- 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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Example: Matrix multiplication
%%cython -a import numpy as np cimport numpy as np def py_mult(u, v): m, n = u.shape n, p = v.shape w = np.zeros((m, p)) for i in range(m): for j in range(p): for k in range(n): w[i, j] += u[i, k] * v[k, j] return w
Generated by Cython 0.22
01:
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03: cimport numpy as np
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@jit def numba_mult(u, v): m, n = u.shape n, p = v.shape w = np.zeros((m, p)) for i in range(m): for j in range(p): for k in range(n): w[i, j] += u[i, k] * v[k, j] return w
%%cython -a import numpy as np cimport numpy as np cimport cython @cython.boundscheck(False) @cython.wraparound(False) def cy_mult(double[:,::1] u, double[:,::1] v): m = u.shape[0] n = u.shape[1] p = v.shape[1] cdef int i, j, k cdef double[:,::1] w = np.zeros((m, p), dtype=np.float64) for i in range(m): for j in range(p): for k in range(n): w[i, j] += u[i, k] * v[k, j] return np.asarray(w)
Generated by Cython 0.22
+01: import numpy as np
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02: cimport numpy as np
03:
04: cimport cython
05: @cython.boundscheck(False)
06: @cython.wraparound(False)
+07: def cy_mult(double[:,::1] u, double[:,::1] v):
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m = 50 n = 30 p = 40 u = np.random.random((m, n)) v = np.random.random((n, p))
%timeit -n 10 np.dot(u, v) %timeit -n 10 py_mult(u, v) %timeit -n 10 numba_mult(u, v) %timeit -n 10 cy_mult(u, v)
10 loops, best of 3: 16 µs per loop 10 loops, best of 3: 46 ms per loop 10 loops, best of 3: 74.2 µs per loop 10 loops, best of 3: 205 µs per loop
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