# How to operate on 2d matrices in a 3D array?

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Alon Rozen on 11 Feb 2020
Commented: Alon Rozen on 11 Feb 2020
Hi,
I have a set of n 3x3 matricies orgenized in a 3D array with dimesions 3x3xn.
I want to operate on all 3x3 matricies: I want to get a vector of determinants and a vector of trace of each 3x3 matrix.
I also want to calculate a 3x3xn array which will hold the 3x3 inverse of each matix.
I can do it using a for loop, of couse, calculating in each iteration for the ith matrix.
Is there a simpler and faster way to do it?
Thanks,
Alon

#### 1 Comment

Stephen Cobeldick on 11 Feb 2020
"Is there a simpler and faster way to do it?"
Calculating the matrix inverse is rarely required or nor efficient when doing numeric computing. Read this to know why:
If you are really interested in efficiency, then use better tools than inv, just as the documentation recommends.
The determinant also tends to be overused by beginners who do not realize how useless it is in numeric computing. Search this forum to know why the determinant is essentially useless in numeric computing.

Bhaskar R on 11 Feb 2020
data = randi([1,10], 3,3,4); % your matrix with n = 4
data_det = arrayfun(@(i)det(data(:,:,i)), 1:size(data,3));
data_trace = arrayfun(@(i)trace(data(:,:,i)), 1:size(data,3));
data_inv = arrayfun(@(i)inv(data(:,:,i)), 1:size(data,3), 'UniformOutput', false);

Alon Rozen on 11 Feb 2020
I tried both - one with a loop and one with these arrayfun.
Indeed a loop works faster! You are right Stepen. Why is that? If I will use only one fuction that returns all calculation results, it also will be slower then a loop?
(Still learning how to do that)
Alon
Stephen Cobeldick on 11 Feb 2020
"Why is that?"
Essentially because repeatedly calling a function handle that runs sme code is slower than just calling that code directly.
"If I will use only one fuction that returns all calculation results, it also will be slower then a loop?"
Probably... try it and find out.
Alon Rozen on 11 Feb 2020
Thanks Stepen!

R2019a

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