Revision as of 15:15, 17 November 2014

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 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

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.

@@ Line 9: / Line 9: @@
 ** inspecting binary formats with od
+=== GNU ODE Integrator ===
+'''vanderpol.ode'''
+<code 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
+</code>
+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
+=== Plotting with Gnuplot ===
+<code lang="gnuplot">
+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"
+</code>
+Run with:
+ gnuplot plot_van.gplot
+=== Python Integrator ===
+=== Working with binary ===
 Example: [http://man7.org/linux/man-pages/man5/elf.5.html ELF] header