- Introduction to Python
- Getting started with Python and the IPython notebook
- Functions are first class objects
- Data science is OSEMN
- Working with text
- Preprocessing text data
- Working with structured data
- Using SQLite3
- Using HDF5
- Using numpy
- Using Pandas
- Computational problems in statistics
- Computer numbers and mathematics
- Algorithmic complexity
- Linear Algebra and Linear Systems
- Linear Algebra and Matrix Decompositions
- Change of Basis
- Optimization and Non-linear Methods
- Practical Optimizatio Routines
- Finding roots
- Optimization Primer
- Using scipy.optimize
- Gradient deescent
- Newton’s method and variants
- Constrained optimization
- Curve fitting
- Finding paraemeters for ODE models
- Optimization of graph node placement
- Optimization of standard statistical models
- Fitting ODEs with the Levenberg–Marquardt algorithm
- 1D example
- 2D example
- Algorithms for Optimization and Root Finding for Multivariate Problems
- Expectation Maximizatio (EM) Algorithm
- Monte Carlo Methods
- Resampling methods
- Resampling
- Simulations
- Setting the random seed
- Sampling with and without replacement
- Calculation of Cook’s distance
- Permutation resampling
- Design of simulation experiments
- Example: Simulations to estimate power
- Check with R
- Estimating the CDF
- Estimating the PDF
- Kernel density estimation
- Multivariate kerndel density estimation
- Markov Chain Monte Carlo (MCMC)
- Using PyMC2
- Using PyMC3
- Using PyStan
- C Crash Course
- Code Optimization
- Using C code in Python
- Using functions from various compiled languages in Python
- Julia and Python
- Converting Python Code to C for speed
- Optimization bake-off
- Writing Parallel Code
- Massively parallel programming with GPUs
- Writing CUDA in C
- Distributed computing for Big Data
- Hadoop MapReduce on AWS EMR with mrjob
- Spark on a local mahcine using 4 nodes
- Modules and Packaging
- Tour of the Jupyter (IPython3) notebook
- Polyglot programming
- What you should know and learn more about
- Wrapping R libraries with Rpy
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Using Multiprocessing
import multiprocessing num_procs = multiprocessing.cpu_count() num_procs
4
def pi_multiprocessing(n): """Split a job of length n into num_procs pieces.""" import multiprocessing m = multiprocessing.cpu_count() pool = multiprocessing.Pool(m) results = pool.map(pi_cython, [n/m]*m) pool.close() return np.mean(results)
For small jobs, the cost of spawning processes dominates
n = int(1e5) %timeit pi_cython(n) %timeit pi_multiprocessing(n)
100 loops, best of 3: 1.95 ms per loop 10 loops, best of 3: 32.6 ms per loop
For larger jobs, we see the expected linear speedup
n = int(1e7) %timeit pi_numpy(n) %timeit pi_multiprocessing(n)
1 loops, best of 3: 718 ms per loop 10 loops, best of 3: 148 ms per loop
Not all tasks are embarassingly parallel. In these problems, we need to communicate across parallel workers. There are two ways to do this - via shared memory (exemplar is OpenMP) and by explicit communication mechanisms (exemplar is MPI). Multiprocessing (and GPU computing) can use both mechanisms.
See MOTW for examples of communicating across processes with multiprocessing.
Using shared memory can lead to race conditions
from multiprocessing import Pool, Value, Array, Lock, current_process n = 4 val = Value('i') arr = Array('i', n) val.value = 0 for i in range(n): arr[i] = 0 def count1(i): "Everyone competes to write to val.""" val.value += 1 def count2(i): """Each process has its own slot in arr to write to.""" ix = current_process().pid % n arr[ix] += 1 pool = Pool(n) pool.map(count1, range(1000)) pool.map(count2, range(1000)) pool.close() print val.value print sum(arr)
500 1000
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