Description
Return one axis gradient of a supplied positively supported weighted Euclidean distance.
Weighted coordinate distances depend on whether weights multiply absolute differences or squared differences. Zero weights can make different vectors equivalent, and derivatives at a zero distance or absolute-value corner need explicit treatment.
Return one axis gradient of a supplied positively supported weighted Euclidean distance.
When to use this tool
Use Weighted Euclidean One Axis Gradient when checking one weighted-axis contribution, support rule or derivative.
How to use the tool and how it works
- Enter difference, weight, distance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gradient. Use the output convention below.
Require nonnegative weight and positive distance. gradient = weight*difference/distance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| difference | Difference | Required. Finite number. |
| weight | Coefficient inside the squared-distance sum, not a weight squared in the gradient. | Required. Finite number. |
| distance | Distance | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gradient | Gradient | Required. Finite number. |
{
"input": {
"difference": 3,
"weight": 2,
"distance": 6
},
"output": {
"gradient": 1
}
}Limitations and assumptions
- This is one axis derivative for distance = sqrt(sum(weight[i]*difference[i]²)); squared-weight conventions differ. The denominator is supplied, not checked against a complete vector, and the zero-distance case is rejected.
- 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
Use a complete distance implementation with an explicit weighting and missing-coordinate convention for vector comparison and optimization.
References
Similar or alternative tools
- Weighted Manhattan Axis Subgradient
For weight*abs(difference), return lower = upper = -weight when difference < 0, +weight when positive, and the interval [-weight,+weight] at zero.
- Signed Distance Axis Reflection Effect Tool
Compute signed distance axis reflection effect from explicit bounded inputs.