有没有办法向量化这个 matlab for 循环？

Question

for i = 2:N
    A(i,i-1:i+1) = [1, -2, 1];
end

Hello, matlab is telling me that this code can be faster by using spalloc for the matrix A (which I have) but also by vectorizing this for loop. I've tried to use the following:

i = 2:N
A(i, i-1:i+1)

but the result obviously turned out to be not what I want.

How can I solve this?

Thank you!

Answer 1

It looks like you're trying to get a second-order difference operator, except your loop winds up missing the first row and including an extra column. The normal (sparse) difference operator is generated like this:

N = 10;
v = ones(N, 1);
A = spdiags([v -2*v v], [-1 0 1], N, N);
full(A)  % for display only

You'll see:

ans =
    -2     1     0     0     0     0     0     0     0     0
     1    -2     1     0     0     0     0     0     0     0
     0     1    -2     1     0     0     0     0     0     0
     0     0     1    -2     1     0     0     0     0     0
     0     0     0     1    -2     1     0     0     0     0
     0     0     0     0     1    -2     1     0     0     0
     0     0     0     0     0     1    -2     1     0     0
     0     0     0     0     0     0     1    -2     1     0
     0     0     0     0     0     0     0     1    -2     1
     0     0     0     0     0     0     0     0     1    -2

If that's not quite what you want (eg, you really don't want the first row), then it's probably faster to generate it as above and then fix it up.