(j) /j1*j%m%/; Set left_left(j) /j2*j%m%/; Parameter R ; R = 2500; Parameter x[i] / i0 0.0 , i1 2.54 , i2 5.08 , i3 7.62001, i4 10.1612, i5 12.7012, i6 15.2412, i7 17.7812, i8 20.3212, i9 22.8612, i10 25.4012, i11 27.9412, i12 30.4812, i13 33.0212, i14 35.5612, i15 38.1012, i16 40.6411, i17 43.1811, i18 45.7231, i19 48.2631, i20 50.8031, i21 53.3431, i22 55.8839, i23 58.4239, i24 60.965 , i25 63.505 , i26 66.045 , i27 68.585 , i28 71.125 , i29 73.665 , i30 76.205 , i31 78.745 , i32 81.285 , i33 83.825 , i34 86.365 , i35 88.905 , i36 91.445 , i37 93.985 , i38 96.525 , i39 99.065 , i40 101.605 , i41 104.145 , i42 106.685 , i43 109.225 , i44 111.766 , i45 114.306 , i46 116.847 , i47 119.387 , i48 121.927 , i49 124.467 , i50 127.008 , i51 129.548 , i52 132.09 , i53 134.63 , i54 137.17 , i55 139.71 , i56 142.251 , i57 144.791 , i58 147.33 , i59 149.87 , i60 152.41 , i61 154.95 , i62 157.49 , i63 160.03 , i64 162.571 , i65 165.111 , i66 167.651 , i67 170.191 , i68 172.731 , i69 175.271 , i70 177.811 , i71 180.351 , i72 182.891 , i73 185.431 , i74 187.972 , i75 190.512 , i76 193.052 , i77 195.592 , i78 198.133 , i79 200.673 , i80 203.213 , i81 205.753 , i82 208.293 , i83 210.833 , i84 213.374 , i85 215.914 , i86 218.456 , i87 220.996 , i88 223.536 , i89 226.076 , i90 228.616 , i91 231.156 , i92 233.696 , i93 236.236 , i94 238.776 , i95 241.316 , i96 243.856 , i97 246.396 , i98 248.936 , i99 251.476 , i100 254.016 , i101 256.556 , i102 259.095 , i103 261.635 , i104 264.176 , i105 266.716 , i106 269.256 , i107 271.797 , i108 274.337 , i109 276.877 , i110 279.417 , i111 281.957 , i112 284.497 , i113 287.037 , i114 289.577 , i115 292.117 , i116 294.657 , i117 297.197 , i118 299.736 , i119 302.276 , i120 304.815 , i121 307.355 , i122 309.895 , i123 312.435 , i124 314.976 , i125 317.516 , i126 320.056 , i127 322.598 , i128 325.138 , i129 327.678 , i130 330.215 , i131 332.755 , i132 335.295 , i133 337.835 , i134 340.375 , i135 342.915 , i136 345.454 , i137 347.994 , i138 350.534 , i139 353.074 , i140 355.615 , i141 358.155 , i142 360.695 , i143 363.235 , i144 365.773 , i145 368.313 , i146 370.853 , i147 373.393 , i148 375.933 , i149 378.473 , i150 381.012 , i151 383.552 , i152 386.09 , i153 388.632 , i154 391.17 , i155 393.71 , i156 396.25 , i157 398.79 , i158 401.329 , i159 403.869 , i160 406.41 , i161 408.95 , i162 411.49 , i163 414.03 , i164 416.57 , i165 419.11 , i166 421.65 , i167 424.19 , i168 426.729 , i169 429.269 , i170 431.81 , i171 434.35 , i172 436.891 , i173 439.431 , i174 441.972 , i175 444.512 , i176 447.052 , i177 449.592 , i178 452.134 , i179 454.674 , i180 457.214 , i181 459.754 , i182 462.295 , i183 464.835 , i184 467.375 , i185 469.915 , i186 472.455 , i187 474.995 , i188 477.535 , i189 480.075 , i190 482.616 , i191 485.156 , i192 487.696 , i193 490.236 , i194 492.776 , i195 495.316 /; Parameter y[i] / i0 3.556 , i1 3.56346 , i2 3.57091 , i3 3.57837 , i4 3.59371 , i5 3.60213 , i6 3.61055 , i7 3.61898 , i8 3.6274 , i9 3.63582 , i10 3.6423 , i11 3.65073 , i12 3.6653 , i13 3.67381 , i14 3.68233 , i15 3.69084 , i16 3.50637 , i17 3.51498 , i18 2.77481 , i19 2.78376 , i20 2.79272 , i21 2.80168 , i22 2.78529 , i23 2.79415 , i24 2.47602 , i25 2.48617 , i26 2.48369 , i27 2.49377 , i28 2.27635 , i29 2.28521 , i30 2.26744 , i31 2.27605 , i32 2.28465 , i33 2.29325 , i34 2.4907 , i35 2.49921 , i36 2.50773 , i37 2.51624 , i38 2.53381 , i39 2.54241 , i40 2.74855 , i41 2.75716 , i42 2.76576 , i43 2.77437 , i44 2.60758 , i45 2.6161 , i46 2.26008 , i47 2.2686 , i48 2.28695 , i49 2.29556 , i50 1.47808 , i51 1.4854 , i52 1.1101 , i53 1.1188 , i54 1.12749 , i55 1.13619 , i56 0.978377 , i57 0.987075 , i58 0.82203 , i59 0.829676 , i60 0.837322 , i61 0.844885 , i62 0.852781 , i63 0.86051 , i64 0.538377 , i65 0.546996 , i66 0.600516 , i67 0.609224 , i68 0.789128 , i69 0.798084 , i70 1.00996 , i71 1.01883 , i72 1.03712 , i73 1.04591 , i74 0.720837 , i75 0.699625 , i76 0.708414 , i77 0.717203 , i78 0.609086 , i79 0.617627 , i80 0.199369 , i81 0.207992 , i82 0.225288 , i83 0.233831 , i84 -0.172432 , i85 -0.163889 , i86 -0.34889 , i87 -0.341233 , i88 -0.333576 , i89 -0.32592 , i90 -0.522016 , i91 -0.514426 , i92 -0.506837 , i93 -0.499248 , i94 -0.491658 , i95 -0.484069 , i96 -0.47648 , i97 -0.46889 , i98 -0.462453 , i99 -0.455008 , i100 -0.447563 , i101 -0.440118 , i102 0.055237 , i103 0.063873 , i104 0.062826 , i105 0.070575 , i106 -0.275144 , i107 -0.275842 , i108 -0.268089 , i109 -0.260335 , i110 -0.118406 , i111 -0.110665 , i112 -0.102923 , i113 -0.095181 , i114 0.103362 , i115 0.111028 , i116 0.131239 , i117 0.138981 , i118 0.27243 , i119 0.280024 , i120 0.421614 , i121 0.429144 , i122 0.436674 , i123 0.444203 , i124 0.484027 , i125 0.491804 , i126 0.515482 , i127 0.571256 , i128 0.580224 , i129 0.589193 , i130 1.11182 , i131 1.12071 , i132 1.34551 , i133 1.35448 , i134 1.38382 , i135 1.39287 , i136 1.77298 , i137 1.78202 , i138 2.00633 , i139 2.01544 , i140 2.41293 , i141 2.42093 , i142 2.39029 , i143 2.39823 , i144 2.89123 , i145 2.89911 , i146 3.33714 , i147 3.34509 , i148 3.40441 , i149 3.41248 , i150 3.70271 , i151 3.71094 , i152 4.15353 , i153 4.12735 , i154 4.56011 , i155 4.56923 , i156 4.77252 , i157 4.78163 , i158 4.89149 , i159 4.89935 , i160 4.96478 , i161 4.97272 , i162 5.16767 , i163 5.17553 , i164 5.38577 , i165 5.39364 , i166 5.40151 , i167 5.40937 , i168 5.28358 , i169 5.29136 , i170 5.14203 , i171 5.14865 , i172 4.80067 , i173 4.80729 , i174 4.86169 , i175 4.86947 , i176 4.56159 , i177 4.56937 , i178 3.78824 , i179 3.79602 , i180 3.8038 , i181 3.81158 , i182 3.66534 , i183 3.67306 , i184 3.67665 , i185 3.6845 , i186 3.6904 , i187 3.69832 , i188 3.70624 , i189 3.71416 , i190 3.50154 , i191 3.50963 , i192 3.51772 , i193 3.52581 , i194 3.5339 , i195 3.54199 /; Parameter dx ; dx = x['i15']-x['i0'] ; Parameter dy ; dy = y['i15']-y['i0'] ; Parameter m_0 ; m_0 = dy/dx; Variable a[j] , p[i] , pprime[i] , pprime2[i] , f ; Equation cons1[i] , cons2[i] , cons3[i] , cons4[i] , cons5 , cons6 , Def_obj ; cons1[i].. sum{j , (a[j]*power(x[i],{ord(j)-1}) ) } -p[i] =e= 0; cons2[i].. sum{j$left(j) , (a[j]*(ord(j)-1) *power(x[i],({ord(j)-1}-1)))} -pprime[i] =e= 0; cons3[i].. sum{j$left_left(j), (a[j]*(ord(j)-1)*({ord(j)-1}-1)*power(x[i],({ord(j)-1}-2)))} -pprime2[i]=e=0; cons4[i].. R*R*pprime2[i]*pprime2[i]-power{ (1+pprime[i]*pprime[i]) ,3 } =l= 0; cons5.. p['i0'] =e= y['i0']; cons6.. pprime['i0'] =e= m_0; Def_obj.. f =e= sum{i,sqr(p[i]-y[i]) }; Model sawpath /all /; Solve sawpath using nlp minimazing f ; display f.l; display p.l, pprime.l, pprime2.l, a.l;