Hints to Exercises: Octave and Matlab
Problem Set 1

Computational Physics with Numerical Recipes
James P. Sethna
Physics 480/680, Spring 2008
http://www.physics.cornell.edu/~sethna/teaching/ComputationalPhysics/



1.1 Preliminaries

Usually I find that typing my commands into a file blah.m, and then executing it
by typing "blah" on the command line, allows me to avoid losing my work when
I crash the program. 

(a) Building an array of equally spaced numbers can be done with the colon
construction
	x = start : step : stop
Functions use parentheses, and can be done on whole arrays, like sin(x)
Using plot(x,y,"g") should make a thin green line. At least on my 
machine (which is using gnuplot), it's complicated making the line thicker.
Use "axis" to set the bounds of the plot; use axis() with no arguments to
reset back to the whole range.

(b) You can use "load" to read in the file:
	yOfT = load NoisyYOfT.dat;
and use slices to pull out the t and y columns (so t = yOfT(:,1)). To
get an array filled with y(i)^2 (rather than the dot product y*y) you
can use y .* y. Plotting blue points is done with an argument "b." to plot.



1.2 Condition Number

You can type in a vector or a matrix using brackets and commas,
	A = [0.780, 0.563; 0.913, 0.659]

(a) A * x applies A to x. 

(b) Try help svd. 

(c) A \ b solves A * x = b. Don't forget to subtract (1,-1) and divide by
the machine precision.



1.3 Sherman Morrison formula

It's not hard to use diag and eye to make the tridiagonal matrices. (Use 
ones(4,1) to make the vector for diag, and set the four corners by hand.)
Use inv(T) to get the inverse of T, and use u*transpose(v) to get the
outer product of two vectors.
You'll either want to make u and v column vectors (separating elements with 
semicolons) or use transpose.



1.4 Timing Sine.

Build x, and then use
	tic; sin(x); toc