Answer to Question #52515 in MatLAB | Mathematica | MathCAD | Maple for jason

Question

Now, for each of the for-loop examples on the next page, write two programs that generate the same arrays (1-D, 2-D and 3-D), with the following changes:
1. Modify the programs to pre-allocate the arrays first
2. Use vectorisation functions to implement the programs without the use of any loops. You may want to
look at ndgrid, and remember to use array versions of your operators!

% 1-D array (3 * i)
n = 10;
for i=1:n
A(i) = 3*i;
end

% 2-D array where
% B(i,j) = i/j
n = 10;
for i=1:n
for j=1:n
B(i,j) = i/j;
end
end

% 3-D array where
% C(i,j,k) = i*j+k
n = 10;
for i=1:n
for j=1:n
for k=1:n
C(i,j,k) = i*j+k;
end
end
end

Answer 1

Now, foreach of the for-loop examples on the next page, write two programs that
generate the same arrays (1-D, 2-D and 3-D), with the following changes:
1. Modify the programs to pre-allocate the arrays first
2. Use vectorisation functions to implement the programs without the use of any
loops. You may want to look at ndgrid, and remember to use array versions of
your operators!
% 1-D array(3 * i)
n = 10;
for i=1:n
A(i) = 3*i;
end

% 2-D array where
% B(i,j) = i/j
n = 10;
for i=1:n
for j=1:n
B(i,j) = i/j;
end
end

% 3-D array where
% C(i,j,k) = i*j+k
n = 10;
for i=1:n
for j=1:n
for k=1:n
C(i,j,k) = i*j+k;
end
end
end

Solve
Pre-allocate vector by set 0 to all elements byfunction zeros(n,n,n).
 
 
% 1-D array (3 * i)
n = 10;
A=zeros(n,1);%pre-allocate arrays
I=zeros(n,1);
I=linspace(1,n,n);
A=I.*3;
% 2-D array where
% B(i,j) = i/j
n = 10;
B=zeros(n,n);
I_1=1./I;
B=I'*I_1;
 
% 3-D array where
% C(i,j,k) = i*j+k
n = 10;
C=zeros(n,n,n);
[X,Y,Z]=ndgrid(I,I,I_1);
C=X.*Y+Z;
%C(i,j,k) = i*j+k;