Test case for option_simple_LCP

[jlperla]

Come up with a test case to ensure no bugs were introduced into the new code.

Save a vector of out put from original HACT code, put it in folder, and then automatically test at the bottom of the new file if it is the same.

[jlperla]

@stevenzhangdx I removed you from this assignment as I decided to change things around a bit. Work at the other ones first, in particular annotation of the sourcecode with math and connection to a latex file with line-numbers.