Description
Calculate a signed scalar component ratio and report whether both nonzero components share a sign.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Calculate a signed scalar component ratio and report whether both nonzero components share a sign.
When to use this tool
Use Signed Component Ratio when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter component, referenceComponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio, sameSign. Inspect sameSign before interpreting the associated values.
Require nonzero referenceComponent. Return ratio=component/referenceComponent and sameSign only when component is nonzero and both scalar signs match.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| component | Component | Required. Finite number. |
| referenceComponent | Reference Component | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Dimensionless ratio under compatible input units and the stated formula. | Required. Finite number. |
| sameSign | Same Sign | Required. Boolean. |
{
"input": {
"component": -6,
"referenceComponent": 3
},
"output": {
"ratio": -2,
"sameSign": false
}
}Limitations and assumptions
- Zero component has ratio zero and sameSign false. The signed ratio is not a vector angle or a complete directional agreement test.
- 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
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Component Cancellation Ratio
Sum components for signedSum and their magnitudes for absoluteMass.
- Vector Component Quantization Error Bound
Calculate half-step coordinate error bounds and their Euclidean bound for a supplied quantization model.