在行列可自由变换的条件下,5点结构有34个
(A,B)---6*30*2---(0,1)(1,0)
让A分别是5a1,2,…,34,让B全是0。当收敛误差为7e-4,收敛199次取迭代次数平均值,得到
迭代次数 | 搜索难度 | |
1 | 3683.965 | 0.99999 |
2 | 3932.508 | 1.067456 |
3 | 4759.392 | 1.291909 |
4 | 8249.643 | 2.239317 |
5 | 9139.653 | 2.480905 |
6 | 9453.382 | 2.566065 |
7 | 9825.925 | 2.667189 |
8 | 11506.23 | 3.123297 |
9 | 11767.83 | 3.194309 |
10 | 12409.84 | 3.368579 |
11 | 13188.83 | 3.58003 |
12 | 13873.26 | 3.765815 |
13 | 16046.96 | 4.355852 |
14 | 19054.19 | 5.172146 |
15 | 19980.3 | 5.423533 |
16 | 21134.39 | 5.736804 |
17 | 22773.47 | 6.181724 |
18 | 22775.07 | 6.182158 |
19 | 23659.18 | 6.422145 |
20 | 24182.31 | 6.564144 |
21 | 25055.74 | 6.801233 |
22 | 25221.65 | 6.846269 |
23 | 25759.79 | 6.992344 |
24 | 26143.76 | 7.09657 |
25 | 27183.99 | 7.378935 |
26 | 28805.32 | 7.819034 |
27 | 29116.43 | 7.903482 |
28 | 29172.19 | 7.918617 |
29 | 32156.56 | 8.728707 |
30 | 33210.32 | 9.014744 |
31 | 33687.66 | 9.144317 |
32 | 40492.64 | 10.99149 |
33 | 45937.17 | 12.46937 |
34 | 65712.91 | 17.83738 |
这里训练集A-B矩阵的高度是5,而结构有5个点,5=5因此这个顺序是5点结构的s1顺序。
在行和列可自由变换的平面上3点结构有6个
这个顺序3a1,3a2,…,3a6是训练集A-B矩阵的高度等于6的顺序,而点的数量为3,6>3因此这个顺序是3点结构的s2顺序。这里用5点结构的s1顺序去标定3点结构的s2顺序。
12(3a1+2a1)=5a1+2*5a3+5a4+5a9+3*5a10+2*5a12+2*5a24
3a1+2a1形成5a1的结构可能有非常多的可能
a | b | |||||||||||
- | - | - | - | 1 | 1 | - | - | - | - | 1 | 1 | |
- | - | - | - | 1 | - | - | - | - | - | 1 | - | |
- | - | - | - | - | 1 | - | - | - | - | - | 1 | |
- | - | - | - | - | 1 | - | - | - | - | - | - | |
- | - | - | - | - | - | - | - | - | - | - | 1 | |
c | d | |||||||||||
- | - | 1 | - | - | 1 | - | 1 | - | - | 1 | - | |
- | - | 1 | - | - | - | - | - | - | - | 1 | - | |
- | - | - | - | - | 1 | - | 1 | - | - | - | - | |
- | - | - | - | - | 1 | - | - | - | - | - | - | |
- | - | - | - | - | - | - | 1 | - | - | - | - |
因为训练集A-B矩阵的列可以自由变换对迭代次数没有影响,所以a和c,b和d是同一个结构。
这里a的迭代次数是3716是5a1的迭代次数的1.01倍,b的迭代次数是3863是5a1迭代次数的1.05倍。所以a和b与结构5a1并不相同,但如果认为训练集A-B矩阵的行也可以自由变换则a,b和5a1相同,虽然这将导致误差,但简化了计算。
再计算搜索难度
(1.00+2*1.29+2.24+3.19+3*3.37+2*3.77+2*7.10)/12=3.40
用3点结构构造5点结构,可以通过3点结构+1+1的方式实现,因为行列可自由变换的平面上2点结构只有3种
因此让3点结构分别加2a1,2,3就相当于实现了+1+1的操作。
3a2
13(3a2+2a1)=5a1+5a12+10*5a25+5a27
(1.00+3.77+10*7.38+7.90)/13=6.65
3a3
23(3a3+2a1)=2*5a1+2*5a2+5a4+5a9+3*5a10+5a12+2*5a15
+6*5a19+3*5a27+2*5a31
(2*1.00+2*1.07+2.24+3.19+3*3.37+3.77+2*5.42+6*6.42+3*7.90+2*9.14)/23=4.99
3a4
