非线性规划lsqcurvefit

1、增加生产、发展经济所依靠的主要因素有增加投资、增加劳动力以及技术革新等，在研究国民经济产值与这些因素的数量关系时，由于技术水平不像资金、劳动力那样容易定量化，作为初步的模型，可认为技术水平不变，只讨论产值和资金、劳动力之间的关系。在科学发展不快时，如资本主义经济发展的前期，这种模型是有意义的。用Q，K，L分别表示产值、资金、劳动力，要寻求数量关系Q（K，L）。经过简化假设与分析，在经济学中，推导出一个著名的Cobb-Douglas生产函数：Q（K，L）=aKL,0,1 (*)式中,，a要由经济统计数据确定。现有美国马萨诸塞州19001926年上述三个经济指数的统计数据，如表1，试用数据拟合的方

2、法，求出（*）式中的参数,，a。表 1TQ K LTQKL19001.051.041.0519131.952.821.6819011.181.061.0819142.013.241.6519021.291.161.1819152.003.241.6219031.301.221.2219162.093.611.8619041.301.271.1719171.964.101.9319051.421.371.3019182.204.361.9619061.501.441.3919192.124.771.9519071.521.531.4719202.164.751.9019081.461.571.3

3、719212.084.541.5819091.602.051.4319222.244.541.6719101.692.511.5819232.564.581.8219111.812.631.5919242.344.581.6019121.932.741.6619252.454.581.6119262.584.541.64第一种方法：由于产值Q、资金K、劳动力L之间满足著名的Cobb-Douglas生产函数关系：Q（K，L）=aKL,0, y=1.04 1.06 1.16 1.22 1.27 1.37 1.44 1.53 1.57 2.05 2.51 2.63 2.74 2.82 3.24 3.

4、24 3.61 4.10 4.36 4.77 4.75 4.54 4.54 4.58 4.58 4.58 4.54;1.05 1.08 1.18 1.22 1.17 1.30 1.39 1.47 1.31 1.43 1.58 1.59 1.66 1.68 1.65 1.62 1.86 1.93 1.96 1.95 1.90 1.58 1.67 1.82 1.60 1.61 1.64;a=1.05 1.18 1.29 1.30 1.30 1.42 1.50 1.52 1.46 1.60 1.69 1.81 1.93 1.95 2.01 2.00 2.09 1.96 2.20 2.12 2.16

5、2.08 2.24 2.56 2.34 2.45 2.58;x0=0.1,0.1,0.2;x=lsqcurvefit (curvefun1,x0,y,a)f = Columns 1 through 15 0.1014 0.1021 0.1049 0.1061 0.1057 0.1088 0.1108 0.1127 0.1104 0.1154 0.1201 0.1209 0.1224 0.1231 0.1243 Columns 16 through 27 0.1239 0.1287 0.1313 0.1326 0.1336 0.1329 0.1275 0.1289 0.1313 0.1279 0

6、.1281 0.1284f = Columns 1 through 15 0.1014 0.1021 0.1049 0.1061 0.1057 0.1088 0.1108 0.1127 0.1104 0.1154 0.1201 0.1209 0.1224 0.1231 0.1243 Columns 16 through 27 0.1239 0.1287 0.1313 0.1326 0.1336 0.1329 0.1275 0.1289 0.1313 0.1279 0.1281 0.1284f = Columns 1 through 15 0.1014 0.1021 0.1049 0.1061

7、0.1057 0.1088 0.1108 0.1127 0.1104 0.1154 0.1201 0.1209 0.1224 0.1231 0.1243 Columns 16 through 27 0.1239 0.1287 0.1313 0.1326 0.1336 0.1329 0.1275 0.1289 0.1313 0.1279 0.1281 0.1284f = Columns 1 through 15 0.1014 0.1021 0.1049 0.1061 0.1057 0.1088 0.1108 0.1127 0.1104 0.1154 0.1201 0.1209 0.1224 0.

