Description
Return coordinate contributions to a unit-direction derivative.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return coordinate contributions to a unit-direction derivative.
When to use this tool
Use Multivariable Directional Derivative Contribution when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter gradient, direction. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contributions, derivative. Use the output convention below.
Return coordinate contributions to a unit-direction derivative. Require aligned gradient/direction arrays with dot(direction,direction) within 1e-12 of one; contributions = gradient_i*direction_i, derivative sums them.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| gradient | Gradient | Required. Array of finite number; maximum items 256. |
| direction | Direction | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contributions | Contributions | Required. Array of finite number; maximum items 256. |
| derivative | Derivative | Required. Finite number. |
{
"input": {
"gradient": [
2,
3
],
"direction": [
1,
0
]
},
"output": {
"contributions": [
2,
0
],
"derivative": 2
}
}Limitations and assumptions
- The gradient and direction are supplied; no function, differentiability or physically compatible coordinate scaling is verified.
- 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
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Gradient Level Set Tangent Orthogonality
Check gradient/direction orthogonality and a regular-level flag.
- Local Logarithmic Second Derivative Tool
Compute local logarithmic second derivative from explicit bounded inputs.