Use nested for loops to perform the following exercises This

Use nested for loops to perform the following exercises. This is FOR MATLAB

(a) Create the 3-D function: T(x, y, z) = x 2 + y 2 + z 2 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 p1a=T.

(b) Compute the average values of T along the z-direction and put the answer into p1b. 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 and put the answer into p1c. The answer should be a vector with the dimension of length(z).

(d) Compute the average value of T over the entire rectangular domain and put the answer into p1d. The answer should be a single number.

Solution

MALTAB CODE

clear all % Clearing the workspace
% The x direction vector
x = -2:0.2:2;
XL = length(x); % Number of points along x direction
y = -1:0.2:1; % The y direction vector
YL = length(y); % Number of points along y direction
z = 0:0.2:1; % The z direction vector
ZL = length(z); % Number of points in
% nested for loops for the evaluvation T;
T = zeros(XL,YL,ZL);
for i = 1:XL % loop for x direction
for j = 1:YL % loop for y direction
for k = 1:ZL % loop for z direction
T(i,j,k) = x(i)^2+y(j)^2+z(k)^2;
end
end
end
p1a = T;
% b part ans
p1b = zeros(XL,YL);
for i = 1:XL
for j = 1:YL
p1b(i,j) = sum(T(i,j,:))/ZL;
end
end
% c part ans
p1c = zeros(1,ZL);
for k =1:ZL
p1c(k) = sum(sum(T(:,:,k)))/(XL*YL);
end
% d part ans
p1d = sum(sum(sum(T)))/(XL*YL*ZL);
% disp% disp
fprintf(\'p1a\')
disp(p1a);
fprintf(\'p1b\')
disp(p1b);
fprintf(\'p1c\')
disp(p1c);
fprintf(\'p1d\')
disp(p1d);

OUTPUT

>> nestedforloop
p1a
(:,:,1) =

Columns 1 through 8

5.0000 4.6400 4.3600 4.1600 4.0400 4.0000 4.0400 4.1600
4.2400 3.8800 3.6000 3.4000 3.2800 3.2400 3.2800 3.4000
3.5600 3.2000 2.9200 2.7200 2.6000 2.5600 2.6000 2.7200
2.9600 2.6000 2.3200 2.1200 2.0000 1.9600 2.0000 2.1200
2.4400 2.0800 1.8000 1.6000 1.4800 1.4400 1.4800 1.6000
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
1.6400 1.2800 1.0000 0.8000 0.6800 0.6400 0.6800 0.8000
1.3600 1.0000 0.7200 0.5200 0.4000 0.3600 0.4000 0.5200
1.1600 0.8000 0.5200 0.3200 0.2000 0.1600 0.2000 0.3200
1.0400 0.6800 0.4000 0.2000 0.0800 0.0400 0.0800 0.2000
1.0000 0.6400 0.3600 0.1600 0.0400 0 0.0400 0.1600
1.0400 0.6800 0.4000 0.2000 0.0800 0.0400 0.0800 0.2000
1.1600 0.8000 0.5200 0.3200 0.2000 0.1600 0.2000 0.3200
1.3600 1.0000 0.7200 0.5200 0.4000 0.3600 0.4000 0.5200
1.6400 1.2800 1.0000 0.8000 0.6800 0.6400 0.6800 0.8000
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
2.4400 2.0800 1.8000 1.6000 1.4800 1.4400 1.4800 1.6000
2.9600 2.6000 2.3200 2.1200 2.0000 1.9600 2.0000 2.1200
3.5600 3.2000 2.9200 2.7200 2.6000 2.5600 2.6000 2.7200
4.2400 3.8800 3.6000 3.4000 3.2800 3.2400 3.2800 3.4000
5.0000 4.6400 4.3600 4.1600 4.0400 4.0000 4.0400 4.1600

