Description
Add dimensions × ln(abs(scale)) to supplied entropy and return that shift.
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Add dimensions × ln(abs(scale)) to supplied entropy and return that shift.
When to use this tool
Use Differential Entropy Coordinate Scale Shift when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter entropy, scale, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read entropy, shift. Use the output convention below.
Require nonzero scale and dimensions 1-256. Add dimensions × ln(abs(scale)) to supplied entropy and return that shift.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entropy | Differential entropy in nats, before or after the stated coordinate scaling. | Required. Finite number. |
| scale | Common nonzero multiplicative coordinate scale applied to all dimensions. | Required. Finite number. |
| dimensions | Dimensions | Required. Safe integer; minimum 1; maximum 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| entropy | Differential entropy in nats, before or after the stated coordinate scaling. | Required. Finite number. |
| shift | Shift | Required. Finite number. |
{
"input": {
"entropy": 2,
"scale": 2,
"dimensions": 1
},
"output": {
"entropy": 2.6931471805599454,
"shift": 0.6931471805599453
}
}Limitations and assumptions
- Entropy is differential entropy in nats for uniform scaling of every coordinate; this is not a discrete-entropy transform or a general Jacobian calculation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate and align complete probability distributions before aggregating terms or interpreting an uncertainty estimate.
References
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