MATLAB: Sum of matrix times scalars

efficientmathmatrixscalar

Hi,

I have a series of 3×3 matrices T1, T2, T3 … TN. In addition, I have a series of scalars a1, a2, … aN. I wish to perform the following sum WITHOUT the use of a for-loop. T1*a1 + T2*a2 + …. TN*aN. I have solved this using a for loop currently, but wish to take advantage of Matlabs superior data structures i.e. 3D arrays, cells, etc.

Thank you for your help !

Best Answer

Hold your 3x3 matrices in a 3x3xN array caled T and your scalars in an Nx1 vector called a and do,

result=reshape(T,9,[])*a(:);
result=reshape(result,3,3);

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MATLAB: Optimization Problem: How to minimize a sum of matrices multipled by a vector

So the question is, how to construct T? It should be as simple as,

T=reshape(  vertcat(A1,A2,..,Am)*X  , N , [] );

Now you can just go and plug into LSQLIN.

MATLAB: Adding Arrays of cells

There is a reason we keep on saying not to create numbered or dynamically named variables. It makes using them extremely difficult.

First step: change your algorithm to create just one variable. Options are a cell array of these cell arrays or concatenating the content of the cells in an extra dimension. Once that's done it's almost trivial to calculate the mean:

A = {A1, A2, ...}  %cell array of cell arrays
meanA = cellfun(@(varargin) mean(cat(ndims(varargin{1})+1, varargin{:}), ndims(varargin{1})+1) , A{:}, 'UniformOutput', false)

The complication here is that I don't know the dimensionality of the matrices you want to average. All the cellfun does is concatenate them all in a higher dimension and take the mean in that dimension.

The result of the concatenation without the mean calculation would be the other way to keep your matrices together

A = {A1, A2, ...}  %cell array of cell arrays
A = cellfun(@(varargin) cat(ndims(varargin{1})+1, varargin{:}), A{:}, 'UniformOutput', false)

Best Answer

Related Solutions

MATLAB: Optimization Problem: How to minimize a sum of matrices multipled by a vector

MATLAB: Adding Arrays of cells

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