Question

2. Neighbor Identification. MATLAB language
Many engineering problems can be solved numerically by dividing a large, compli- cated geometry into a multitude of smaller easier-to-solve cells. The quantities rep- resented in an individual cell (for example, temperature, velocity, and/or pressure) depend only on the values of those quantities stored at the cell’s nearest neighbors. In this problem, we will write a script to identify all the neighbors of a given cell in a rectangular array. Consider the numbered setup shown below.

N = 6 1 5 9 13 17 21 2 6 10 14 18 22 M = 4 3 7 11 15 19 23 4 8 12 16 20 24

The neighbors of cells 4 and 18 identified on a linearly-indexed grid with M = 4 and N = 6. Two different sets of neighbors have been identified in the figure above: (1) cell 4 has neighbors 3, 7, 8, and (2) cell 18 has neighbors 13, 14, 15, 17, 19, 21, 22, and 23. This configuration of cell s uses the concept of linear indexing, in which a single number (as opposed to two, e.g. (x, y)) is used to represent a cell’s location in a 2D grid. In this problem, we will assume that cell numbering always starts in the upper-left corner, proceeds down the first column, then down the second column, etc., as shown.

1. (a) Begin by asking the user to input three separate values representing the num- ber of rows in the array, M, the number of columns, N, and the cell for which we will be identifying neighbors, P. Your code must produce an error if eitherM or N is less than 2 or a non-integer value. Similarly your code must produce an error if the value of P is a non-integer or does not fall in the range of valid cellnumber,1≤P ≤(M×N).

2. (b) Once the values of M, N, and P have been collected and validated, we can begin identifying all the neighbors of P . You may find it helpful to write down in your pseudo-code the numerical rules and patterns that let us classify a cell, P , as being located on the walls (left, right, top, bottom), or corners (top left, top right, bottom left, bottom right). Note that the maximum number of neighbors is

2

8 (4 orthogonal + 4 diagonal), while the ones located on the walls each has 5 neighbors, and the ones located in the corners each has 3 neighbors.

(c) Print the neighbors of the user-input cell ID, P, to the command window. Use the formate shown below.

Cell ID: 4

Neighbors: 3 7 8

The neighbors needs to be in ascending order. Keep your logic as concise and organized as possible.

(d) Can a linear indexing scheme be used for a 3D grid? If so, explain the number- ing convention you would employ, using examples to explain your convention if necessary. In 2D, we can classify every cell as either: (1) corner, (2) edge, or (3) interior. Extend this classification system for a 3D grid and define how many neighbors surround each of these different cell types.

Note: Your code should work for any valid values of M and N, do not rely on hard- codedlogicaltestthatpresupposeaparticularvalueforMandN,e.g.if P == 24to catch the bottom-right corner in the grid above. Keep everything defined in terms of M and N, and/or other derived quantities.

Answer 1

ANSWER:

• You can find the answers for question a-c in the code below.
  • Answer d: Yes we use linear indexing in 3-D. Here, Cell numbering always starts from the first 2-D grid (i.e. wall) in the upper-left corner, proceeds down the first column, then down the second column continuing to cover complete wall and then the 2nd grid and till the last wall. We can classify every cell as either: (1) corner, (2) edge, (3) Surface, or (4) interior. Having, 7, 11, 17, and 26 neighbors respectively.
• I have provided the properly commented code in both text and image format so you can easily copy the code as well as check for correct indentation.
• I have provided the output image of the code so you can easily cross-check for the correct output of the code.
• Have a nice and healthy day!!

CODE TEXT

clc;

clear;

% Prompting user to enter M, N and P and converting it to integer

M=int32(input('Enter Number of rows: '));

N=int32(input('Enter Number of columns: '));

P=int32(input('Enter Cell Number: '));

% Checking for integer and P limit

if ~isinteger(M) || ~isinteger(N) || ~isinteger(P)

fprintf('%d %d %d',isinteger(M),isinteger(N),isinteger(P))

disp('Please enter integer only in all feilds');

elseif M<2 || N<2

disp('Please enter value of row and column >= 2');

elseif P<=0 || P>(M*N)

fprintf('Value of P should be in between 1 and %d',(M*N));

else

% Now every thing is correct, we can work further

% Finding left neighbours if exist and storing in neigh

neighs=[];

i=1; % index counter

% left neighbour is (P-M)th cell if its lies between 1 to N*M

if (P-M) > 0

% finding upper left neighbour if P%M != 1 i.e. P is not upperrow cell

if mod(P, M) ~=1

neighs(i)=P-M-1; % storing in index

i=i+1; % incementing counter

end

neighs(i)=P-M; % storing in index

i=i+1; % incementing counter

% finding bottom left neighbour if P%M != 0 i.e. P is not lowest row cell

if mod(P, M) ~=0

neighs(i)=P-M+1; % storing in index

i=i+1; % incementing counter

end

end

% upper and lower neighbour of Pth cell

% finding upper neighbour if P%M != 1 i.e. P is not upperrow cell

if mod(P, M) ~=1

neighs(i)=P-1; % storing in index

i=i+1; % incementing counter

end

% finding bottom neighbour if P%M != 0 i.e. P is not lowest row cell

if mod(P, M) ~=0

neighs(i)=P+1; % storing in index

i=i+1; % incementing counter

end

% left neighbour is (P-M)th cell if its lies between 1 to N*M

if (P+M) <= (N*M)

