Description
Sum the row with magnitude-aware compensation and independently sum absolute values the same way.
Opposing signs can cancel in a row sum even when individual magnitudes are large. Compensated summation tracks some lost low-order information but remains finite-precision arithmetic.
Sum the row with magnitude-aware compensation and independently sum absolute values the same way.
When to use this tool
Use Row Signed Sum Cancellation Term when you need a diagnostic for signed-sum cancellation.
How to use the tool and how it works
- Enter row. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedSum, absoluteSum, cancellation. Use the output convention below.
Sum the row with magnitude-aware compensation and independently sum absolute values the same way. Return max(0, absoluteSum - abs(signedSum)) as cancellation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedSum | Signed Sum | Required. Finite number. |
| absoluteSum | Absolute Sum | Required. Finite number. |
| cancellation | Cancellation | Required. Finite number. |
{
"input": {
"row": [
3,
-2
]
},
"output": {
"signedSum": 1,
"absoluteSum": 5,
"cancellation": 4
}
}Limitations and assumptions
- Compensation reduces some rounding error but does not guarantee exact arithmetic or a condition-number 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
Use higher precision or a validated numerical method when cancellation materially affects the downstream result.
References
Similar or alternative tools
- Matrix Row Balanced Sign Count
Count strictly positive, strictly negative, and exact-zero row entries.
- Matrix Two Row Inner Product Term
Require equal-length left and right arrays, multiply corresponding elements into terms, and sum those products.