least_square_fit_3d.java
fit u 3 degree polynomial in 3 dimensions
terms used to find fit 
0   a^0 * b^0 * c^0
 
1   a^1 * b^0 * c^0
2   a^0 * b^1 * c^0
3   a^0 * b^0 * c^1
 
4   a^2 * b^0 * c^0
5   a^1 * b^1 * c^0
6   a^1 * b^0 * c^1
7   a^0 * b^2 * c^0
8   a^0 * b^1 * c^1
9   a^0 * b^0 * c^2
 
10   a^3 * b^0 * c^0
11   a^2 * b^1 * c^0
12   a^2 * b^0 * c^1
13   a^1 * b^2 * c^0
14   a^1 * b^1 * c^1
15   a^1 * b^0 * c^2
16   a^0 * b^3 * c^0
17   a^0 * b^2 * c^1
18   a^0 * b^1 * c^2
19   a^0 * b^0 * c^3
 
C[0]=-3242.387250238933
C[1]=4112.508377509684
C[2]=4963.5655203668775
C[3]=4712.222663224122
C[4]=-2034.5359521546275
C[5]=-2227.7104254453307
C[6]=-2033.1104254453542
C[7]=-2713.250237868938
C[8]=-2497.710425445328
C[9]=-2823.964523583276
C[10]=452.8112908341508
C[11]=487.53364142994394
C[12]=506.53364142994633
C[13]=556.5336414299486
C[14]=390.94709800191947
C[15]=497.53364142995235
C[16]=648.8112908341518
C[17]=675.5336414299469
C[18]=615.533641429945
C[19]=749.8112908341594
check_3d k=124, amin=0.0, amax=4.0, bmin=0.0, bmax=4.0
         cmin=0.0, cmax=4.0, umin=60.0, umax=181397.0
rms_err=360.8648823650948, avg_err=270.62396883372696, max_err=1549.4124235417112
 
fit u 4 degree polynomial in 3 dimensions
terms used to find fit 
0   a^0 * b^0 * c^0
 
1   a^1 * b^0 * c^0
2   a^0 * b^1 * c^0
3   a^0 * b^0 * c^1
 
4   a^2 * b^0 * c^0
5   a^1 * b^1 * c^0
6   a^1 * b^0 * c^1
7   a^0 * b^2 * c^0
8   a^0 * b^1 * c^1
9   a^0 * b^0 * c^2
 
10   a^3 * b^0 * c^0
11   a^2 * b^1 * c^0
12   a^2 * b^0 * c^1
13   a^1 * b^2 * c^0
14   a^1 * b^1 * c^1
15   a^1 * b^0 * c^2
16   a^0 * b^3 * c^0
17   a^0 * b^2 * c^1
18   a^0 * b^1 * c^2
19   a^0 * b^0 * c^3
 
20   a^4 * b^0 * c^0
21   a^3 * b^1 * c^0
22   a^3 * b^0 * c^1
23   a^2 * b^2 * c^0
24   a^2 * b^1 * c^1
25   a^2 * b^0 * c^2
26   a^1 * b^3 * c^0
27   a^1 * b^2 * c^1
28   a^1 * b^1 * c^2
29   a^1 * b^0 * c^3
30   a^0 * b^4 * c^0
31   a^0 * b^3 * c^1
32   a^0 * b^2 * c^2
33   a^0 * b^1 * c^3
34   a^0 * b^0 * c^4
 
C[0]=1.0000000014294415
C[1]=1.9999999990057802
C[2]=2.999999998979007
C[3]=3.999999998322437
C[4]=5.999999999678053
C[5]=7.00000000065431
C[6]=8.000000001017355
C[7]=9.999999999887734
C[8]=11.000000001144372
C[9]=13.000000000422688
C[10]=16.000000000336502
C[11]=16.999999999845606
C[12]=17.99999999973685
C[13]=19.999999999939224
C[14]=20.999999999750322
C[15]=22.999999999821355
C[16]=26.000000000182013
C[17]=26.99999999977008
C[18]=28.999999999722647
C[19]=31.000000000038426
C[20]=34.99999999994619
C[21]=36.00000000001534
C[22]=37.00000000002821
C[23]=39.000000000001116
C[24]=40.0000000000237
C[25]=42.00000000000836
C[26]=45.000000000000874
C[27]=46.000000000019874
C[28]=1.645883429546302E-11
C[29]=48.0000000000164
C[30]=51.99999999997177
C[31]=53.000000000016946
C[32]=55.00000000001857
C[33]=58.00000000002622
C[34]=61.99999999998337
check_3d k=124, amin=0.0, amax=4.0, bmin=0.0, bmax=4.0
         cmin=0.0, cmax=4.0, umin=60.0, umax=181397.0
rms_err=1.7606169929008373E-10, avg_err=1.3951644141050038E-10, max_err=6.111804395914078E-10