Description
Return recovered=sign(transformed)*expm1(abs(transformed)) and residual=original-recovered.
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 recovered=sign(transformed)*expm1(abs(transformed)) and residual=original-recovered.
When to use this tool
Use Signed Log Transform Inverse Residual 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 original, transformed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read recovered, residual. Use the output convention below.
Return recovered=sign(transformed)*expm1(abs(transformed)) and residual=original-recovered.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| original | Supplied original-coordinate value or inverse result under the stated convention. | Required. Finite number. |
| transformed | Transformed | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| recovered | Unscaled inverse value; a nonunit forward reference scale is not restored. | Required. Finite number. |
| residual | Signed supplied-minus-reconstructed discrepancy under the stated formula. | Required. Finite number. |
{
"input": {
"original": 3,
"transformed": 1.3862943611198906
},
"output": {
"recovered": 3,
"residual": 0
}
}Limitations and assumptions
- This is the unit-reference inverse of sign(x)*ln(1+abs(x)). It applies no external reference scale; outputs from a scaled forward transform need that scale restored separately before comparison in original units.
- 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: Signed Log1p Reference Scale
Apply an odd signed-log1p transform with an explicitly supplied positive reference scale, preserving zero without imposing an undefined logarithm on negatives.
- Normalizer Center Inverse Offset
For nonzero signed scale return original=normalized*scale+center and offsetContribution=center.