Asked by Harshavardhan K
on 15 Jun 2018 at 6:47

CL = 0:0.5:8;

for i=1:1:17

fcn = @(CR) sind(CL(i)).^2 + sind(CR).^2 - ((0.5)*(sind(2*CL(i)))*(sind(2*CR))) - (2*(sind(CL(i)).^2)*(sind(CR).^2)) - sind(CL(i)-CR).^2;

CR(i) = fzero(fcn,1 );

disp(CR);

end

Iam trying to get a CR value for each value of CL but CR values come out to be always near 1 (which I know is incorrect).

Answer by Steven Lord
on 15 Jun 2018 at 13:52

Accepted Answer

When I run your code and store the results in a `table` array:

CL = 0:0.5:8; results = table(CL.', zeros(size(CL.')), zeros(size(CL.')), 'VariableNames', {'CL', 'CR', 'solution'}); for i=1:1:17

fcn = @(CR) sind(CL(i)).^2 + sind(CR).^2 - ((0.5)*(sind(2*CL(i)))*(sind(2*CR))) - (2*(sind(CL(i)).^2)*(sind(CR).^2)) - sind(CL(i)-CR).^2;

CR(i) = fzero(fcn,1 );

%disp(CR); results{i, 'CL'} = CL(i); results{i, 'CR'} = CR(i); results{i, 'solution'} = fcn(CL(i)); end

displaying that `table` shows that the value of your function for the solution found by `fzero` is extremely small for each value of CL.

results = 17×3 table

CL CR solution ___ _______ ___________

0 1 0 0.5 1 2.3366e-20 1 0.97978 -4.124e-20 1.5 0.97376 -2.6978e-19 2 0.97172 -3.3119e-19 2.5 1.04 7.5217e-19 3 0.97172 8.0976e-19 3.5 0.9755 8.3687e-19 4 1 1.0639e-18 4.5 0.98637 -6.0986e-19 5 0.97172 -2.575e-19 5.5 -1.2817 -2.3852e-18 6 -2.5999 -2.4937e-18 6.5 0.96 -2.6563e-18 7 0.99967 -6.2884e-18 7.5 -6.0998 -2.9273e-18 8 0.98114 -7.5894e-19

The values of CR found by `fzero` may not be ** the solution** you expected, but they seem from these results to each be

If we plot one of your functions, I see one reason why you may be confused. I'm using just one of the CL values over which you iterated, so I was able to simplify your function by removing the indexing on CL:

CL = 4; fcn = @(CR) sind(CL).^2 + sind(CR).^2 - ((0.5)*(sind(2*CL))*(sind(2*CR))) - (2*(sind(CL).^2)*(sind(CR).^2)) - sind(CL-CR).^2; CR2 = linspace(-3, 3, 1000); plot(CR2, fcn(CR2))

Look at the Y limits. The *maximum* value of your function over that interval is about 7e-18. That's pretty small.

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Answer by Walter Roberson
on 16 Jun 2018 at 6:34

Your function is an identity for all real values of CR and CL (I wouldn't want to promise for complex values.) **Everything** is a solution, and any plot of the function is just plotting numeric noise.

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