Question

Using basic programming (for loops, while loops, and if statements), write two MATLAB functions, both taking as input:

Answer 1

Answer:

For n = 100

• (AB)x: 10100
• A(Bx): 200

For n = 200

• (AB)x: 40200
• A(Bx): 400

For n = 400

• (AB)x: 160400
• A(Bx): 800

For n = 800

• (AB)x: 640800
• A(Bx): 1600

The faster approach is A(Bx)

Explanation step by step functions:

A(Bx) is faster because requires fewer interactions to find a result: for (AB)x you have (n*n)+n interactions while for A(Bx) you have n+n, to understand why please see the step by step:

a) Function for (AB)x:

function loopcount1 = FirstAB(A,B,x)  

 n = size(A)(1);

 AB = zeros(n,n);

 ABx = zeros(n,1);

 loopcount1 = 0;  

 for i = 1:n

   for j = 1:n

     AB(i,j) = A(i,:)*B(:,j);

     loopcount1 += 1;

   end

 end

 for k = 1:n

   ABx(k) = AB(k,:)*x;

   loopcount1 += 1;

 end

end

b) Function for A(Bx):

function loopcount2 = FirstBx(A,B,x)

 n = size(A)(1);

 Bx = zeros(n,1);

 ABx = zeros(n,1);

 loopcount2 = 0;  

 for i = 1:n

   Bx(i) = B(i,:)*x;

   loopcount2 += 1;

 end

 for j = 1:n

   ABx(j) = A(j,:)*Bx;

   loopcount2 += 1;

 end

end