Random projection algorithm pseudo code

I am trying to apply Random Projections method on a very sparse dataset. I found papers and tutorials about Johnson Lindenstrauss method, but every one of them is full of equations which makes no meaningful explanation to me. For example, this document on Johnson-Lindenstrauss Unfortunately, from this document, I can get no idea about the implementation steps of the algorithm. It's a long shot but is there anyone who can tell me the plain English version or very simple pseudo code of the algorithm? Or where can I start to dig this equations? Any suggestions? For example, what I understand from the algorithm by reading this paper concerning Johnson-Lindenstrauss is that: - Assume we have a `AxB` matrix where `A` is number of samples and `B` is the number of dimensions, e.g. `100x5000`. And I want to reduce the dimension of it to `500`, which will produce a `100x500` matrix. As far as I understand: first, I need to construct a `100x500` matrix and fill the entries randomly with `+1` and `-1` (with a 50% probability). Edit: Okay, I think I started to get it. So we have a matrix `A` which is `mxn`. We want to reduce it to `E` which is `mxk`. What we need to do is, to construct a matrix `R` which has `nxk` dimension, and fill it with `0`, `-1` or `+1`, with respect to `2/3`, `1/6` and `1/6` probability. After constructing this `R`, we'll simply do a matrix multiplication `AxR` to find our reduced matrix `E`. But we don't need to do a full matrix multiplication, because if an element of `Ri` is `0`, we don't need to do calculation. Simply skip it. But if we face with `1`, we just add the column, or if it's `-1`, just subtract it from the calculation. So we'll simply use summation rather than multiplication to find `E`. And that is what makes this method very fast. It turned out a very neat algorithm, although I feel too stupid to get the idea.