Problem 2237. Mmm! Multi-dimensional Matrix Multiplication

Created by J-G van der Toorn

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You have got a couple of multi-dimensional matrices, A and B. And want to multiply them. For the first 2 dimensions, an ordinary matrix multiplication applies. And in the other dimensions? Well, they just act as parallel worlds. All 2D matrices are multiplied, for every element in the other dimensions. You may assume that the size in the 1st two dimensions allows simple matrix multiplication: A(:,:,1)*B(:,:,1), so size(A(:,:,1),2) == size(B(:,:,1),1), or either A(:,:,1) is a scalar or B(:,:,1) is a scalar. In the other dimensions, the sizes of A and B should be eqaal, size(A,n) == size(B,n), for n&gt;2, or either ndims(A)&lt;n or ndims(B)&lt;n, or either size(A,n)==1 or size(B,n)==1, so one of them is a scalar.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>mtimesm</w:t></w:r><w:r><w:t> that does this, and ask Mathworks to include it in the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>elmat</w:t></w:r><w:r><w:t> toolbox of the Next Release.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

59 Solutions
20 Solvers

Last Solution submitted on Oct 21, 2022

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

J.R.! Menzinger on 6 Mar 2014

The 5th case should be: C_correct = cat(3,A(:,:,1)*B,A(:,:,2)*B,A(:,:,3)*B); ??

Swapnali Gujar on 6 Mar 2014

I gave the solution which passes all given test cases, but I am sure it will fail, if there are multiple combinations of sizes of A and B.
I believe, to get a full-proof solution, more test cases are needed. Or such solution can work for limited combination of sizes of multidimensional matrices to be multiplied.

J-G van der Toorn on 7 Mar 2014

José Ramón, You are absolutely right. I will fix it.

Jonathan Agg on 14 Jan 2021

Have a look in 20b! :)

Problem Recent Solvers20

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 2237. Mmm! Multi-dimensional Matrix Multiplication

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author31

Problem Tags

Community Treasure Hunt

Problem 2237. Mmm! Multi-dimensional Matrix Multiplication

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author31

Problem Tags

Community Treasure Hunt

Players