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hudie012荣誉版主 (文坛精英)
小兔爱吃萝卜
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[求助]
matlab数据拟合问题求助
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已知一组数据y，x。根据这组数据要拟合一个公式，确定其中的参数，拟合公式的形式为：y=A*x^n，其中A，n是要拟合的参数。 没有接触过matlab，所以也不懂咋弄，有没有帮忙拟合一下，写一下程序。[ Last edited by hudie012 on 2012-9-6 at 15:04 ] |
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2012-09-06 15:04:09, 27.62 K
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2楼2012-09-06 10:50:05
【答案】应助回帖
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感谢参与，应助指数 +1
csgt0: 金币+1, 多谢应助 2012-09-06 13:20:48
hudie012: 金币+5 2012-09-10 17:38:40
感谢参与，应助指数 +1
csgt0: 金币+1, 多谢应助 2012-09-06 13:20:48
hudie012: 金币+5 2012-09-10 17:38:40
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Sample TextSample Text 这个其实并不难，在研一的课上会学数值分析方法，看上去这是一个非线性函数的拟合，其实可以通过对左右取自然对数将其转化为线性函数的拟合。取对数得到：ln(y)=n*ln(a*x)=n*（ln(a)+ln(x)）=n*ln(a)+n*ln(x)这样就可以把原来的式子化为拟合数据y=a*x+b 方法如下：x1=log(x); y1=log(y)； m=ployfit(x1,y1,1) 然后会出现两个数（这里写成m1,m2)，则式子就是ln(y)=m1*ln(x)+m2 所以n=m1,n*ln(a)=m2. |
3楼2012-09-06 11:36:29
4楼2012-09-06 16:26:11
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代码如下！ 结果在图上 function F=hu(x,xdata) %x=[] A=x(1); n=x(2); x=xdata; y=A.*x.^n; F=[y]; end data=[19.409 1.9918 19.548 2.0058 19.657 2.0168 19.768 2.0273 19.88 2.0393 20.005 2.0518 20.11 2.0613 20.215 2.0723 20.341 2.0843 20.455 2.0953 20.565 2.1058 20.676 2.1173 20.803 2.1303 20.933 2.1438 21.044 2.1548 21.141 2.1663 21.252 2.1778 21.353 2.1888 21.454 2.1983 21.556 2.2103 21.665 2.2233 21.759 2.2333 21.862 2.2438 21.971 2.2538 22.077 2.2658 22.173 2.2768 22.29 2.2913 22.375 2.3003 22.46 2.3083 22.554 2.3208 22.639 2.3303 22.723 2.3388 22.811 2.3488 22.915 2.3608 23.01 2.3713 23.103 2.3838 23.197 2.3943 23.303 2.4063 23.408 2.4178 23.497 2.4278 23.602 2.4398 23.691 2.4498 23.777 2.4603 23.878 2.4728 23.984 2.4848 24.091 2.4978 24.187 2.5083 24.298 2.5208 24.383 2.5318 24.465 2.5413 24.567 2.5538 24.66 2.5643 24.747 2.5758 24.847 2.5878 24.945 2.5993 25.032 2.6108 25.125 2.6218 25.216 2.6333 25.294 2.6438 25.389 2.6563 25.47 2.6658 25.563 2.6778 25.644 2.6883 25.742 2.7003 25.822 2.7103 25.904 2.7213 25.991 2.7333 26.072 2.7443 26.156 2.7548 26.246 2.7663 26.336 2.7763 26.424 2.7878 26.513 2.7998 26.6 2.8113 26.681 2.8218 26.769 2.8338 26.85 2.8453 26.93 2.8558 27.015 2.8678 27.096 2.8788 27.183 2.8913 27.26 2.9023 27.343 2.9138 27.417 2.9248 27.497 2.9363 27.571 2.9468 27.654 2.9598 27.722 2.9688 27.802 2.9808 27.878 2.9913 27.952 3.0018 28.03 3.0133 28.108 3.0258 28.176 3.0358 28.252 3.0478 28.318 3.0578 28.388 3.0683 28.456 3.0783 28.537 3.0908 28.606 3.1023 28.674 3.1123 28.763 3.1268 28.836 3.1378 28.905 3.1483 28.974 3.1593 29.047 3.1708 29.114 3.1813 29.178 3.1918 29.245 