IF statement if == "A variable" not working

Trying to do a heat conduction simulation my and my IF statement not working

I have a variable called 'b' which equal to 'maximum timestep - 1' and I want to use and IF to record maximum temperature

The IF statement not working when I use IF == b, but works with IF = 9999

[Stephen23]

"IF statement if == "A variable" not working"

IF statement is working: you are comparing two different values, ergo EQ returns FALSE. You need to learn how to work with binary floating point numbers. For example, either ROUND the result or compare the absolute difference against a tolerance:

abs(A-B)<tol

This is a completely expected result with binary floating point numbers:

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

and also a brief overview of the topic:

https://0.30000000000000004.com/

Answer 1

[Fangjun Jiang]

Most likely it is a floating point data equal comparison problem. b is somewhere near 9999 but not exactly. Use round() or integer data type.

a=1-1/3

a = 0.6667

b=2/3

b = 0.6667

a==b

ans = logical
   0

Answer 2

[Voss]

"The IF statement not working when I use IF == b, but works with IF = 99999"

The behavior is not the same when using b vs when using 99999 because b is not exactly equal to 99999.

format long g

T= 1; %simulation time seconds
del_t= 1E-5; %time step size
N = T/del_t %Number of time discretization

N = 
                    100000

b=(T/del_t)-1 % N-1

b = 
                     99999

b looks like it is equal to 99999, but it's not.

b == 99999 % nope

ans = logical
   0

It's actually slightly smaller:

fprintf('%.40f',b)

99998.9999999999854480847716331481933593750000

Why? Because of https://en.wikipedia.org/wiki/Floating-point_arithmetic. See also https://www.mathworks.com/matlabcentral/answers/57444-why-is-0-3-0-2-0-1-not-equal-to-zero.

Consider the behavior of the following two loops:

counter = 1;
counter_hit_b = false;
while counter < N
    counter = counter+1;
    if counter == b
        counter_hit_b = true;
    end
end
disp(counter_hit_b)

   0

counter = 1;
counter_hit_99999 = false;
while counter < N
    counter = counter+1;
    if counter == 99999
        counter_hit_99999 = true;
    end
end
counter_hit_99999

counter_hit_99999 = logical
   1

The counter is 99999 at some point, but it is never b.

To get the right behavior using b instead of hard-coding 99999, you can define b to be exactly 99999 by using round.

b = round(T/del_t-1)

b = 
       99999

fprintf('%.40f',b)

99999.0000000000000000000000000000000000000000

b == 99999 % now b is exactly 99999

ans = logical
   1