Thanks for all the comments about the attributes of Python and Julia. It seems to me that the most prudent choice is to learn Python and Julia. However, what I would really like to know is just how fast these languages really are and here is the test. What I want to do is to fit networks of coupled ODEs (and PDEs) to data using MCMC (see here). This means I need a language that loops fast. An example in pseudo-Matlab code would be
for n = 1:N
for i = 1:T
y(i+1) = M\y(i)
end
Compare to data and set new parameters
end
where h is a parameter and M is some matrix (say 1000 dimensional), which is sometimes a Toeplitz matrix but not always. Hence, in each time step I need to invert a matrix, which can depend on time so I can’t always precompute, and do a matrix multiplication. Then in each parameter setting step I need to sum an objective function like the mean square error over all the data points. The code to do this in C or Fortran can be pretty complicated because you have to keep track of all the indices and call linear algebra libraries. I thus want something that has the simple syntax of Matlab but is as fast as C. Python seems to be too slow for our needs but maybe we haven’t optimized the code. Julia seems like the perfect fit but let me know if I am just deluded.
