24小时热门版块排行榜

返回列表

bella_虫虫

新虫 (小有名气)

应助: 0 (幼儿园)
金币: 389.8
帖子: 59
在线: 14.7小时
虫号: 2013381
注册: 2012-09-19
专业: 无机非金属基复合材料

[求助] MATLAB或者1stOpt自定义公式曲线拟合已有1人参与

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

回复此楼

» 猜你喜欢

深圳大学2026年秋博士招生-物理学-活性胶体方向-高永祥课题组已经有18人回复
论物质与能量的统一模型及物理现象解释已经有0人回复
物理学I论文润色/翻译怎么收费? 已经有115人回复
基于基元I统一理论的数学相关应用推导已经有0人回复
基元I统一理论：宇宙本质、层级演化与修炼文明的本源规律已经有1人回复
基元I理论下三大核心空间现象精准推导与细节解析已经有0人回复
基于基元 I 统一理论的反重力理论推导已经有0人回复
基于基元I统一理论的量子力学本源推导已经有1人回复
推荐一款可以AI辅助写作的Latex编辑器SmartLatexEditor，超级好用，AI润色，全免费已经有20人回复
【EI|Scopus 双检索】第六届智能机器人系统国际会议（ISoIRS 2026）已经有0人回复
2026年第四届电动车与车辆工程国际会议（CEVVE 2026）已经有0人回复

1楼 2018-10-22 17:07:50

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

独孤神宇

版主 (知名作家)

应助: 490 (硕士)
贵宾: 0.008
金币: 31016.3
散金: 802
红花: 122
沙发: 1
帖子: 5600
在线: 856.5小时
虫号: 3522474
注册: 2014-11-06
性别: GG
专业: 机械动力学
管辖: 计算模拟

【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

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