3.18  Serious bug exists in HW4 Problem3 code!!
3.16  HW5 sol added
3.4:  HW4 problem3, added cvx toolbox for lasso.
3.4:  HW4 problem3, timing bug and error2 bug fixed
3.1:  Added midterm report draft
3.1:  Added HW4 problem 3;
2.22: Added HW4 problem1; still working on problem2.
1.26: Serious bugs solved for sol1.m.
      and added runtime analysis plot.


--------HW1----------
--------------flop count analysis-------------
A is of size n*m, r is the number of non-zero entries in x.
1) MP: O(m*n*r)
2) OMP: O(m*n*r+n*r*r)
3) LSOMP: O(m*n*r*r)
4) WMP: O(k*n*r) k is the mean of number of cols a_l, such that a_l^T b_{p-1}>t |b_{p-1}|_2
5) Thresholding: O(n*r*r)

---------------Optional Problem---------------
A vast of literature talks about the asymptotic distribution of this problem. We note the original problem is equivalent to finding the pdf of the minimum pair-wise angles of m points uniformly sampled on a n-dimensional unit sphere. We refer to the following journal for a asymptotic distribution of this.

Cai, Tony, Jianqing Fan, and Tiefeng Jiang. 
"Distributions of angles in random packing on spheres." 
The Journal of Machine Learning Research 14.1 (2013): 1837-1864.

Simulation results show that the bias of this asymptotic distribution goes down as m increases. And in extreme of m->\inf, the pdf will be a delta at \mu(A)=1, meaning that \mu(A) will converge to 1 in probability as m goes to infinity. This is intuitively correct, since when we adding more columns into A, the probability of two colinear columns occurs increases.


--------HW3-----------
See HW3 folder.
.\eps_0.001\ is better. (lambda=0.001)