matlab 多项式拟合EXCEL中复杂数据
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有如下原始數(shù)據(jù)x,y,它對(duì)應(yīng)的曲線圖形為：
| -9552 | -2036.81 |
| -9328 | -2025.62 |
| -9168 | -2014.43 |
| -9024 | -2003.25 |
| -8928 | -1992.06 |
| -8800 | -1980.87 |
| -8688 | -1969.68 |
| -8592 | -1958.49 |
| -8496 | -1947.3 |
| -8416 | -1936.11 |
| -8336 | -1924.93 |
| -8240 | -1913.74 |
| -8112 | -1902.55 |
| -8016 | -1891.36 |
| -7920 | -1880.17 |
| -7824 | -1868.98 |
| -7744 | -1857.8 |
| -7648 | -1846.61 |
| -7552 | -1835.42 |
| -7472 | -1824.23 |
| -7392 | -1813.04 |
| -7328 | -1801.85 |
| -7248 | -1790.66 |
| -7136 | -1779.48 |
| -7072 | -1768.29 |
| -7008 | -1757.1 |
| -6944 | -1745.91 |
| -6896 | -1734.72 |
| -6848 | -1723.53 |
| -6752 | -1712.34 |
| -6688 | -1701.16 |
| -6592 | -1689.97 |
| -6512 | -1678.78 |
| -6400 | -1667.59 |
| -6288 | -1656.4 |
| -6192 | -1645.21 |
| -6096 | -1634.02 |
| -6016 | -1622.84 |
| -5920 | -1611.65 |
| -5840 | -1600.46 |
| -5744 | -1589.27 |
| -5664 | -1578.08 |
| -5568 | -1566.89 |
| -5504 | -1555.7 |
| -5440 | -1544.52 |
| -5360 | -1533.33 |
| -5280 | -1522.14 |
| -5168 | -1510.95 |
| -5088 | -1499.76 |
| -5024 | -1488.57 |
| -4960 | -1477.39 |
| -4896 | -1466.2 |
| -4848 | -1455.01 |
| -4800 | -1443.82 |
| -4720 | -1432.63 |
| -4656 | -1421.44 |
| -4592 | -1410.25 |
| -4512 | -1399.07 |
| -4448 | -1387.88 |
| -4400 | -1376.69 |
| -4336 | -1365.5 |
| -4304 | -1354.31 |
| -4272 | -1343.12 |
| -4208 | -1331.93 |
| -4144 | -1320.75 |
| -4096 | -1309.56 |
| -4048 | -1298.37 |
| -3984 | -1287.18 |
| -3952 | -1275.99 |
| -3888 | -1264.8 |
| -3824 | -1253.61 |
| -3776 | -1242.43 |
| -3712 | -1231.24 |
| -3680 | -1220.05 |
| -3632 | -1208.86 |
| -3584 | -1197.67 |
| -3504 | -1186.48 |
| -3456 | -1175.3 |
| -3408 | -1164.11 |
| -3360 | -1152.92 |
| -3328 | -1141.73 |
| -3296 | -1130.54 |
| -3264 | -1119.35 |
| -3200 | -1108.16 |
| -3152 | -1096.98 |
| -3120 | -1085.79 |
| -3072 | -1074.6 |
| -3024 | -1063.41 |
| -2992 | -1052.22 |
| -2928 | -1041.03 |
| -2880 | -1029.84 |
| -2832 | -1018.66 |
| -2816 | -1007.47 |
| -2768 | -996.279 |
| -2720 | -985.09 |
| -2688 | -973.902 |
| -2656 | -962.713 |
| -2624 | -951.525 |
| -2576 | -940.336 |
| -2544 | -929.148 |
| -2512 | -917.959 |
| -2480 | -906.77 |
| -2432 | -895.582 |
| -2416 | -884.393 |
| -2368 | -873.205 |
| -2336 | -862.016 |
| -2320 | -850.828 |
| -2272 | -839.639 |
| -2224 | -828.451 |
| -2192 | -817.262 |
| -2160 | -806.074 |
| -2144 | -794.885 |
| -2112 | -783.697 |
| -2080 | -772.508 |
| -2032 | -761.32 |
| -2000 | -750.131 |
| -1984 | -738.943 |
| -1952 | -727.754 |
| -1936 | -716.566 |
| -1904 | -705.377 |
| -1888 | -694.189 |
| -1856 | -683 |
| -1824 | -671.811 |
| -1792 | -660.623 |
| -1760 | -649.434 |
| -1744 | -638.246 |
| -1712 | -627.057 |
| -1696 | -615.869 |
| -1680 | -604.68 |
| -1648 | -593.492 |
| -1616 | -582.303 |
| -1584 | -571.115 |
| -1568 | -559.926 |
| -1552 | -548.738 |
| -1536 | -537.549 |
| -1504 | -526.361 |
| -1488 | -515.172 |
| -1472 | -503.984 |
| -1456 | -492.795 |
| -1440 | -481.607 |
| -1408 | -470.418 |
| -1392 | -459.23 |
| -1376 | -448.041 |
| -1344 | -436.852 |
