How can I solve a linear system of equation Ax=b where A and b are changing in a for loop

Hi there.

I'm doing a dynamic force analysis problem and i need to determinate forces and torque on a four-bar linkage.

So I wrote a linear system Ax = b , but this is in a for loop (i = 1:360) and the components of A and b change at every step. (see photo)

For matrix A, I thought I need a 9x9 matrix that changes ad every step so,

for i = 1:360

.....

.....

A(9, 9, i) = [ 1,0,-1,0,0,0,0,0,0;

0,1,0,-1,0,0,0,0,0;

Ra2y(i),-Ra2x(i),Rb2y(i),-Rb2x(i),0,0,0,0,1;

0,0,1,0,-1,0,0,0,0;

0,0,0,1,0,-1,0,0,0;

0,0,-Rb3y(i),Rb3x(i),Rc3y(i),-Rc3x(i),0,0,0;

0,0,0,0,1,0,1,0,0;

0,0,0,0,0,1,0,1,0;

0,0,0,0,-Rc4y(i),Rc4x(i),-Rd4y(i),Rd4x(i),0];

and

b(9,1,i) = [m2*ag2x(i);

m2*ag2y(i) - W2;

Ig2*alfa2(i);

m3*ag3x(i);

m3*ag3y(i) - W3;

Ig3*alfa3(i);

m4*ag4x(i);

m4*ag4y(i) - W4;

Ig4*alfa4(i)];

and then calculate x = A\b where x is a 9x1x360, so 360 column vector 9x1;

But matlab tell me "Unable to perform assignment because the indices on the left side are

not compatible with the size of the right side";

I don't know what to do..

Anyone can help me ?

Sorry for my not-so-perfect english.

Thanks in advance,

Luca

Answer 1

[Jon]

You could do it like this:

% preallocate arrays to hold results
x = zeros(9,360);
A = zeros(9,9,360);
b = zeros(9,1,360);

% loop through angular positions
for i = 1:360
    A(:,:,i) = ... % assign all rows and and all columns of 9 by 9 to the ith "page"
    b(:,i) = ... % assign all rows of 9 by 1 to the ith "page"
    
    % solve and store result in ith column of x result matrix
    x(:,i) = A\b

end

By the way, I see you are storing the A and b matrices as 3 dimensional arrays, if you don't need them after the analysis is done you don't need to save them at all, you could just compute A and B at each increment. In this case don't preallocate the A an b arrays and just assign A = ... and b = ...

Finally, It's good to avoid screenshots of code. Instead if you want to include code in your post you can use the "Code" button in the MATLAB Answers toolbar to have it formatted nicely.

[Luca Amicucci]

Thanks a lot for the answer, this is my first ever made question!

First I tried with the simple

for i = 1:360
    ...
    A = [   ];
    b = [   ];
    x = A\b

end

But in this way matlab store only the last i_th step.

Therefore I tried with

for i = 1:360
    ...
    A(:,:,i) = ... 
    b(:,i) = ...
    
    x(:,i) = A(:,:,i)\b(:,i)
end

And It works.

So I have the x vector with size 9x360, with the components of the forces and torque that are:

F12x = x(1,:);
F12y = x(2,:);
...
...
Torque = x(9,:);

Thanks again!

[Jon]

Glad to hear that you are now able to get it to work. As I mentioned earlier, in case it wasn't so clear, if you only need to have the x results for every step but don't need the A's and B's you could also use

for i = 1:360
    ...
    A = ... 
    b = ...
    
    x(:,i) = A\b
end

And you wouldn't have to use memory to store all of those A and b values for each iteration.

[Luca Amicucci]

Ahhh you’re right, it’s more efficient. Thanks again! Can I ask you another question ?

[Jon]

yes of course, but if it's a completely new topic you might want to post it as a new question in case other people might be interested in following it.

[Luca Amicucci]

Ok, I post a new question.