optimization for nonlinear equation using fminunc

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FATHIMA JAMSHEENA P
编辑： Torsten 2023-7-10
i have an equation . i have to do optimization for this to get unknown parameters z a and b. , and are matrixes of size 364x441.after getting z a and b i have to put those values in above equation to get estimated LHS. how to do this using fminunc funtion in matlab

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Torsten
Torsten 2023-7-10
编辑：Torsten 2023-7-10
x0 = [1 1 1];
fun = @(x) x(1)*dsdt + x(2)*s.^x(3);
f = @(x) sum(sum((fun(x) - p).^2));
x = fminsearch(f,x0)
lhs = fun(x)
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Torsten
Torsten 2023-7-10
编辑：Torsten 2023-7-10
Ran in:
s = load("s.mat");
s = s.s;
s = s(:);
size(s)
ans = 1×2
160524 1
idx = s > 0;
s = s(idx);
size(s)
ans = 1×2
160491 1
dsdt = load("dsdt.mat");
dsdt = dsdt.dsdt;
dsdt = dsdt(:);
dsdt = dsdt(idx);
p = load("p.mat");
p = p.p;
p = p(:);
p = p(idx);
x0 = [1 1 1];
fun = @(x) x(1)*dsdt + x(2)*s.^x(3);
f = @(x) sum((fun(x) - p).^2);
x = fminsearch(f,x0,optimset('MaxFunEvals',10000,'MaxIter',10000,'Display','iter'))
Iteration Func-count f(x) Procedure 0 1 1.20927e+07 1 4 1.20778e+07 initial simplex 2 6 1.20398e+07 expand 3 7 1.20398e+07 reflect 4 9 1.19714e+07 expand 5 11 1.18792e+07 expand 6 13 1.17615e+07 expand 7 15 1.13954e+07 expand 8 17 1.08876e+07 expand 9 19 1.07885e+07 reflect 10 21 1.07565e+07 contract outside 11 23 1.07565e+07 contract inside 12 25 1.07565e+07 contract outside 13 27 1.07565e+07 contract inside 14 28 1.07565e+07 reflect 15 30 1.07565e+07 contract inside 16 32 1.07565e+07 contract outside 17 34 1.07565e+07 contract inside 18 35 1.07565e+07 reflect 19 37 1.07501e+07 expand 20 39 1.07501e+07 contract inside 21 40 1.07501e+07 reflect 22 42 1.07501e+07 contract inside 23 43 1.07501e+07 reflect 24 44 1.07501e+07 reflect 25 46 1.07499e+07 reflect 26 48 1.07421e+07 expand 27 49 1.07421e+07 reflect 28 50 1.07421e+07 reflect 29 52 1.07395e+07 expand 30 54 1.07261e+07 expand 31 56 1.07178e+07 expand 32 57 1.07178e+07 reflect 33 59 1.06921e+07 expand 34 60 1.06921e+07 reflect 35 62 1.06768e+07 expand 36 64 1.06581e+07 expand 37 66 1.06415e+07 expand 38 68 1.06069e+07 expand 39 69 1.06069e+07 reflect 40 71 1.0574e+07 expand 41 73 1.0574e+07 contract inside 42 75 1.0574e+07 contract outside 43 76 1.0574e+07 reflect 44 78 1.05512e+07 expand 45 80 1.05512e+07 contract outside 46 81 1.05512e+07 reflect 47 83 1.05512e+07 contract inside 48 85 1.05496e+07 reflect 49 87 1.05453e+07 reflect 50 88 1.05453e+07 reflect 51 90 1.05421e+07 expand 52 92 1.05343e+07 expand 53 93 1.05343e+07 reflect 54 95 1.05308e+07 expand 55 97 1.05308e+07 contract inside 56 99 1.05308e+07 contract outside 57 100 1.05308e+07 reflect 58 101 1.05308e+07 reflect 59 103 1.05302e+07 contract inside 60 105 1.053e+07 reflect 61 107 1.053e+07 contract outside 62 109 1.053e+07 contract inside 63 111 1.05299e+07 reflect 64 113 1.05299e+07 contract inside 65 115 1.05299e+07 contract inside 66 117 1.05299e+07 contract inside 67 119 1.05299e+07 contract inside 68 121 1.05299e+07 contract inside 69 123 1.05299e+07 contract inside 70 125 1.05299e+07 reflect 71 127 1.05299e+07 reflect 72 128 1.05299e+07 reflect 73 130 1.05299e+07 contract inside 74 132 1.05299e+07 reflect 75 134 1.05299e+07 contract inside 76 136 1.05299e+07 contract inside 77 138 1.05298e+07 reflect 78 139 1.05298e+07 reflect 79 141 1.05298e+07 contract inside 80 143 1.05298e+07 expand 81 144 1.05298e+07 reflect 82 145 1.05298e+07 reflect 83 147 1.05298e+07 reflect 84 149 1.05298e+07 expand 85 151 1.05298e+07 contract outside 86 152 1.05298e+07 reflect 87 153 1.05298e+07 reflect 88 155 1.05298e+07 expand 89 156 1.05298e+07 reflect 90 157 1.05298e+07 reflect 91 159 1.05298e+07 expand 92 161 1.05297e+07 expand 93 163 1.05297e+07 expand 94 165 1.05296e+07 expand 95 166 1.05296e+07 reflect 96 168 1.05294e+07 expand 97 170 1.05292e+07 expand 98 171 1.05292e+07 reflect 99 173 1.05288e+07 expand 100 175 1.05283e+07 expand 101 176 1.05283e+07 reflect 102 178 1.05273e+07 expand 103 180 1.05264e+07 expand 104 182 1.05254e+07 expand 105 184 1.05251e+07 expand 106 186 1.0524e+07 reflect 107 187 1.0524e+07 reflect 108 189 1.0524e+07 