least_square_fit.c
fitting u=1.0+2.0*x+3.0*t+4.0*x*x+5.0*x*t+6.0*t*t+7.0*x*x*x+ 
          8.0*x*x*t+9.0*x*t*t+10.0*t*t*t; 
terms used to find fit 
a^0 b^0  

a^1 b^0  
a^0 b^1  
 
the function generating data set  
fit with 2 variables to 1 power using 3 terms 
the function generating data set  
check_2d k=35, amin=0, amax=2.5, bmin=0, bmax=1 
               umin=1, umax=216.135 

Least Square Fit is u = 
   -38.7832 * a^0 * b^0  
   66.0013 * a^1 * b^0  
   45.7315 * a^0 * b^1  
rms_err=21.5716, avg_err=18.6921, max_err=53.3299 

terms used to find fit 
a^0 b^0  

a^1 b^0  
a^0 b^1  
 
a^2 b^0  
a^1 b^1  
a^0 b^2  
 
the function generating data set  
fit with 2 variables to 2 power using 6 terms 
the function generating data set  
check_2d k=35, amin=0, amax=2.5, bmin=0, bmax=1 
               umin=1, umax=216.135 

Least Square Fit is u = 
   7.03326 * a^0 * b^0  
   -30.6774 * a^1 * b^0  
   -14.1527 * a^0 * b^1  
   33.5185 * a^2 * b^0  
   31.4919 * a^1 * b^1  
   27.678 * a^0 * b^2  
rms_err=3.07644, avg_err=2.58996, max_err=6.929 

terms used to find fit 
a^0 b^0  

a^1 b^0  
a^0 b^1  
 
a^2 b^0  
a^1 b^1  
a^0 b^2  
 
a^3 b^0  
a^2 b^1  
a^1 b^2  
a^0 b^3  
 
the function generating data set  
fit with 2 variables to 3 power using 10 terms 
the function generating data set  
check_2d k=35, amin=0, amax=2.5, bmin=0, bmax=1 
               umin=1, umax=216.135 

Least Square Fit is u = 
   1 * a^0 * b^0  
   2 * a^1 * b^0  
   3 * a^0 * b^1  
   4 * a^2 * b^0  
   5 * a^1 * b^1  
   6 * a^0 * b^2  
   7 * a^3 * b^0  
   8 * a^2 * b^1  
   9 * a^1 * b^2  
   10 * a^0 * b^3  
rms_err=2.79503e-13, avg_err=2.03881e-13, max_err=9.55236e-13