i1 16 64 400 25 8 8 i2 1 1 1 4 3 3 i3 4 20 40 4 100 200 min 10 15 35 14 30 35 max 10 20 45 16 30 45
How can I get the function of this correlation?
i1 16 64 400 25 8 8 i2 1 1 1 4 3 3 i3 4 20 40 4 100 200 min 10 15 35 14 30 35 max 10 20 45 16 30 45
How can I get the function of this correlation?
If we can assume the function has the form: $f(i_1,i_2,i_3)=a\times i_1 +b\times i_1+c\times i_1$
If we had the exact value of the function at 3 different$(i_1,i_2,i_3)$ then the coefficients could be driven deterministically by solving a $3\times 3$ matrix equation.
Here we are given max and min value of a given combination so a good approach will be:
1.choose 3 equations out of 6 (20 cases)
2.solve the $3\times 3$ matrix equation once for min and once for max and derive eight(two cases for each equation) $f(i_1,i_2,i_3)$
3.check that $f(i_1,i_2,i_3)$ meets the constraints imposed by other 3 equations and chosen 3 equations( 3*2+3 = 9 in total)
If met, one possible $f(i_1,i_2,i_3)$ is found and go back to step 1
else If not met and there is a 6C3(all 20 cases are NOT checked) go back to step1
else If there is no more 6C3(all 20 cases are checked) output functions found