Description
Calculate half-step coordinate error bounds and their Euclidean bound for a supplied quantization model.
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 half-step coordinate error bounds and their Euclidean bound for a supplied quantization model.
When to use this tool
Use Vector Component Quantization Error Bound 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 steps. 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 coordinateBounds, euclideanBound. Use the output convention below.
Require nonnegative steps and return coordinateBounds=steps/2 and euclideanBound=hypot(coordinateBounds).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| steps | Nonnegative coordinate quantization increments under a half-step error model. | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coordinateBounds | Coordinate Bounds | Required. Array of Finite number.; maximum items 256. |
| euclideanBound | Euclidean Bound | Required. Finite number. |
{
"input": {
"steps": [
6,
8
]
},
"output": {
"coordinateBounds": [
3,
4
],
"euclideanBound": 5
}
}Limitations and assumptions
- This bounds coordinate errors under a nearest-step half-increment assumption. It does not quantize a vector, specify tie handling, model bias or probability, or apply to arbitrary truncation rules.
- 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 Cancellation Ratio
Sum components for signedSum and their magnitudes for absoluteMass.