3.2028 29.302 3.2123 29.366 3.2223 29.433 3.2338 29.51 3.2463 29.57 3.2568 29.628 3.2663 29.695 3.2773 29.752 3.2863 29.818 3.2973 29.88 3.3078 29.937 3.3183 30.005 3.3308 30.07 3.3413 30.136 3.3528 30.195 3.3628 30.257 3.3738 30.32 3.3843 30.379 3.3948 30.439 3.4058 30.498 3.4173 30.559 3.4263 30.614 3.4368 30.677 3.4493 30.732 3.4593 30.792 3.4703 30.851 3.4813 30.911 3.4928 30.971 3.5038 31.031 3.5153 31.092 3.5268 31.146 3.5373 31.203 3.5483 31.259 3.5588 31.314 3.5693 31.37 3.5808 31.425 3.5913 31.485 3.6028 31.542 3.6143 31.593 3.6243 31.649 3.6353 31.698 3.6458 31.754 3.6568 31.811 3.6688 31.862 3.6788 31.916 3.6898 31.965 3.7003 32.014 3.7103 32.069 3.7213 32.116 3.7313 32.168 3.7423 32.22 3.7533 32.275 3.7648 32.326 3.7758 32.378 3.7868 32.425 3.7978 32.47 3.8073 32.518 3.8178 32.57 3.8288 32.615 3.8393 32.666 3.8508 32.716 3.8613 32.765 3.8728 32.813 3.8838 32.859 3.8938 32.909 3.9058 32.958 3.9168 33.005 3.9278 33.054 3.9388 33.101 3.9503 33.141 3.9593 33.189 3.9703 33.235 3.9813 33.278 3.9918 33.324 4.0033 33.369 4.0143 33.417 4.0258 33.458 4.0353 33.5 4.0453 33.543 4.0553 33.586 4.0668 33.629 4.0773 33.673 4.0888 33.716 4.0998 33.758 4.1108 33.806 4.1228 33.851 4.1338 33.891 4.1443 33.931 4.1543 33.97 4.1648 34.008 4.1748 34.052 4.1858 34.094 4.1978 34.133 4.2083 34.175 4.2193 34.217 4.2308 34.254 4.2408 34.294 4.2498 34.334 4.2613 34.374 4.2733 34.409 4.2838 34.446 4.2933 34.483 4.3033 34.52 4.3128 34.559 4.3243 34.597 4.3348 34.635 4.3458 34.672 4.3568 34.71 4.3673 34.745 4.3768 34.781 4.3888 34.818 4.3983 34.854 4.4093 34.889 4.4193 34.924 4.4293 34.962 4.4413 34.996 4.4533 35.03 4.4633 35.064 4.4723 35.097 4.4823 35.13 4.4928 35.166 4.5038 35.202 4.5148 35.237 4.5268 35.271 4.5368 35.305 4.5478 35.34 4.5588 35.371 4.5683 35.403 4.5783 35.437 4.5898 35.47 4.6003 35.502 4.6103 35.533 4.6203 35.564 4.6308 35.595 4.6413 35.627 4.6518 35.66 4.6623 35.692 4.6733 35.721 4.6828 35.756 4.6948 35.786 4.7053 35.817 4.7153 35.846 4.7258 35.877 4.7363 35.907 4.7468 35.936 4.7568 35.967 4.7678 35.996 4.7778 36.026 4.7883 36.055 4.7983 36.083 4.8098 36.111 4.8198 36.142 4.8308 36.17 4.8413 36.198 4.8513 36.226 4.8618 36.255 4.8723 36.282 4.8823 36.312 4.8938 36.341 4.9048 36.369 4.9148 36.397 4.9258 36.422 4.9358 36.45 4.9458 36.476 4.9558 36.503 4.9663 36.528 4.9768 36.556 4.9873 36.583 4.9978 36.61 5.0083 36.637 5.0188 36.664 5.0298 36.687 5.0388 36.713 5.0498 36.737 5.0598 36.764 5.0703 36.791 5.0813 36.815 5.0918 36.841 5.1023 36.867 5.1138 36.891 5.1243 36.916 5.1348 36.94 5.1448 36.965 5.1553 36.989 5.1668 37.012 5.1768 37.037 5.1873 37.06 5.1973 37.083 5.2073 37.105 5.2178 37.129 5.2278 37.151 5.2378 37.174 5.2478 37.196 5.2578 37.218 5.2678 37.239 5.2783 37.261 5.2873 37.284 5.2983 37.307 5.3108 37.329 5.3208 37.35 