Description
Compute axial=dot(unitVector,perturbation) and derivative=(perturbation-unitVector*axial)/norm componentwise.
Normalization depends on the supplied center, scale, norm, range, reference distribution, or denominator. A zero spread and a missing denominator need an explicit policy, and clipping differs from fitting a scaler. Evaluating one scalar or derivative term does not estimate every parameter or establish a distributional improvement.
Compute axial=dot(unitVector,perturbation) and derivative=(perturbation-unitVector*axial)/norm componentwise.
When to use this tool
Use Unit Vector Normalization Tangent Term when you already have the required normalization parameters and need this local scalar, range, policy, or derivative term.
How to use the tool and how it works
- Enter unitVector, perturbation, norm. 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 derivative. Use the output convention below.
Require aligned unitVector and perturbation, unit-vector norm within 1e-12 of one, and positive supplied norm. Compute axial=dot(unitVector,perturbation) and derivative=(perturbation-unitVector*axial)/norm componentwise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| unitVector | Unit Vector | Required. Array of finite number; maximum items 256. |
| perturbation | Perturbation | Required. Array of finite number; maximum items 256. |
| norm | Positive norm of the intended original vector; consistency with direction is not checked. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Local derivative term under the supplied parameter and norm assumptions. | Required. Array of finite number; maximum items 256. |
{
"input": {
"unitVector": [
1,
0
],
"perturbation": [
2,
3
],
"norm": 2
},
"output": {
"derivative": [
0,
1.5
]
}
}Limitations and assumptions
- This is the differential of vector normalization under the supplied direction and original norm. Their consistency with an underlying vector is not checked, and the result is a local derivative rather than a finite perturbed normalized vector.
- 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
Fit or verify the intended scaler parameters and statistical model separately. Check units, zero policies, missingness, clipping, inverse conventions, and whether supplied norms or denominators belong to the same data.
References
Similar or alternative tools
- Scalar L2 Norm Gradient Coordinate
For positive norm require abs(coordinate)<=norm and return derivative=coordinate/norm.
- L1 Normalized One Coordinate Sensitivity
Return derivative=(norm-value*coordinateSign)/(norm^2).