8、1231 0.1243 Columns 16 through 27 0.1239 0.1287 0.1313 0.1326 0.1336 0.1329 0.1275 0.1289 0.1313 0.1279 0.1281 0.1284f = Columns 1 through 15 1.1859 1.1458 1.2183 1.3675 2.1124 1.9051 1.8009 1.9109 3.9341 11.3056 21.3237 26.8402 27.2102 30.1095 71.7457 Columns 16 through 27 78.6560 72.1463 122.3372

9、159.8159 271.3147 301.8438 590.3906 447.2670 305.2897 582.2508 564.3515 489.8016f = Columns 1 through 15 1.1859 1.1458 1.2183 1.3675 2.1124 1.9051 1.8009 1.9109 3.9341 11.3056 21.3237 26.8402 27.2102 30.1095 71.7457 Columns 16 through 27 78.6560 72.1463 122.3372 159.8159 271.3147 301.8438 590.3906 4

10、47.2671 305.2897 582.2509 564.3515 489.8016f = Columns 1 through 15 1.1859 1.1458 1.2183 1.3675 2.1124 1.9051 1.8009 1.9109 3.9341 11.3056 21.3237 26.8402 27.2102 30.1095 71.7457 Columns 16 through 27 78.6560 72.1463 122.3373 159.8159 271.3147 301.8438 590.3907 447.2671 305.2898 582.2509 564.3515 48

11、9.8017f = Columns 1 through 15 1.1859 1.1458 1.2183 1.3675 2.1124 1.9051 1.8009 1.9109 3.9341 11.3056 21.3237 26.8402 27.2102 30.1095 71.7457 Columns 16 through 27 78.6560 72.1463 122.3372 159.8159 271.3146 301.8437 590.3906 447.2670 305.2897 582.2508 564.3515 489.8016f = Columns 1 through 15 1.4977

12、 1.5046 1.5809 1.6415 1.7643 1.8045 1.8340 1.9002 2.1018 2.7090 3.2178 3.3827 3.4536 3.5439 4.2062 Columns 16 through 27 4.2540 4.4259 5.0107 5.3282 5.9291 5.9957 6.3761 6.1620 5.9032 6.3912 6.3667 6.2313f = Columns 1 through 15 1.4977 1.5046 1.5809 1.6415 1.7643 1.8045 1.8340 1.9002 2.1018 2.7090 3

13、.2178 3.3827 3.4536 3.5439 4.2062 Columns 16 through 27 4.2540 4.4259 5.0107 5.3282 5.9291 5.9957 6.3761 6.1620 5.9032 6.3912 6.3667 6.2313f = Columns 1 through 15 1.4977 1.5046 1.5809 1.6415 1.7643 1.8045 1.8340 1.9002 2.1018 2.7090 3.2178 3.3827 3.4536 3.5439 4.2062 Columns 16 through 27 4.2540 4.

14、4259 5.0107 5.3282 5.9291 5.9957 6.3761 6.1620 5.9032 6.3912 6.3667 6.2313f = Columns 1 through 14 1.4977 1.5046 1.5809 1.6415 1.7643 1.8045 1.8340 1.9002 2.1018 2.7090 3.2178 3.3827 3.4536 3.5439 Columns 15 through 27 4.2062 4.2540 4.4259 5.0107 5.3282 5.9291 5.9957 6.3761 6.1620 5.9032 6.3912 6.36

15、67 6.2313f = Columns 1 through 14 0.5851 0.5905 0.6106 0.6199 0.6180 0.6400 0.6546 0.6689 0.6546 0.6954 0.7334 0.7397 0.7516 0.7569 Columns 15 through 27 0.7701 0.7670 0.8041 0.8267 0.8374 0.8481 0.8427 0.8033 0.8133 0.8300 0.8067 0.8078 0.8100f = Columns 1 through 14 0.5851 0.5905 0.6106 0.6199 0.6

