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How to generate a vector with the required values

Dear all, I just noticed that if I create a vector like x=[.1:.1:.9] the result apparently is the same as creating it manually as x=[.1 .2 .3 .4 .5 .6 .7 .8 .9]; but it is not like that!
For example
>> x=[.1:.1:.9]
x =
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
>> x(3)==.3
ans =
0
how can you explain that? And how can I be sure to create vectors with the required values???
FIY I'm using Matlab 2009b on a Unix environment. Cheers, -Luca

  1 Comment

Jan
on 15 Feb 2011
Should we vote this question, because it is asked very frequently? Or should we not vote it, because the best answer would be not to ask the question at all? (sorry for this illogical formulation)

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3 Answers

Answer by Davide Ferraro on 15 Feb 2011
 Accepted Answer

The syntax:
x=[.1:.1:.9]
is creating a vector incrementally and due to Floating Point arithmetic approximation the obtained value may be different from the exact value from the vector definition.
Page, Troubleshooting Common Floating-Point Arithmetic Problems perfectly explains this with some possible approaches you may consider, especially if you are planning to do some "exact" comparison with ==.

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Answer by Jan
on 15 Feb 2011

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Answer by Bruno Luong
on 15 Feb 2011

As Davide wrote, colon() operator will build the array by increment of the step (actually half incremental from both ends), and numerical errors will accumulate.
A more accurate way is using linspace(), which is computed by integer multiplication of the step.
a = linspace(0,1,11)
a == [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]
For what you want, probably the only way to get the exact value as command line is
a = eval('[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]')

  3 Comments

Hmm, why use the eval ...
a = eval('[0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]')
b = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1]
isequal(a,b)
Right Jos, I should write
eval(['[ ' sprintf('0.%d ',0:10) ']'])
Jan
on 15 Feb 2011
I assume the suggested EVAL method will increase the OP's misunderstanding of using floating point numbers in Matlab.

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