学习对象对神经网络迭代次数的影响
制作一个81*30*2的神经网络
输入minst数据集的1的图片，让这个网络向1,0收敛，
y[0]=1,y[1]=0
收敛标准
while (Math.abs(f2[0] - y[0]) > δ || Math.abs(f2[1] - y[1]) > δ )
这个网络用
S（minst1）81*30*2-（1,0）表示
本文尝试了从δ=1e-5到δ=1e-100共37个梯度，实验了minst数据集1中的前200张图片，
|
δ |
f2[0] |
f2[1] |
迭代次数 |
耗时ms |
耗时min |
|
1.00E-05 |
0.999998767 |
2.14412E-06 |
12.60301508 |
538 |
0.008966667 |
|
1.00E-06 |
0.999999456 |
1.71233E-08 |
237.3869347 |
1452 |
0.0242 |
|
1.00E-07 |
0.999999905 |
2.18655E-10 |
1127.78392 |
4623 |
0.07705 |
|
9*1e-8 |
0.999999917 |
3.15809E-10 |
1035.763819 |
4294 |
0.071566667 |
|
8*1e-8 |
0.999999923 |
1.0114E-10 |
1098.522613 |
4538 |
0.075633333 |
|
7*1e-8 |
0.999999933 |
6.30542E-11 |
1191.849246 |
4891 |
0.081516667 |
|
6*1e-8 |
0.999999942 |
4.99584E-11 |
1225.180905 |
5178 |
0.0863 |
|
5*1e-8 |
0.999999952 |
9.37548E-11 |
1278.170854 |
5356 |
0.089266667 |
|
4*1e-8 |
0.999999961 |
4.89244E-11 |
1398.537688 |
5836 |
0.097266667 |
|
3*1e-8 |
0.99999997 |
2.12962E-11 |
1429.738693 |
5868 |
0.0978 |
|
2*1e-8 |
0.99999998 |
3.93178E-11 |
1590.713568 |
6518 |
0.108633333 |
|
1.00E-08 |
0.99999999 |
1.1666E-12 |
1786.728643 |
7173 |
0.11955 |
|
9*1e-9 |
0.999999991 |
3.3773E-12 |
1745.658291 |
7253 |
0.120883333 |
|
8*1e-9 |
0.999999992 |
0 |
1797.226131 |
7569 |
0.12615 |
|
7*1e-9 |
0.999999993 |
0 |
1757.663317 |
7326 |
0.1221 |
|
6*1e-9 |
0.999999994 |
4.55909E-12 |
1755.934673 |
7279 |
0.121316667 |
|
5*1e-9 |
0.999999995 |
5.725E-252 |
1876.286432 |
7651 |
0.127516667 |
|
4*1e-9 |
0.999999996 |
9.9559E-196 |
1991.919598 |
8135 |
0.135583333 |
|
3*1e-9 |
0.999999997 |
3.276E-226 |
1979.291457 |
7951 |
0.132516667 |
|
2*1e-9 |
0.999999998 |
0 |
2216.160804 |
9070 |
0.151166667 |
|
1.00E-09 |
0.999999999 |
7.0075E-278 |
2347.341709 |
9280 |
0.154666667 |
|
1.00E-10 |
1 |
0 |
3385.070352 |
13249 |
0.220816667 |
|
1.00E-11 |
1 |
0 |
3306.542714 |
12790 |
0.213166667 |
|
1.00E-12 |
1 |
0 |
3578.98995 |
13771 |
0.229516667 |
|
1.00E-13 |
1 |
0 |
5316.045226 |
20239 |
0.337316667 |
|
1.00E-14 |
1 |
0 |
6040.467337 |
21185 |
0.353083333 |
|
1.00E-15 |
1 |
0 |
6332.708543 |
22035 |
0.36725 |
|
1.00E-16 |
1 |
0 |
7156.442211 |
24539 |
0.408983333 |
|
1.00E-17 |
1 |
0 |
7230.18593 |
24539 |
0.408983333 |
|
1.00E-18 |
1 |
0 |
7186.788945 |
24495 |
0.40825 |
|
1.00E-19 |
1 |
0 |
6177.095477 |
21098 |
0.351633333 |
|
1.00E-20 |
1 |
0 |
6805.40201 |
23117 |
0.385283333 |
|
1.00E-21 |
1 |
0 |
6529.226131 |
22288 |
0.371466667 |
|
1.00E-30 |
1 |
0 |
6281.366834 |
22129 |
0.368816667 |
|
1.00E-40 |
1 |
0 |
7388.201005 |
25981 |
0.433016667 |
|
1.00E-50 |
1 |
0 |
6792.452261 |
23902 |
0.398366667 |
|
1.00E-100 |
1 |
0 |
6561.286432 |
23033 |
0.383883333 |
整条迭代次数曲线在1e-17前变化都比较规则，在1e-17以后开始在顶点附近波动。
观察从1e-7<=δ<=1e-9这一段的图像
发现迭代次数与对数坐标-ln（δ）几乎成一条直线，
所以用1e-7到1e-17的所有数据去拟合曲线
|
x |
16.11809565,16.22345617,16.3412392,16.47477059,16.62892127,16.81124283,17.03438638,17.32206846,17.72753356,18.42068074,18.52604126,18.6438243,18.77735569,18.93150637,19.11382792,19.33697148,19.62465355,20.03011866,20.72326584,23.02585093,25.32843602,27.63102112,29.93360621,32.2361913,34.53877639,36.84136149,39.14394658 |
|
y |
1127.78392,1035.763819,1098.522613,1191.849246,1225.180905,1278.170854,1398.537688,1429.738693,1590.713568,1786.728643,1745.658291,1797.226131,1757.663317,1755.934673,1876.286432,1991.919598,1979.291457,2216.160804,2347.341709,3385.070352,3306.542714,3578.98995,5316.045226,6040.467337,6332.708543,7156.442211,7230.18593 |
|
拟合方程式：Y = a + b·X |
|
|
a = -3485.76777297036 |
|
|
b = 282.494876711601 |
|
|
相关系数 R2：0.98642214549575 |
再用1e-7到1e-9的数据去拟合
|
x |
16.11809565,16.22345617,16.3412392,16.47477059,16.62892127,16.81124283,17.03438638,17.32206846,17.72753356,18.42068074,18.52604126,18.6438243,18.77735569,18.93150637,19.11382792,19.33697148,19.62465355,20.03011866,20.72326584 |
|
y |