5.3308 37.371 5.3403 37.391 5.3508 37.413 5.3603 37.435 5.3713 37.456 5.3813 37.477 5.3918 37.497 5.4018 37.519 5.4123 37.539 5.4218 37.559 5.4323 37.581 5.4433 37.601 5.4533 37.622 5.4638 37.643 5.4763 37.663 5.4863 37.682 5.4963 37.702 5.5068 37.722 5.5168 37.741 5.5268 37.76 5.5363 37.78 5.5473 37.799 5.5568 37.818 5.5678 37.838 5.5788 37.855 5.5878 37.873 5.5978 37.892 5.6078 37.911 5.6178 37.929 5.6278 37.948 5.6383 37.966 5.6483 37.984 5.6593 38.001 5.6693 38.019 5.6793 38.037 5.6893 38.055 5.6993 38.072 5.7093 38.089 5.7188 38.106 5.7308 38.124 5.7413 38.141 5.7508 38.159 5.7613 38.176 5.7718 38.193 5.7818 38.21 5.7918 38.226 5.8018 38.242 5.8133 38.26 5.8218 38.278 5.8323 38.294 5.8428 38.311 5.8533 38.327 5.8633 38.344 5.8743 38.36 5.8858 38.376 5.8958 38.393 5.9068 38.407 5.9163 38.424 5.9268 38.439 5.9388 38.455 5.9498 38.471 5.9608 38.487 5.9713 38.502 5.9818 38.518 5.9923 38.532 6.0033 38.547 6.0133 38.562 6.0248 38.578 6.0353 38.593 6.0463 38.607 6.0568 38.622 6.0688 38.636 6.0788 38.651 6.0893 38.665 6.0993 38.68 6.1113 38.694 6.1208 38.708 6.1318 38.721 6.1418 38.735 6.1528 38.748 6.1628 38.762 6.1728 38.776 6.1838 38.789 6.1938 38.803 6.2048 38.816 6.2163 38.831 6.2283 38.844 6.2388 38.857 6.2488 38.87 6.2598 38.883 6.2703 38.897 6.2818 38.91 6.2928 38.923 6.3033 38.935 6.3138 38.947 6.3243 38.96 6.3343 38.972 6.3458 38.985 6.3568 38.997 6.3673 39.009 6.3773 39.021 6.3888 39.033 6.3988 39.045 6.4093 39.057 6.4193 39.068 6.4313 39.08 6.4413 39.091 6.4513 39.102 6.4613 39.114 6.4728 39.125 6.4828 39.136 6.4933 39.147 6.5033 39.158 6.5143 39.169 6.5258 39.18 6.5353 39.191 6.5418 39.202 6.5523 39.212 6.5633 39.222 6.5728 39.233 6.5838 39.244 6.5943 39.254 6.6043 39.265 6.6158 39.275 6.6248 39.285 6.6353 39.295 6.6453 39.306 6.6573 39.316 6.6673 39.326 6.6773 39.336 6.6888 39.346 6.6993 39.355 6.7098 39.365 6.7208 39.375 6.7308 39.384 6.7408 39.394 6.7518 39.403 6.7623 39.413 6.7733 39.422 6.7833 39.432 6.7948 39.442 6.8053 39.451 6.8158 39.46 6.8258 39.469 6.8373 39.478 6.8473 39.486 6.8568 39.496 6.8673 39.504 6.8788 39.513 6.8888 39.521 6.8983 39.53 6.9088 39.538 6.9193 39.546 6.9288 39.554 6.9403 39.563 6.9513 39.572 6.9613 39.58 6.9718 39.588 6.9813 39.596 6.9928 39.604 7.0023 39.612 7.0128 39.62 7.0228 39.628 7.0348 39.636 7.0448 39.643 7.0543 39.651 7.0658 39.659 7.0758 39.666 7.0863 39.674 7.0963 39.682 7.1083 39.689 7.1183 39.697 7.1288 39.704 7.1398 39.711 7.1473 39.718 7.1573 39.726 7.1678 39.733 7.1793 39.74 7.1888 39.746 7.1988 39.754 7.2103 39.761 7.2203 39.767 7.2303 39.774 7.2408 39.781 7.2518 39.787 7.2618 39.794 7.2718 39.801 7.2833 39.807 7.2933 39.814 7.3033 39.82 7.3143 39.826 7.3238 39.833 7.3353 39.839 7.3448 39.845 7.3553 39.851 7.3663 39.857 7.3763 39.863 7.3858 39.869 7.3968 39.875 7.4068 39.881 