Description
Return (rightX - leftX)/(rightY - leftY) as derivative of inverse position with respect to value.
Linear interpolation blends endpoint values by a normalized coordinate. Its value weights, inverse slope, and sensitivities to moving nodes answer different questions and use different units.
Return (rightX - leftX)/(rightY - leftY) as derivative of inverse position with respect to value.
When to use this tool
Use Linear Interpolant Inverse Sensitivity when you need one explicitly defined linear interpolation term.
How to use the tool and how it works
- Enter leftX, rightX, leftY, rightY. 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.
Require increasing x endpoints and unequal y values. Return (rightX - leftX)/(rightY - leftY) as derivative of inverse position with respect to value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftX | Left X | Required. Finite number. |
| rightX | Right X | Required. Finite number. |
| leftY | Left Y | Required. Finite number. |
| rightY | Right Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"leftX": 0,
"rightX": 4,
"leftY": 2,
"rightY": 10
},
"output": {
"derivative": 0.5
}
}Limitations and assumptions
- This local inverse sensitivity can be negative; a near-flat segment is not rejected by tolerance.
- 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
Validate endpoints and units and use a complete evaluator when clamping, extrapolation, or uncertainty propagation is required.
References
Similar or alternative tools
- Inverse Linear Extrapolation Domain Flag
Compute x0 + (targetY - y0) × (x1 - x0)/(y1 - y0) and flag target values outside the endpoint y range.
- Inverse Interpolation Flat Segment Flag
Mark flat when left equals right.