1127.78392,1035.763819,1098.522613,1191.849246,1225.180905,1278.170854,1398.537688,1429.738693,1590.713568,1786.728643,1745.658291,1797.226131,1757.663317,1755.934673,1876.286432,1991.919598,1979.291457,2216.160804,2347.341709 |
|
拟合方程式：Y = a + b·X |
|
|
a = -3307.56214257176 |
|
|
b = 272.670470518643 |
|
|
相关系数 R2：0.982938988083221 |
用这组数据去验证准确率
|
a = -3307.56214257176 |
|
|
b = 272.670470518643 |
|
δ |
实测迭代次数 n |
计算迭代次数n |
计算值/实测值 |
|
1.00E-05 |
12.60301508 |
-1.68E+02 |
-1.34E+01 |
|
1.00E-06 |
237.3869347 |
459.5196217 |
1.935740998 |
|
1.00E-07 |
1127.78392 |
1087.366582 |
0.964162162 |
|
9.00E-08 |
1035.763819 |
1116.095284 |
1.077557705 |
|
8.00E-08 |
1098.522613 |
1148.21124 |
1.045232229 |
|
7.00E-08 |
1191.849246 |
1184.621307 |
0.993935526 |
|
6.00E-08 |
1225.180905 |
1226.653646 |
1.00120206 |
|
5.00E-08 |
1278.170854 |
1276.36735 |
0.998588996 |
|
4.00E-08 |
1398.537688 |
1337.212007 |
0.956150141 |
|
3.00E-08 |
1429.738693 |
1415.654413 |
0.990149053 |
|
2.00E-08 |
1590.713568 |
1526.212775 |
0.959451661 |
|
1.00E-08 |
1786.728643 |
1715.213543 |
0.95997428 |
|
9.00E-09 |
1745.658291 |
1743.942245 |
0.999016963 |
|
8.00E-09 |
1797.226131 |
1776.0582 |
0.988221888 |
|
7.00E-09 |
1757.663317 |
1812.468268 |
1.031180574 |
|
6.00E-09 |
1755.934673 |
1854.500606 |
1.05613303 |
|
5.00E-09 |
1876.286432 |
1904.214311 |
1.014884656 |
|
4.00E-09 |
1991.919598 |
1965.058968 |
0.986515204 |
|
3.00E-09 |
1979.291457 |
2043.501374 |
1.03244086 |
|
2.00E-09 |
2216.160804 |
2154.059736 |
0.971978086 |
|
1.00E-09 |
2347.341709 |
2343.060504 |
0.998176148 |
|
1.00E-10 |
3385.070352 |
2970.907465 |
0.877650139 |
|
1.00E-11 |
3306.542714 |
3598.754425 |
1.08837379 |
|
1.00E-12 |
3578.98995 |
4226.601386 |
1.180948101 |
|
1.00E-13 |
5316.045226 |
4.85E+03 |
0.913169121 |
|
1.00E-14 |
6040.467337 |
5.48E+03 |
0.907594562 |
|
1.00E-15 |
6332.708543 |
6.11E+03 |
0.96485449 |
|
1.00E-16 |
7156.442211 |
6.74E+03 |
0.941527791 |
|
1.00E-17 |
7230.18593 |
7.37E+03 |
1.02E+00 |
|
1.00E-18 |
7186.788945 |
7.99E+03 |
1.112274649 |
|
1.00E-19 |
6177.095477 |
8.62E+03 |
1.395725571 |
|
1.00E-20 |
6805.40201 |
9.25E+03 |
1.359122805 |
|
1.00E-21 |
6529.226131 |
9.88E+03 |
1.512771014 |
可以看到在1e-7到1e-17的区间上
|
a = -3307.56214257176 |
|
b = 272.670470518643 |
符合度还是很好的，在这个区间上计算值/实测值的比值相对稳定
如果迭代次数用n表示，在1e-7到1e-17的区间上
S（minst1）81*30*2-（1,0）的迭代次数可以相对精确的表示为
n= -3307.56214257176+272.670470518643（-ln δ）
为了验证这种算法的有效性，制作了
S（minst0）81*30*2-（1,0），用minst的0向1,0收敛看看是否依然有这种关系，同样也做了前200张图片，收集到的数据
|
δ |
f2[0] |
f2[1] |
迭代次数n |
耗时ms |
耗时min |
|
1.00E-05 |
0.999998923 |
2.46145E-06 |
7.708542714 |
560 |
0.00933333 |
|
1.00E-06 |
0.999999524 |
6.20923E-08 |
136.2261307 |
1085 |
0.01808333 |
|
1.00E-07 |
0.999999913 |
1.48981E-10 |
1209.934673 |
4954 |
0.08256667 |
|
9*1e-8 |
0.999999918 |
1.17055E-10 |
1421.145729 |
5624 |
0.09373333 |
|
8*1e-8 |
0.999999927 |
1.04366E-10 |
1644.38191 |
6383 |
0.10638333 |
|
7*1e-8 |
0.999999936 |
1.00675E-10 |
1699.180905 |
6591 |
0.10985 |
|
6*1e-8 |
0.999999942 |
5.60869E-11 |
2013.98995 |
7675 |
0.12791667 |
|
5*1e-8 |
0.999999952 |
7.29598E-11 |
2044.592965 |
7377 |
0.12295 |
|
4*1e-8 |
0.999999961 |
8.41249E-12 |
2423.824121 |
8610 |
0.1435 |
|
3*1e-8 |
0.999999971 |
3.15976E-11 |
2582.422111 |
9157 |
0.15261667 |
|
2*1e-8 |
0.99999998 |
1.89992E-11 |
3003.592965 |
10490 |
0.17483333 |
|
1.00E-08 |
0.99999999 |
2.39506E-11 |
3712.859296 |
12876 |
0.2146 |
|
9*1e-9 |
0.999999991 |
6.77043E-13 |
4286.18593 |
14883 |
0.24805 |
|
8*1e-9 |
0.999999992 |
0 |
4302.025126 |
14594 |
0.24323333 |
|
7*1e-9 |
0.999999993 |
1.81922E-12 |
4208.959799 |
14336 |
0.23893333 |
|
6*1e-9 |
0.999999994 |
0 |
4872.673367 |
16558 |
0.27596667 |
|
5*1e-9 |
0.999999995 |
0 |
5254.140704 |
17848 |
0.29746667 |
|
4*1e-9 |
0.999999996 |
0 |
5111.964824 |
17354 |
0.28923333 |
|
3*1e-9 |
0.999999997 |
0 |
5183.090452 |
17612 |
0.29353333 |
|
2*1e-9 |
0.999999998 |
