Goals this year are to get healthier.  Make my body healthier, make my finances healthier and my relationships with people and society healthier.  But since that is a little lofty here are my 10 resolutions for 2011 that are hopefully measurable.

1. Take 10,000 pictures.
2. Use Sea Salt instead of iodized table salt.
3. Cook a healthy dinner at least once a week.
4. Pack Lunch at least 3 times each work week.
5. Get a passport.
6. Use Anti-RSI software while at work (and really get up and stretch!)
7. Take at least 2 trips for vacation.
8. Document and release open-source a steady-state, inviscid flow solver.
9. NOT buy a new computer.
10. Recycle!

So you kind of know what eigenvalues are.  And you’ve been presented the Power Method.  But what is a half ass-ed description on how it works.

As a reminder the power method’s iteration is

x(k+1) = Ax(k)

And we are looking for the eigenvectors for A.  You may already know that the simple version of the power method yields the largest magnitude eigenvalue and eigenvector pair (if you didn’t I just told you).  But how can this be thought of.

First off lets think of A as a collection of directions, those directions are given by the eigenvectors.  We will start at x(0) and just go in the direction that A tells us.  After one iteration we get to x(1).  Then we take a step again in the direction A tells us to go, we get to x(2).  After taking a whole bunch of steps in the direction of A we realize that our feet hurt, also we can draw a vector from where we were to where we are.  That vector is the dominant eigenvector of A (the vector of the largest magnitude).  So after a bunch of iterations, x(k) -x(0) is basically along the an eigenvector for A.  If eigenvectors are similar in magnitude, it will take a long time for that direction to look more like one eigenvector and less like a combination of the two largest.  Which is why the Power Method converges faster if the eigenvalues are far apart in magnitude.

One eigenvector is shouting go west, one speaking go north, so you go northwest.  After a while you can only hear the eigenvector that shouts go west so you just head west.  After walking far, you steps west look like you are just going west. Thus you are just left with the eigenvector west.

All finished, with the front bare to expose its true nature.

So aquired some sturdy double corrugated cardboard that was used to move servers.  (If its good enough for a computing cluser its good enough for my butt).  My roommate used Hermite interpolation (for more information see Works-> Interpolation)  to tweak the curvature of the couch for comfort.

After deciding on the curve we traced out 24 curved pieces, that would be placed 3 inches apart for the full length of the 6 foot couch.  Cut some slots vertically so we could just slide the couch together, once they were all cut (this took about 4 days of lunch breaks).    

A few pieces together in the cross design.

Almost full length couch put together

And just finished it off with a twin sized memory foam mattress and some pillows.  The only thing missing is a true back support so that it could go in the middle of our living room.  But really there are two options here, buy a freaking huge tv and put the couch across the room, or buy a slightly smaller tv and build a support.  We’ll let Black Friday Sales decide.

After gcc couldn’t even compile a simple Hello World in either c or c++ I knew something was up.  I had actually had a few compilers floating around on my machine, none of which were working any longer, all complaining about finding standard library files.  I tired reinstalling them manually, double and triple checking paths.  I tired binary packages from http://hpc.sourceforge.net/ (love that site).  Thinking it was an issue with multiple compilers I decided to take the big stick approach and wiped by hard drive and reinstalled Snow Leopard.  Still no luck.

Not 20 minutes later I tripped across a post by Brian Pane that set me in the right direction.  This could have saved me days of time if I knew then.

The skinny:

Insert Snow Leopard DVD

Go to Option Installs folder

Run Xcode.mpkg

Compile and collect loot.

Having just reinstalled Snow Leopard (yes, REinstalled) I’m going through the steps I take to get everything “just right”.  The first thing I need configured on a new machine is a fancy terminal.  The default configuration gives no visual cue for the difference between different items in your directory.

Begin by opening up terminal and opening our bash_profile.  This file can hold all the configurations we want to make to the default bash (beginners read: terminal).  Chances are this file isn’t on your computer yet, no problem.  Type in:

vim ~/.bash_profile

hit “i” to open vim to insert mode, and add the following two lines at the end.

export CLICOLOR=1

export LSCOLORS=ExFxCxDxBxegedabagacad

now hit “esc” , then “wq” and “return”.

Close Terminal and relog os x. When you return to terminal and enter a command such as ls, directories will now be highlighted and thus easily distinguishable from regular files.

Much more useful