MATLAB: Do I get different results for this division

divisionMATLAB

Hello,

I have the following piece of code. I expect to get b = 0:

R1 = 1e3;
Cond = 2e-12;
b = 1/R1/Cond - 1/(R1*Cond); % The result is not zero

But if I try the following, the result is zero:

A = 4;
B = 2;
C = 1/A/B - 1/(A*B);

I thought that the operation 1/a/b was always equal to 1/(a*b). Maybe it's due to the fact that the variable Cond is small. I'd like to know why there are differences.

Thanks.

Best Answer

"I thought that the operation 1/a/b was always equal to 1/(a*b). "

Mathematically they are the same. But for numeric computations they are not at all the same, especially when you are using values large differences in magnitude. Basically you have forgotten to take into account the precision limits of floating-point values, and how floating-point errors propagate through a calculation.

"I expect to get b = 0:"

The values of R1 and Cond differ by fifteen orders, which is right on the limit of double precision. There is no reason to expect the two calculations to produce the same output..

This is a topic that has been discussed many times before:

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/69-why-does-1-2-3-1-3-not-equal-zero#answer_271

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

https://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0

https://www.mathworks.com/matlabcentral/answers/20830-1-0010-does-not-equal-1-0010

etc, etc, etc

Related Solutions

MATLAB: Bucle doesn’t end

Because the number 0.1 cannot be represented exactly in typical floating point systems. It will be off in approximately the 16th decimal place, and so will not be exactly 10 after 100 times through this loop.

You need to include a tolerance, if you want to check equality of floating point numbers.

You can read more details if you search for these keywords, but here is one good place.

MATLAB: Didn’t I get “Hello” word by running following script? if I change the value in if loop except 13.2 it gives me correct answer.

clc
tol = 10^-3 ;
display('code executing');
for number=1:0.1:15
    if abs(number-13.2)<=tol
        disp('Hello');
    end 
end

You should not compare flottant numbers using ==..you should subtract and check is the absolute value of difference is less then a specified tolerance.

Best Answer

Related Solutions

MATLAB: Bucle doesn’t end

MATLAB: Didn’t I get “Hello” word by running following script? if I change the value in if loop except 13.2 it gives me correct answer.

Related Question