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I have 2 vectors:

a = 1.0e-04*[0.110000000000000   0.140000000000000   0.140000000000000   0.140000000000000];
b =         [0.000011000000000   0.000014000000000   0.000014000000000   0.000014000000000];

by look at by eyes, it seems similar; but when I use this command:

a == b

then I got:

ans = 
  1×4 logical array  
   0   0   0   0

The expectation is:

ans = 
      1×4 logical array  
       1   1   1   1

Does anyone knows what wrong with this command in the matlab?

Thank you.

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2
  • $\begingroup$ See this SO question. $\endgroup$
    – Peter K.
    May 17, 2017 at 20:37
  • $\begingroup$ One way to fix it can be abs(a-b)<1e-15. $\endgroup$
    – msm
    May 18, 2017 at 0:14

3 Answers 3

1
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Floating point numbers are stored with a limited precision according to the IEEE754 conventions (search for this term in the net for further details).

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1
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Neither 0.11 nor 1E-4 can be exactly represented in floating point arithmetic. And the product of 2 numbers will introduce an extra error.

Testing for equality in floating point arithmetic is therefore more complex than it seems.

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0
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Have you tried subtracting them? I'm pretty sure this is due to the limited precision of the floating point numbers

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4
  • $\begingroup$ I tried, and I got all zeros, such as: [ 0.0000000000 -0.0000000000 0.0000000000 0.0000000000 0.0000000000] $\endgroup$ May 17, 2017 at 19:35
  • $\begingroup$ @phuc nguyen Despite that you have what seems to be a zero vector, it has actually been rounded down. $\endgroup$
    – Envidia
    May 17, 2017 at 20:42
  • $\begingroup$ @phucnguyen That negative sign in front of one of the numbers should make you suspect that these are not actually zeros. See also the documentation for the format command.. $\endgroup$
    – MBaz
    May 17, 2017 at 22:46
  • $\begingroup$ @Envidia: if they are rounded down, anyway to detect those very small numbers (for ex: 0.00000000000000002), I still cant detect them even use the format long command $\endgroup$ May 18, 2017 at 13:19

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