This contains some examples for using numpy array operations. The iPython notebook file is a good starting point.

The examples include:

• diffusion
• gaussian walk

What's shown below is shown in more detail in the iPython notebook.

• Python loops have python overhead
• Numpy operations are lower level

x = 0 for i in range(10): x+=1 

• Useful when performing the same operation to many numerical pieces of data.
• Ex: Adding all the elements from two lists of numbers

• Addition two lists of numbers
• numpy array functions
  • np.sum(), np.cumsum(), np.exp()

Under the hood, complex operations will automatically be run on multiple processors.

• SIMD
• Intel MKL
• To get these benefits in anaconda:

conda install mkl 

• Grid data - possibly regularly spaced
• Point data

• Finite Difference Examples: diffusion.py
  • Grid data
  • Write equation
  • Draw arrays and arrows referencing location to array
• 1-D
  • For loop: diff1d_loop()
  • array version: diff1d_vec()
  • Show 2-d plot of all results to compare to gaussian motion
• 2-D
  • For loop: diff2d_loop()
  • array version: diff2d_vec()
• Draw overlapping boxes to show how slice indexing should work
• lineprofiler: https://github.com/rkern/line_profiler

Basic iPython Usage:

run diffusion # Visualized the 1-D computations diff1d_vec() # test the time difference %timeit diff1d_loop(plotUpdate=Fase) %timeit diff1d_vec(plotUpdate=Fase) # Visualized the 2-D computations diff2d_vec() # test the time difference %timeit diff2d_loop(plotUpdate=Fase) %timeit diff2d_vec(plotUpdate=Fase) 

• Gaussian motion
• Individual particles

• Array views
• Rotating 2-D grid of points
• Rotating 2-D list of points from gaussian motion

• numexpr
• cython
• pyOpenCl