MATLAB Use nested for loops to perform the following exercis

MATLAB

Use nested for loops to perform the following exercises.

(a) Create the 3-D function: T(x,y,z) = x² + y² + z² in a rectangular domain with x = [-2:0.2:2]; y = [-1:0.2:1] and z = [0:0.2:1]. Matrix T should have the dimension of length(x) by length(y) by length(z). Set a=T.

(b) Compute the average values of T along the z-direction. The answer should be a 2-D matrix with the dimension of length(x) by length(y).

(c) Compute the average values of T over the x-y planes. The answer should be a vector with the dimension of length(z).

(d) Compute the average value of T over the entire rectangular domain. The answer should be a single number.

Solution

Solution:

%***********************************

clear all;
clc;

x = [-2:0.2:2];
y = [-1:.2:1];
z = [0:.2:1];

T = zeros(length(x) , length(y) , length(z));
%1 definition of T
for i= 1:length(x)
    for j=1:length(y)
        for k=1:length(z)
            T(i,j,k)=(x(i))^2 + (y(j))^2 +(z(k))^2 ;
        end
    end
end

%2 average along z
ans1 = zeros(length(x),length(y));
for i= 1:length(x)
    for j=1:length(y)
      
            ans1(i,j)= sum(T(i,j,:))/length(z) ;
     
    end
end

%2 average along z
ans2 = zeros(1,length(z));
for k=1:length(z)
      for i= 1:length(x)
           for j=1:length(y)
         ans2(k)= sum(sum(T(:,:,k)))/(length(x)*length(y)) ;
        end
    end
end

%2 average along z
anst = zeros(1,length(z));
for k=1:length(z)
      for i= 1:length(x)
           for j=1:length(y)
         anst(k)= sum(sum(T(:,:,k)))/(length(x)*length(y)) ;
        end
    end
end
ans3 = sum(anst)/length(z);

%**********************************************************

answer are there in matrix :

a-> T

b-> ans1

ans1 =

    5.3667    5.0067    4.7267    4.5267    4.4067    4.3667    4.4067    4.5267    4.7267    5.0067    5.3667
    4.6067    4.2467    3.9667    3.7667    3.6467    3.6067    3.6467    3.7667    3.9667    4.2467    4.6067
    3.9267    3.5667    3.2867    3.0867    2.9667    2.9267    2.9667    3.0867    3.2867    3.5667    3.9267
    3.3267    2.9667    2.6867    2.4867    2.3667    2.3267    2.3667    2.4867    2.6867    2.9667    3.3267
    2.8067    2.4467    2.1667    1.9667    1.8467    1.8067    1.8467    1.9667    2.1667    2.4467    2.8067
    2.3667    2.0067    1.7267    1.5267    1.4067    1.3667    1.4067    1.5267    1.7267    2.0067    2.3667
    2.0067    1.6467    1.3667    1.1667    1.0467    1.0067    1.0467    1.1667    1.3667    1.6467    2.0067
    1.7267    1.3667    1.0867    0.8867    0.7667    0.7267    0.7667    0.8867    1.0867    1.3667    1.7267
    1.5267    1.1667    0.8867    0.6867    0.5667    0.5267    0.5667    0.6867    0.8867    1.1667    1.5267
    1.4067    1.0467    0.7667    0.5667    0.4467    0.4067    0.4467    0.5667    0.7667    1.0467    1.4067
    1.3667    1.0067    0.7267    0.5267    0.4067    0.3667    0.4067    0.5267    0.7267    1.0067    1.3667
    1.4067    1.0467    0.7667    0.5667    0.4467    0.4067    0.4467    0.5667    0.7667    1.0467    1.4067
    1.5267    1.1667    0.8867    0.6867    0.5667    0.5267    0.5667    0.6867    0.8867    1.1667    1.5267
    1.7267    1.3667    1.0867    0.8867    0.7667    0.7267    0.7667    0.8867    1.0867    1.3667    1.7267
    2.0067    1.6467    1.3667    1.1667    1.0467    1.0067    1.0467    1.1667    1.3667    1.6467    2.0067
    2.3667    2.0067    1.7267    1.5267    1.4067    1.3667    1.4067    1.5267    1.7267    2.0067    2.3667
    2.8067    2.4467    2.1667    1.9667    1.8467    1.8067    1.8467    1.9667    2.1667    2.4467    2.8067
    3.3267    2.9667    2.6867    2.4867    2.3667    2.3267    2.3667    2.4867    2.6867    2.9667    3.3267
    3.9267    3.5667    3.2867    3.0867    2.9667    2.9267    2.9667    3.0867    3.2867    3.5667    3.9267
    4.6067    4.2467    3.9667    3.7667    3.6467    3.6067    3.6467    3.7667    3.9667    4.2467    4.6067
    5.3667    5.0067    4.7267    4.5267    4.4067    4.3667    4.4067    4.5267    4.7267    5.0067    5.3667

c->ans2

ans2 =

    1.8667    1.9067    2.0267    2.2267    2.5067    2.8667

d->ans3

ans3 =

    2.2333