Part II: Comparing the Speed of Matlab versus Python/Numpy

In this note, I extend a previous post on comparing run-time speeds of various econometrics packages by

  1. Adding Stata to the original comparison of Matlab and Python
  2. Calculating runtime speeds by
    • Comparing full OLS estimation functions for each package
      • Stata: reg
      • Matlab: fitlm
      • Python: regression.linear_model.OLS from the statsmodels module.
    • Comparing the runtimes for calculations using linear algebra code for the OLS model: $ (x'x)^{-1}x'y $
  3. Since Stata and Matlab automatically parralelize some calculations, we parallelize the python code using the Parallel module.

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Comparing the Speed of Matlab versus Python/Numpy

Update 1: A more complete and updated speed comparison can be found here.

Update 2: Python and Matlab code edited on 4/5/2015.

In this short note, we compare the speed of matlab and the scientific computing platform of python for a simple bootstrap of an ordinary least squares model. Bottom line (with caveats): matlab is faster than python with this code. One might be able to further optimize the python code below, but it isn't an obvious or easy process (see for example advanced optimization techniques).

As an aside, this note demonstrates that even if one can't optimize python code significantly enough, it is possible to do computationally expensive calculations in matlab and return results to the ipython notebook.

Data Setup

We will bootstrap the ordinary least squares model (ols) using 1000 replicates. For generating the toy dataset, the true parameter values are $$ \beta=\begin{bmatrix} 10\\-.5\\.5 \end{bmatrix} $$

We perform the experiment for 3 different sample sizes ($n = \begin{bmatrix}1,000 & 10,000 & 100,000 \end{bmatrix}$). For each of the observations in the toy dataset, the independent variables are drawn from

$$ \mu_x = \begin{bmatrix} 10\\10 \end{bmatrix}, \sigma_x = \begin{bmatrix} 4 & 0 \\ 0 & 4 \end{bmatrix} $$

The dependent variable is constructed by drawing a vector of random normal variates from Normal(0,1). Denoting this vector as $\epsilon$ calculate the dependent variable as $$ \mathbf{Y=Xb+\epsilon} $$

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Tapping MariaDB / MySQL data from Ipython

In this short post, I will outline how one can access data stored in a database like MariaDB or MySQL for analysis inside an Ipython Notebook. There are many reasons why you might want to store your data in a proper database. For me the most important are:

  1. All of my data resides in a password protected and more secure place than having a multitude of csv, mat, and dta files scattered all over my file system.

  2. If you access the same data for multiple projects, any changes to the underlying data will be propagated to your analysis, without having to update copies of project data.

  3. Having data in a central repository makes backup and recover significantly easier.

  4. This allows for two-way interaction with your database. You can read and write tables from/to your database. Rather than use SQL, you can create database tables using pandas/ipython.

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