Operations on portions of matrices to the end of the matrices.

First, let me start off by thanking this matlab answers community for its tremendous support for those of us new to the mathematical programming world. I've already been helped immensely by many great minds.

I'm running across an issue at the moment that I cannot wrap my head around and could use some help. I have two matrices, K & Beta. K is always 'n' rows by 4 columns. Beta is also always 'n' rows but can possibly have more columns than K.

The problem is to do mathematical operations on portions of the K and Beta matrices and combine the results in a K_structure matrix. Essentially I want to do the following:

    K_structure = Beta(1:4,:)'*K(1:4,:)*Beta(1:4,:) + Beta(5:8,:)'*K(5:8,:)*Beta(5:8,:) + Beta(9:12,:)'*K(9:12,:)*Beta(9:12,:) + ...

So, the first 4 rows of Beta' times the first 4 rows of K times the first 4 rows of Beta then plus the next 4 rows of Beta' times the next 4 rows of K times the next 4 rows of Beta + ... and so on until the end of Beta and K are reached. Based on the program the end row is a multiple of 4 (i.e. 4, 8, 12, 16, etc.)

Any help would be terrific.

Answer 1

[Matt J]

Another approach, using FEX:mat2tiles

    Kd=mat2tiles(sparse(K),[4,4]);
      Kd=blkdiag(Kd{:});

    K_structure = Beta.'*Kd*Beta;

Essentially, you should really be maintaining K as a (sparse) block diagonal matrix with 4x4 blocks instead of stacking the 4x4 blocks in an 4mx4 matrix.

[Mark]

I think I need to buy you a drink if I ever meet you Matt.

I'm getting an error with the 'mat2tiles' function. Perhaps it's in a library I don't have or not included with the student version? I see on the link you sent that it only mentions 2012b I have student 2012a grrr.

Undefined function 'mat2tiles' for input arguments of type 'double'.

Error in Truss_2D (line 68) Kd=mat2tiles(sparse(K),[4,4]);

[Mark]

I figured out it was a function needed that you so kindly provided. Thanks again. I'll have to see if I can spend some time trying to understand how the function works. Thanks

http://www.mathworks.com/matlabcentral/fileexchange/35085-split-nd-array-into-equal-sized-cells

Answer 2

[Honglei Chen]

Why not just use a for loop?

Let's say your K is 12 rows, so

Niteration = 12/4;
K_structure = zeros(size(Beta,2));
for m = 1:Niteration
  idx = (1:4)+(m-1)*4;
  K_structure = K_structure + Beta(idx,:)'*K(idx,:)*Beta(idx,:);
end

[Mark]

I modified it a little to be:

Niteration = 12/4; K_structure = zeros(size(Beta,2)) for m = 1:Niteration idx5 = 1:4+(m-1)*4; K_structure = K_structure + Beta(idx5,:)'*K(idx5,:)*Beta(idx5,:); end K_structure

and I got an error:

Error using * Inner matrix dimensions must agree.

Error in Truss_2D (line 71) K_structure = K_structure + Beta(idx5,:)'*K(idx5,:)*Beta(idx5,:);

To be honest, I'm not sure why I'm getting this error. it should be the transpose of a 4 row by 6 column matrix times a 4 row by 4 column matrix times a 4 row by 6 column matrix and each of those results added together. I must be missing something.

[Mark]

if I run the program with just

K_structure = Beta(1:4,:)'*K(1:4,:)*Beta(1:4,:)+Beta(5:8,:)'*K(5:8,:)*Beta(5:8,:)+Beta(9:12,:)'*K(9:12,:)*Beta(9:12,:)

I get the following results:

    1.0000         0   -1.0000         0         0         0
         0    1.0000         0         0         0   -1.0000
   -1.0000         0    1.3600   -0.4800   -0.3600    0.4800
         0         0   -0.4800    0.6400    0.4800   -0.6400
         0         0   -0.3600    0.4800    0.3600   -0.4800
         0   -1.0000    0.4800   -0.6400   -0.4800    1.6400

[Honglei Chen]

I forgot a bracket in my answer. I updated it.