Problem Set 8

This week's coverage was on function fitting---that is choosing what parameters of a particular
function best fit existing data. I found this section particularly useful for my final project, and
interests in general, but the scope was really broad. Therefore I chose to focus on the problems
that have most relevance to my work outside class (I think!). The hardest bit was setting up the
right environments to make some of my code work. For example, I found a pandas package that
was especially helpful for calculating the bootstrap method, but it was a real headache getting
python to read the import---I had to modify PYTHONPATH. Which is all news to me, I didn't even
know there was such a thing before starting the problem set! I'm discovering that in my case
the learning happens in the process of trying to translate a mathematical concept into code.

For this p-set, I learned how to build arrays in python, downloaded Xcode to write a "git"
command from terminal to pull directly from github, figured out how to edit python paths, learned
a TON of numpy functions, and figured out how to write the output of a python script to .csv, also
how to import and modify .csv and .txt files in Matlab and R. Not to mention a variety of
idiosyncrasies about my computer's workflow. I also picked up a little on good programming
habits. Since I was forced to re-examine my PYTHONPATH, I discovered the file architecture
inherent to my computer, which was really confusing. Now I put all my modules in a specific
folder. Wow!

11.1: Singular Value Decomposition & Bootstrap Sampling

SVD input file (generated) here
Python Code here

The output of the SVD program (singular values, wi)

**I had some kind of bug in my bootstrap method, the program wouldn't print output for my
original and resampled mean. Not sure why, I'll leave it for further examination.

You can find the script commented out of the code linked above.

12.3: Variance and Eigenvalues

Some math work for problem 12.3