0 |
6082.698492 |
20465 |
0.34108333 |
|
1.00E-09 |
0.999999999 |
0 |
6494.728643 |
21881 |
0.36468333 |
|
1.00E-10 |
1 |
0 |
10189.42714 |
33988 |
0.56646667 |
|
1.00E-11 |
1 |
0 |
13439.73367 |
44875 |
0.74791667 |
|
1.00E-12 |
1 |
0 |
17556.1809 |
58167 |
0.96945 |
|
1.00E-13 |
1 |
0 |
19906.98492 |
65831 |
1.09718333 |
|
1.00E-14 |
1 |
0 |
23540.1809 |
81247 |
1.35411667 |
|
1.00E-15 |
1 |
0 |
33767.99497 |
117164 |
1.95273333 |
|
1.00E-16 |
1 |
0 |
34384.37688 |
118141 |
1.96901667 |
|
1.00E-17 |
1 |
0 |
28723.54774 |
97890 |
1.6315 |
|
1.00E-18 |
1 |
0 |
40934.60302 |
139877 |
2.33128333 |
|
1.00E-19 |
1 |
0 |
32035.70352 |
107708 |
1.79513333 |
|
1.00E-20 |
1 |
0 |
33375.62814 |
111770 |
1.86283333 |
|
1.00E-21 |
1 |
0 |
34949.13065 |
117591 |
1.95985 |
|
1.00E-30 |
1 |
0 |
29546.60302 |
99119 |
1.65198333 |
|
1.00E-40 |
1 |
0 |
35771.70854 |
121475 |
2.02458333 |
|
1.00E-50 |
1 |
0 |
34268.64322 |
116553 |
1.94255 |
|
1.00E-100 |
1 |
0 |
34817.75377 |
121115 |
2.01858333 |
将迭代次数画成图
和minst1 的图像向差不多，在δ>1e-17的区间上都相对平滑，在1e-17以后变得波动，如果将0和1的迭代次数画在一起
0的迭代次数曲线要陡一些。用同样的办法在1e-7到1e-9的区间上拟合曲线
|
x |
16.11809565,16.22345617,16.3412392,16.47477059,16.62892127,16.81124283,17.03438638,17.32206846,17.72753356,18.42068074,18.52604126,18.6438243,18.77735569,18.93150637,19.11382792,19.33697148,19.62465355,20.03011866,20.72326584 |
|
y |
1209.934673,1421.145729,1644.38191,1699.180905,2013.98995,2044.592965,2423.824121,2582.422111,3003.592965,3712.859296,4286.18593,4302.025126,4208.959799,4872.673367,5254.140704,5111.964824,5183.090452,6082.698492,6494.728643 |
|
拟合方程式：Y = a + b·X |
|
|
a = -17686.9878549532 |
|
|
b = 1177.34374258058 |
|
|
相关系数 R2：0.987287995583678 |
得到数据
|
δ |
实测迭代次数 n |
计算迭代次数n |
计算值/实测值 |
|
1.00E-05 |
7.708542714 |
-4132.3171 |
-536.0698193 |
|
1.00E-06 |
136.2261307 |
-1421.382949 |
-10.43399634 |
|
1.00E-07 |
1209.934673 |
1289.551202 |
1.065802337 |
|
9.00E-08 |
1421.145729 |
1413.596746 |
0.994688101 |
|
8.00E-08 |
1644.38191 |
1552.267866 |
0.943982573 |
|
7.00E-08 |
1699.180905 |
1709.480215 |
1.006061339 |
|
6.00E-08 |
2013.98995 |
1890.968554 |
0.938916579 |
|
5.00E-08 |
2044.592965 |
2105.623698 |
1.02984982 |
|
4.00E-08 |
2423.824121 |
2368.340362 |
0.977109 |
|
3.00E-08 |
2582.422111 |
2707.041049 |
1.048256611 |
|
2.00E-08 |
3003.592965 |
3184.412857 |
1.060201197 |
|
1.00E-08 |
3712.859296 |
4000.485353 |
1.077467535 |
|
9.00E-09 |
4286.18593 |
4124.530897 |
0.962284643 |
|
8.00E-09 |
4302.025126 |
4263.202017 |
0.99097562 |
|
7.00E-09 |
4208.959799 |
4420.414366 |
1.050239151 |
|
6.00E-09 |
4872.673367 |
4601.902705 |
0.944430779 |
|
5.00E-09 |
5254.140704 |
4816.557849 |
0.916716571 |
|
4.00E-09 |
5111.964824 |
5079.274513 |
0.993605138 |
|
3.00E-09 |
5183.090452 |
5417.9752 |
1.045317509 |
|
2.00E-09 |
6082.698492 |
5895.347008 |
0.969199281 |
|
1.00E-09 |
6494.728643 |
6711.419504 |
1.033364113 |
|
1.00E-10 |
10189.42714 |
9422.353655 |
0.924718684 |
|
1.00E-11 |
13439.73367 |
12133.28781 |
0.90279228 |
|
1.00E-12 |
17556.1809 |
14844.22196 |
0.845526828 |
|
1.00E-13 |
19906.98492 |
17555.15611 |
0.881859115 |
|
1.00E-14 |
23540.1809 |
20266.09026 |
0.860914805 |
|
1.00E-15 |
33767.99497 |
22977.02441 |
0.680437924 |
|
1.00E-16 |
34384.37688 |
25687.95856 |
0.747082277 |
|
1.00E-17 |
28723.54774 |
28398.89271 |
0.988697252 |
|
1.00E-18 |
40934.60302 |
31109.82686 |
0.759988483 |
|
1.00E-19 |
32035.70352 |
33820.76101 |
1.055720877 |
|
1.00E-20 |
33375.62814 |
36531.69516 |
1.094562026 |
|
1.00E-21 |
34949.13065 |
39242.62932 |
1.122849942 |
将迭代次数画成曲线
相对近似。所以
S（minst0）81*30*2-（1,0）的迭代次数可以相对精确的表示为
n=-17686.9878549532+1177.34374258058*（-ln δ）
同样将迭代次数的倒数理解成频率，就得到了
S（minst1）81*30*2-（1,0） … 1/（-3307.56+272.67（-ln δ））
S（minst0）81*30*2-（1,0） …1/（-17686.98+1177.34*（-ln δ））
所以minst0和minst1的图像对应不同的收敛标准δ都有各自的特征频率。
实验数据
Random rand1 =new Random();
int ti1=rand1.nextInt(98)+1;