| -1312 | -425.664 |
| -1296 | -414.475 |
| -1296 | -403.287 |
| -1248 | -392.098 |
| -1232 | -380.91 |
| -1216 | -369.721 |
| -1216 | -358.533 |
| -1184 | -347.344 |
| -1168 | -336.156 |
| -1136 | -324.967 |
| -1120 | -313.779 |
| -1104 | -302.59 |
| -1088 | -291.402 |
| -1072 | -280.213 |
| -1040 | -269.025 |
| -1024 | -257.836 |
| -1008 | -246.648 |
| -992 | -235.459 |
| -976 | -224.27 |
| -944 | -213.082 |
| -944 | -201.893 |
| -912 | -190.705 |
| -896 | -179.516 |
| -880 | -168.328 |
| -880 | -157.139 |
| -848 | -145.951 |
| -848 | -134.762 |
| -832 | -123.574 |
| -800 | -112.385 |
| -768 | -101.197 |
| -752 | -90.0082 |
| -752 | -78.8197 |
| -736 | -67.6311 |
| -704 | -56.4426 |
| -688 | -45.2541 |
| -656 | -34.0656 |
| -656 | -22.877 |
| -624 | -11.6885 |
| -608 | -0.5 |
| -608 | 10.68852 |
| -576 | 21.87705 |
| -560 | 33.06557 |
| -544 | 44.2541 |
| -528 | 55.44262 |
| -528 | 66.63115 |
| -496 | 77.81967 |
| -464 | 89.0082 |
| -448 | 100.1967 |
| -432 | 111.3852 |
| -416 | 122.5738 |
| -400 | 133.7623 |
| -384 | 144.9508 |
| -352 | 156.1393 |
| -336 | 167.3279 |
| -320 | 178.5164 |
| -304 | 189.7049 |
| -272 | 200.8934 |
| -256 | 212.082 |
| -240 | 223.2705 |
| -208 | 234.459 |
| -208 | 245.6475 |
| -192 | 256.8361 |
| -160 | 268.0246 |
| -128 | 279.2131 |
| -112 | 290.4016 |
| -96 | 301.5902 |
| -80 | 312.7787 |
| -48 | 323.9672 |
| -32 | 335.1557 |
| 0 | 346.3443 |
| 32 | 357.5328 |
| 48 | 368.7213 |
| 80 | 379.9098 |
| 112 | 391.0984 |
| 128 | 402.2869 |
| 144 | 413.4754 |
| 176 | 424.6639 |
| 192 | 435.8525 |
| 208 | 447.041 |
| 240 | 458.2295 |
| 272 | 469.418 |
| 288 | 480.6066 |
| 320 | 491.7951 |
| 336 | 502.9836 |
| 368 | 514.1721 |
| 400 | 525.3607 |
| 416 | 536.5492 |
| 448 | 547.7377 |
| 480 | 558.9262 |
| 512 | 570.1148 |
| 544 | 581.3033 |
| 576 | 592.4918 |
| 608 | 603.6803 |
| 640 | 614.8689 |
| 656 | 626.0574 |
| 688 | 637.2459 |
| 720 | 648.4344 |
| 752 | 659.623 |
| 784 | 670.8115 |
| 816 | 682 |
| 848 | 693.1885 |
| 880 | 704.377 |
| 912 | 715.5656 |
| 944 | 726.7541 |
| 976 | 737.9426 |
| 1008 | 749.1311 |
| 1056 | 760.3197 |
| 1088 | 771.5082 |
| 1104 | 782.6967 |
| 1152 | 793.8852 |
| 1184 | 805.0738 |
| 1216 | 816.2623 |
| 1248 | 827.4508 |
| 1280 | 838.6393 |
| 1312 | 849.8279 |
| 1344 | 861.0164 |
| 1392 | 872.2049 |
| 1424 | 883.3934 |
| 1472 | 894.582 |
| 1504 | 905.7705 |
| 1552 | 916.959 |
| 1584 | 928.1475 |
| 1632 | 939.3361 |
| 1680 | 950.5246 |
| 1728 | 961.7131 |
| 1776 | 972.9016 |
| 1824 | 984.0902 |
| 1856 | 995.2787 |
| 1904 | 1006.467 |
| 1952 | 1017.656 |
| 2000 | 1028.844 |
| 2048 | 1040.033 |
| 2096 | 1051.221 |
| 2128 | 1062.41 |
| 2176 | 1073.598 |
| 2224 | 1084.787 |
| 2288 | 1095.975 |
| 2320 | 1107.164 |
| 2384 | 1118.352 |
| 2432 | 1129.541 |
| 2480 | 1140.73 |
| 2544 | 1151.918 |
| 2576 | 1163.107 |
| 2640 | 1174.295 |
| 2704 | 1185.484 |
| 2752 | 1196.672 |
| 2800 | 1207.861 |
| 2864 | 1219.049 |
| 2912 | 1230.238 |
| 2960 | 1241.426 |
| 3008 | 1252.615 |
| 3072 | 1263.803 |
| 3136 | 1274.992 |
| 3200 | 1286.18 |
| 3264 | 1297.369 |
| 3328 | 1308.557 |
| 3392 | 1319.746 |
| 3440 | 1330.934 |
| 3520 | 1342.123 |
