Creating a Pattern of set values within a Matrix

function B = inf_analysis(i,j,k,N)
A = ones(N^2)
B = diag(diag(A))

for rows = 1:N^2;
    for cols = 1:N^2;
        B(rows,rows+4:rows+4) = -1/4;
        break;
    end
end

I want to create a matrix with the value -1/4 is specific diagonals and locations based off a specific pattern i found. I was able to place the value in one specific diagonal but it added four more columns which i did not want.

[Stephen23]

@Braeden Elbers: show us the matrix that you want to achieve.

[Walter Roberson]

What is the purpose of those break statements? In context, your code is equivalent to

function B = inf_analysis(i,j,k,N)
A = ones(N^2)
B = diag(diag(A))
for rows = 1:N^2
    cols = 1;
        B(rows,rows+4:rows+4) = -1/4;

end
for rows = 1:N^2;
    cols = 1
        B(3,1:rows+4) = -1/4;
end

[Braeden Elbers]

I took the break statemnt out, this is the code i am working with:

function B = inf_analysis(i,j,k,N)
A = ones(N^2)
B = diag(diag(A))
for rows = 1:N^2;
    for cols = 1:N^2;
        B(rows,rows+4:rows+4) = -1/4;
    end
end

I want a matrix with ones in the diagoinal and -1/4 in a digonal for a size (N^2,N^2) in the (N,N+1), (N, N+4), (N+1,N), & (N+3,N) position for a N = 4 matrix

[Braeden Elbers]

But i dont want the four extra columns added after i run the function. So for a N = 4 matrix i only want size(B) = 64x64

[David Hill]

It would be much clearer if you just showed us an example.

[Braeden Elbers]

%% Ax = b system of equations found from values of inside of 5x5 matrix -->

% 3x3 matrix, using average of the four values touching the corresponding

% entry + 1

A = [1 -1/4 0 -1/4 0 0 0 0 0;

-1/4 1 -1/4 0 -1/4 0 0 0 0;

0 -1/4 1 0 0 -1/4 0 0 0;

-1/4 0 0 1 -1/4 0 -1/4 0 0;

0 -1/4 0 -1/4 1 -1/4 0 -1/4 0;

0 0 -1/4 0 -1/4 1 0 0 -1/4;

0 0 0 -1/4 0 0 1 -1/4 0;

0 0 0 0 -1/4 0 -1/4 1 -1/4;

0 0 0 0 0 -1/4 0 -1/4 1];

b = [6;3.5;6;3.5;1;3.5;6;3.5;6];

x = inv(A)*b

This is the matrix i created from setting up my system of equations. I need to create this matrix for size N^2.

[Braeden Elbers]

All border values of the 5x5 matrix were set and that is how i got the b matrix

Answer 1

[Walter Roberson]

inf_analysis([],[],[],4)

ans = 16×16

1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0

function B = inf_analysis(i,j,k,N)
    z = zeros(N^2,1);
    e = ones(N^2,1);
    e4 = -e/4;
    B = spdiags([e4, z, e4, e, e4, z, z, e4],-3:4,N^2,N^2);
    B = full(B);
end

[Braeden Elbers]

Thank you

[Walter Roberson]

Slightly improved:

inf_analysis([],[],[],4)

ans = 16×16

1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0

function B = inf_analysis(i,j,k,N)
    e = ones(N^2,1);
    e4 = -e/4;
    B = spdiags([e4, e4, e, e4, e4], [-3, -1, 0, 1, 4], N^2, N^2);
    B = full(B);
end

[Walter Roberson]

inf_analysis([],[],[],4)

ans = 16×16

1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 0 0 -0.2500 1.0000 0 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 0 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 0 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 0 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 -0.2500 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 -0.2500 1.0000 0 0 0 -0.2500 0 0 0 0 0 0 0 0 0 -0.2500 0 0 1.0000 -0.2500 0 0 -0.2500 0 0

function B = inf_analysis(i,j,k,N)
    e = ones(N^2,1);
    e4 = -e/4;
    e4m1 = e4; e4m1(3:3:end) = 0;
    e4p1 = e4; e4p1(1:3:end) = 0;
    B = spdiags([e4, e4m1, e, e4p1, e4], [-3, -1, 0, 1, 4], N^2, N^2);
    B = full(B);
end

Answer 2

[Braeden Elbers]

for the diagonals touching the diagonal containing ones, every third entry still needs to be zero. that is the only problem i am running into.

Will i use a similar method to creat the b vector to solve for x in Ax=b?

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/1657905-creating-a-pattern-of-set-values-within-a-matrix#comment_2005530 for the modification for every 3rd.

You did not give the rule for the b vector.

[Braeden Elbers]

the values within y, [N^2x1] matrix, need to be placed in specific locations within the array.

these are the rules that need to fill an [N^2x1]

y = zeros(N^2,1);

y1 = ((2*k)/4)+1

y2 = (k/4)+1

y3 = 1

The first 1:N terms need to follow the pattern

[y1 y2 y2 y2 y2... y1

followed by

[y2 y3 y3 y3 y3... y2

until the terms reach N^2-N:N^2

[y1 y2 y2 y2 y2... y1

[Walter Roberson]

I suggest using repelem(), such as

repelem([y1, y2, y1, y2, y3, y2, y1, y2, y1], [1, N-2, 1, 1, ?, 1, N-2, 1])

where ? is a value you would need to calculate.