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[求助]
MATLAB或者1stOpt自定义公式曲线拟合 已有1人参与
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自定义公式是y^2-1=A*x^2/(x^2-B^2)+C*x^2/(x^2-D^2) 其中x是波长，y是折射率。求参数A,B,C,D.万分感谢！数据如下： x y 0.4 1.76854 0.401 1.76835 0.402 1.76817 0.403 1.768 0.404 1.76782 0.405 1.76764 0.406 1.76747 0.407 1.7673 0.408 1.76713 0.409 1.76696 0.41 1.76679 0.411 1.76662 0.412 1.76646 0.413 1.76629 0.414 1.76613 0.415 1.76597 0.416 1.76581 0.417 1.76565 0.418 1.76549 0.419 1.76533 0.42 1.76518 0.421 1.76502 0.422 1.76487 0.423 1.76472 0.424 1.76457 0.425 1.76442 0.426 1.76427 0.427 1.76412 0.428 1.76398 0.429 1.76383 0.43 1.76369 0.431 1.76355 0.432 1.76341 0.433 1.76327 0.434 1.76313 0.435 1.76299 0.436 1.76285 0.437 1.76272 0.438 1.76258 0.439 1.76245 0.44 1.76232 0.441 1.76218 0.442 1.76205 0.443 1.76192 0.444 1.76179 0.445 1.76167 0.446 1.76154 0.447 1.76141 0.448 1.76129 0.449 1.76116 0.45 1.76104 0.451 1.76092 0.452 1.7608 0.453 1.76068 0.454 1.76056 0.455 1.76044 0.456 1.76032 0.457 1.7602 0.458 1.76009 0.459 1.75997 0.46 1.75986 0.461 1.75974 0.462 1.75963 0.463 1.75952 0.464 1.75941 0.465 1.7593 0.466 1.75919 0.467 1.75908 0.468 1.75897 0.469 1.75886 0.47 1.75875 0.471 1.75865 0.472 1.75854 0.473 1.75844 0.474 1.75833 0.475 1.75823 0.476 1.75813 0.477 1.75803 0.478 1.75793 0.479 1.75783 0.48 1.75773 0.481 1.75763 0.482 1.75753 0.483 1.75743 0.484 1.75733 0.485 1.75724 0.486 1.75714 0.487 1.75705 0.488 1.75695 0.489 1.75686 0.49 1.75677 0.491 1.75667 0.492 1.75658 0.493 1.75649 0.494 1.7564 0.495 1.75631 0.496 1.75622 0.497 1.75613 0.498 1.75604 0.499 1.75596 0.5 1.75587 0.501 1.75578 0.502 1.7557 0.503 1.75561 0.504 1.75553 0.505 1.75544 0.506 1.75536 0.507 1.75528 0.508 1.75519 0.509 1.75511 0.51 1.75503 0.511 1.75495 0.512 1.75487 0.513 1.75479 0.514 1.75471 0.515 1.75463 0.516 1.75455 0.517 1.75447 0.518 1.75439 0.519 1.75432 0.52 1.75424 0.521 1.75416 0.522 1.75409 0.523 1.75401 0.524 1.75394 0.525 1.75386 0.526 1.75379 0.527 1.75372 0.528 1.75364 0.529 1.75357 0.53 1.7535 0.531 1.75343 0.532 1.75336 0.533 1.75329 0.534 1.75321 0.535 1.75315 0.536 1.75307 0.537 1.75301 0.538 1.75294 0.539 1.75287 0.54 1.7528 0.541 1.75273 0.542 1.75267 0.543 1.7526 0.544 1.75253 0.545 1.75247 0.546 1.7524 0.547 1.75234 0.548 1.75227 0.549 1.75221 0.55 1.75215 0.551 1.75208 0.552 1.75202 0.553 1.75196 0.554 1.75189 0.555 1.75183 0.556 1.75177 0.557 1.75171 0.558 1.75165 0.559 1.75159 0.56 1.75153 0.561 1.75147 0.562 1.75141 0.563 1.75135 0.564 1.75129 0.565 1.75123 0.566 1.75117 0.567 1.75111 0.568 1.75106 0.569 1.751 0.57 1.75094 0.571 1.75088 0.572 1.75083 0.573 1.75077 0.574 1.75072 0.575 1.75066 0.576 1.75061 0.577 1.75055 0.578 1.7505 0.579 1.75044 0.58 1.75039 0.581 1.75034 0.582 1.75028 0.583 1.75023 0.584 1.75018 0.585 1.75012 0.586 1.75007 0.587 1.75002 0.588 1.74997 0.589 1.74992 0.59 1.74987 0.591 1.74981 0.592 1.74977 0.593 1.74971 0.594 1.74966 0.595 1.74961 0.596 