Problem with equating for loop index to a variable.

I run the following code and it does not produce the expected results:

 % code
clear all

 FlowRate=0.6;
 for ThermalImpCurve = 0.2:0.2:1.6

    if FlowRate==ThermalImpCurve
        ThermalImpCurve
        break;
    end

 end

if the variable FlowRate is 0.6 or 1.4 the loop does not break.

[Stephen23]

Welcome to the world of floating point number calculations!. This is such a common topic that the wiki has an explanation of it too:

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

There are hundreds of threads asking the same question (with the same answer)

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

http://www.mathworks.com/matlabcentral/answers/69-why-does-1-2-3-1-3-not-equal-zero

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

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

http://www.mathworks.com/matlabcentral/answers/17391-round-error-using-if-statement-two-things-don-t-equal-each-other

and finally:

http://www.mathworks.com/matlabcentral/answers/97069-how-can-i-compare-numbers-for-equality-within-a-tolerance-in-matlab-8-0-r2012b

Answer 1

[Roger Stafford]

You should read Cleve Moler's document on the subject at

   http://www.mathworks.com/company/newsletters/news_notes/pdf/Fall96Cleve.pdf

The trouble in this particular example is that binary floating point numbers are incapable of being exactly equal to values such as 0.6 or 1.4, so matlab must approximate these values. As it happens, its approximation for the original ‘FlowRate’ is slightly different from that generated by the colon operator in ThermalImpCurve, hence the failure to recognize your intended equalities. You should not demand exact equality in such situations but allow tiny error tolerances.

[Jake G]

Thank you! That was very helpful

[Roger Stafford]

To add to the discussion above, here are the two differing binary representations of 0.6 . FlowRate=0.6 in matlab’s binary double is actually represented by:

   0.10011001100110011001100110011001100110011001100110011

whereas ThermalImpCurve = 0.2:0.2:1.6 at the third element is represented by:

   0.10011001100110011001100110011001100110011001100110100

As you can see, they differ only by 1 in the least bit out of 53 bits. Neither value is exactly 0.6, which would require infinitely many binary digits. FlowRate is rounded down, whereas ThermalImpCurve(3) was rounded up and is a bit farther off the correct value. This latter is probably due to the fact that the 0.2 increment itself in ThermalImpCurve cannot be exactly represented and so there is possibly a cumulative effect.