{"id":2534,"date":"2024-05-29T05:35:16","date_gmt":"2024-05-29T09:35:16","guid":{"rendered":"https:\/\/blogs.mathworks.com\/matlab\/?p=2534"},"modified":"2024-05-29T05:35:16","modified_gmt":"2024-05-29T09:35:16","slug":"paged-matrix-functions-in-matlab-2024-edition","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/matlab\/2024\/05\/29\/paged-matrix-functions-in-matlab-2024-edition\/","title":{"rendered":"Paged Matrix Functions in MATLAB (2024 edition)"},"content":{"rendered":"
Back in 2021, Loren Shure posted an <\/span>article that introduced the first page-wise matrix functions in MATLAB<\/span><\/a>: A page-wise matrix multiply <\/span>pagemtimes<\/span><\/a>, along with page-wise transpose <\/span>pagetranspose<\/span><\/a>, and complex conjugate transpose <\/span>pagectranspose<\/span><\/a>; all of which were added to MATLAB R2020b. <\/span><\/div>
The following diagram is helpful to visualize what's going on in the 3D case. Each 3D array is considered as a set of matrices (or pages) <\/span><\/div>
\"\"<\/img><\/div>
A demo I like to show is this one. Image that A and B are stacks of 100,000 matrices, each of size 3x3. We want to multiply each pair together to form the stack C. Here's the old way of doing this using a loop.<\/span><\/div>
A = rand(3,3,100000);<\/span><\/span><\/div><\/div>
B = rand(3,3,100000);<\/span><\/span><\/div><\/div>
C = zeros(3,3,100000); <\/span>% preallocate the results<\/span><\/span><\/div><\/div>
 <\/div><\/div>
tic<\/span><\/span><\/div><\/div>
for <\/span>i=1:100000<\/span><\/span><\/div><\/div>
    C(:,:,i) = A(:,:,i) * B(:,:,i);<\/span><\/span><\/div><\/div>
end<\/span><\/span><\/div><\/div>
loopTime = toc<\/span><\/span><\/div>
loopTime = <\/span> 0.156962100000000<\/div><\/div><\/div><\/div><\/div><\/div>
and this is how I'd do it using <\/span>pagemtimes.<\/span><\/div>
tic<\/span><\/span><\/div><\/div>
C1 = pagemtimes(A,B);<\/span><\/span><\/div><\/div>
pagedTime = toc<\/span><\/span><\/div>
pagedTime = <\/span> 0.003961600000000<\/div><\/div><\/div><\/div><\/div><\/div>
The result is a lot faster.<\/span><\/div>
fprintf(<\/span>\"The pagemtimes version is %f times faster than the loop\\n\"<\/span>,loopTime\/pagedTime)<\/span><\/span><\/div>
The pagemtimes version is 39.620886 times faster than the loop<\/div><\/div><\/div><\/div><\/div>
That's a lot of speedup! Indeed, this demo has been carefully selected to show about the most amount of speed-up you can expect on your machine for <\/span>pagemtimes<\/span> for reasons we'll get into later.<\/span><\/div>
The idea of page-wise matrix functions turned out to be both a popular and useful idea! Here at MathWorks, we found uses for them all over our products and the user community made requests for several more variants. Page-wise matrix-multiply was a great start but you also wanted page-wise SVD, backslash, eig and more. MathWork's development team delivered!<\/span><\/div>
So, let's take a closer look at the state of play for paged matrix functions as of R2024a.<\/span><\/div>

The full list of page-wise matrix functions in MATLAB<\/span><\/h2>
Here's a list of all of the page-wise matrix functions we have in MATLAB, along with when they were introduced.<\/span><\/div>