tw[a][b]=((double)ti1/100);
学习率0.1
S（minst0）81*30*2-（1,0）的数据
1.00E-05
f2[0] f2[1] 迭代次数
0.999998 7.62E-06 5
0.999999 4.50E-07 5
1 8.72E-06 5
1 2.63E-06 5
1 8.90E-07 5
1 2.79E-06 5
0.999999 1.13E-09 6
1 2.00E-06 5
1 9.81E-10 6
1 1.07E-09 6
0.999999 4.84E-06 5
0.999999 9.67E-10 6
1 1.51E-06 5
0.999999 3.16E-06 5
1 1.11E-09 6
1 9.48E-10 6
0.99999 ######## 41
1 1.15E-09 6
0.999998 1.14E-09 6
1 3.56E-06 5
0.999998 9.30E-10 6
0.999999 2.60E-06 5
1 8.88E-07 5
0.999999 1.49E-06 5
1 3.99E-06 5
0.999998 1.42E-06 5
0.999999 9.32E-07 5
0.999999 1.86E-06 5
1 3.24E-06 5
1 1.51E-06 5
0.999998 6.83E-06 5
0.999999 1.16E-09 6
0.99999 0 135
1 7.46E-06 5
0.999999 8.65E-07 5
1 1.01E-09 6
0.999998 5.64E-06 5
0.999997 3.92E-07 5
0.999999 1.99E-06 5
1 7.55E-06 5
1 7.38E-07 5
1 7.65E-07 5
0.999999 1.71E-06 5
1 8.41E-07 5
0.999999 1.15E-09 6
1 1.13E-09 6
0.999999 1.62E-06 5
1 6.34E-06 5
1 9.38E-07 5
1 5.41E-06 5
1 9.91E-06 5
0.999997 1.23E-09 6
0.999999 1.15E-09 6
0.999998 1.16E-06 5
1 9.75E-07 5
0.999999 9.38E-06 5
1 1.15E-09 6
1 3.73E-07 5
1 1.14E-09 6
1 9.14E-06 5
1 3.67E-06 5
0.999999 1.27E-06 5
1 4.63E-06 5
0.999999 1.28E-06 5
1 1.15E-09 6
1 1.37E-06 5
1 1.22E-09 6
0.999999 8.34E-06 5
0.999999 7.08E-07 5
0.999996 3.07E-06 5
0.999998 2.96E-06 5
0.99999 0 150
1 1.15E-09 6
1 4.19E-07 5
0.999998 7.17E-06 5
1 2.58E-06 5
1 5.06E-07 5
0.999997 1.14E-09 6
0.999998 2.28E-06 5
1 8.82E-07 5
0.999999 5.21E-06 5
1 9.29E-06 5
1 1.30E-06 5
1 9.78E-10 6
1 1.05E-09 6
1 1.24E-06 5
1 1.03E-06 5
0.999999 1.94E-06 5
0.999999 5.98E-06 5
1 1.98E-06 5
1 3.73E-06 5
1 1.72E-06 5
1 2.35E-06 5
1 1.16E-09 6
1 1.98E-06 5
1 9.91E-07 5
1 6.29E-06 5
0.999994 1.15E-06 5
0.999999 6.34E-07 5
1 7.80E-07 5
0.999999 1.07E-09 6
1 1.15E-09 6
1 4.64E-06 5
1 1.63E-06 5
1 9.91E-10 6
0.999999 6.25E-06 5
1 6.51E-07 5
0.999999 3.54E-06 5
1 9.38E-07 5
0.999999 6.65E-07 5
0.999999 7.32E-07 5
0.999999 9.09E-06 5
1 2.07E-06 5
0.999999 1.54E-06 5
1 9.67E-07 5
1 1.04E-09 6
1 7.58E-06 5
0.999999 2.67E-06 5
0.999999 2.44E-06 5
0.999999 1.18E-09 6
1 1.07E-09 6
1 8.52E-07 5
1 2.59E-06 5
0.999999 3.59E-06 5
0.999997 5.87E-07 5
0.999996 7.76E-07 5
1 9.34E-06 5
1 1.13E-09 6
1 8.44E-06 5
0.999997 1.08E-09 6
1 5.02E-10 6
1 1.80E-06 5
0.999999 2.00E-06 5
1 2.86E-07 5
0.999999 3.11E-06 5
1 1.15E-09 6
0.999996 1.15E-09 6
0.999993 1.12E-09 6
0.999995 1.14E-09 6
1 2.82E-06 5
0.999999 1.14E-09 6
0.999999 3.69E-06 5
0.999999 1.08E-06 5
0.999995 6.39E-06 5
1 1.03E-09 6
1 1.15E-09 6
1 9.14E-06 5
1 4.60E-06 5
0.999995 8.47E-06 5
1 9.77E-06 5
1 1.17E-09 6
1 7.58E-07 5
0.999999 3.40E-06 5
0.999998 1.09E-09 6
0.999999 1.16E-09 6
0.999998 2.07E-06 5
1 6.63E-06 5
0.999998 2.27E-06 5
1 1.14E-09 6
1 8.69E-07 5
1 4.02E-06 5
1 9.60E-10 6
1 1.15E-09 6
0.999997 4.19E-07 5
1 3.44E-06 5
1 1.29E-06 5
0.999999 3.79E-07 5
1 5.28E-07 5
0.99999 0 181
1 4.92E-06 5
1 4.60E-06 5
0.999997 1.18E-09 6
1 4.07E-06 5
1 2.90E-06 5
0.999997 2.59E-06 5
0.999999 1.05E-09 6
0.999999 8.89E-09 6
1 4.74E-06 5
1 8.39E-06 5
0.999999 1.69E-06 5
1 6.51E-06 5
1 7.86E-06 5
0.999999 8.94E-06 5
1 9.82E-07 5
1 3.31E-06 5
1 4.14E-06 5
1 3.10E-07 5
1 8.46E-06 5
0.999991 7.89E-06 5
1 8.97E-06 5
1 4.09E-07 5
0.999999 7.84E-06 5
1 1.43E-09 6
0.999991 2.81E-07 5
1 1.14E-09 6
0.999999 1.09E-09 6
0.999998 1.33E-06 5
1 3.59E-06 5
1 9.35E-06 5
0.999999 2.46E-06 7.708543
1.00E-06
0.999999 1.39E-10 6
1 5.31E-10 6
0.999999 0 436
0.999999 0 543
0.999999 9.02E-10 6
0.999999 0 354
1 1.32E-10 6
1 6.86E-10 6
0.999999 0 499
0.999999 0 405
1 1.13E-09 6
0.999999 0 540
1 7.83E-10 6
1 3.13E-07 5
1 7.15E-10 6
1 1.09E-09 6
1 3.37E-10 6
1 3.54E-07 5
1 8.63E-10 6
1 1.05E-09 6
1 7.90E-07 5
0.999999 0 537
0.999999 0 395
0.999999 4.99E-10 6
0.999999 9.91E-10 6
1 1.84E-10 6
0.999999 5.95E-10 6
0.999999 7.93E-10 6
1 5.17E-10 6
1 9.82E-07 5
1 6.51E-07 5
0.999999 5.14E-10 6
0.999999 0 495
1 2.63E-10 6
1 1.87E-10 6
1 7.18E-10 6
1 1.52E-10 6
1 3.95E-07 5
