Inverse a cell of matrices

The MVP Walter was great and helped me created a cell of matrices but I ran into the problem the I will need to find the inverse matrices of each matrix. My code is:

T1_theta = [-90:5:90];
M = sind(T1_theta);
N = cosd(T1_theta);
T1 = arrayfun(@(m,n)[m^2 n^2 0 0 0 2*m*n; 
  n^2 m^2 0 0 0 -2*m*n;
  0 0 1 0 0 0;
  0 0 0 m -n 0;
  0 0 0 n m 0; 
  -m*n m*n 0 0 0 m^2-n^2], M, N, 'uniform', 0);

This code produces a 1x37 cell comprised of 6x6 matrices. I thought that the code:

inv(T1)

would work but I understand why it doesnt. I was thinking of possibly doing another "arrayfun" function over top of the cell if that is possible?

Answer 1

[James Tursa]

Yes, you can do something like this:

T1inv = cellfun(@inv,T1,'uni',false);

That being said, this begs the question of what you will be doing with this downstream in your code, and if maybe there isn't a better formulation for your overall problem that uses backslash instead. How will you be using the T1 inverses downstream in your code?

Answer 2

[Walter Roberson]

T1inv = cellfun(@inv, T1, 'uniform', 0);

However, most of the time you should avoid using inv() . It is not common that you need the inverse of a matrix in its own right: you normally need to multiply the inverse by another matrix. In such situations you should replace inv(A)*B with A\B and you should replace B*inv(A) with B/A

For example if you were planning to do T1inv{1}*B with constant B, then instead of forming T1inv do

T1invB = cellfun(@(A)A\B, T1, 'uniform', 0);

[andrew krugle]

Both Walter and James thank you very much for your quick response. I've been creating a finite element model which is repersented by:

[𝐶_bar]=[𝑇1]^−1*[𝐶]*[𝑇2].

Both T1 and T2 are transformation matrices which are dependent on the input theta (Walter helped me with that part). The [C] matrix is all of constants. [T1]^-1 and [T2] change per the different theta range of -90 to 90 inputed into them by the 'arrayfun' function. My plan was take each individual cell of the arrayfun(each matrix) and plug it into the above formula and create a seperate array that I could take out the first column with

col1mat = horzcat(col1{:});

and produce an XY graph of value vs theta.

I really hope that makes sense. Thanks for your help guys

[Walter Roberson]

C_bar = cellfun(@(t1, t2) t1\C*t2, T1, T2, 'uniform', 0);
col1mat = cell2mat(cellfun(@(c) c(:,1), C_bar(:).', 'uniform', 0));

The C_bar(:).' is an idiom for ensuring that C_bar is a row vector of cells instead of potentially being a column vector of cells. There is no "reshape to row vector" operator, but there is a "reshape to column vector" operator and a transpose operator, so (:).' forces column and makes it row afterwards. You can remove the (:).' if you are sure that C_bar will be a row vector of cells.