Columns 9 through 11

4.3600 4.6400 5.0000
3.6000 3.8800 4.2400
2.9200 3.2000 3.5600
2.3200 2.6000 2.9600
1.8000 2.0800 2.4400
1.3600 1.6400 2.0000
1.0000 1.2800 1.6400
0.7200 1.0000 1.3600
0.5200 0.8000 1.1600
0.4000 0.6800 1.0400
0.3600 0.6400 1.0000
0.4000 0.6800 1.0400
0.5200 0.8000 1.1600
0.7200 1.0000 1.3600
1.0000 1.2800 1.6400
1.3600 1.6400 2.0000
1.8000 2.0800 2.4400
2.3200 2.6000 2.9600
2.9200 3.2000 3.5600
3.6000 3.8800 4.2400
4.3600 4.6400 5.0000

(:,:,2) =

Columns 1 through 8

5.0400 4.6800 4.4000 4.2000 4.0800 4.0400 4.0800 4.2000
4.2800 3.9200 3.6400 3.4400 3.3200 3.2800 3.3200 3.4400
3.6000 3.2400 2.9600 2.7600 2.6400 2.6000 2.6400 2.7600
3.0000 2.6400 2.3600 2.1600 2.0400 2.0000 2.0400 2.1600
2.4800 2.1200 1.8400 1.6400 1.5200 1.4800 1.5200 1.6400
2.0400 1.6800 1.4000 1.2000 1.0800 1.0400 1.0800 1.2000
1.6800 1.3200 1.0400 0.8400 0.7200 0.6800 0.7200 0.8400
1.4000 1.0400 0.7600 0.5600 0.4400 0.4000 0.4400 0.5600
1.2000 0.8400 0.5600 0.3600 0.2400 0.2000 0.2400 0.3600
1.0800 0.7200 0.4400 0.2400 0.1200 0.0800 0.1200 0.2400
1.0400 0.6800 0.4000 0.2000 0.0800 0.0400 0.0800 0.2000
1.0800 0.7200 0.4400 0.2400 0.1200 0.0800 0.1200 0.2400
1.2000 0.8400 0.5600 0.3600 0.2400 0.2000 0.2400 0.3600
1.4000 1.0400 0.7600 0.5600 0.4400 0.4000 0.4400 0.5600
1.6800 1.3200 1.0400 0.8400 0.7200 0.6800 0.7200 0.8400
2.0400 1.6800 1.4000 1.2000 1.0800 1.0400 1.0800 1.2000
2.4800 2.1200 1.8400 1.6400 1.5200 1.4800 1.5200 1.6400
3.0000 2.6400 2.3600 2.1600 2.0400 2.0000 2.0400 2.1600
3.6000 3.2400 2.9600 2.7600 2.6400 2.6000 2.6400 2.7600
4.2800 3.9200 3.6400 3.4400 3.3200 3.2800 3.3200 3.4400
5.0400 4.6800 4.4000 4.2000 4.0800 4.0400 4.0800 4.2000

Columns 9 through 11

4.4000 4.6800 5.0400
3.6400 3.9200 4.2800
2.9600 3.2400 3.6000
2.3600 2.6400 3.0000
1.8400 2.1200 2.4800
1.4000 1.6800 2.0400
1.0400 1.3200 1.6800
0.7600 1.0400 1.4000
0.5600 0.8400 1.2000
0.4400 0.7200 1.0800
0.4000 0.6800 1.0400
0.4400 0.7200 1.0800
0.5600 0.8400 1.2000
0.7600 1.0400 1.4000
1.0400 1.3200 1.6800
1.4000 1.6800 2.0400
1.8400 2.1200 2.4800
2.3600 2.6400 3.0000
2.9600 3.2400 3.6000
3.6400 3.9200 4.2800
4.4000 4.6800 5.0400

