Description
Return excess=max(0,intersection-min(leftSize,rightSize)), feasible when that is zero, and denominator=leftSize+rightSize.
A similarity term depends on the comparison universe, missing-value policy, treatment of repeated features, and normalization. A score can also have a caller-selected value when its mathematical denominator vanishes. Those conventions matter before interpreting a threshold or comparing methods.
Return excess=max(0,intersection-min(leftSize,rightSize)), feasible when that is zero, and denominator=leftSize+rightSize.
When to use this tool
Use Dice Count Feasibility Residual when you need this particular comparison term, normalization, domain condition, or empty-result policy in a larger matching workflow.
How to use the tool and how it works
- Enter intersection, leftSize, rightSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read feasible, excess, denominator. Inspect feasible before interpreting the associated values.
Return excess=max(0,intersection-min(leftSize,rightSize)), feasible when that is zero, and denominator=leftSize+rightSize. Require nonnegative integer counts.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intersection | Intersection | Required. Safe integer; minimum 0. |
| leftSize | Left Size | Required. Safe integer; minimum 0. |
| rightSize | Right Size | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| feasible | Whether overlap is no greater than either size; not whole-set validation. | Required. Boolean. |
| excess | Excess | Required. Safe integer. |
| denominator | Denominator | Required. Safe integer. |
{
"input": {
"intersection": 3,
"leftSize": 2,
"rightSize": 5
},
"output": {
"feasible": false,
"excess": 1,
"denominator": 7
}
}Limitations and assumptions
- Impossible overlap counts are reported with feasible false rather than rejected. This checks count arithmetic without an actual set intersection or a Dice score.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Compare methods only after aligning feature definitions, missingness, empty policies, multiplicities, and normalizers. Use a complete comparison when the tool returns only one contribution or count check.
References
Similar or alternative tools
- Dice Overlap Count Contribution
Return exact decimal numerator twice overlap and denominator firstSize+secondSize using BigInt, plus numeric dice.
- Cosine Norm Rescale Invariance Residual
Return cosine=dot/(firstNorm*secondNorm), scaledCosine=sign(firstScale*secondScale)*cosine, and their residual.