16、180 0.6400 0.6546 0.6689 0.6546 0.6954 0.7334 0.7397 0.7516 0.7569 Columns 15 through 27 0.7701 0.7670 0.8041 0.8267 0.8374 0.8481 0.8427 0.8033 0.8133 0.8300 0.8067 0.8078 0.8100f = Columns 1 through 14 0.5851 0.5905 0.6106 0.6199 0.6180 0.6400 0.6546 0.6689 0.6546 0.6954 0.7334 0.7397 0.7516 0.756

17、9 Columns 15 through 27 0.7701 0.7670 0.8041 0.8267 0.8374 0.8481 0.8427 0.8033 0.8133 0.8300 0.8067 0.8078 0.8100f = Columns 1 through 14 0.5851 0.5905 0.6106 0.6199 0.6180 0.6400 0.6546 0.6689 0.6546 0.6954 0.7334 0.7397 0.7516 0.7569 Columns 15 through 27 0.7701 0.7670 0.8041 0.8267 0.8374 0.8481

18、 0.8427 0.8033 0.8133 0.8300 0.8067 0.8078 0.8100f = Columns 1 through 14 1.2225 1.2335 1.2979 1.3395 1.3917 1.4439 1.4800 1.5326 1.5975 1.9201 2.1937 2.2694 2.3212 2.3666 Columns 15 through 27 2.6363 2.6455 2.7949 3.0541 3.1893 3.4157 3.4219 3.4262 3.3901 3.3569 3.4406 3.4365 3.4019f = Columns 1 th

19、rough 14 1.2225 1.2335 1.2979 1.3395 1.3917 1.4439 1.4800 1.5326 1.5975 1.9201 2.1937 2.2694 2.3212 2.3666 Columns 15 through 27 2.6363 2.6455 2.7949 3.0541 3.1893 3.4157 3.4219 3.4262 3.3901 3.3569 3.4406 3.4365 3.4019f = Columns 1 through 14 1.2225 1.2335 1.2979 1.3395 1.3917 1.4439 1.4800 1.5326

20、1.5975 1.9201 2.1937 2.2694 2.3212 2.3666 Columns 15 through 27 2.6363 2.6455 2.7949 3.0541 3.1893 3.4157 3.4219 3.4262 3.3901 3.3569 3.4406 3.4365 3.4019f = Columns 1 through 14 1.2225 1.2335 1.2979 1.3395 1.3917 1.4439 1.4800 1.5326 1.5975 1.9201 2.1937 2.2694 2.3212 2.3666 Columns 15 through 27 2

21、.6363 2.6455 2.7949 3.0541 3.1893 3.4157 3.4219 3.4262 3.3901 3.3569 3.4406 3.4365 3.4019f = Columns 1 through 14 1.2341 1.2396 1.2777 1.3037 1.3430 1.3692 1.3873 1.4168 1.4698 1.6644 1.8170 1.8603 1.8850 1.9095 Columns 15 through 27 2.0632 2.0708 2.1337 2.2663 2.3344 2.4511 2.4584 2.4899 2.4626 2.4

22、320 2.4953 2.4922 2.4715f = Columns 1 through 14 1.2341 1.2396 1.2777 1.3037 1.3430 1.3692 1.3873 1.4168 1.4698 1.6644 1.8170 1.8603 1.8850 1.9095 Columns 15 through 27 2.0632 2.0708 2.1337 2.2663 2.3344 2.4511 2.4584 2.4899 2.4626 2.4320 2.4953 2.4922 2.4715f = Columns 1 through 14 1.2341 1.2396 1.