(:,:,3) =

Columns 1 through 8

5.1600 4.8000 4.5200 4.3200 4.2000 4.1600 4.2000 4.3200
4.4000 4.0400 3.7600 3.5600 3.4400 3.4000 3.4400 3.5600
3.7200 3.3600 3.0800 2.8800 2.7600 2.7200 2.7600 2.8800
3.1200 2.7600 2.4800 2.2800 2.1600 2.1200 2.1600 2.2800
2.6000 2.2400 1.9600 1.7600 1.6400 1.6000 1.6400 1.7600
2.1600 1.8000 1.5200 1.3200 1.2000 1.1600 1.2000 1.3200
1.8000 1.4400 1.1600 0.9600 0.8400 0.8000 0.8400 0.9600
1.5200 1.1600 0.8800 0.6800 0.5600 0.5200 0.5600 0.6800
1.3200 0.9600 0.6800 0.4800 0.3600 0.3200 0.3600 0.4800
1.2000 0.8400 0.5600 0.3600 0.2400 0.2000 0.2400 0.3600
1.1600 0.8000 0.5200 0.3200 0.2000 0.1600 0.2000 0.3200
1.2000 0.8400 0.5600 0.3600 0.2400 0.2000 0.2400 0.3600
1.3200 0.9600 0.6800 0.4800 0.3600 0.3200 0.3600 0.4800
1.5200 1.1600 0.8800 0.6800 0.5600 0.5200 0.5600 0.6800
1.8000 1.4400 1.1600 0.9600 0.8400 0.8000 0.8400 0.9600
2.1600 1.8000 1.5200 1.3200 1.2000 1.1600 1.2000 1.3200
2.6000 2.2400 1.9600 1.7600 1.6400 1.6000 1.6400 1.7600
3.1200 2.7600 2.4800 2.2800 2.1600 2.1200 2.1600 2.2800
3.7200 3.3600 3.0800 2.8800 2.7600 2.7200 2.7600 2.8800
4.4000 4.0400 3.7600 3.5600 3.4400 3.4000 3.4400 3.5600
5.1600 4.8000 4.5200 4.3200 4.2000 4.1600 4.2000 4.3200

Columns 9 through 11

4.5200 4.8000 5.1600
3.7600 4.0400 4.4000
3.0800 3.3600 3.7200
2.4800 2.7600 3.1200
1.9600 2.2400 2.6000
1.5200 1.8000 2.1600
1.1600 1.4400 1.8000
0.8800 1.1600 1.5200
0.6800 0.9600 1.3200
0.5600 0.8400 1.2000
0.5200 0.8000 1.1600
0.5600 0.8400 1.2000
0.6800 0.9600 1.3200
0.8800 1.1600 1.5200
1.1600 1.4400 1.8000
1.5200 1.8000 2.1600
1.9600 2.2400 2.6000
2.4800 2.7600 3.1200
3.0800 3.3600 3.7200
3.7600 4.0400 4.4000
4.5200 4.8000 5.1600

(:,:,4) =

Columns 1 through 8

5.3600 5.0000 4.7200 4.5200 4.4000 4.3600 4.4000 4.5200
4.6000 4.2400 3.9600 3.7600 3.6400 3.6000 3.6400 3.7600
3.9200 3.5600 3.2800 3.0800 2.9600 2.9200 2.9600 3.0800
3.3200 2.9600 2.6800 2.4800 2.3600 2.3200 2.3600 2.4800
2.8000 2.4400 2.1600 1.9600 1.8400 1.8000 1.8400 1.9600
2.3600 2.0000 1.7200 1.5200 1.4000 1.3600 1.4000 1.5200
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
1.7200 1.3600 1.0800 0.8800 0.7600 0.7200 0.7600 0.8800
1.5200 1.1600 0.8800 0.6800 0.5600 0.5200 0.5600 0.6800
1.4000 1.0400 0.7600 0.5600 0.4400 0.4000 0.4400 0.5600
1.3600 1.0000 0.7200 0.5200 0.4000 0.3600 0.4000 0.5200
1.4000 1.0400 0.7600 0.5600 0.4400 0.4000 0.4400 0.5600
1.5200 1.1600 0.8800 0.6800 0.5600 0.5200 0.5600 0.6800
1.7200 1.3600 1.0800 0.8800 0.7600 0.7200 0.7600 0.8800
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
2.3600 2.0000 1.7200 1.5200 1.4000 1.3600 1.4000 1.5200
2.8000 2.4400 2.1600 1.9600 1.8400 1.8000 1.8400 1.9600
3.3200 2.9600 2.6800 2.4800 2.3600 2.3200 2.3600 2.4800
3.9200 3.5600 3.2800 3.0800 2.9600 2.9200 2.9600 3.0800
4.6000 4.2400 3.9600 3.7600 3.6400 3.6000 3.6400 3.7600
5.3600 5.0000 4.7200 4.5200 4.4000 4.3600 4.4000 4.5200

