Description
Calculate newDot=dot-2*firstAxis*secondAxis, newCosine=newDot/(firstNorm*secondNorm), and the corresponding delta.
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.
Calculate newDot=dot-2*firstAxis*secondAxis, newCosine=newDot/(firstNorm*secondNorm), and the corresponding delta.
When to use this tool
Use Cosine Signed One Axis Flip Effect 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 dot, firstAxis, secondAxis, firstNorm, secondNorm. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read newDot, newCosine, delta. Use the output convention below.
Calculate newDot=dot-2*firstAxis*secondAxis, newCosine=newDot/(firstNorm*secondNorm), and the corresponding delta. Require positive norms, feasible axis magnitudes, and dot bounds with the implemented 1e-12 allowance on the updated dot.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dot | Dot | Required. Finite number. |
| firstAxis | First Axis | Required. Finite number. |
| secondAxis | Second Axis | Required. Finite number. |
| firstNorm | First Norm | Required. Finite number; strictly above 0. |
| secondNorm | Second Norm | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| newDot | New Dot | Required. Finite number. |
| newCosine | New Cosine | Required. Finite number. |
| delta | Delta | Required. Finite number. |
{
"input": {
"dot": 5,
"firstAxis": 1,
"secondAxis": 2,
"firstNorm": 3,
"secondNorm": 4
},
"output": {
"newDot": 1,
"newCosine": 0.08333333333333333,
"delta": -0.3333333333333333
}
}Limitations and assumptions
- This models flipping one input coordinate's sign. The allowance is absolute in dot-product units and output is not clamped to cosine bounds; supplied summaries may not represent consistent full vectors.
- 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
- Cosine Antiparallel Negative Score Label
Return negative for score<0 and antiparallel when abs(score+1)<=tolerance.
- Cosine Dot Product Roundoff Clamp
Clamp cosine to minus one through one when it is within the supplied tolerance outside that interval.