Creating a matrix such as a = [1 1 1 1 1 1 1; ... 1 2 2 2 2 2 2; ... 1 2 3 3 3 3 3; ... 1 2 3 4 4 4 4; ... 1 2 3 4 5 5 5; ... 1 2 3 4 5 6 6; ...

Hello I am currently working on a project in which we must use the flexibility matrix of a mass-spring system in order to calculate its natural frequency. I've derived the flexibility matrix by hand and noticed the pattern below. How can I do this for N numbers instead of having to update by hand each time I increase N?

a = [1 1 1 1 1 1 1; ...
     1 2 2 2 2 2 2; ...
     1 2 3 3 3 3 3; ...
     1 2 3 4 4 4 4; ...
     1 2 3 4 5 5 5; ...
     1 2 3 4 5 6 6; ...
     1 2 3 4 5 6 7]

Answer 1

[Image Analyst]

Here is one way - a simple for loop

N = 7;
% First way
a = ones(7);
for col = 1 : N
    a(2:col, col) = 2 : col;
    a(col : end, col) = col;
end
% Show in command window:
a

a = 7×7

1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 3 3 3 3 3 1 2 3 4 4 4 4 1 2 3 4 5 5 5 1 2 3 4 5 6 6 1 2 3 4 5 6 7

% Second way
a = repmat((1:N)', 1, N);
for col = 1 : N
    a(col:end, col) = col;
end
a

a = 7×7

1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 3 3 3 3 3 1 2 3 4 4 4 4 1 2 3 4 5 5 5 1 2 3 4 5 6 6 1 2 3 4 5 6 7

[Jose Del Rio]

thanks!

Answer 2

[John D'Errico]

Hint #1. Can you just create the matrix from scratch each time? So, is there a simple formula for a(i,j) in the order n matrix? Answer: yes. All you need to see is that a(i,j) = min(i,j). If that is the case, then can you create the matrix using meshgrid? In fact, you can create it in one line of code, without needing meshgrid.

a_n = @(n) min(ones(n,1)*(1:n),(1:n)'*ones(1,n))

a_n = function_handle with value:
    @(n)min(ones(n,1)*(1:n),(1:n)'*ones(1,n))

a_n(5)

ans = 5×5

1 1 1 1 1 1 2 2 2 2 1 2 3 3 3 1 2 3 4 4 1 2 3 4 5

So this function creats the entire matrix, given only the number n.

As an alternative hint, could you go from the matrix of order N, to N+1? How might you do that? For example, suppose you padded the previous order matriix with zeros on the left and top, and then added 1 to every element. Could you do that simply? (Of course.)

a_update = @(a) [zeros(1,size(a,2)+1);[zeros(size(a,1),1),a]] + 1;

a = 1

a = 1

a = a_update(a)

a = 2×2

1 1 1 2

a = a_update(a)

a = 3×3

1 1 1 1 2 2 1 2 3

a = a_update(a)

a = 4×4

1 1 1 1 1 2 2 2 1 2 3 3 1 2 3 4

So a_update creates the order n+1 matrix from the order n matrix.

Answer 3

[Stephen23]

N = 7;
A = min(1:N,(1:N).')

A = 7×7

1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 3 3 3 3 3 1 2 3 4 4 4 4 1 2 3 4 5 5 5 1 2 3 4 5 6 6 1 2 3 4 5 6 7

Answer 4

[Steven Lord]

A = gallery('minij', 7)

A = 7×7

1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 3 3 3 3 3 1 2 3 4 4 4 4 1 2 3 4 5 5 5 1 2 3 4 5 6 6 1 2 3 4 5 6 7

See the documentation for the gallery function for a list of the other types of matrices it can create.