numpy

Numpy

Numpy is the de facto standard for efficient matrix representations and (BLAS level 1-3) computations. Scipy implements more high-level algorithms for scientific computing (Lapack, statistics,...).

What is it?

1. data_plot.py: reads a CSV file containing data, performs linear regression, and plots the data and the line representing the regression; numpy is used to represent the data, scipy to perform the linear regression, matplotlib for plotting the result
2. data_writer.py: produces data for the data_plot.py script, linear with noise added
3. data.csv: example data set for data_plot.py
4. diffusion.ipynb: solving the PDE describing thermal diffusion in 2D.
5. fft.py: creates a signal consisting of a sum of cosine functions with specified amplitudes and frequencies, adding noise; plots the resulting function, uses FFT to determine the frequency spectrum, and plot the latter
6. fft_experiments.ipynb: notebook with some experiments on signal analysis using FFT.
7. game_of_life.ipynb: jupyter notebook implementing Game of Life.
8. logistic_map.ipynb: analysis and visualization of the logistic map.
9. numeexpr.ipynb: Jupyter notebook illustrating some use cases of the numexpr module.
10. numpy.ipynb: Jupyter notebook illustrating some numpy aspects like array slicing, adding dimension to arrays, and so on.
11. indexing_arrays.ipynb: indexing using ..., np.newaxis
12. structured_arrays.ipynb: Jupyter notebook illustration creating of and working with structured numpy arrays.
13. optimization.py: illustration of how to use the scipy.optimize for unconstrained multivariate optimization
14. target_function_plot.py: script that creates a surface plot of the target function in optimization.py
15. pendulum_ode.py: solves the ODE of a damped, driven pendulum that is optionally anharmonic. Optionally plots results.
16. dynamic_programming.ipynb: example of string alignment using dynamic programming.
17. vector_write.py: script to create a file containing a specified number of floating point values, either in text or binary format to test I/O performance characteristics.
18. vector_sum.py: reads files generated by vector_write.py and computes the sum of the values; intended for I/O performance tests.
19. genetic_drift.ipynb: Jupyter notebook illustrating how to use numpy to model systems of arbitrary dimensions.
20. exponentiation.ipynb: Jupyter notebook to illustrate that the algorithm can have a significant impact on performance.
21. io_performance.ipynb: Jupyter notebook to illustrate the performance of different I/O methods (text, binary, HDF5).
22. broadcast.ipynb: Jupyter notebook illustrating the use of broadcasting in numpy.

Pendulum

For chaotic regime, choose the following parameters:

• l = 9.81
• q = 0.5
• F_d = 1.2
• omega_d = 0.66667 (2/3)
• theta0 = 0.2
• anharmonic

To easily obtain as many points as possible for the Poicare section, choose delta_t ~ 3pi, e.g., delta_t = 0.009424778.