Description
Return leftWeight = 1 - parameter, rightWeight = parameter, and the sum of their absolute values as amplification.
An interpolation weight, geometric extrapolation distance, and mathematical error bound describe different quantities. A curvature-based bound needs assumptions about the underlying function, not just a computed coordinate.
Return leftWeight = 1 - parameter, rightWeight = parameter, and the sum of their absolute values as amplification.
When to use this tool
Use Linear Extrapolation Horizon Amplification when you need one explicit interpolation error or amplification component.
How to use the tool and how it works
- Enter parameter. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftWeight, rightWeight, amplification. Use the output convention below.
Return leftWeight = 1 - parameter, rightWeight = parameter, and the sum of their absolute values as amplification.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parameter | Normalized interpolation coordinate under the stated domain; may permit extrapolation. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftWeight | Left Weight | Required. Finite number. |
| rightWeight | Right Weight | Required. Finite number. |
| amplification | Amplification | Required. Finite number. |
{
"input": {
"parameter": 2
},
"output": {
"leftWeight": -1,
"rightWeight": 2,
"amplification": 3
}
}Limitations and assumptions
- Inside [0, 1] amplification is one; outside it measures value-error amplification under these linear weights, not a probabilistic error estimate.
- 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
Establish valid derivative bounds and compare methods or measurements before claiming a prediction-error guarantee.
References
Similar or alternative tools
- Interpolant Extrapolated Weight Sign
Mark leftNegative for t > 1, rightNegative for t < 0, and extrapolated outside [0, 1].
- Extrapolation Distance In Knot Units
Return (value - lowerKnot)/span and distance outside either endpoint divided by span, or zero outsideDistance within the interval.