23、2777 1.3037 1.3430 1.3692 1.3873 1.4168 1.4698 1.6644 1.8170 1.8603 1.8850 1.9095 Columns 15 through 27 2.0632 2.0708 2.1337 2.2663 2.3344 2.4511 2.4584 2.4899 2.4626 2.4320 2.4953 2.4922 2.4715f = Columns 1 through 14 1.2341 1.2396 1.2777 1.3037 1.3430 1.3692 1.3873 1.4168 1.4698 1.6644 1.8170 1.86

24、03 1.8850 1.9095 Columns 15 through 27 2.0632 2.0708 2.1337 2.2663 2.3344 2.4511 2.4584 2.4899 2.4626 2.4320 2.4953 2.4922 2.4715f = Columns 1 through 14 1.2408 1.2469 1.2845 1.3089 1.3414 1.3693 1.3885 1.4171 1.4575 1.6302 1.7666 1.8039 1.8276 1.8492 Columns 15 through 27 1.9777 1.9827 2.0454 2.159

25、1 2.2171 2.3135 2.3173 2.3281 2.3102 2.2920 2.3335 2.3315 2.3160f = Columns 1 through 14 1.2408 1.2469 1.2845 1.3089 1.3414 1.3693 1.3885 1.4171 1.4575 1.6302 1.7666 1.8039 1.8276 1.8492 Columns 15 through 27 1.9777 1.9827 2.0454 2.1591 2.2171 2.3135 2.3173 2.3281 2.3102 2.2920 2.3335 2.3315 2.3160f

26、 = Columns 1 through 14 1.2408 1.2469 1.2845 1.3089 1.3414 1.3693 1.3885 1.4171 1.4575 1.6302 1.7666 1.8039 1.8276 1.8492 Columns 15 through 27 1.9777 1.9827 2.0454 2.1591 2.2171 2.3135 2.3173 2.3281 2.3102 2.2920 2.3335 2.3315 2.3160f = Columns 1 through 14 1.2408 1.2469 1.2845 1.3089 1.3414 1.3693

27、 1.3885 1.4171 1.4575 1.6302 1.7666 1.8039 1.8276 1.8492 Columns 15 through 27 1.9777 1.9827 2.0454 2.1591 2.2171 2.3135 2.3173 2.3281 2.3102 2.2920 2.3335 2.3315 2.3160f = Columns 1 through 14 1.2392 1.2456 1.2839 1.3085 1.3402 1.3693 1.3892 1.4184 1.4567 1.6291 1.7658 1.8028 1.8271 1.8487 Columns

28、15 through 27 1.9755 1.9802 2.0450 2.1584 2.2162 2.3115 2.3147 2.3209 2.3045 2.2886 2.3266 2.3247 2.3099f = Columns 1 through 14 1.2392 1.2456 1.2839 1.3085 1.3402 1.3693 1.3892 1.4184 1.4567 1.6291 1.7658 1.8028 1.8271 1.8487 Columns 15 through 27 1.9755 1.9802 2.0450 2.1584 2.2162 2.3115 2.3147 2.

29、3209 2.3045 2.2886 2.3266 2.3247 2.3099f = Columns 1 through 14 1.2392 1.2456 1.2839 1.3085 1.3402 1.3693 1.3892 1.4184 1.4567 1.6291 1.7658 1.8028 1.8271 1.8487 Columns 15 through 27 1.9755 1.9802 2.0450 2.1584 2.2162 2.3115 2.3147 2.3209 2.3045 2.2886 2.3266 2.3247 2.3099f = Columns 1 through 14 1

30、.2392 1.2456 1.2839 1.3085 1.3402 1.3693 1.3892 1.4184 1.4567 1.6291 1.7658 1.8028 1.8271 1.8487 Columns 15 through 27 1.9755 1.9802 2.0450 2.1584 2.2162 2.3115 2.3147 2.3209 2.3045 2.2886 2.3266 2.3247 2.3099f = Columns 1 through 14 1.2392 1.2457 1.2840 1.3086 1.3402 1.3693 1.3892 1.4185 1.4567 1.6291 1.7659 1.8029 1.8272 1.8487 Columns 15 through 27 1.9755 1.9802 2.0450 2.1584 2.2161 2.3114 2.3146 2.3209 2.3045 2.2886 2.3265 2.3247 2.3099f = Columns 1 t