Description
Return p × (ln(p) - ln(q))/ln(base), or zero for p zero.
Divergences and information densities compare probabilities on a common support. A weighted cell contribution and an unweighted logarithmic ratio differ, and zero-support cases require explicit limits.
Return p × (ln(p) - ln(q))/ln(base), or zero for p zero.
When to use this tool
Use Information: Relative Entropy Single Cell Term when you need one precisely defined information-comparison term.
How to use the tool and how it works
- Enter p, q, base. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require p and q in [0, 1], base > 1, and positive q whenever p is positive. Return p × (ln(p) - ln(q))/ln(base), or zero for p zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| p | P | Required. Finite number. |
| q | Q | Required. Finite number. |
| base | Numeric base or source quantity interpreted under the specific calculation above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.relativeEntropyTerm | Relative Entropy Term | Calculated result member: number. |
{
"input": {
"p": 0.5,
"q": 0.25,
"base": 2
},
"output": {
"result": {
"relativeEntropyTerm": 0.5
}
}
}Limitations and assumptions
- A single relative-entropy term can be negative; infinite positive-p/zero-q cases are rejected instead of returned as infinity.
- Outputs are nested inside result. 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
Align and validate complete distributions before summing terms or interpreting a full divergence or dependence measure.
References
Similar or alternative tools
- Information Gain Zero Cell Limit
Return cell × (ln(cell) - ln(reference)), with zero at a zero cell and zeroCellLimit flagged.
- Information: Mutual Information Single Cell Term
Validate marginals in [0, 1] and jointProbability between max(0, row + column - 1) and min(row, column).