How do can I solve for 2 unknowns in one equation given a data set for x and y.

The equation is (A/2)*[1+(alpha/2)+cos(2*pi*x)-(alpha/4)*cos(4*pi*x)]:

I need to solve for A and alpha, given 50 points for x and y:

x = [0, 0.013824885, 0.034562212, 0.057603687, 0.073732719, 0.094470046, 0.119815668, 0.142857143, 0.168202765, 0.188940092, 0.198156682, 0.223502304, 0.246543779, 0.264976959, 0.274193548, 0.290322581, 0.299539171, 0.315668203, 0.331797235, 0.359447005, 0.380184332, 0.398617512, 0.421658986, 0.447004608, 0.474654378, 0.497695853, 0.525345622, 0.525345622, 0.548387097, 0.571428571, 0.599078341, 0.629032258, 0.652073733, 0.665898618, 0.68202765, 0.695852535, 0.711981567, 0.730414747, 0.748847926, 0.767281106, 0.783410138, 0.797235023, 0.813364055, 0.841013825, 0.866359447, 0.882488479, 0.896313364, 0.914746544 ,0.928571429, 0.958525346];

y = [0.002808989, 0.008426966, 0.019662921, 0.030898876, 0.047752809, 0.06741573, 0.098314607, 0.146067416, 0.188202247, 0.22752809, 0.25, 0.303370787, 0.342696629, 0.379213483, 0.390449438, 0.401685393, 0.412921348, 0.424157303, 0.424157303, 0.426966292, 0.424157303, 0.424157303, 0.415730337, 0.407303371, 0.401685393, 0.398876404, 0.401685393, 0.401685393, 0.407303371, 0.41011236, 0.421348315, 0.426966292, 0.429775281, 0.429775281, 0.424157303, 0.415730337, 0.398876404, 0.379213483, 0.345505618, 0.311797753, 0.278089888, 0.25, 0.216292135, 0.162921348, 0.115168539, 0.087078652, 0.070224719, 0.050561798, 0.033707865, 0.016853933];

[Walter Roberson]

Do you want one solution per point, or do you want a least-squared fit?

Answer 1

[the cyclist]

Having plotted (x,y), I'm guessing that the answer to Walter's question is that you want a single best-fit equation to those points.

If you have the Statistics Toolbox, you can do that with the nlinfit() function.

doc nlinfit

for details.

Also, if you search this forum on "cyclist" and "nlinfit", you should be able to find a couple examples I have posted here.

Answer 2

[SooShiant]

Here is a simple example which you can change the equation and range and solve yours. The equation is 12x+9y+7z-60=0 where x,y,z are integers varies 0 to 10:

x=[0:1:10];
y=[0:1:10];
z=[0:1:10];
[X,Y,Z]=ndgrid(x,y,z);
F=12.*X+9.*Y+7.*Z-60;
idx=find(F==0);
[X(idx(:)),Y(idx(:)),Z(idx(:))];

Equations of this type are known as Diophantine equations.