Description
Sum weights and return residual=sum-1.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Sum weights and return residual=sum-1.
When to use this tool
Use Vector Affine Combination Weight Residual when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter weights. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sum, residual. Use the output convention below.
Sum weights and return residual=sum-1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weights | Weights | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sum | Sum | Required. Finite number. |
| residual | Supplied weight sum minus one; no automatic normalization. | Required. Finite number. |
{
"input": {
"weights": [
0.2,
0.3,
0.4
]
},
"output": {
"sum": 0.9,
"residual": -0.09999999999999998
}
}Limitations and assumptions
- Weights may be negative and are not normalized. An empty array gives sum zero and residual minus one; the tool neither combines points nor tests convexity or a full geometric affine relation.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Three Point Affine Dependence Residual
Calculate the vector residual for a supplied point's affine relation to two other points at a fixed parameter.
- Homogeneous Point Weight Flag
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.