Difference between revisions of "CompSciWeek13"
From Predictive Chemistry
(→Numerical Integration) |
(→Numerical Integration + Binary Output Format) |
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Binary comes in lots of units |
Binary comes in lots of units |
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| − | 8 bits = 1 byte |
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| + | |||
| − | 4 bits = 1 nibble |
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| + | {| div class="wikitable" |
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| − | 1 byte = 1 ascii character |
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| + | ! 8 bits |
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| − | + | ! = 1 byte |
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| − | + | |- |
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| − | + | ! 4 bits |
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| − | + | ! = 1 nibble |
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| + | |- |
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| + | ! 1 byte |
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| + | ! = 1 ascii character |
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| + | |- |
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| + | ! 2 bytes |
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| + | ! = 1 short |
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| + | |- |
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| + | ! 4 bytes |
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| + | ! = 1 32-bit int = 1 float |
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| + | |- |
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| + | ! 8 bytes |
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| + | ! = 1 64-bit int = 1 64-bit address = 1 double = 1 float complex |
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| + | |- |
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| + | ! 16 bytes |
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| + | ! = 1 long double = 1 double complex |
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| + | |} |
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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) |
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Revision as of 16:11, 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
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
