You can find some information about the Drift Diffusion Model here. There are probably several versions of the Drift Diffusion Model coded in MATLAB. I coded my own for two purposes:
1) If I code something, I better understand it
2) I wanted to have a flexible version that I can easily modify.
I attach to this post my MATLAB code for the DDM. It is optimized to the best of my skill. It can be used to simulate a model with two choices (as usual) or one choice, with or without variability across trial (so it can actually be used to simulate a Pure DDM or a Extended DDM). The code is highly commented.
If you take a look at the code, you could get confused about the presence at the same time of the for loop and the cumsum function. The cumsum is a really fast way in MATLAB to operate a cumulative sum of a vector. However, in this case I have to sum an undefined number of points (since the process stops when it hits the threshold, and it is not possible to know it beforehand). I could just use an incredibly high number of points and hope the process hits the threshold at some point. Or I could use a for loop to keep summing points until it hits a threshold. Both these methods are computationally expensive. So I used a compromise: the software runs cumsum for the first maxWalk points,and, if the threshold has not been hit, runs cumsum again (starting from the end of the previous run) within a loop (it repeats the loop for 100 times, every time for maxWalk points). After some testing, this version is generally much faster than a version with only cumsum or only a for loop.
This is an example of the resulting RT distribution with a high drift rate (e.g., the correct stimulus is easily identifiable):
I will soon post an alternative version of this file. They are less efficient, but allow to plot the process as it accumulates, which is quite cool.