How to avoid loops for the following matrix manipulcation

I need to do the following operations on a series of matrix A1,A2,...,A_m\in\reals^{n\times n}, and two vectors c,x\in\reals^{n}.

• H\in\reals^{n\times n} = \sum_{i=1}{m}(A_i*x)(A_i*x)^T,
• b\in\reals^{n} = \sum_{i=1}{m}c_i*(A_i*x).

I guess no-loop implementation will be faster. However, I tried and failed. Any ideas, guys?

Appreciate your time in advance!

[Chuangchuang Sun]

btw, A_i is sparse if that matters here.

[Walter Roberson]

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

[James Tursa]

Are you sure the calculation isn't (A_i*x)^T * (A_i*x) ?

[Stephen23]

"I need to do the following operations on a series of matrix A1,A2,...,A_m..."

"I guess no-loop implementation will be faster."

Accessing numbered variables in a loop is slow. It is not fast.

You could change your data design to use one array, in which case you could write fast code.

[Chuangchuang Sun]

@James Tursa yeah (A_i*x)(A_i*x)^T is a matrix while (A_i*x)^T * (A_i*x) is a scale. The former is what i need.

[Walter Roberson]

Chuangchuang Sun comments to me:

I am not naming them dynamically. I stack them in one matrix, or in a structure. does that make a difference?

[James Tursa]

How large is n?

[Stephen23]

Chuangchuang Sun's "Flag" moved here:

n is around 100

Answer 1

[James Tursa]

Since the A_i are sparse, you are probably stuck with your loop. Consider storing them as A{i} instead of A_i, however, to make looping easier. And code it such that you do the A{i}*x calculation only once.