Numerical Integration + Binary Output Format

Van der Pol Oscillator: <math>\ddot u - \mu (1-u^2) \dot u + u = 0</math>
- Implementations in OpenOffice Spreadsheet, GNU ODE, and Python
- Perturbed initial conditions, Lyapunov exponents, and large deviation principles
Working well with others: text
Working with machines: binary
- This is preferable when you have lots and lots of data
- The relevant numpy methods are x.tofile("file") and x = fromfile("file") -- but save("file", x) and x = load("file") are preferred
- inspecting binary formats with od

vanderpol.ode

<source lang="python"> mu = %MU

u = 1.0 y = 0.0

u' = y y' = mu*(1-u*u)*y - u

print t, u, y, y! every 10 from 50 step 0, 100 </source>

You can do the substitution with sed and run all dynamics with:

 for((i=0;i<10;i++)); do
   sed -e "s|%MU|$i|" vanderpol.ode >vanderpol-$i.ode
   ode -f vanderpol-$i.ode >out-$i.dat </dev/null
 done

set term postscript enh color lw 3 "Times-Roman" 28 set out 'van.eps'

set xlabel "u" set ylabel "y" plot 'out-0.dat' u 2:3 w l title "0", \


    'out-1.dat' u 2:3 w l title "1", \
    'out-4.dat' u 2:3 w l title "{/Symbol m} = 4"

Run with:

gnuplot plot_van.gplot

Example: ELF header

od -t x1 -t c -N 8 /bin/bash

Binary comes in lots of units

8 bits	= 1 byte
4 bits	= 1 nibble
1 byte	= 1 ascii character
2 bytes	= 1 short
4 bytes	= 1 32-bit int = 1 float
8 bytes	= 1 64-bit int = 1 64-bit address = 1 double = 1 float complex
16 bytes	= 1 long double = 1 double complex

Byte ordering on most modern 64-bit processors is little-endian (Intel, AMD)

in base 10, this would mean the 4-digit representation of the number 123 is

The binary together would read:

0011 0010 0001 0000

Since we have to use 4 digits, but the little end (least significant byte) goes first.

Basis Functions