1 5.56E-07 5
0.999999 0 597
1 7.52E-10 6
1 1.03E-09 6
1 3.63E-10 6
1 8.45E-10 6
1 3.76E-10 6
0.999999 0 444
1 3.64E-10 6
0.999999 1.46E-10 6
1 1.36E-10 6
1 1.15E-09 6
0.999999 6.35E-10 6
0.999999 0 828
1 1.05E-09 6
1 2.89E-07 5
0.999999 0 1282
1 1.15E-09 6
1 1.14E-09 6
1 1.34E-10 6
0.999999 0 538
0.999999 0 538
1 7.53E-10 6
1 9.59E-10 6
1 9.57E-07 5
0.999999 0 512
0.999999 0 367
0.999999 0 569
1 1.22E-09 6
1 1.12E-09 6
1 9.69E-10 6
0.999999 7.21E-07 5
0.999999 9.78E-10 6
1 9.27E-10 6
1 6.46E-10 6
1 9.59E-10 6
1 1.13E-09 6
1 9.87E-10 6
1 1.89E-10 6
1 3.11E-10 6
0.999999 0 402
1 5.41E-10 6
1 9.68E-07 5
0.999999 7.02E-07 5
1 2.55E-10 6
0.999999 5.00E-10 6
1 6.92E-10 6
1 3.41E-07 5
0.999999 7.77E-07 5
1 8.16E-10 6
1 1.11E-09 6
1 6.06E-10 6
0.999999 9.54E-10 6
0.999999 0 533
0.999999 0 505
0.999999 1.16E-09 6
0.999999 0 355
1 5.42E-10 6
0.999999 3.82E-07 5
1 2.03E-07 5
0.999999 0 546
1 3.38E-10 6
1 6.63E-10 6
1 3.59E-10 6
1 6.51E-10 6
1 2.67E-10 6
0.999999 0 1032
1 1.68E-10 6
1 1.60E-10 6
1 1.15E-09 6
0.999999 0 368
0.999999 0 516
1 9.78E-07 5
1 4.56E-10 6
1 8.30E-10 6
1 3.87E-10 6
1 7.85E-10 6
0.999999 1.01E-09 6
0.999999 0 403
0.999999 1.12E-09 6
0.999999 1.89E-10 6
1 1.03E-09 6
0.999999 0 647
1 3.39E-07 5
1 1.16E-09 6
1 6.81E-10 6
0.999999 1.28E-09 6
0.999999 3.18E-10 6
1 1.81E-10 6
0.999999 0 538
1 3.18E-10 6
1 4.56E-10 6
0.999999 0 502
0.999999 0 1048
0.999999 0 179
0.999999 1.11E-09 6
0.999999 0 490
1 8.34E-10 6
1 9.57E-10 6
1 4.88E-10 6
1 8.98E-10 6
1 6.42E-10 6
1 8.83E-07 5
0.999999 0 286
0.999999 2.81E-10 6
1 2.37E-10 6
0.999999 0 540
1 2.80E-10 6
1 5.56E-10 6
0.999999 0 1903
0.999999 0 266
1 1.05E-09 6
1 3.97E-10 6
1 5.36E-10 6
1 1.18E-09 6
0.999999 0 396
1 7.44E-10 6
1 4.50E-07 5
0.999999 0 385
0.999999 0 507
1 1.09E-09 6
0.999999 1.12E-09 6
0.999999 2.74E-10 6
1 1.64E-10 6
1 5.34E-10 6
1 7.43E-10 6
0.999999 0 325
0.999999 0 143
1 6.36E-10 6
1 1.04E-09 6
0.999999 6.21E-10 6
1 8.45E-10 6
1 5.47E-10 6
0.999999 1.66E-10 6
1 7.59E-10 6
0.999999 0 335
0.999999 0 514
1 2.07E-10 6
1 1.28E-09 6
1 2.54E-10 6
1 1.15E-09 6
0.999999 0 544
1 5.47E-10 6
1 1.17E-09 6
0.999999 0 916
0.999999 0 296
1 4.58E-10 6
0.999999 1.02E-09 6
1 3.36E-10 6
1 2.12E-10 6
0.999999 0 523
1 2.65E-10 6
1 5.14E-10 6
1 6.85E-10 6
0.999999 5.49E-10 6
1 5.63E-10 6
0.999999 6.82E-10 6
0.999999 0 408
1 2.68E-10 6
1 1.10E-09 6
0.999999 2.40E-07 5
1 6.21E-08 136.2261
1.00E-07
1 0 1111
1 0 1281
1 4.65E-11 6
1 0 1716
1 0 1619
1 0 1179
1 0 1014
1 0 875
1 6.66E-10 6
1 1.14E-09 6
1 0 809
1 0 772
1 0 1688
1 4.15E-10 6
1 1.18E-10 6
1 0 1579
1 5.38E-10 6
1 0 1098
1 0 1721
1 0 1562
1 0 1433
1 0 776
1 1.62E-10 6
1 0 1712
1 0 1818
1 0 1694
1 0 1384
1 0 1705
1 1.57E-10 6
1 0 1603
1 0 685
1 0 1548
1 0 1593
1 0 1435
1 0 2297
1 3.75E-10 6
1 0 1468
1 0 1161
1 1.11E-09 6
1 0 1759
1 4.32E-10 6
1 0 708
1 0 2065
1 0 1548
1 0 1556
1 0 1713
1 5.56E-10 6
1 9.70E-10 6
1 0 1866
1 0 1712
1 0 833
1 1.32E-09 6
1 0 1602
1 0 3829
1 0 1767
1 0 1704
1 0 1279
1 0 1486
1 0 1277
1 0 1500
1 0 1564
1 0 1505
1 6.32E-10 6
1 0 1393
1 0 689
1 0 921
1 0 3551
1 0 1613
1 0 1633
1 0 1514
1 6.08E-10 6
1 0 2205
1 0 1553
1 0 682
1 0 1652
1 0 1120
1 0 1761
1 0 1466
1 0 960
1 0 1680
1 0 2437
1 0 972
1 0 1813
1 5.94E-10 6
1 9.83E-10 6
1 1.26E-10 6
1 0 3068
1 0 1579
1 6.12E-10 6
1 0 1695
1 0 1632
1 0 1050
1 8.11E-11 6
1 0 1713
1 0 1699
1 0 1391
1 0 678
1 0 1711
1 0 2803
1 0 1091
1 0 1694
1 0 1637
1 0 963
1 0 1709
1 0 2186
1 0 2256
1 0 1707
1 0 1975
1 0 1805
1 6.10E-10 6
1 0 1943
1 4.48E-10 6
1 0 1278
1 0 4192
1 0 1964
1 1.39E-10 6
1 0 1427
1 0 1056
1 0 1413
1 0 2570
1 3.82E-10 6
1 5.29E-10 6
1 0 1044
1 0 1699
1 7.50E-11 6
1 0 1595
1 1.11E-09 6
1 0 1472
1 0 2027
1 0 600
1 0 1648
1 0 2883
1 2.74E-10 6
1 0 2033
1 0 612
1 0 1521
1 0 1454
1 0 1358
1 0 4486
1 0 1598
1 5.75E-10 6
1 0 1358
1 0 2682
1 7.08E-10 6
1 0 1570
1 4.15E-10 6
1 1.04E-09 6
1 5.98E-10 6
1 0 1271
1 0 1485
1 0 1537
