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New Algorithm Required for Nonlinear Fit

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[quote][i]Originally posted by alexsha[/i]
[br]In OriginPro, there are two algorithms used for nonlinear fit: LM and Simplex, both of them require the end-users to provide initial start values of each parameter. Unfortunately, in most cases, it is not easy for common users to decided so-called correct start values. We just known a software named 1stOpt (in Chinese, http://www.7d-soft.cn), an algorithm called ��Universal Global Optimization �C UGO) has been proposed for nonlinear regression, with the robust and reliable are much better than LM and Simplex, specially, what a amazing is no initial start values are required!!! By testing lots of examples, 1stOpt show overall superior to OriginPro in nonlinear fit areas. Is it possible for OriginPro to acquire and add UGO in next version?

The followings is an example which is very hard for OriginPro to find correct answers (not easy for identifying start values) , but very easy for 1stOpt (no need start values).

Fit Function: y=1/(P+B*X^c)+A*x^n
Parameters needed to be found: P, B, c, A, n

Data:
//x	y
160.73	6266.7
159.82	6151.9
158.84	6035.1
157.86	5920.9
156.87	5812.6
155.88	5702.2
154.89	5594.9
153.96	5491.3
152.97	5385
151.98	5282.2
150.99	5181.3
150.06	5084.8
149.08	4988.8
148.09	4892.2
147.1	4796.9
146.17	4701
145.18	4608
144.2	4515.2
143.2	4429.6
142.21	4342.9
141.25	4255.6
140.2	4167.1
139.14	4077.6
138.05	3987.9
136.96	3898.9
135.94	3808.5
134.84	3717.7
133.74	3628.9
132.65	3543
131.57	3456.3
130.55	3372.5
129.47	3292.8
128.4	3212.7
127.33	3133.6
126.34	3056.6
125.29	2985.5
124.26	2912.5
123.23	2842.9
122.21	2774.1
121.21	2708.3
120.27	2642.1
119.27	2580.2
118.29	2518.7
117.32	2459.1
116.42	2401.1
115.48	2344.3
114.55	2290.9
113.62	2237.5
112.7	2189
111.85	2138.8
110.94	2089.4
110.03	2042.4
109.13	1998.1
108.28	1953.6
107.38	1906.6
106.48	1867.8
105.6	1824.5
104.72	1784.3
103.91	1745
103.05	1704.5
102.2	1668.7
101.35	1629
100.51	1590.4
99.739	1552.5
98.913	1514.7
98.103	1476.4
97.308	1444.3
96.513	1411.4
95.78	1378.5
95.002	1344.8
94.239	1307.8
93.482	1276.1
92.776	1243.5
92.039	1212.9
91.314	1178.7
90.604	1148.4
89.942	1115.9
89.244	1084.5
88.559	1051.5
87.889	1029.7
87.226	996.16
86.569	965.86
85.963	937.72
85.323	907.87
84.694	877.58
84.081	838.17
83.473	819.48
82.876	797.76
82.287	768.54
81.811	749.96
81.178	724.39
80.614	697.24
80.118	674.67
79.574	649.49
79.011	629.83
78.478	614.6
78.012	591.87
77.494	573.43
76.927	558.94
76.512	539.45
75.962	526.99
75.472	514.14
75.014	504.11
74.566	484.4
74.123	473.23
73.608	468.93
73.183	453.77
72.774	448.58
72.369	447.73
71.897	431.79
71.503	432.45
71.116	432.15
70.741	420.71
70.3	427.26
69.935	419.76
69.572	407.28
69.148	408.04
68.796	393.71
68.448	403.74
68.114	408.8
67.717	401.26
67.374	400.81
67.037	401.89
66.741	408.68
66.416	398.49
66.015	414.14
65.373	419.78
64.769	426.82
64.109	418.42
63.44	446.32
62.772	451.55
62.111	473.27
61.508	499.69
60.908	523.66
60.219	551.47
59.699	593.53
59.119	608.69
58.547	658.08
57.992	712.27
57.483	769.4
56.969	826.48
56.472	896.05
55.989	957.57
55.513	1065.1
55.088	1114.1
54.651	1195
54.237	1271.5
53.836	1355.6
53.318	1483.2
52.701	1690
52.08	2245.9
51.431	2470.4
50.877	2719.1
50.298	2957.5
49.74	3155.2
49.2	3279.4
48.702	3546.4
48.182	3741
47.681	4021
47.213	4015.1
46.768	4304.7
46.368	4127.9
45.956	4530.9
45.55	4802.9
45.157	5047.4
44.799	4804.3
44.43	5164.1
44.078	4781
43.727	5175.5
43.384	5708.6
43.079	5679.6
42.899	5161.8
42.719	5399.1
42.547	5483
42.253	4839.4
41.962	5360.7
41.691	5622
40.602	5772.3

