Let's say I've got a vector like this one:
A = [101:105]
Which is really:
[ 101, 102, 103, 104, 105 ]
And I'd like to use only vector/matrix functions and operators to produces the matrix:
101 102 103 104 105
102 103 104 105 0
103 104 105 0 0
104 105 0 0 0
105 0 0 0 0
or the following matrix:
101 102 103 104 105
0 101 102 103 104
0 0 101 102 103
0 0 0 101 102
0 0 0 0 101
Any ideas anyone?
(I'm very much a novice in MATLAB, but I've been saddled this stuff...)
hankel(A) will get you the first matrix
triu(toeplitz(A)) will get you the second one.
--Loren
The best solutions are listed by Loren. It's also possible to create these matrices using SPDIAGS:
vec = 101:105;
A = full(spdiags(repmat(vec,5,1),0:4,5,5)); % The second matrix
B = fliplr(full(spdiags(repmat(fliplr(vec),5,1),0:4,5,5))); % The first matrix
I recall creating banded matrices like this before I found out about some of the built-in functions Loren mentioned. It's not nearly as simple and clean as using those, but it worked. =)
The way I'd go about it is to create a matrix A:
101 102 103 104 105 101 102 103 104 105 101 102 103 104 105 101 102 103 104 105 101 102 103 104 105
And then find a matrix B such that when you multiply A*B you'll get the result you want. Basically do the linear algebra on paper first and then have Matlab do the calculation.
For generating such triangular matrices with such a regular pattern, use the toeplitz function, e.g.
m=toeplitz([1,0,0,0],[1,2,3,4])
for the other case, use rot90(m)