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ZanzabumX [31]
2 years ago
6

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

Computers and Technology
1 answer:
borishaifa [10]2 years ago
5 0

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

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Answer:

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Explanation:

The program has been written in Java. The source code file has been attached to this response. Please download it for better readability. The code contains comments explaining what goes on on each segment of the code.

Hope this helps!

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