Difference between revisions of "CompSciWeek13"
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| − | Byte ordering on most modern 64-bit processors is little-endian (Intel, AMD) |
+ | Byte ordering on most modern 64-bit processors is little-endian (Intel, AMD). For more info, see [http://betterexplained.com/articles/understanding-big-and-little-endian-byte-order/]. |
| − | + | In an imaginary system where base 10 numbers are encoded by 4-bit nibbles, a 4-digit representation of the number 123 is |
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0011 0010 0001 0000 |
0011 0010 0001 0000 |
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| − | Since we have to use 4 digits, but the little end (least significant byte) goes first. |
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| + | Since we have to use 4 digits, the most significant digit is set to all zeros, and goes last. The little end (least significant byte) goes first. Notice that within the 4-bit nibbles, the least-significant bit is still on the right. So the number is encoded using this left-to right (within a digit) and bottom to top (digits within a word) order. |
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| + | Real binary encoding is just like the above, except that each 'digit' is a byte, so every 8 bits are in order, but the bytes are reversed. |
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= Basis Functions = |
= Basis Functions = |
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Revision as of 20:18, 17 November 2014
Contents
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
GNU ODE Integrator
vanderpol.ode
<source lang="haskell"> 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
Plotting with Gnuplot
<source 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"
</source>
Run with:
gnuplot plot_van.gplot
Python Integrator
Working with binary
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 = 1 word |
| 4 bytes | = 1 32-bit int = 1 float |
| 8 bytes | = 1 64-bit int = 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). For more info, see [1].
In an imaginary system where base 10 numbers are encoded by 4-bit nibbles, a 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, the most significant digit is set to all zeros, and goes last. The little end (least significant byte) goes first. Notice that within the 4-bit nibbles, the least-significant bit is still on the right. So the number is encoded using this left-to right (within a digit) and bottom to top (digits within a word) order.
Real binary encoding is just like the above, except that each 'digit' is a byte, so every 8 bits are in order, but the bytes are reversed.
Basis Functions
- Constructing B-splines - tensor method
- Representing the differentiation operator
- Solving PDEs using the implicit method