| 3584 | 1353.311 |
| 3648 | 1364.5 |
| 3712 | 1375.689 |
| 3776 | 1386.877 |
| 3856 | 1398.066 |
| 3920 | 1409.254 |
| 3984 | 1420.443 |
| 4032 | 1431.631 |
| 4128 | 1442.82 |
| 4192 | 1454.008 |
| 4272 | 1465.197 |
| 4320 | 1476.385 |
| 4400 | 1487.574 |
| 4464 | 1498.762 |
| 4544 | 1509.951 |
| 4608 | 1521.139 |
| 4704 | 1532.328 |
| 4752 | 1543.516 |
| 4832 | 1554.705 |
| 4896 | 1565.893 |
| 4960 | 1577.082 |
| 5040 | 1588.27 |
| 5120 | 1599.459 |
| 5184 | 1610.648 |
| 5264 | 1621.836 |
| 5328 | 1633.025 |
| 5392 | 1644.213 |
| 5472 | 1655.402 |
| 5520 | 1666.59 |
| 5616 | 1677.779 |
| 5696 | 1688.967 |
| 5776 | 1700.156 |
| 5840 | 1711.344 |
| 5904 | 1722.533 |
| 6000 | 1733.721 |
| 6064 | 1744.91 |
| 6144 | 1756.098 |
| 6208 | 1767.287 |
| 6272 | 1778.475 |
| 6352 | 1789.664 |
| 6400 | 1800.852 |
| 6480 | 1812.041 |
| 6528 | 1823.23 |
| 6592 | 1834.418 |
| 6672 | 1845.607 |
| 6736 | 1856.795 |
| 6800 | 1867.984 |
| 6864 | 1879.172 |
| 6928 | 1890.361 |
| 6992 | 1901.549 |
| 7040 | 1912.738 |
| 7104 | 1923.926 |
| 7152 | 1935.115 |
| 7184 | 1946.303 |
| 7248 | 1957.492 |
| 7280 | 1968.68 |
| 7328 | 1979.869 |
| 7376 | 1991.057 |
| 7408 | 2002.246 |
| 7456 | 2013.434 |
| 7488 | 2024.623 |
| 7536 | 2035.811 |
| 7568 | 2047 |
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如果想得到該曲線的函數(shù)表達(dá)式（多項(xiàng)式擬合的表達(dá)式），在Excel 自帶圖表工具中可以能過為曲線加趨勢(shì)線方式實(shí)現(xiàn)：
選擇多項(xiàng)式，調(diào)整階數(shù)讓擬合后在結(jié)果與原始曲線盡量重合，并勾選顯示公式：
EXCEL趨勢(shì)曲線多項(xiàng)式最高的階數(shù)是6階，但是實(shí)際效果與原始數(shù)據(jù)相差還是較大，看到是我們數(shù)據(jù)太復(fù)雜，EXCEL也無能為力了，這時(shí)也只能請(qǐng)出強(qiáng)大的matlab來解決，把上述原始數(shù)據(jù)保存于EXCEL中，并強(qiáng)excel文件（.xls/xlsx）保存于matlab工作目錄下，然后運(yùn)行如下代碼（可以把下面代碼保存為.m文件，然后運(yùn)行）：
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% 清屏，清除變量
clear,clc,close all
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% 從excel中得到數(shù)據(jù)
x = xlsread('test.xlsx');
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% 數(shù)據(jù)轉(zhuǎn)置
x = x';
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% 畫出原始數(shù)據(jù)
plot(x(1,:),x(2,:),'r');
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% 多項(xiàng)式擬合，如果擬合效果不好，可以得高多項(xiàng)式的階數(shù)，也就是下面最后一個(gè)參數(shù)，多項(xiàng)式越高，計(jì)算量就越大，
% P是多項(xiàng)式的表達(dá)式
[p,s]=polyfit(x(1,:),x(2,:),15); % 15是多項(xiàng)式階數(shù)
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% 用上面擬合出的多項(xiàng)式計(jì)算對(duì)應(yīng)的結(jié)果及與原始數(shù)據(jù)的偏差
[y_fit,DELTA]=polyval(p,x(1,:),s);
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% 畫出擬合后的結(jié)果
hold on
plot(x(1,:),y_fit,'b');
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% 給曲線加標(biāo)注
legend('原始曲線','擬合后曲線');
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% 顯示多項(xiàng)式各階系數(shù)
p
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4階多項(xiàng)式擬合效果：
6階多項(xiàng)式擬合效果：
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10階多項(xiàng)式擬合效果：
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15階多項(xiàng)式擬合效果：
20階多項(xiàng)式擬合效果：
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微信關(guān)注圖中張十三的博客公眾號(hào)，學(xué)習(xí)更多技術(shù)干貨:
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