Trouble with spdiags and how it produces Tridiagonal matrix?

matrix = repelem([1 2 3]',[4 , 1 ,5])
matrix2 = repelem([0.5 1.5]',[5,5] )

TridiagonalMatrix = spdiags([matrix matrix2 matrix], -1:1, 10, 10)
full(TridiagonalMatrix)

Output:
matrix    matrix2
1         0.5
1         0.5
1         0.5
1         0.5
2         0.5
3         1.5
3         1.5
3         1.5
3         1.5
3         1.5

As you can see although there are 4 1s in the matrix named matrix, however, on the 1st diagonal there are only 3 1s listed.

Why is this the case and how can I fix it so that it has 4 1s, whilst still having 4 1s in the -1st diagonal aswell

Answer 1

[Matt J]

Why is this the case and how can I fix it so that it has 4 1s, whilst still having 4 1s in the -1st diagonal as well

From the documentation:

With the syntax S = spdiags(Bin,d,m,n), if a column of Bin has more elements than the diagonal it is replacing, and m >= n, then spdiags takes elements of super-diagonals from the lower part of the column of Bin.

Solution:

matrix = repelem([1 2 3]',[4 , 1 ,5]);
matrix2 = repelem([0.5 1.5]',[5,5] );
matrix3=repelem([1 2 3].', [5,1,4]);

TridiagonalMatrix = spdiags([matrix matrix2 matrix3], -1:1, 10, 10);

>> full(TridiagonalMatrix)

ans =

    0.5000    1.0000         0         0         0         0         0         0         0         0
    1.0000    0.5000    1.0000         0         0         0         0         0         0         0
         0    1.0000    0.5000    1.0000         0         0         0         0         0         0
         0         0    1.0000    0.5000    1.0000         0         0         0         0         0
         0         0         0    1.0000    0.5000    2.0000         0         0         0         0
         0         0         0         0    2.0000    1.5000    3.0000         0         0         0
         0         0         0         0         0    3.0000    1.5000    3.0000         0         0
         0         0         0         0         0         0    3.0000    1.5000    3.0000         0
         0         0         0         0         0         0         0    3.0000    1.5000    3.0000
         0         0         0         0         0         0         0         0    3.0000    1.5000

[arthurk]

Yeah, I guess if you can't get around it this is the best way. thanks

[Matt J]

You are welcome but please Accept-click the answer to indicate that it solves the problem.

Answer 2

[Matt J]

matrix = repelem([1 2 3]',[4 , 1 ,5]);
matrix2 = repelem([0.5 1.5]',[5,5] );

T=spdiags([matrix matrix2/2], -1:0, 10, 10);
TridiagonalMatrix = T+T.';

[arthurk]

Code:

    matrix = repelem([1 2 3], [4, 1, 5])
    matrix2 = repelem([0.5 1.5], [5, 5])
    
    T=spdiags([matrix matrix2/2], -1:0, 10, 10);
    TridiagonalMatrix = T+T.';

Receiving the error:

Error using spdiags (line 95)
For the syntax spdiags(B,d,m,n), the size of B must be min(m,n)-by-length(d).

Error in test (line 4)
     T=spdiags([matrix matrix2/2], -1:0, 10, 10);

[Matt J]

Your repelem's should be applied to column vectors, not row vectors.