Columns 9 through 11

4.7200 5.0000 5.3600
3.9600 4.2400 4.6000
3.2800 3.5600 3.9200
2.6800 2.9600 3.3200
2.1600 2.4400 2.8000
1.7200 2.0000 2.3600
1.3600 1.6400 2.0000
1.0800 1.3600 1.7200
0.8800 1.1600 1.5200
0.7600 1.0400 1.4000
0.7200 1.0000 1.3600
0.7600 1.0400 1.4000
0.8800 1.1600 1.5200
1.0800 1.3600 1.7200
1.3600 1.6400 2.0000
1.7200 2.0000 2.3600
2.1600 2.4400 2.8000
2.6800 2.9600 3.3200
3.2800 3.5600 3.9200
3.9600 4.2400 4.6000
4.7200 5.0000 5.3600

(:,:,5) =

Columns 1 through 8

5.6400 5.2800 5.0000 4.8000 4.6800 4.6400 4.6800 4.8000
4.8800 4.5200 4.2400 4.0400 3.9200 3.8800 3.9200 4.0400
4.2000 3.8400 3.5600 3.3600 3.2400 3.2000 3.2400 3.3600
3.6000 3.2400 2.9600 2.7600 2.6400 2.6000 2.6400 2.7600
3.0800 2.7200 2.4400 2.2400 2.1200 2.0800 2.1200 2.2400
2.6400 2.2800 2.0000 1.8000 1.6800 1.6400 1.6800 1.8000
2.2800 1.9200 1.6400 1.4400 1.3200 1.2800 1.3200 1.4400
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
1.8000 1.4400 1.1600 0.9600 0.8400 0.8000 0.8400 0.9600
1.6800 1.3200 1.0400 0.8400 0.7200 0.6800 0.7200 0.8400
1.6400 1.2800 1.0000 0.8000 0.6800 0.6400 0.6800 0.8000
1.6800 1.3200 1.0400 0.8400 0.7200 0.6800 0.7200 0.8400
1.8000 1.4400 1.1600 0.9600 0.8400 0.8000 0.8400 0.9600
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
2.2800 1.9200 1.6400 1.4400 1.3200 1.2800 1.3200 1.4400
2.6400 2.2800 2.0000 1.8000 1.6800 1.6400 1.6800 1.8000
3.0800 2.7200 2.4400 2.2400 2.1200 2.0800 2.1200 2.2400
3.6000 3.2400 2.9600 2.7600 2.6400 2.6000 2.6400 2.7600
4.2000 3.8400 3.5600 3.3600 3.2400 3.2000 3.2400 3.3600
4.8800 4.5200 4.2400 4.0400 3.9200 3.8800 3.9200 4.0400
5.6400 5.2800 5.0000 4.8000 4.6800 4.6400 4.6800 4.8000

Columns 9 through 11

5.0000 5.2800 5.6400
4.2400 4.5200 4.8800
3.5600 3.8400 4.2000
2.9600 3.2400 3.6000
2.4400 2.7200 3.0800
2.0000 2.2800 2.6400
1.6400 1.9200 2.2800
1.3600 1.6400 2.0000
1.1600 1.4400 1.8000
1.0400 1.3200 1.6800
1.0000 1.2800 1.6400
1.0400 1.3200 1.6800
1.1600 1.4400 1.8000
1.3600 1.6400 2.0000
1.6400 1.9200 2.2800
2.0000 2.2800 2.6400
2.4400 2.7200 3.0800
2.9600 3.2400 3.6000
3.5600 3.8400 4.2000
4.2400 4.5200 4.8800
5.0000 5.2800 5.6400

