Description
First-order norm uncertainty for independent supplied component errors; excludes the nondifferentiable zero vector.
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.
First-order norm uncertainty for independent supplied component errors; excludes the nondifferentiable zero vector.
When to use this tool
Use Vector Uncertain Norm First Order Factor 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 vector, standardDeviations. 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 norm, standardUncertainty. Use the output convention below.
Require matching vector and nonnegative standardDeviations arrays and a nonzero vector. Return its norm and first-order standardUncertainty as hypot of component/norm times its corresponding standard deviation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| standardDeviations | Nonnegative component standard uncertainties on matching vector-unit bases. | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| norm | Norm | Required. Finite number. |
| standardUncertainty | First-order norm uncertainty under independent component errors. | Required. Finite number. |
{
"input": {
"vector": [
3,
4
],
"standardDeviations": [
1,
1
]
},
"output": {
"norm": 5,
"standardUncertainty": 1
}
}Limitations and assumptions
- This uncertainty propagation assumes uncorrelated components and a local linear approximation away from zero norm. It does not estimate uncertainties, include covariance, or calculate a coverage interval.
- 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 Angle Bisector Equal Norm Case
Normalize the sum of equal-norm vectors to obtain a bisector direction, rejecting a zero sum.
- Vector Rejection Norm Roundoff Gap
Subtract squaredProjection from squaredNorm for raw.