Description
Multiply firstCoordinate/firstNorm by secondCoordinate/secondNorm.
A vector has ordered coordinates. Its length and direction are different properties: scaling changes length, while normalization retains direction when the vector is nonzero. Coordinate order and the chosen axes determine the interpretation.
Multiply firstCoordinate/firstNorm by secondCoordinate/secondNorm.
When to use this tool
Use Cosine Coordinate Term when you need a small coordinate transformation or a direction calculation under an explicit axis convention.
How to use the tool and how it works
- Enter firstCoordinate, secondCoordinate, 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 contribution. Use the output convention below.
Require positive norms and absolute coordinates no greater than their respective norms. Multiply firstCoordinate/firstNorm by secondCoordinate/secondNorm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstCoordinate | First Coordinate | Required. Finite number. |
| secondCoordinate | Second Coordinate | 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 |
|---|---|---|
| contribution | Contribution | Required. Finite number. |
{
"input": {
"firstCoordinate": 3,
"secondCoordinate": 4,
"firstNorm": 5,
"secondNorm": 5
},
"output": {
"contribution": 0.48
}
}Limitations and assumptions
- This is one cosine-similarity contribution, potentially signed; supplied norms and vector correspondence are not independently computed or verified.
- 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
Verify the coordinate system and use a complete transformation matrix when several transformations must be composed.
References
Similar or alternative tools
- Unit L2 Coordinate Contribution
Divide coordinate by norm and square it for squaredNormShare.
- Squared Distance Coordinate Contribution
Subtract secondCoordinate from firstCoordinate and square for squaredContribution.