(:,:,6) =

Columns 1 through 8

6.0000 5.6400 5.3600 5.1600 5.0400 5.0000 5.0400 5.1600
5.2400 4.8800 4.6000 4.4000 4.2800 4.2400 4.2800 4.4000
4.5600 4.2000 3.9200 3.7200 3.6000 3.5600 3.6000 3.7200
3.9600 3.6000 3.3200 3.1200 3.0000 2.9600 3.0000 3.1200
3.4400 3.0800 2.8000 2.6000 2.4800 2.4400 2.4800 2.6000
3.0000 2.6400 2.3600 2.1600 2.0400 2.0000 2.0400 2.1600
2.6400 2.2800 2.0000 1.8000 1.6800 1.6400 1.6800 1.8000
2.3600 2.0000 1.7200 1.5200 1.4000 1.3600 1.4000 1.5200
2.1600 1.8000 1.5200 1.3200 1.2000 1.1600 1.2000 1.3200
2.0400 1.6800 1.4000 1.2000 1.0800 1.0400 1.0800 1.2000
2.0000 1.6400 1.3600 1.1600 1.0400 1.0000 1.0400 1.1600
2.0400 1.6800 1.4000 1.2000 1.0800 1.0400 1.0800 1.2000
2.1600 1.8000 1.5200 1.3200 1.2000 1.1600 1.2000 1.3200
2.3600 2.0000 1.7200 1.5200 1.4000 1.3600 1.4000 1.5200
2.6400 2.2800 2.0000 1.8000 1.6800 1.6400 1.6800 1.8000
3.0000 2.6400 2.3600 2.1600 2.0400 2.0000 2.0400 2.1600
3.4400 3.0800 2.8000 2.6000 2.4800 2.4400 2.4800 2.6000
3.9600 3.6000 3.3200 3.1200 3.0000 2.9600 3.0000 3.1200
4.5600 4.2000 3.9200 3.7200 3.6000 3.5600 3.6000 3.7200
5.2400 4.8800 4.6000 4.4000 4.2800 4.2400 4.2800 4.4000
6.0000 5.6400 5.3600 5.1600 5.0400 5.0000 5.0400 5.1600

Columns 9 through 11

5.3600 5.6400 6.0000
4.6000 4.8800 5.2400
3.9200 4.2000 4.5600
3.3200 3.6000 3.9600
2.8000 3.0800 3.4400
2.3600 2.6400 3.0000
2.0000 2.2800 2.6400
1.7200 2.0000 2.3600
1.5200 1.8000 2.1600
1.4000 1.6800 2.0400
1.3600 1.6400 2.0000
1.4000 1.6800 2.0400
1.5200 1.8000 2.1600
1.7200 2.0000 2.3600
2.0000 2.2800 2.6400
2.3600 2.6400 3.0000
2.8000 3.0800 3.4400
3.3200 3.6000 3.9600
3.9200 4.2000 4.5600
4.6000 4.8800 5.2400
5.3600 5.6400 6.0000

p1b Columns 1 through 8

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

Columns 9 through 11

4.7267 5.0067 5.3667
3.9667 4.2467 4.6067
3.2867 3.5667 3.9267
2.6867 2.9667 3.3267
2.1667 2.4467 2.8067
1.7267 2.0067 2.3667
1.3667 1.6467 2.0067
1.0867 1.3667 1.7267
0.8867 1.1667 1.5267
0.7667 1.0467 1.4067
0.7267 1.0067 1.3667
0.7667 1.0467 1.4067
0.8867 1.1667 1.5267
1.0867 1.3667 1.7267
1.3667 1.6467 2.0067
1.7267 2.0067 2.3667
2.1667 2.4467 2.8067
2.6867 2.9667 3.3267
3.2867 3.5667 3.9267
3.9667 4.2467 4.6067
4.7267 5.0067 5.3667

p1c 1.8667 1.9067 2.0267 2.2267 2.5067 2.8667

p1d 2.2333

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