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Improving modal analysis code

Asked by Pinco on 6 Aug 2012

Hi everyone!

My code resolves a dynamic problem with coupled equation, so I study this problem in the modal space.

I have the matrix of MODAL solution (each column is the solution for time t*, with t* = 0,1,2,.. T) but I want to know the NODAL SOLUTION, so I wrote this code to execute inverse modal transformation (PHI is the modal matrix while BI2 is a translation coordinates matrix, such as g = BI2*PHI*y, where g is in the nodal space while y in the modal):

```% y is the modal solution matrix
% g is the nodal solution matrix
g = zeros(size(y));
for i=1:length(y)
g(:,i) = BI2*PHI*y(:,i);
end
```

In fact, the modal inverse relation is true column by column [y(:,i) -> g(:,i)].

How can I improve my code? This for loop is very slow when I have a lot of dof.. I think I have to rewrite it, but I don't know how.

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Answer by Matt Kindig on 6 Aug 2012

Hi Pinco,

What are the dimensions of BI2, PHI, and y? You might be able to use matrix multiplication directly to eliminate the loop. You may just be able to write it as:

```g = BI2*PHI*y;
```

Pinco on 8 Aug 2012

```size(y) = (n,1)
size(BI2) = (n,n)
size(PHI) = (n,n)
size(g) = (n,t)
```

where n is the number of dof selected and t is the number of time-point used (i.e if T = 250s and I use a discretization dt = 1s, t=0:250).

Now I can test your code ;)

Pinco on 18 Aug 2012

It works very well! I'm sorry for this time in my answer. Thank you very much!!!