Matlab equality problem. Please help.

Question

Jenny Chen 2018-10-3

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/422077-matlab-equality-problem-please-help

编辑： Stephen23 2018-10-4

Hi, this is my code.

theta(k) = 45
l = x.*cosd(theta(k))+y.*sind(theta(k));
l(1,1) == l(3,3);
x(1,1)*cosd(45)+ y(1,1)*sind(45) == x(3,3)*cosd(45)+ y(3,3)*sind(45);
x(1,1)+ y(1,1)==x(3,3)+ y(3,3);

However, matlab it saying

l(1,1) == l(3,3)

is false,

x(1,1)*cosd(45)+ y(1,1)*sind(45) == x(3,3)*cosd(45)+ y(3,3)*sind(45)

is false, and

x(1,1)+ y(1,1)==x(3,3)+ y(3,3)

is true. I am wondering why because I believe l(1,1) == l(3,3) is true.

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Rik 2018-10-3

在 MATLAB Online 中打开

Your code is not self-contained (i.e. we cannot run it independently of the code you have before this), and I don't understand what you mean with your code/notation.

A wild guess would be that you are checking equality on a non-integer data type, which means you might be encountering float rounding errors. If you run the code below, you can clearly see that 1.0000 does not equal 1.0000

a=1+eps*2;%very close to 1
b=sqrt(a);b=b^2;%do an operation and reverse it
clc,isequal(a,b)
disp(a)
disp(b)

Jenny Chen 2018-10-3

编辑：Stephen23 2018-10-4

在 MATLAB Online 中打开

Hello, sorry, this should be enough to run.

theta = [45];
[Pr,Pc] = size(P);
nt = length(theta);
x = zeros(Pr,Pc);
y = zeros(Pr,Pc);
for i = 1:Pr
    for j = 1:Pc
        x(i,j) = j - 1;
        y(i,j) = Pr - i;
    end
end
for k = 1:nt
    l = x.*cosd(theta(k))+y.*sind(theta(k));
    l(1,1) == l(3,3)
    x(1,1)*cosd(45)+ y(1,1)*sind(45) == x(3,3)*cosd(45)+ y(3,3)*sind(45)
    x(1,1)+ y(1,1)==x(3,3)+ y(3,3)
end

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Answer 1

Stephen23 2018-10-4

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/422077-matlab-equality-problem-please-help#answer_339672

编辑：Stephen23 2018-10-4

在 MATLAB Online 中打开

You have to learn about floating point numbers, and why you should not test them for equality like that. Always compare the absolute difference against a tolerance, like this:

abs(A-B)<tol

Start by reading these:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

To see the "real" value download James Tursa's FEX submission:

https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

"I am wondering why because I believe l(1,1) == l(3,3) is true"

If you use num2strExact on both of those values, you will find that they are not the same, and MATLAB's output is correct. That is why you should compare the absolute difference against a tolerance.