If statement not working for trig quad check

Hello all,

I've tried to make a simple trig quad check progam for one of my school classes, but I've ran into an error on the if statement that returns what angle my cartesian vector points to. I know that the math is correct and working as seen in the output, but the if statement is not selecting the correct value even though I'm pretty sure that the code should be.

Here is the code and output:

clear all
close all
clc

% Sample vectors
vec1 = [0.8373, 2.9192];
vec2 = [2.0376, 1.2927];
vec3 = [2.0508, -0.7287];
vec4 = [0.8720, -2.3708];
vec5 = [-1.0475, -3.0047];
vec6 = [-2.9724, -2.3876];
vec7 = [-4.1656, 0.7559];
vec8 = [-4.1700, 1.2655];
vec9 = [-2.9840, 2.9025];
vec10 = [-1.0618, 3.5280];

% Matrix with line-by-line function. For output readability
vel = [cart2polar(vec1); cart2polar(vec2); cart2polar(vec3);... 
    cart2polar(vec4); cart2polar(vec5); cart2polar(vec6); ...
    cart2polar(vec7); cart2polar(vec8);cart2polar(vec9); ...
    cart2polar(vec10)];


velT = array2table(vel,"VariableNames",{'Magnitues','Angle','Asin', ...
    'pi-sin', 'cosine','2pi-cosine'});
disp(velT)

    Magnitues     Angle       Asin      pi-sin    cosine     2pi-cosine
    _________    _______    ________    ______    _______    __________

     3.0369      0.27933     0.27933    2.8623    0.27933      6.0039  
     2.4131       1.0054      1.0054    2.1361     1.0054      5.2777  
     2.1764            0      1.2294    1.9122     1.9122       4.371  
     2.5261            0     0.35245    2.7891     2.7891       3.494  
     3.1821        3.477    -0.33545     3.477     2.8061       3.477  
     3.8126       4.0357    -0.89407    4.0357     2.2475      4.0357  
     4.2336            0     -1.3913    4.5329     1.3913      4.8919  
     4.3578            0     -1.2762    4.4177     1.2762       5.007  
     4.1628            0    -0.79924    3.9408    0.79924      5.4839  
     3.6843            0    -0.29234    3.4339    0.29234      5.9908  

Correct values are the values of sine and cosine that match in magnitude.

Row 3 would be 1.9122

Row 7 would be 1.3913

% Function
function vec_o = cart2polar(vec_i)

    % Magnitude of vector
    v = norm(vec_i);
    
    % Returns sine and cosine values
    theta_s = [asin(vec_i(1)/v), pi-asin(vec_i(1)/v)];
    theta_c = [acos(vec_i(2)/v), 2*pi-acos(vec_i(2)/v)];

    % Combines as vector
    theta = [theta_s, theta_c];
    gamma = 0;
    
    % If statement
    if (theta(1) == theta(3)) && (theta(1) ~= theta(2)) && (theta(1) ~= theta(4))
        gamma = theta(1);
        % Quad 1

    elseif theta(2) == theta(3) && (theta(2) ~= theta(1)) && (theta(2) ~= theta(4))
        gamma = theta(2);
        % Quad 2

    elseif theta(2) == theta(4)
        gamma = theta_c(2);
        % Quad 3

    elseif -theta(1) == theta(3)
        gamma = 2*pi-theta_c(1);
        % Quad 4

    else
    end

    % Returns values
    vec_o = [v, gamma, theta];
end

Thanks to anyone ahead of time

[Andrew Matteson]

Comment

The 1st set of zeros under the angles column is quad 2. The 2nd set is quad 4

Answer 1

[the cyclist]

I did not look in detail, but I'd be willing to bet that the problem lies in making comparisons between floating-point numbers, which may not be represented exactly.

Try making those comparisons to within a tolerance, for example

if abs(theta(1)-theta(3)) < 1.e-9

[Andrew Matteson]

Can do

[Andrew Matteson]

worked

[the cyclist]

Glad it worked out