Description
Sum components for signedSum and their magnitudes for absoluteMass.
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.
Sum components for signedSum and their magnitudes for absoluteMass.
When to use this tool
Use Vector Component Cancellation 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 components. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedSum, absoluteMass, retainedRatio, defined. Inspect defined before interpreting the associated values.
Sum components for signedSum and their magnitudes for absoluteMass. Return retainedRatio=abs(signedSum)/absoluteMass when any component is nonzero, otherwise zero with defined false.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| components | Components | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedSum | Signed Sum | Required. Finite number. |
| absoluteMass | Absolute Mass | Required. Finite number. |
| retainedRatio | Retained Ratio | Required. Finite number. |
| defined | Whether the associated denominator or quantity is defined; inspect before interpreting a placeholder. | Required. Boolean. |
{
"input": {
"components": [
3,
-2
]
},
"output": {
"signedSum": 1,
"absoluteMass": 5,
"retainedRatio": 0.2,
"defined": true
}
}Limitations and assumptions
- Nonzero components can cancel completely while defined remains true. The ratio measures scalar-sum cancellation rather than a vector norm or an error estimate; summation is ordinary floating point.
- 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
- Signed Component Ratio
Calculate a signed scalar component ratio and report whether both nonzero components share a sign.
- Vector Component Quantization Error Bound
Calculate half-step coordinate error bounds and their Euclidean bound for a supplied quantization model.