Sum of matrix times scalars

Hi,

I have a series of 3x3 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 !

[KALYAN ACHARJYA]

Are these matrices in cell array or different individuals variables names?

[Stephen23]

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

Use indexing, then your task is trivial.

[Mohammed Kagalwala]

They are in different individual variable names however no reason they can't be grouped in a cell or 3D matrix

Answer 1

[Matt J]

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);

[Guillaume]

Note that if a is a Nx1 vector, then a(:) and a are the same.

Another option is:

result = sum(T .* reshape(a, 1, 1, []), 3);

[Mohammed Kagalwala]

Thank you for your help ! The reshape solutions both work, however on average Matt's solution is faster ( I tested with N = 10000). My other method was coming up with an S1 and S2 such that T*S1*q*S2 = to the 3x3 sum I want. Here T is 3x3N, and q is Nx1. I'm going to try and extend the reshape idea to the following double sum, , where = 3x3 matrix.