1.74957 0.597 1.74952 0.598 1.74947 0.599 1.74942 0.6 1.74937 0.601 1.74932 0.602 1.74927 0.603 1.74923 0.604 1.74918 0.605 1.74913 0.606 1.74909 0.607 1.74904 0.608 1.74899 0.609 1.74895 0.61 1.7489 0.611 1.74886 0.612 1.74881 0.613 1.74877 0.614 1.74872 0.615 1.74868 0.616 1.74863 0.617 1.74859 0.618 1.74854 0.619 1.7485 0.62 1.74845 0.621 1.74841 0.622 1.74837 0.623 1.74833 0.624 1.74828 0.625 1.74824 0.626 1.7482 0.627 1.74816 0.628 1.74811 0.629 1.74807 0.63 1.74803 0.631 1.74799 0.632 1.74795 0.633 1.74791 0.634 1.74787 0.635 1.74783 0.636 1.74779 0.637 1.74775 0.638 1.74771 0.639 1.74767 0.64 1.74763 0.641 1.74759 0.642 1.74755 0.643 1.74751 0.644 1.74747 0.645 1.74743 0.646 1.7474 0.647 1.74736 0.648 1.74732 0.649 1.74728 0.65 1.74725 0.651 1.74721 0.652 1.74717 0.653 1.74714 0.654 1.7471 0.655 1.74706 0.656 1.74703 0.657 1.74699 0.658 1.74695 0.659 1.74692 0.66 1.74688 0.661 1.74685 0.662 1.74681 0.663 1.74678 0.664 1.74674 0.665 1.74671 0.666 1.74667 0.667 1.74664 0.668 1.7466 0.669 1.74657 0.67 1.74653 0.671 1.7465 0.672 1.74647 0.673 1.74643 0.674 1.7464 0.675 1.74637 0.676 1.74633 0.677 1.7463 0.678 1.74627 0.679 1.74623 0.68 1.7462 0.681 1.74617 0.682 1.74614 0.683 1.74611 0.684 1.74607 0.685 1.74604 0.686 1.74601 0.687 1.74598 0.688 1.74595 0.689 1.74592 0.69 1.74588 0.691 1.74585 0.692 1.74582 0.693 1.74579 0.694 1.74576 0.695 1.74573 0.696 1.7457 0.697 1.74567 0.698 1.74564 0.699 1.74561 0.7 1.74558 0.701 1.74555 0.702 1.74552 0.703 1.74549 0.704 1.74547 0.705 1.74544 0.706 1.74541 0.707 1.74538 0.708 1.74535 0.709 1.74532 0.71 1.74529 0.711 1.74526 0.712 1.74524 0.713 1.74521 0.714 1.74518 0.715 1.74515 0.716 1.74513 0.717 1.7451 0.718 1.74507 0.719 1.74504 0.72 1.74502 0.721 1.74499 0.722 1.74496 0.723 1.74493 0.724 1.74491 0.725 1.74488 0.726 1.74486 0.727 1.74483 0.728 1.7448 0.729 1.74478 0.73 1.74475 0.731 1.74472 0.732 1.7447 0.733 1.74467 0.734 1.74465 0.735 1.74462 0.736 1.7446 0.737 1.74457 0.738 1.74455 0.739 1.74452 0.74 1.7445 0.741 1.74447 0.742 1.74445 0.743 1.74442 0.744 1.7444 0.745 1.74437 0.746 1.74435 0.747 1.74433 0.748 1.7443 0.749 1.74428 0.75 1.74425 0.751 1.74423 0.752 1.74421 0.753 1.74418 0.754 1.74416 0.755 1.74414 0.756 1.74411 0.757 1.74409 0.758 1.74407 0.759 1.74404 0.76 1.74402 0.761 1.744 0.762 1.74398 0.763 1.74395 0.764 1.74393 0.765 1.74391 0.766 1.74389 0.767 1.74386 0.768 1.74384 0.769 1.74382 0.77 1.7438 0.771 1.74377 0.772 1.74375 0.773 1.74373 0.774 1.74371 0.775 1.74369 0.776 1.74367 0.777 1.74364 0.778 1.74362 0.779 1.7436 0.78 1.74358 0.781 1.74356 0.782 1.74354 0.783 1.74352 0.784 1.7435 0.785 1.74348 0.786 1.74346 0.787 1.74344 0.788 1.74342 0.789 1.7434 0.79 1.74337 0.791 1.74335 0.792 1.74333 0.793 1.74331 0.794 1.74329 0.795 1.74327 0.796 1.74326 0.797 1.74323 0.798 1.74322 0.799 1.7432 0.8 1.74318 0.801 1.74316 0.802 1.74314 0.803 1.74312 0.804 1.7431 0.805 1.74308 0.806 1.74306 0.807 1.74304 0.808 1.74302 0.809 1.743 