Different matrix multiplication results from the sparse and full version of the same matrix

Hello everyone,

I found that for some matrix, if its sparse form and full form multiplied by the same vector, it could get the different results:

clearvars
v1 = [0 0 1 0 1 3;0 0 0 0 0 0];
v2 = sparse(v1);
gene = sqrt([2 3 5 7 11 13])';
disp(v1*gene==v2*gene)

The code above generates 0 1, which means that the first element of the matrix multiplication is inconsistent.

However if you have only v1 = [0 0 1 0 1 3], which is the inconsistent line, it gets correct again.

I've tried it on matlab 2016a,2017b,2019a,all got 0 and 1.

How spooky it is ! Can anybody tells me why it is like this?

[KALYAN ACHARJYA]

It generated

   1
   1
>> 

[pages larry]

I tried it on matlab 2016a,2017b and 2019a, what about you?

Answer 1

[Alex Mcaulley]

That is the floating point error (it is not related with sparse or full matrix). See this:

clearvars
v1 = [0 0 1 0 1 3;0 0 0 0 0 0];
v2 = sparse(v1);
gene = sqrt([2 3 5 7 11 13])';
v1*gene-v2*gene

ans =

   1.0e-14 *

    0.3553
         0
         

Then, the command "==" is not a good idea to deal with this. Use ismembertol for example:

 ismembertol(v1*gene,v2*gene,eps)

ans =

  2×1 logical array

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   1