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Matlab-matrix-multiplication and transposition precision

The following script should print out a 7x7 all-ones matrix because the equation is satisfied.

A = rand(5,7);
B = rand(5,7);

C = (A' * B)';
D =  B' * A;

C == D

Instead of this answer:

ans =

 1     1     1     1     0     1     1
 1     1     1     1     0     1     0
 1     1     1     1     1     1     1
 1     1     1     1     0     0     0
 1     0     1     1     1     1     1
 0     0     1     1     1     1     1
 0     1     1     0     1     1     1

I think this is a floating point precision issue because when the format long

numbers are different in C and D.

  • What am I doing wrong?
  • Where is this happening?
  • How can I avoid this?
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1 answer


You are not doing anything wrong - the computer has finite precision and your calculation shows it - just like 1e6 + 0.1 - 1e6

(try it in Matlab). One way to avoid this is to use some arbitrary precision library - but it will not "solve" it, it will just push the problem towards lower and lower numbers.

See these links for more information:

http://floating-point-gui.de/errors/comparison/



http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

By the way, format long

has nothing to do with actual precision, it just sets up how the numbers are formatted to be displayed .

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