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

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pages larry
pages larry 2019-6-11
回答： Alex Mcaulley 2019-6-11
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?

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Alex Mcaulley
Alex Mcaulley 2019-6-11
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
1
1

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