0.81 1.74299 0.811 1.74297 0.812 1.74295 0.813 1.74293 0.814 1.74291 0.815 1.74289 0.816 1.74287 0.817 1.74286 0.818 1.74284 0.819 1.74282 0.82 1.7428 0.821 1.74278 0.822 1.74276 0.823 1.74275 0.824 1.74273 0.825 1.74271 0.826 1.74269 0.827 1.74268 0.828 1.74266 0.829 1.74264 0.83 1.74262 0.831 1.74261 0.832 1.74259 0.833 1.74257 0.834 1.74255 0.835 1.74254 0.836 1.74252 0.837 1.7425 0.838 1.74249 0.839 1.74247 0.84 1.74245 0.841 1.74244 0.842 1.74242 0.843 1.7424 0.844 1.74239 0.845 1.74237 0.846 1.74235 0.847 1.74234 0.848 1.74232 0.849 1.74231 0.85 1.74229 0.851 1.74227 0.852 1.74226 0.853 1.74224 0.854 1.74222 0.855 1.74221 0.856 1.74219 0.857 1.74218 0.858 1.74216 0.859 1.74215 0.86 1.74213 0.861 1.74212 0.862 1.7421 0.863 1.74208 0.864 1.74207 0.865 1.74205 0.866 1.74204 0.867 1.74202 0.868 1.74201 0.869 1.74199 0.87 1.74198 0.871 1.74196 0.872 1.74195 0.873 1.74193 0.874 1.74192 0.875 1.7419 0.876 1.74189 0.877 1.74187 0.878 1.74186 0.879 1.74185 0.88 1.74183 0.881 1.74182 0.882 1.7418 0.883 1.74179 0.884 1.74177 0.885 1.74176 0.886 1.74174 0.887 1.74173 0.888 1.74172 0.889 1.7417 0.89 1.74169 0.891 1.74167 0.892 1.74166 0.893 1.74165 0.894 1.74163 0.895 1.74162 0.896 1.7416 0.897 1.74159 0.898 1.74158 0.899 1.74156 0.9 1.74155 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独孤神宇
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【答案】应助回帖
★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★
感谢参与，应助指数 +1
bella_虫虫: 金币+20, ★★★很有帮助, 大神，有拟合后的数据吗？我还需要画出拟合曲线。谢谢！ 2018-10-23 09:30:04
感谢参与，应助指数 +1
bella_虫虫: 金币+20, ★★★很有帮助, 大神，有拟合后的数据吗？我还需要画出拟合曲线。谢谢！ 2018-10-23 09:30:04
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结果不唯一，模型和数据匹配度太高了，如果是实验数据，感觉就有点假了，。 模型公式: y = sqrt(a*x^2/(x^2-b^2)+c*x^2/(x^2-d^2)+1) y = sqrt((-1.18379266454923)*x^2/(x^2-18.1057685843^2)+2.00785118048099*x^2/(x^2-0.0945636570305277^2)+1) 迭代数: 515 计算用时(时:分:秒:微秒): 00:00:08:244 优化算法: 标准简面体爬山法 + 通用全局优化算法(SM1) 计算结束原因: 达到收敛判断标准 均方差(RMSE): 3.2249045091751E-5 残差平方和(SSR): 5.21040455574223E-7 相关系数(R): 0.999989750571742 相关系数之平方(R^2): 0.999979501248535 修正R平方(Adj. R^2): 0.999979418924232 确定系数(DC): 0.999979501177371 卡方系数(Chi-Square): 1.48486804223232E-7 F统计(F-Statistic): 8081713.58220345 参数 最佳估算 ---------- ------------- a -1.18379266454923 b 18.1057685843 c 2.00785118048099 d 0.0945636570305277 ********************** 迭代数: 727 计算用时(时:分:秒:微秒): 00:00:09:450 优化算法: 标准简面体爬山法 + 通用全局优化算法(SM1) 计算结束原因: 达到收敛判断标准 均方差(RMSE): 3.22347590799856E-5 残差平方和(SSR): 5.20578926165303E-7 相关系数(R): 0.999989759928103 相关系数之平方(R^2): 0.999979519961065 修正R平方(Adj. R^2): 0.999979437711913 确定系数(DC): 0.999979519334905 卡方系数(Chi-Square): 1.48357855659539E-7 F统计(F-Statistic): 8089167.49117066 参数 最佳估算 ---------- ------------- a 2.00784753166354 b 0.094565365438321 c -1.88301602220581 d 22.8151229510075 |
2楼2018-10-22 19:26:16
独孤神宇
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3楼2018-10-23 10:17:52
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