1 /*Quadratic Curve Fitting Solution

2

3 Find a plausable quadratic fit to a sample of points

4

5 Nigel_Galloway@operamail.com

6 February 1st., 2009

7 */

8 set Sample;

9 param Sx {z in Sample};

10 param Sy {z in Sample};

11

12 var a;

13 var b;

14 var c;

15

16 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];

17 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];

18 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];

19

20 solve;

21

22 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);

23

24 data;

25

26 param:

27 Sample: Sx Sy :=

28 1 0 1

29 2 0.5 0.9

30 3 1 0.7

31 4 1.5 1.5

32 5 1.9 2

33 6 2.5 2.4

34 7 3 3.2

35 8 3.5 2

36 9 4 2.7

37 10 4.5 3.5

38 11 5 1

39 12 5.5 4

40 13 6 3.6

41 14 6.6 2.7

42 15 7 5.7

43 16 7.6 4.6

44 17 8.5 6

45 18 9 6.8

46 19 10 7.3

47 ;

48

49 end;