Matlab vector times cell array

Question

I have a vector x = [1 2 3] and a 3 by 3 cell array C that consists of N by N matrices. E.g. C{1,1} is an N by N matrix.

I want to multiply x and C and get a cell array D of size 1 by 3:

D{1,1} = x(1)C{1,1) + x(2)C{2,1} + x(3)C{3,1} 
D{1,2} = x(1)C{1,2) + x(2)C{2,2} + x(3)C{3,2} 
D{1,3} = x(1)C{1,3) + x(2)C{2,3} + x(3)C{3,3}

Honestly, your data is begging to be stored in matrices rather than cell arrays. — Dennis Jaheruddin
– Dennis Jaheruddin, Commented Nov 21, 2013 at 10:20

chappjc · Accepted Answer · 2013-11-22 05:41:38Z

3

No unrolled loops

For a vector x of length M=3, and an M-by-M cell array C, the idea is to form an M*N-by-M matrix, where column i is composed of all the values in the cells C{i,:}. Then you can use matrix multiplication with x.' to get the values in D, and mat2cell to break up the result into a new cell array.

Ct = C';
Dvals = reshape([Ct{:}],[],M)*x.';
D = mat2cell(reshape(Dvals,N,[]),N,N*ones(M,1))

Test Data:

N = 4; M = 3; x = 1:M;
C = mat2cell(rand(N*M,N*M),N*ones(M,1),N*ones(M,1));

Note: This requires that each sub-matrix is the same size, as in the question.

edited Nov 22, 2013 at 5:41

answered Nov 21, 2013 at 6:03

chappjc

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Comments

Simon · Accepted Answer · 2013-11-21 04:24:44Z

0

With no loops:

D = cell(1, 3);
D{1} = x(1) * C{1,1} + x(2) * C{2,1} + x(3) * C{3,1};
D{2} = x(1) * C{1,2} + x(2) * C{2,2} + x(3) * C{3,2};
D{3} = x(1) * C{1,3} + x(2) * C{2,3} + x(3) * C{3,3};

With one loop:

D = cell(1, 3);
for i=1:3
    D{i} = x(1) * C{1,i} + x(2) * C{2,i} + x(3) * C{3,i};
end

With two loops:

D = cell(1, 3);
for i=1:3
    D{i} = x(1) * C{1,i};
    for j=2:3
        D{i} = D{i} + x(j) * C{j,i};
    end
end

answered Nov 21, 2013 at 4:24

Simon

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3 Comments

Eitan T Over a year ago

"no loops" doesn't really automate the calculation, does it?

Simon Over a year ago

Well, the OP didn't ask for automation, did (s)he? ;)

Eitan T Over a year ago

In that case you could multiply everything by hand and just feed in the results, right? You should know better :)

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Matlab vector times cell array

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