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

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Adam
Adam 2013-8-27
回答： SooShiant 2014-2-20
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];

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回答（2 个）

the cyclist
the cyclist 2013-8-27
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.
SooShiant
SooShiant 2014-2-20
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.

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