1 6.67E-10 6
1 6.54E-10 6
1 0 1528
1 0 1589
1 0 1442
1 0 1706
1 0 1545
1 0 1456
1 0 1587
1 0 1553
1 1.81E-10 6
1 2.46E-10 6
1 0 1223
1 1.82E-10 6
1 0 1158
1 1.02E-09 6
1 9.26E-10 6
1 0 1427
1 0 1653
1 0 3642
1 0 2025
1 7.07E-10 6
1 0 1699
1 2.30E-10 6
1 8.77E-10 6
1 0 632
1 3.60E-10 6
1 1.02E-09 6
1 0 1677
1 0 814
1 1.09E-09 6
1 0 1943
1 1.16E-09 6
1 7.50E-10 6
1 0 1678
1 1.04E-09 6
1 0 1710
1 0 1699
1 0 1434
1 0 1676
1 0 490
1 0 1594
1 0 1708
1 0 2677
1 0 1707
1 0 1576
1 0 1648
1 0 1539
1 1.49E-10 1209.935
9*1e-8
1 0 3217
1 0 1863
1 7.73E-11 6
1 0 1094
1 0 815
1 0 1791
1 4.57E-10 6
1 4.93E-10 6
1 0 2518
1 0 1795
1 0 1767
1 5.64E-10 6
1 0 2163
1 0 4059
1 0 3715
1 5.09E-10 6
1 0 1802
1 0 1755
1 9.92E-10 6
1 0 1720
1 0 1815
1 0 900
1 0 1356
1 4.65E-10 6
1 0 1100
1 0 1779
1 0 1443
1 3.51E-10 6
1 5.21E-10 6
1 5.42E-10 6
1 0 698
1 9.74E-10 6
1 0 568
1 0 1595
1 1.19E-09 6
1 1.15E-09 6
1 0 1777
1 0 1215
1 0 1197
1 0 3602
1 0 1398
1 0 1258
1 0 1568
1 0 1327
1 9.02E-10 6
1 0 1739
1 5.59E-10 6
1 0 1735
1 0 2405
1 0 1752
1 0 896
1 3.20E-10 6
1 1.14E-10 6
1 0 1491
1 0 1448
1 1.08E-09 6
1 0 1689
1 0 1527
1 0 1554
1 0 1499
1 1.70E-10 6
1 0 1648
1 0 1687
1 0 1338
1 0 1784
1 3.16E-10 6
1 0 3262
1 0 1560
1 0 1303
1 0 1696
1 0 1130
1 3.55E-10 6
1 0 1040
1 0 897
1 1.15E-09 6
1 0 1362
1 6.21E-10 6
1 1.36E-10 6
1 0 2154
1 0 1131
1 0 1040
1 5.07E-10 6
1 0 2467
1 0 2132
1 0 1784
1 0 2689
1 0 2747
1 0 1543
1 0 1532
1 0 1902
1 1.10E-09 6
1 0 1820
1 0 1562
1 0 1405
1 0 1801
1 0 1453
1 0 1223
1 0 170
1 0 2199
1 0 3776
1 0 1674
1 0 1119
1 7.69E-11 6
1 0 1813
1 0 2318
1 0 3697
1 0 418
1 0 1686
1 2.56E-10 6
1 0 2111
1 0 1542
1 0 1969
1 0 1785
1 2.91E-10 6
1 0 1799
1 1.32E-10 6
1 0 1805
1 0 1703
1 1.03E-09 6
1 6.21E-10 6
1 0 2739
1 0 3789
1 0 189
1 0 1804
1 0 1967
1 0 1553
1 0 1725
1 0 1296
1 1.16E-10 6
1 0 2479
1 0 1786
1 0 2139
1 0 1634
1 0 3377
1 0 1708
1 0 1783
1 0 1835
1 0 1767
1 0 3700
1 0 1803
1 0 2285
1 0 1306
1 0 2434
1 2.42E-10 6
1 0 1620
1 0 1736
1 0 1688
1 0 3244
1 0 1426
1 0 1761
1 0 1707
1 0 726
1 0 1911
1 7.90E-11 6
1 0 1208
1 0 1208
1 0 1227
1 0 1475
1 0 1299
1 0 1600
1 1.04E-09 6
1 0 1539
1 0 1539
1 0 1423
1 0 1633
1 0 1666
1 0 1711
1 0 1671
1 1.17E-09 6
1 8.23E-10 6
1 0 4421
1 0 1874
1 0 2103
1 1.14E-09 6
1 0 3001
1 0 1815
1 0 497
1 2.36E-10 6
1 4.29E-10 6
1 0 746
1 0 1670
1 0 2955
1 0 2604
1 0 1455
1 0 2547
1 0 1318
1 0 1743
1 0 1788
1 0 1800
1 0 2279
1 0 1192
1 0 1799
1 0 1603
1 0 1754
1 0 2152
1 0 1579
1 0 1782
1 0 1086
1 0 1802
1 1.17E-10 1421.146
8*1e-8
1 0 2866
1 0 1919
1 0 1506
1 0 1706
1 0 2137
1 7.53E-10 6
1 0 1360
1 0 1672
1 0 1448
1 0 1736
1 0 1901
1 0 2506
1 0 1234
1 0 5209
1 0 2824
1 2.41E-10 6
1 3.11E-10 6
1 0 1905
1 0 1889
1 1.70E-10 6
1 0 1390
1 2.87E-10 6
1 0 2115
1 0 1781
1 0 1530
1 0 1283
1 0 1324
1 0 1856
1 1.06E-09 6
1 0 957
1 0 1622
1 0 2617
1 0 3674
1 0 1344
1 0 4364
1 0 1703
1 0 1498
1 0 1758
1 0 1428
1 5.22E-10 6
1 0 1871
1 0 1642
1 0 1896
1 0 1597
1 0 1878
1 0 1765
1 1.06E-09 6
1 0 1589
1 4.50E-10 6
1 0 1889
1 1.38E-09 6
1 0 2990
1 0 1458
1 0 2234
1 0 3360
1 1.08E-09 6
1 0 1265
1 9.82E-11 6
1 0 2054
1 0 1869
1 0 1550
1 0 2264
1 0 1784
1 0 1240
1 0 1853
1 6.73E-10 6
1 0 3310
1 0 1861
1 1.07E-09 6
1 0 1409
1 1.03E-09 6
1 0 1122
1 2.96E-10 6
1 0 1491
1 7.05E-10 6
1 0 1841
1 0 1471
1 0 1686
1 0 2279
1 0 922
1 0 1834
1 0 1942
1 0 1840
1 0 1928
1 9.24E-10 6
1 0 1254
1 0 3717
1 0 3104
1 0 1887
1 1.23E-10 6
1 0 1857
1 0 1912
1 0 1766
1 0 2819
1 0 1696
1 0 1739
1 0 1870
1 0 1893
1 0 1578
1 1.19E-09 6
1 0 1287
1 0 1262
1 0 1665
1 0 1327
1 0 2830
1 0 5894
1 1.65E-10 6
1 2.82E-10 6
1 0 1946
1 0 1634
1 2.63E-10 6
1 0 4497
1 0 1141
1 1.02E-09 6
1 0 3796
1 0 1605
1 0 1612
1 0 1829
1 0 2907
1 0 3297
1 0 1473
1 0 1067
1 0 1840
1 7.90E-11 6
1 0 2623
1 0 1799
1 0 1619
1 1.15E-09 6
1 1.45E-10 6
1 0 2015
1 0 1450
1 0 2053
1 4.42E-10 6
1 0 1308
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1 1.04E-10 1644.382
