Description
Return invertible=(scale!=0).
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 invertible=(scale!=0).
When to use this tool
Use Scalar Affine Inverse Existence 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 scale, offset. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read invertible, inverseScale, inverseOffset. Inspect invertible before interpreting the associated values.
Return invertible=(scale!=0). When invertible return inverseScale=1/scale and inverseOffset=-offset/scale; otherwise return both coefficients as zero placeholders.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| scale | Supplied nonzero or positive multiplier under the stated transform convention. | Required. Finite number. |
| offset | Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| invertible | Invertible | Required. Boolean. |
| inverseScale | 1/scale when invertible; zero placeholder otherwise. | Required. Finite number. |
| inverseOffset | Inverse Offset | Required. Finite number. |
{
"input": {
"scale": 2,
"offset": 3
},
"output": {
"invertible": true,
"inverseScale": 0.5,
"inverseOffset": -1.5
}
}Limitations and assumptions
- The forward convention is y=scale*x+offset. A nonzero finite scale can still produce unrepresentable inverse coefficients; this does not recover an observation or infer a fitted affine model.
- 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
- Affine Normalizer Parameter Compose
For first transform y=firstScale*x+firstOffset followed by z=secondScale*y+secondOffset return scale=secondScale*firstScale and offset=secondScale*firstOffset+secondOffset.
- Normalizer Center Inverse Offset
For nonzero signed scale return original=normalized*scale+center and offsetContribution=center.