CompSciWeek13

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

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

3 = 0011
2 = 0010
1 = 0001
0 = 0000

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

• Constructing B-splines - tensor method
• Representing the differentiation operator
• Solving PDEs using the implicit method