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1 7.3E-11 2044.593
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4*1e-9
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1.00E-21
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1.00E-30
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1 0 16432
1 0 29546.6
1.00E-40
1 0 52117
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1 0 35771.71
1.00E-50
1 0 77039
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1 0 34268.64
1.00E-100
1 0 183885
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1 0 10405
1 0 10411
1 0 22138
1 0 23021
1 0 17146
1 0 9476
1 0 34817.75
S（minst1）81*30*2-（1,0） 的数据
1.00E-05
0.999999 7.47E-06 5
1 6.94E-06 5
1 2.06E-06 5
0.999999 7.99E-06 5
1 1.54E-09 6
0.999999 7.12E-06 5
1 1.65E-09 6
1 6.15E-06 5
1 2.55E-06 5
1 1.09E-09 6
0.999998 3.63E-06 5
0.999999 1.40E-09 6
0.999998 1.62E-09 6
1 1.83E-06 5
0.999999 8.70E-06 5
0.999999 1.53E-06 5
1 1.70E-06 5
0.999998 1.96E-09 6
1 5.81E-06 5
0.999999 6.56E-09 6
0.99999 0 295
1 4.39E-06 5
1 3.66E-09 6
1 1.63E-06 5
0.999999 3.77E-09 6
0.999998 2.18E-09 6
0.999998 2.30E-06 5
0.999999 2.15E-06 5
1 3.51E-09 6
0.999998 2.64E-07 5
0.999993 9.53E-06 5
0.999999 8.74E-07 5
1 3.74E-07 5
1 2.37E-09 6
1 1.69E-09 6
0.999999 1.36E-09 6
0.999995 2.81E-09 6
0.999999 2.06E-09 6
1 5.86E-06 5
1 9.67E-09 6
0.999998 2.47E-09 6
0.999998 5.07E-06 5
0.999996 1.80E-09 6
1 3.02E-09 6
1 5.42E-09 6
0.999999 3.66E-06 5
0.999999 6.92E-06 5
0.999999 2.97E-09 6
0.999998 2.29E-09 6
1 4.31E-09 6
0.999998 2.60E-06 5
0.999998 2.60E-06 5
1 1.66E-06 5
0.999992 8.95E-06 5
1 6.63E-06 5
1 1.01E-09 6
0.999997 1.16E-07 6
1 8.52E-09 6
0.999999 2.82E-06 5
0.999999 1.66E-09 6
1 3.60E-09 6
0.999994 2.00E-08 6
0.999999 9.58E-06 5
0.999998 1.80E-09 6
1 4.99E-06 5
1 1.85E-06 5
1 2.76E-06 5
0.999999 4.78E-06 5
0.999995 7.40E-09 6
0.999999 8.30E-09 6
0.999997 1.12E-09 6
0.999999 5.10E-09 6
1 2.52E-09 6
1 3.17E-07 5
0.999999 4.55E-09 6
1 5.12E-06 5
0.999997 1.95E-09 6
0.999999 4.51E-06 5
0.999998 8.34E-09 6
1 1.30E-09 6
0.999998 1.37E-09 6
1 7.22E-06 5
0.999999 7.84E-09 6
0.99999 0 361
1 4.04E-06 5
1 1.78E-09 6
1 8.47E-10 6
0.999998 1.84E-09 6
0.999999 3.02E-09 6
0.999996 1.07E-09 6
0.999999 2.96E-06 5
1 4.98E-06 5
0.999998 4.11E-09 6
0.999999 1.98E-09 6
1 3.56E-09 6
1 1.10E-08 6
1 2.19E-09 6
0.999999 6.46E-07 5
1 2.45E-09 6
0.999999 2.74E-09 6
1 7.56E-06 5
1 4.05E-09 6
0.999999 8.86E-09 6
0.999999 1.74E-09 6
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0.999999 2.14E-06 12.60302
1.00E-06
0.999999 0 1066
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1 1.91E-09 6
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1 2.49E-09 6
0.999999 0 923
0.999999 5.21E-09 6
0.999999 4.50E-10 6
1 2.06E-07 5
0.999999 ######## 227
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1 1.17E-09 6
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0.999999 2.52E-09 6
1 7.14E-10 6
0.999999 1.74E-09 6
0.999999 0 551
0.999999 4.25E-10 6
0.999999 ######## 347
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1 5.22E-10 6
1 5.19E-10 6
1 3.23E-10 6
1 9.06E-07 5
1 1.41E-09 6
0.999999 0 655
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0.999999 0 1001
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0.999999 0 1034
0.999999 0 1049
1 1.94E-10 6
1 8.23E-09 6
0.999999 1.71E-08 237.3869
1.00E-07
1 0 1510
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1 2.64E-10 6
1 0 3202
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1 0 745
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1 0 2768
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1 1.42E-09 6
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1 1.11E-09 6
1 1.04E-09 6
1 0 3258
1 0 875
1 ######## 261
1 0 3258
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1 4.08E-10 6
1 0 818
1 0 635