[/quote]

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T O P I C R E V I E W

alexsha

Posted - 04/28/2006 : 02:15:52 AM

In OriginPro, there are two algorithms used for nonlinear fit: LM and Simplex, both of them require the end-users to provide initial start values of each parameter. Unfortunately, in most cases, it is not easy for common users to decided so-called correct start values. We just known a software named 1stOpt (in Chinese, http://www.7d-soft.cn), an algorithm called ��Universal Global Optimization �C UGO) has been proposed for nonlinear regression, with the robust and reliable are much better than LM and Simplex, specially, what a amazing is no initial start values are required!!! By testing lots of examples, 1stOpt show overall superior to OriginPro in nonlinear fit areas. Is it possible for OriginPro to acquire and add UGO in next version?

The followings is an example which is very hard for OriginPro to find correct answers (not easy for identifying start values) , but very easy for 1stOpt (no need start values).

Fit Function: y=1/(P+B*X^c)+A*x^n
Parameters needed to be found: P, B, c, A, n

Data:
//x y
160.73 6266.7
159.82 6151.9
158.84 6035.1
157.86 5920.9
156.87 5812.6
155.88 5702.2
154.89 5594.9
153.96 5491.3
152.97 5385
151.98 5282.2
150.99 5181.3
150.06 5084.8
149.08 4988.8
148.09 4892.2
147.1 4796.9
146.17 4701
145.18 4608
144.2 4515.2
143.2 4429.6
142.21 4342.9
141.25 4255.6
140.2 4167.1
139.14 4077.6
138.05 3987.9
136.96 3898.9
135.94 3808.5
134.84 3717.7
133.74 3628.9
132.65 3543
131.57 3456.3
130.55 3372.5
129.47 3292.8
128.4 3212.7
127.33 3133.6
126.34 3056.6
125.29 2985.5
124.26 2912.5
123.23 2842.9
122.21 2774.1
121.21 2708.3
120.27 2642.1
119.27 2580.2
118.29 2518.7
117.32 2459.1
116.42 2401.1
115.48 2344.3
114.55 2290.9
113.62 2237.5
112.7 2189
111.85 2138.8
110.94 2089.4
110.03 2042.4
109.13 1998.1
108.28 1953.6
107.38 1906.6
106.48 1867.8
105.6 1824.5
104.72 1784.3
103.91 1745
103.05 1704.5
102.2 1668.7
101.35 1629
100.51 1590.4
99.739 1552.5
98.913 1514.7
98.103 1476.4
97.308 1444.3
96.513 1411.4
95.78 1378.5
95.002 1344.8
94.239 1307.8
93.482 1276.1
92.776 1243.5
92.039 1212.9
91.314 1178.7
90.604 1148.4
89.942 1115.9
89.244 1084.5
88.559 1051.5
87.889 1029.7
87.226 996.16
86.569 965.86
85.963 937.72
85.323 907.87
84.694 877.58
84.081 838.17
83.473 819.48
82.876 797.76
82.287 768.54
81.811 749.96
81.178 724.39
80.614 697.24
80.118 674.67
79.574 649.49
79.011 629.83
78.478 614.6
78.012 591.87
77.494 573.43
76.927 558.94
76.512 539.45
75.962 526.99
75.472 514.14
75.014 504.11
74.566 484.4
74.123 473.23
73.608 468.93
73.183 453.77
72.774 448.58
72.369 447.73
71.897 431.79
71.503 432.45
71.116 432.15
70.741 420.71
70.3 427.26
69.935 419.76
69.572 407.28
69.148 408.04
68.796 393.71
68.448 403.74
68.114 408.8
67.717 401.26
67.374 400.81
67.037 401.89
66.741 408.68
66.416 398.49
66.015 414.14
65.373 419.78
64.769 426.82
64.109 418.42
63.44 446.32
62.772 451.55
62.111 473.27
61.508 499.69
60.908 523.66
60.219 551.47
59.699 593.53
59.119 608.69
58.547 658.08
57.992 712.27
57.483 769.4
56.969 826.48
56.472 896.05
55.989 957.57
55.513 1065.1
55.088 1114.1
54.651 1195
54.237 1271.5
53.836 1355.6
53.318 1483.2
52.701 1690
52.08 2245.9
51.431 2470.4
50.877 2719.1
50.298 2957.5
49.74 3155.2
49.2 3279.4
48.702 3546.4
48.182 3741
47.681 4021
47.213 4015.1
46.768 4304.7
46.368 4127.9
45.956 4530.9
45.55 4802.9
45.157 5047.4
44.799 4804.3
44.43 5164.1
44.078 4781
43.727 5175.5
43.384 5708.6
43.079 5679.6
42.899 5161.8
42.719 5399.1
42.547 5483
42.253 4839.4
41.962 5360.7
41.691 5622
40.602 5772.3

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