Description
Return derivative=(norm-value*coordinateSign)/(norm^2).
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.
Return derivative=(norm-value*coordinateSign)/(norm^2).
When to use this tool
Use L1 Normalized One Coordinate Sensitivity 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 value, norm, coordinateSign. 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.
For positive norm require abs(value)<=norm, coordinateSign in {-1,1}, and value*coordinateSign>=0. Return derivative=(norm-value*coordinateSign)/(norm^2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Supplied scalar or returned value under the stated operation. | Required. Finite number. |
| norm | Positive supplied norm for the same vector or coordinate model, not recomputed here. | Required. Finite number; strictly above 0. |
| coordinateSign | Exactly -1 or 1, consistent with the supplied value's sign. | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Local derivative term under the supplied parameter and norm assumptions. | Required. Finite number. |
{
"input": {
"value": 2,
"norm": 5,
"coordinateSign": 1
},
"output": {
"derivative": 0.12
}
}Limitations and assumptions
- This is the selected coordinate's sensitivity under an L1 normalization sign branch, using a supplied total norm. No full vector, norm consistency, or finite perturbation is evaluated; numeric squaring can underflow or overflow at extreme norms.
- 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
- Unit Vector Normalization Tangent Term
Compute axial=dot(unitVector,perturbation) and derivative=(perturbation-unitVector*axial)/norm componentwise.
- Scalar L2 Norm Gradient Coordinate
For positive norm require abs(coordinate)<=norm and return derivative=coordinate/norm.