# How can i do fast a sum of products?

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Le Dung on 15 Jan 2018
Edited: Matt J on 18 Jan 2018
Hi everyone! My problem is: I have an array of matrix 2x2, [A],[B],....[Z] (elements in the matrix are integer (or complex) numbers) and an array: 1/(s-a),1/(s-b),....,1/(s-z). And a,b,c,...,z are also integer (or complex) numbers. But s is a variable, s=1 to 100. And, i must calculate:
H=[A]*1/(s-a)+[B]*1/(s-b)+.....+[Z]*1/(s-z)
So, If i want to create a code that do fast (exactly is general), how can i do? I created two variables consist of cells, H1=cell(n,1) where n is number of matrix. So, H1 is a row vector, nx1, H1 consist of the matrix above. H2=cell(1,n) where n is number of matrix. So, H2 is a column vector, 1xn, H2 consist of 1/(s-a),1/(s-b),....,1/(s-z).
So, instead of writing a code:
H=[A]*1/(s-a)+[B]*1/(s-b)+.....+[Z]*1/(s-z) % (of course, i need do: syms s)
i will write:
H=H1xH2, % (H is not only a matrix 2x2 but also function of s variable)
That is problem i want to talk. But, you know, Matlab returns a warning
Undefined function 'mtimes' for input arguments of type 'cell'.
So, who can help me? thank you so much.
Matt J on 15 Jan 2018
Edited: Matt J on 15 Jan 2018
H1 is a row vector, nx1...H2 is a column vector, 1xn
Things that are nx1 are columns and things that are 1xn are rows.
of course, i need do: syms s
Are you sure you need to do this symbolically? If speed is a priority, this is working against you.
Le Dung on 16 Jan 2018
Edited: Le Dung on 16 Jan 2018
First, thank you for your comment. Oh yes, I had a mistake. Of course, nx1 is a row vector, and 1xn is a column vector. Yes, i want to write a code that more general (not is running speed of code but my code is more general or exactly is more profession) as i described above. And, " i need do: syms s". That is only my ideal to solve this my problem. May be you can have different methods (code) to solve my problem. Could you help me? Again,thank you so much.

Matt J on 16 Jan 2018
If you're not doing it symbolically, it becomes very simple matrix arithematic:
H1stack=cat(3,H1{:});
H2stack=cat(3,H2{:});
s=5; %for example
result=H1stack./(s-H2stack);
Le Dung on 18 Jan 2018
Edited: Le Dung on 18 Jan 2018
Yes, but can "s" be a vector? for example, s=1:100. If not, if s=1:1000, you must call the function 1000 times according to each value of s. It is a inconvenience in the cases where s has many values unless you use a loop.
A=[1 2;3 4];
B=[5 6;7 8];
a=0.5;
b=3.5;
H1=cell(2,1);
H2=cell(1,2);
H1{1,1}=A;
H1{2,1}=B;
H2{1,1}=a;
H2{1,2}=b;
H1stack=cat(3,H1{:});
H2stack=cat(3,H2{:});
s=5;
result1=H1stack./(s-H2stack);
Matlab returns:
Array dimensions must match for binary array op.
Matt J on 18 Jan 2018
Edited: Matt J on 18 Jan 2018
Array dimensions must match for binary array op.
To get rid of this, upgrade to R2016b or higher! If you can't, you'll have to use bsxfun().
Yes, but can "s" be a vector?
Yes, you can modify the code to
function result = myFunc(s,H1stack,H2stack)
s=reshape(s,1,1,1,[]);
result=H1stack./(s-H2stack);
end