Column Circulant Matrix

Hello,

How to create the following coulumn circulant matrix in matlab:

X=
[
x_0 x_{p-1} .... x_{P-L}
x_1 x_0     .... x_{P-L+1}
.
.
.
x_{p-1} x_{p-2} ... x_{P-L-1}
]

where p>L and both are positive integers.

Thanks

Answer 1

[Honglei Chen]

gallery('circul',[1 2 3])'

You can then take the first L columns

[S. David]

May be I was not clear. I have the first column, but I need to create the whole matrix using it. The question is how? Thanks

[Honglei Chen]

Just pass your first column in the place of [1 2 3] in the above code and see what the output is. The last transpose should restore your circulant matrix on columns.

[S. David]

Ok, good. Now how can I control the number of column's circular shifts? I mean, I do not want the circulant matrix to be square. For example, say I want something like:

X=[

1 5 4

2 1 5

3 2 1

4 3 2

5 4 3

]

Thanks.

[S. David]

Very simple

x=[1 2 3 4 5];

P=gallery('circul',x)';

G=P(:,1:3);