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1 2.19E-10 1127.784
9*1e-8
1 0 1280
1 0 876
1 0 1932
1 1.78E-09 6
1 0 894
1 6.51E-10 6
1 0 1040
1 0 1027
1 4.75E-10 6
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1 6.66E-10 6
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1 9.49E-10 6
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1 1.56E-09 6
1 0 645
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1 4.66E-09 6
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1 ######## 259
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1 2.30E-09 6
1 7.34E-10 6
1 1.03E-09 6
1 0 618
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1 9.17E-10 6
1 0 797
1 0 980
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1 ######## 234
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1 2.92E-10 6
1 0 965
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1 0 859
1 1.41E-09 6
1 0 662
1 0 3755
1 0 2079
1 0 850
1 0 1818
1 0 1239
1 5.67E-10 6
1 0 389
1 3.16E-10 1035.764
8*1e-8
1 0 1188
1 0 938
1 0 1484
1 0 784
1 0 1271
1 0 3245
1 0 1468
1 0 1315
1 1.24E-09 6
1 0 1977
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1 1.27E-09 6
1 0 1097
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1 6.28E-10 6
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1 0 2856
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1 0 687
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1 9.46E-10 6
1 0 2385
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1 2.41E-09 6
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1 1.36E-09 6
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1 9.62E-10 6
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1 0 595
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1 0 675
1 1.46E-09 6
1 0 1520
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1 1.01E-10 1098.523
7*1e-8
1 0 1307
1 1.74E-09 6
1 0 3592
1 0 1984
1 1.40E-09 6
1 0 1840
1 0 1453
1 0 1705
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1 3.62E-10 6
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1 0 1029
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1 1.98E-09 6
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1 6.10E-10 6
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1 0 568
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1 4.26E-10 6
1 2.07E-10 6
1 0 288
1 0 767
1 0 480
1 0 2363
1 0 632
1 0 467
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1 1.87E-10 6
1 0 2384
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1 2.86E-10 6
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1 1.26E-09 6
1 1.44E-10 6
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1 0 864
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1 0 689
1 0 3112
1 0 478
1 1.36E-10 6
1 0 767
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1 0 1265
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1 0 448
1 5.79E-10 6
1 0 5336
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1 0 336
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1 1.54E-09 6
1 0 1416
1 0 781
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1 0 3529
1 0 2626
1 0 609
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1 0 935
1 0 1420
1 0 674
1 0 627
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1 4.97E-10 6
1 5.68E-10 6
1 2.89E-10 6
1 0 1809
1 0 1078
1 0 603
1 0 1337
1 0 1455
1 0 1506
1 0 513
1 6.31E-11 1191.849
6*1e-8
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3*1e-8
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2*1e-8
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1 3.93E-11 1590.714
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1 1.17E-12 1786.729
9*1e-9
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1 1E-195 1991.92
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1 3.3E-226 1979.291
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