matlab 多項式擬合EXCEL中複雜數據

有如下原始數據x,y,它對應的曲線圖形爲：

-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

如果想得到該曲線的函數表達式（多項式擬合的表達式），在Excel 自帶圖表工具中可以能過爲曲線加趨勢線方式實現：

選擇多項式，調整階數讓擬合後在結果與原始曲線儘量重合，並勾選顯示公式：

EXCEL趨勢曲線多項式最高的階數是6階，但是實際效果與原始數據相差還是較大，看到是我們數據太複雜，EXCEL也無能爲力了，這時也只能請出強大的matlab來解決，把上述原始數據保存於EXCEL中，並強excel文件（.xls/xlsx）保存於matlab工作目錄下，然後運行如下代碼（可以把下面代碼保存爲.m文件，然後運行）：

% 清屏，清除變量

clear,clc,close all

% 從excel中得到數據

x = xlsread('test.xlsx');

% 數據轉置

x = x';

% 畫出原始數據

plot(x(1,:),x(2,:),'r');

% 多項式擬合，如果擬合效果不好，可以得高多項式的階數，也就是下面最後一個參數，多項式越高，計算量就越大，

% P是多項式的表達式

[p,s]=polyfit(x(1,:),x(2,:),15); % 15是多項式階數

% 用上面擬合出的多項式計算對應的結果及與原始數據的偏差