contract inside 109 191 1.05222e+07 expand 110 192 1.05222e+07 reflect 111 194 1.0521e+07 expand 112 195 1.0521e+07 reflect 113 197 1.05167e+07 expand 114 198 1.05167e+07 reflect 115 200 1.05151e+07 expand 116 202 1.05063e+07 expand 117 203 1.05063e+07 reflect 118 204 1.05063e+07 reflect 119 206 1.05003e+07 expand 120 208 1.04913e+07 expand 121 210 1.04842e+07 reflect 122 212 1.04725e+07 expand 123 214 1.04549e+07 expand 124 215 1.04549e+07 reflect 125 217 1.04491e+07 reflect 126 219 1.04491e+07 contract inside 127 221 1.0444e+07 reflect 128 222 1.0444e+07 reflect 129 224 1.04438e+07 contract outside 130 226 1.0443e+07 contract inside 131 228 1.04426e+07 contract inside 132 230 1.0442e+07 contract inside 133 232 1.0442e+07 contract outside 134 234 1.0442e+07 contract inside 135 236 1.0442e+07 contract inside 136 238 1.04419e+07 reflect 137 240 1.04419e+07 reflect 138 242 1.04418e+07 contract inside 139 244 1.04417e+07 expand 140 245 1.04417e+07 reflect 141 247 1.04417e+07 contract outside 142 249 1.04413e+07 expand 143 250 1.04413e+07 reflect 144 251 1.04413e+07 reflect 145 253 1.04406e+07 expand 146 254 1.04406e+07 reflect 147 256 1.04402e+07 expand 148 258 1.04396e+07 expand 149 260 1.04379e+07 expand 150 261 1.04379e+07 reflect 151 263 1.04377e+07 reflect 152 265 1.04363e+07 expand 153 267 1.0435e+07 expand 154 269 1.0435e+07 contract inside 155 271 1.04348e+07 reflect 156 273 1.04348e+07 contract inside 157 275 1.04341e+07 reflect 158 277 1.04341e+07 contract inside 159 279 1.04339e+07 expand 160 280 1.04339e+07 reflect 161 282 1.04339e+07 contract inside 162 284 1.04339e+07 contract outside 163 285 1.04339e+07 reflect 164 287 1.04338e+07 reflect 165 289 1.04338e+07 contract inside 166 291 1.04338e+07 reflect 167 293 1.04338e+07 contract outside 168 294 1.04338e+07 reflect 169 296 1.04338e+07 contract inside 170 298 1.04338e+07 contract inside 171 300 1.04338e+07 contract inside 172 302 1.04338e+07 contract inside 173 303 1.04338e+07 reflect 174 305 1.04338e+07 contract outside 175 306 1.04338e+07 reflect 176 308 1.04338e+07 contract inside 177 310 1.04338e+07 contract inside 178 312 1.04338e+07 contract inside 179 314 1.04338e+07 contract inside 180 316 1.04338e+07 contract inside 181 318 1.04338e+07 contract inside 182 320 1.04338e+07 reflect 183 322 1.04338e+07 contract inside 184 323 1.04338e+07 reflect 185 325 1.04338e+07 contract inside 186 326 1.04338e+07 reflect 187 328 1.04338e+07 contract inside 188 330 1.04338e+07 contract inside 189 332 1.04338e+07 expand 190 333 1.04338e+07 reflect 191 335 1.04338e+07 contract inside 192 336 1.04338e+07 reflect 193 338 1.04338e+07 contract inside 194 340 1.04338e+07 contract outside 195 342 1.04338e+07 contract inside 196 344 1.04338e+07 reflect 197 346 1.04338e+07 contract inside 198 348 1.04338e+07 contract inside 199 350 1.04338e+07 contract inside 200 352 1.04338e+07 contract inside 201 354 1.04338e+07 contract inside 202 356 1.04338e+07 contract inside 203 358 1.04338e+07 contract inside 204 360 1.04338e+07 contract inside 205 362 1.04338e+07 contract inside 206 363 1.04338e+07 reflect 207 364 1.04338e+07 reflect 208 366 1.04338e+07 contract outside 209 368 1.04338e+07 contract inside 210 370 1.04338e+07 contract inside 211 371 1.04338e+07 reflect 212 372 1.04338e+07 reflect 213 374 1.04338e+07 contract inside 214 376 1.04338e+07 contract outside 215 378 1.04338e+07 contract inside 216 380 1.04338e+07 contract inside 217 382 1.04338e+07 contract outside 218 384 1.04338e+07 contract inside 219 385 1.04338e+07 reflect 220 387 1.04338e+07 contract inside 221 389 1.04338e+07 contract outside 222 391 1.04338e+07 contract outside 223 393 1.04338e+07 contract inside 224 395 1.04338e+07 contract outside 225 397 1.04338e+07 contract inside 226 398 1.04338e+07 reflect 227 400 1.04338e+07 contract inside 228 402 1.04338e+07 contract inside 229 404 1.04338e+07 contract outside Optimization terminated: the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-04 and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-04
x = 1×3
111.0799 29.1041 1.7976
f(x)
ans = 1.0434e+07
lhs = fun(x)
lhs = 160491×1
2.9934 3.3399 3.1968 3.2387 3.2808 3.3120 3.3416 3.3916 3.4217 3.4499

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