Thread Subject: sparse matrix and precision???

Please consider the following commands and outputs:
________________________________
K>> K(60884208)

ans =

   0.162500000000000

K>> KK(60884208)

ans =

   0.162500000000000

K>> KK(60884208) - K(60884208)

ans =

    -2.775557561562891e-17
___________________________________

K is a sparse matrix and KK is a full matrix. My question: How to make K uses the same numeric data as KK, since the min function on K and KK produces different results? :((

"Duc" wrote in message <is0m4o$7pc$1@newscl01ah.mathworks.com>...
> Please consider the following commands and outputs:
> ________________________________
> K>> K(60884208)
>
> ans =
>
> 0.162500000000000
>
> K>> KK(60884208)
>
> ans =
>
> 0.162500000000000
>
> K>> KK(60884208) - K(60884208)
>
> ans =
>
> -2.775557561562891e-17
> ___________________________________
>
> K is a sparse matrix and KK is a full matrix. My question: How to make K uses the same numeric data as KK, since the min function on K and KK produces different results? :((

You have not convinced us, (not even remotely convinced)
that those two numbers were ever identical from the two
sources.

>> format long g
>> K = 0.162500000000000;
>> Ksparse = sparse(K);
>> K - Ksparse
ans =
     0

Just because the two numbers are displayed as the same
to 15 digits, does not make them identical to the full 52
bits of precision afforded by a double.

Even if these two numbers were produced by the same
operations on a full versus sparse array, does not make
them assuredly identical.

Welcome to the world of floating point arithmetic.

John

Hi John,

So sorry for my deficiencies here. My first approach is the full matrix operations, then I switch to sparse matrix. So, it is assumed that K and KK is the same numeric data, but they're the same only few first iterations.

inside a for loop:
__________________________________________________________________
k = B_s'*C_shear *B_s*gaussWeights(q)*det(Jacob);
K = K + sparse(colMap, rowMap,k,GDof,GDof);
KK(elementDof,elementDof)=KK(elementDof,elementDof)+k;
___________________________________________________________________

After the loop, KK - K is not a zero matrix :(

"Duc" wrote in message <is0op4$dua$1@newscl01ah.mathworks.com>...
> Hi John,
>
> So sorry for my deficiencies here. My first approach is the full matrix operations, then I switch to sparse matrix. So, it is assumed that K and KK is the same numeric data, but they're the same only few first iterations.
>
> inside a for loop:
> __________________________________________________________________
> k = B_s'*C_shear *B_s*gaussWeights(q)*det(Jacob);
> K = K + sparse(colMap, rowMap,k,GDof,GDof);
> KK(elementDof,elementDof)=KK(elementDof,elementDof)+k;
> ___________________________________________________________________
>
> After the loop, KK - K is not a zero matrix :(

The point is that when you add more than two numbers in
floating point arithmetic, the sequence that you add them
matters.

>> (.3 + .2 + .6) == (.6 + .3 + .2)
ans =
     0

There is NO presumption that the sequence of operations
is identical for a sparse versus floating point operation,
nor should you EVER trust the least significant bits of
such an operation.

As I said, welcome to the floating point world.

John

Very happy to enter the world of floating point arithmetic :)

I've fixed the problem after two hours of debugging. It was my mistake (K\f instead of K(active,active)\f(active)) leads to the confusion :D

Thank you very much, John. Have a nice time!