12(3a4+2a1)=5a5+5a7+2*5a8+5a13+2*5a14+3*5a17+5a22+5a29
(2.48+2.67+2*3.12+4.36+2*5.17+3*6.18+6.85+8.73)/12=5.02
3a5
9(3a5+1)=5a6+2*5a7+5a14+3*5a20+5a21+5a28
(2.57+2*2.67+5.17+3*6.56+6.80+7.92)/9=5.28
3a6
3(3a6+2a1)=5a8+5a11+5a26
(3.12+3.58+7.82)/3=4.84
得到第一组顺序
2a1 |
3.404 |
6.651 |
4.992 |
5.018 |
5.276 |
4.841 |
用同样的方法计算第二组数据3ax+2a2
3a1
30(3a1+2a2)=2*5a1+2*5a2+2*5a3+5a4+2*5a5+5a6+2*5a7
+4*5a8+2*5a12+2*5a14+4*5a15+2*5a21+2*5a24+2*5a29
(2*1.00+2*1.07+2*1.29+2.24+2*2.48+2.57+2*2.67+4*3.12+2*3.77+2*5.17+4*5.42+2*6.80+2*7.10+2*8.73)/30=3.97
3a2
10(3a2+2a2)=5a7+3*5a10+5a14+4*5a19+5a20
(2.67+3*3.37+5.17+4*6.42+6.56)/10=5.02
3a3
49(3a3+2a2)=3*5a1+2*5a2+2*5a4+2*5a6+3*5a7+3*5a9+2*5a12+2*5a13+2*5a14+6*5a17+6*5a20+5a21+2*5a22+6*5a27+3*5a28+4*5a31
(3*1.00+2*1.07+2*2.24+2*2.57+3*2.67+3*3.19+2*3.77+2*4.36+2*5.17+6*6.18+6*6.56+6.80+2*6.85+6*7.90+3*7.92+4*9.14)/49=5.38
3a4
49(3a4+2a2)=5a2+2*5a3+2*5a4+3*5a5+2*5a6+2*5a9+3*5a13+6*5a16+3*5a18+2*5a21+2*5a22+2*5a24+6*5a26+3*5a29+4*5a30+6*5a32
(1.07+2*1.29+2*2.24+3*2.48+2*2.57+2*3.19+3*4.36+6*5.74+3*6.18+2*6.80+2*6.85+2*7.10+6*7.82+3*8.73+4*9.01+6*10.99)/49=6.32
3a5
48(3a5+2a2)=2*5a2+5a4+3*5a6+2*5a9+2*5a13+2*5a15+6*5a18+2*5a21+4*5a22+6*5a28+4*5a30+4*5a31+10*5a33
(2*1.07+2.24+3*2.57+2*3.19+2*4.36+2*5.42+6*6.18+2*6.80+4*6.85+6*7.92+4*9.01+4*9.14+10*12.47)/48=7.52
3a6
10(3a6+2a2)=5a3+5a5+3*5a11+5a16+4*5a23
(1.29+2.48+3*3.58+5.74+4*6.99)/10=4.82
得到第二组数据
2a2 |
3.971 |
5.02 |
5.38 |
6.321 |
7.52 |
4.822 |
计算第三组数据3ax+2a3
3a1
12(3a1+2a3)=5a4+3*5a11+2*5a12+5a13+2*5a14+2*5a24+5a29
(2.24+3*3.58+2*3.77+4.36+2*5.17+2*7.10+8.73)/12=4.84
3a2
3(3a2+2a3)=5a8+5a10+5a17
(3.12+3.37+6.18)/3=4.22
3a3
12(3a3+2a2)=5a1+2*5a3+5a5+5a7+2*5a8+5a9+5a22+3*5a26
(1.00+2*1.29+2.48+2.67+2*3.12+3.19+6.85+3*7.82)/12=4.04
3a4
23(3a4+2a3)=5a4+3*5a11+5a13+2*5a15+2*5a21+6*5a23
+5a24+2*5a29+2*5a30+3*5a32
(2.24+3*3.58+4.36+2*5.42+2*6.80+6*6.99+7.10+2*8.73+2*9.01+3*10.99)/23=6.93
3a5
9(3a5+2a3)=5a2+5a3+2*5a5+5a6+3*5a16+5a18
(1.07+1.29+2*2.48+2.57+3*5.74+6.18)/9=3.70
3a6
13(3a6+2a3)=5a24+5a29+5a32+10*5a34
(7.10+8.73+10.99+10*17.84)/13=15.78
计算3组搜索难度数据的平均值
2a1 | 2a2 | 2a3 | 平均 | |
3.404 | 3.971 | 4.844 | 4.07321 | |
6.651 | 5.02 | 4.225 | 5.29833 | |
4.992 | 5.38 | 4.04 | 4.80408 | |
5.018 | 6.321 | 6.926 | 6.08826 | |
5.276 | 7.52 | 3.698 | 5.49783 | |
4.841 | 4.822 | 15.78 | 8.48219 |
将平均值画图
尽管第3点,5点的数据略小,但曲线整体上是增的。暗示了5s1与3s2内在顺序的相似性。