7.4163 39.886 7.4268 39.892 7.4368 39.898 7.4468 39.904 7.4568 39.909 7.4683 39.915 7.4778 39.921 7.4893 39.926 7.4988 39.931 7.5088 39.937 7.5193 39.942 7.5298 39.948 7.5413 39.953 7.5513 39.958 7.5613 39.964 7.5718 39.969 7.5818 39.974 7.5928 39.979 7.6038 39.984 7.6148 39.99 7.6248 39.995 7.6353 39.999 7.6458 40.004 7.6563 40.009 7.6668 40.014 7.6763 40.019 7.6878 40.023 7.6978 40.028 7.7093 40.033 7.7188 40.037 7.7293 40.042 7.7398 40.046 7.7493 40.051 7.7603 40.055 7.7703 40.059 7.7808 40.064 7.7913 40.068 7.8023 40.072 7.8118 40.076 7.8223 40.08 7.8328 40.085 7.8433 40.089 7.8538 40.093 7.8643 40.097 7.8748 40.101 7.8848 40.105 7.8943 40.109 7.9048 40.113 7.9148 40.117 7.9258 40.121 7.9373 40.124 7.9468 40.128 7.9563 40.132 7.9673 40.135 7.9768 40.139 7.9878 40.143 7.9978 40.147 8.0088 40.15 8.0188 40.154 8.0298 40.157 8.0398 40.16 8.0503 40.164 8.0603 40.167 8.0708 40.17 8.0808 40.174 8.0913 40.177 8.1023 40.18 8.1133 40.184 8.1238 40.187 8.1333 40.19 8.1443 40.193 8.1548 40.196 8.1653 40.199 8.1758 40.202 8.1848 40.205 8.1958 40.208 8.2058 40.211 8.2168 40.214 8.2273 40.217 8.2368 40.22 8.2478 40.223 8.2578 40.225 8.2678 40.228 8.2778 40.231 8.2888 40.234 8.2998 40.236 8.3098 40.239 8.3203 40.242 8.3298 40.244 8.3403 40.247 8.3503 40.249 8.3608 40.252 8.3708 40.254 8.3813 40.257 8.3923 40.259 8.4023 40.262 8.4123 40.264 8.4228 40.266 8.4343 40.269 8.4438 40.271 8.4543 40.273 8.4648 40.276 8.4743 40.278 8.4848 40.28 8.4948 40.282 8.5053 40.285 8.5158 40.287 8.5268 40.289 8.5363 40.291 8.5468 40.293 8.5573 40.295 8.5673 40.297 8.5773 40.299 8.5878 40.301 8.5983 40.303 8.6088 40.305 8.6198 40.307 8.6293 40.309 8.6398 40.311 8.6498 40.313 8.6603 40.314 8.6713 40.316 8.6808 40.318 8.6913 40.32 8.7013 40.322 8.7118 40.323 8.7218 40.325 8.7318 40.327 8.7423 40.328 8.7528 40.33 8.7623 40.331 8.7728 40.333 8.7833 40.335 8.7923 40.336 8.8033 40.338 8.8133 40.339 8.8243 40.341 8.8348 40.342 8.8458 40.344 8.8553 40.345 8.8653 40.347 8.8758 40.348 8.8868 40.35 8.8968 40.351 8.9073 40.352 8.9178 40.354 8.9283 40.355 8.9388 40.356 8.9498 40.358 8.9598 40.359 8.9703 40.36 8.9808 40.361 8.9913 40.363 9.0013 40.364 9.0113 40.365 9.0218 40.366 9.0318 40.367 9.0423 40.368 9.0528 40.37 9.0633 40.371 9.0733 40.372 9.0833 40.373 9.0938 40.374 9.1043 40.375 9.1143 40.376 9.1253 40.377 9.1353 40.378 9.1458 40.379 9.1563 40.38 9.1663 40.381 9.1763 40.382 9.1863 40.383 9.1973 40.384 9.2073 40.385 9.2188 40.386 9.2288 40.387 9.2388 40.387 9.2493 40.388 9.2593 40.389 9.2698 40.39 9.2808 40.391 9.2913 40.392 9.3018 40.392 9.3118 40.393 9.3218 40.394 9.3328 40.395 9.3433 40.396 9.3533 40.396 9.3638 40.397 9.3743 40.398 9.3853 40.398 9.3953 40.399 9.4053 40.4 9.4158 40.4 9.4263 40.401 9.4368 40.402 9.4468 40.402 9.4568 40.403 9.4678 40.404 9.4778 