% finding upper right neighbour if P%M != 1 i.e. P is not upperrow cell

if mod(P, M) ~=1

neighs(i)=P+M-1; % storing in index

i=i+1; % incementing counter

end

neighs(i)=P+M; % storing in index

i=i+1; % incementing counter

% finding upper left neighbour if P%M != 0 i.e. P is not lowest row cell

if mod(P, M) ~=0

neighs(i)=P+M+1; % storing in index

i=i+1; % incementing counter

end

end

% display

fprintf('Cell ID: %d\n',P);

fprintf('Neighbors: ');

fprintf('%d ',neighs);

end

CODE IMAGE

1 - clc; clear; 3 4 5 - % Prompting user to enter M, N and P and converting it to integer M=int32(input('Enter Number of rows: ')); N=int32(input('Enter Number of columns : ')); Print32(input('Enter Cell Number: ')); 6- 8 9 10 - 11 - 12 13 - 14 - 15 - 16 17 - 18 19 20 - 21 - % Checking for integer and P limit if visinteger(M) || ~isinteger(N) || ~isinteger(P) fprintf("%d %d %d', isinteger(M), isinteger(N), isinteger(P)) disp('Please enter integer only in all feilds'); elseif M<2 || N<2 disp('Please enter value of row and column >= 2'); elseif P<=0 || P>(M*N) fprintf("Value of P should be in between 1 and %d',(M*N)); else % Now every thing is correct, we can work further % Finding left neighbours if exist and storing in neigh neighs=[]; i=1; % index counter % left neighbour is (P-M)th cell if its lies between 1 to N*M if (P-M) > 0 % finding upper left neighbour if P%M != 1 i.e. P is not upperrow cell if mod(P, M) -=1 neighs(i)=P-M-1; % storing in index i=i+1; % incementing counter end neighs(i)=P-M; % storing in index i=i+1; % incementing counter % finding bottom left neighbour if p%M != 0 i.e. P is not lowest row cell if mod(P, M) ~=0 neighs (i)=P-M+1; % storing in index 22 23 - 24 25 - 26 27 - 28 29 - 30 31 32 - 33 -

32 33 34 35 - 36 37 38 39 - 40 41 - 42 43 44 - 45 - 46 47 - 48 if mod(P, M) ~=0 neighs (i)=P-M+1; % storing in index i=i+1; % incementing counter end end % upper and lower neighbour of Pth cell % finding upper neighbour if P%M != 1 i.e. P is not upperrow cell if mod(P, M) ~=1 neighs (i)=P-1; % storing in index i=i+1; % incementing counter end % finding bottom neighbour if P%M != 0 i.e. P is not lowest row cell if mod(P, M) -=0 neighs(i)=P+1; % storing in index i=i+1; % incementing counter end % left neighbour is (P-M)th cell if its lies between 1 to N*M if (P+M) <= (N*M) % finding upper right neighbour if p%M != 1 i.e. P is not upperrow cell if mod(P, M) ~=1 neighs (i)=P+M-1; % storing in index i=i+1; % incementing counter end neighs (i)=P+M; % storing in index i=i+1; % incementing counter % finding upper left neighbour if P%M != 0 i.e. P is not lowest row cell if mod(P, M) -=0 neighs (i)=P+M+1; % storing in index i=i+1; % incementing counter end end % display fprintf('Cell ID: %d\n',P); 49 - 50 51 - 52 53 - 54 55 56 57 58 59 - 60 61 - 62 63 64

1 63 64 65 66 % display fprintf('Cell ID: %d\n',P); fprintf('Neighbors: '); fprintf('%d', neighs); end - 67 -

OUTPUT IMAGE

1.

Enter Number of rows: 1 Enter Number of columns: 3 Enter Cell Number: 1 Please enter value of row and column >= 2

2.

Enter Number of rows: 4 Enter Number of columns: 6 Enter Cell Number: 27 Value of p should be in between 1 and 24

3.

Enter Number of rows: 4 Enter Number of columns: 6 Enter Cell Number: 4 Cell ID: 4 Neighbors: 378

4.
Enter Number of rows: 4 Enter Number of columns: 6 Enter Cell Number: 18 Cell ID: 18 Neighbors: 13 14 15 17 19 21 22 23