Description
For nonnegative norm return defined=(norm>0) and normalized=value/norm when positive, otherwise the supplied zeroValue.
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.
For nonnegative norm return defined=(norm>0) and normalized=value/norm when positive, otherwise the supplied zeroValue.
When to use this tool
Use Scalar Norm Reference Zero Policy 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, zeroValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read defined, normalized. Inspect defined before interpreting the associated values.
For nonnegative norm return defined=(norm>0) and normalized=value/norm when positive, otherwise the supplied zeroValue.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. |
| zeroValue | Caller-selected fallback returned exactly when norm==0. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| defined | Whether the stated denominator or quantity is defined; inspect before using a placeholder. | Required. Boolean. |
| normalized | Scalar transformed under the stated formula and zero policy. | Required. Finite number. |
{
"input": {
"value": 0,
"norm": 0,
"zeroValue": 0
},
"output": {
"defined": false,
"normalized": 0
}
}Limitations and assumptions
- The denominator is supplied and not checked against an underlying vector or the value's magnitude. ZeroValue is an explicit fallback, not a mathematical normalization at a zero norm, and output need not lie within a unit range.
- 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
- Normalization: Robust Scaler Zero Spread Policy
Compute one robust-reference normalized scalar with an explicit reject/zero policy for a supplied zero spread, preserving defined status.
- Signed L1 Mass Factor
Return l1Mass=sum(abs(values)), defined when any element is nonzero, and reciprocalMass=1/l1Mass when defined or zero otherwise.