40.404 9.4883 40.405 9.4983 40.405 9.5093 40.406 9.5198 40.407 9.5303 40.407 9.5398 40.408 9.5498 40.408 9.5598 40.409 9.5703 40.409 9.5803 40.41 9.5913 40.41 9.6018 40.411 9.6118 40.411 9.6218 40.412 9.6323 40.412 9.6423 40.413 9.6523 40.413 9.6623 40.414 9.6733 40.414 9.6833 40.414 9.6933 40.415 9.7033 40.415 9.7143 40.416 9.7248 40.416 9.7348 40.417 9.7453 40.417 9.7453 40.417 9.7668 40.418 9.7763 40.418 9.7763 40.418 9.7968 40.419 9.8068 40.419 9.8178 40.419 9.8283 40.42 9.8383 40.42 9.8383 40.42 9.8578 40.421 9.8688 40.421 9.8688 40.421 9.8888 40.421 9.8988 40.422 9.9098 40.422 9.9198 40.422 9.9298 40.423 9.9403 40.423 9.9403 40.423 9.9603 40.423 9.9703 40.424 9.9808 40.424 9.9808 40.424 9.9808 40.424 10.0108 40.424 10.0208 40.425 10.0313 40.425 10.0313 40.425 10.0523 40.425 10.0628 40.425 10.0733 40.426 10.0833 40.426 10.0833 40.426 10.1038 40.426 10.1138 40.426 10.1243 40.427 10.1348 40.427 10.1348 40.427 10.1348 40.427 10.1348 40.427 10.1758 40.427 10.1868 40.427 10.1973 40.428 10.2083 40.428 10.2083 40.428 10.2083 40.428 10.2083 40.428 10.2488 40.428 10.2593 40.428 10.2698 40.428 10.2798 40.429 10.2898 40.429 10.2898 40.429 10.2898 40.429 10.2898 40.429 10.2898 40.429 10.3423 40.429 10.3523 40.429 10.3633 40.429 10.3733 40.429 10.3833 40.429 10.3933 40.43 10.4038 40.43 10.4038 40.43 10.4038 40.43 10.4038 40.43 10.4038 40.43 10.4038 40.43 10.4663 40.43 10.4763 40.43 10.4868 40.43 10.4968 40.43 10.5048 40.43 10.5153 40.43 10.5258 40.43 10.5358 40.43 10.5468 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.5568 40.431 10.6983 40.431 10.7083 40.431 10.7183 40.431 10.7293 40.431 10.7413 40.431 10.7523 40.431 10.7648 40.431 10.7753 40.431 10.7858 40.431 10.7968 40.431 10.8083 40.431 10.8198 40.431 10.8323 40.431 10.8448 40.431 10.8548 40.431 10.8648 40.431 10.8748 40.431 10.8853 40.431 10.8963 40.431 10.9083 40.431 10.9198 40.431 10.9333 40.431 10.9463 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 10.9603 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508 40.432 11.1508]; xdata=data(:,1); %Im ydata=data(:,2); % options= optimset('MaxFunEvals',5000,'Maxiter',1000); lb=[]; ub=[]; t=1; for i=1:1:11 x0(1) = -100 + 200*rand; x0(2) = -100 + 200*rand; [x(t,  ,resnorm(t)]=lsqcurvefit(@hu,x0,xdata,ydata,lb,ub,options);t=t+1; end m=find(resnorm==min(resnorm)); xm=x(m, y=hu(xm,xdata); plot(xdata,ydata,'.',xdata,y,'r')  _W]LNKVZJBL0MZQ4C6(PUHW.jpg |
5楼2012-09-10 11:03:18
hudie012
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6楼2012-09-10 17:40:34
xxz903
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7楼2012-09-10 18:01:07
|
我先按你的建了一个curvefun3.m的函数，然后打开curve11.m可以进行拟合，x0是初始的向量，可以改动，看看效果 我另外建了一个指数形式的拟合curve22，希望能帮到你，可以自己去修改，形式很简单  |
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8楼2015-07-11 15:59:29
