Vectorizing Code - how can I populate elements of a matrix from a vector without a FOR loop?

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Eric
Eric 2011-9-26
I need to populate a large matrix from elements of a vector without using a FOR loop. The sizes of my vector and matrix can be quite large but the problem has the form of this shortened version:
a = [a1 a2 a3]
B = [a1 a1 0 0 0 0;...
a1 a1 0 0 0 0;...
0 0 a2 a2 0 0;...
0 0 a2 a2 0 0;...
0 0 0 0 a3 a3;...
0 0 0 0 a3 a3]
This is for a time simulation where the elements of "a" change every time step. The form of "B" does not change, only the elements from "a".
Again, this is easily done with a FOR loop, but in the interest of speed, I really need to avoid using loops here. I'm hoping there is a simple answer but for now, I'm stumped.
Thoughts and suggestions please!
Cheers,
- Eric

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回答（3 个）

Fangjun Jiang
Fangjun Jiang 2011-9-26
a=[1 2 3];
B=arrayfun(@(x) x*ones(2),a,'uni',0);
B=blkdiag(B{:})
Jan
Jan 2011-9-26
a = rand(1, 3);
B = kron(diag(a), ones(2));
David Holdaway
David Holdaway 2012-5-29
Do you NEED to make B as a matrix? Fangjun Jiang and Jan Simon's methods will work fine for what you have asked, but I've found if your vectors get big the ordinary "*" multiplication in Matlab is not very efficient for large block-diagonal matrices and it takes masses of memory to store and you are better off looping over the blocks anyway. (This is assuming there are no clever inbuilt tools in Matlab for block diagonal matrices I have never heard of).

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