alpar@1: /*Quadratic Curve Fitting Solution
alpar@1: 
alpar@1:   Find a plausable quadratic fit to a sample of points
alpar@1: 
alpar@1:   Nigel_Galloway@operamail.com
alpar@1:   February 1st., 2009
alpar@1: */
alpar@1: set Sample;
alpar@1: param Sx {z in Sample};
alpar@1: param Sy {z in Sample};
alpar@1: 
alpar@1: var a;
alpar@1: var b;
alpar@1: var c;
alpar@1: 
alpar@1: equalz1 :sum{z in Sample} a*Sx[z]*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} c*Sx[z]*Sx[z] = sum{z in Sample} Sy[z]*Sx[z]*Sx[z];
alpar@1: equalz2 :sum{z in Sample} a*Sx[z]*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z]*Sx[z] + sum{z in Sample} c*Sx[z] = sum{z in Sample} Sy[z]*Sx[z];
alpar@1: equalz3 :sum{z in Sample} a*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z] + sum{z in Sample} c = sum{z in Sample} Sy[z];
alpar@1: 
alpar@1: solve;
alpar@1: 
alpar@1: printf "\nbest quadratic fit is:\n\ty = %f %s %fx %s %fx^2\n\n", c, if b < 0 then "-" else "+", abs(b), if a < 0 then "-" else "+", abs(a);
alpar@1: 
alpar@1: data;
alpar@1: 
alpar@1: param:
alpar@1: Sample:   Sx    Sy :=
alpar@1:   1         0    1
alpar@1:   2       0.5  0.9
alpar@1:   3         1  0.7
alpar@1:   4       1.5  1.5
alpar@1:   5       1.9    2
alpar@1:   6       2.5  2.4
alpar@1:   7         3  3.2
alpar@1:   8       3.5    2
alpar@1:   9         4  2.7
alpar@1:  10       4.5  3.5
alpar@1:  11         5    1
alpar@1:  12       5.5    4
alpar@1:  13         6  3.6
alpar@1:  14       6.6  2.7
alpar@1:  15         7  5.7
alpar@1:  16       7.6  4.6
alpar@1:  17       8.5    6
alpar@1:  18         9  6.8
alpar@1:  19        10  7.3
alpar@1: ;
alpar@1: 
alpar@1: end;