How to stop unwanted rows being added when constructing a matrix in a for loop
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Hi there,
just a simple question I think.
I am trying to construct a matrix in a quick way using a for loop. Because the values for diagonals are the same I can using indexing like (i,i) and (i+1,i) etc. However, apart from the first diagonal I input (i,i), the second diagonal (i,i+1) adds an extra row and column to my original matrix.
Here is my code:
clear, clc, close all
mat = zeros(7,7)
n = size(mat,1)
for i = 1:n
mat(i,i) = 6
mat(i,i+1) = -4
end
If you run the code, the diagonal containing -4 adds on a extra row and column at the end; making a 7x7 matrix to an 8x8. This is very frustraing and I do not want this!
Can I ask what its the trick to getting around this, please?
Many thanks
Scott
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Accepted Answer
Star Strider
on 5 Sep 2024
The reason is that there are the same number of ‘6’ and ‘-4’ being created in the loop. There needs to be one less ‘-4’.
clear, clc, close all
mat = zeros(7,7);
n = size(mat,1);
for i = 1:n
mat(i,i) = 6;
mat(i,i+1) = -4;
end
mat
N = 7;
mat2 = diag(ones(1,N)*6); % Use 'diag'
mat2 = + mat2 + diag(ones(1,N-1)*-4, 1)
.
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More Answers (3)
ScottB
on 5 Sep 2024
mat = zeros(7,7)
n = size(mat,1)
for i = 1:n
mat(i,i) = 6
if i ==7
else
mat(i,i+1) = -4
end
end
mat =
6 -4 0 0 0 0 0
0 6 -4 0 0 0 0
0 0 6 -4 0 0 0
0 0 0 6 -4 0 0
0 0 0 0 6 -4 0
0 0 0 0 0 6 -4
0 0 0 0 0 0 6
1 Comment
Voss
on 5 Sep 2024
Or
mat = zeros(7,7);
n = size(mat,1);
for i = 1:n
mat(i,i) = 6;
if i ~= n
mat(i,i+1) = -4;
end
end
mat
Steven Lord
on 5 Sep 2024
Since you're creating matrices with diagonal bands, consider using the diag or spdiags functions.
n = 7;
mainDiagonal = diag(6*ones(n, 1))
upperDiagonal = diag(-4*ones(n-1, 1), 1)
A = mainDiagonal + upperDiagonal
Note that when I created upperDiagonal I used a vector of all -4 values that had length one shorter than the vector of 6 values I used to create mainDiagonal. This made it so upperDiagonal was n-by-n rather than (n+1)-by-(n+1) as it would have been had I used -4*ones(n, 1).
B = diag(-4*ones(n, 1), 1)
For bands below the diagonal, use a negative value as the second input.
lowerDiagonal = diag(-8*ones(n-1, 1), -1)
Here are the numbers for which band contains each element of the matrix.
bandNumbers = toeplitz(0:-1:-(n-1), 0:(n-1))
For spdiags you don't have to create each band individually, though the syntax is a little bit more complicated. The command below puts 6 on the 0 (main) diagonal of S and -4 on the +1 (upper) diagonal, and makes S an n-by-n matrix.
S = spdiags([6 -4], [0 1], n, n)
Since S is sparse it's displayed slightly differently. Convert it to full and it looks like A above.
F = full(S)
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