Description
Choose a valid pivotColumn and use the largest absolute row entry as scale.
Triangular storage can leave structural zeros and unit diagonals implicit. Solving or inverting requires usable diagonal entries, but a diagonal threshold alone does not measure conditioning.
Choose a valid pivotColumn and use the largest absolute row entry as scale.
When to use this tool
Use Matrix Row Pivot Scale Ratio when you need a triangular-entry convention or pivot diagnostic.
How to use the tool and how it works
- Enter row, pivotColumn. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read ratio, scale, zeroRow. Inspect zeroRow before interpreting the associated values.
Choose a valid pivotColumn and use the largest absolute row entry as scale. Return abs(pivot) / scale, or ratio zero and zeroRow true for an all-zero row.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Array of finite number; maximum items 256. |
| pivotColumn | Pivot Column | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| ratio | Dimensionless ratio when numerator and denominator use compatible units. | Required. Finite number. |
| scale | Scale | Required. Finite number. |
| zeroRow | Zero Row | Required. Boolean. |
{
"input": {
"row": [
2,
-4
],
"pivotColumn": 0
},
"output": {
"ratio": 0.5,
"scale": 4,
"zeroRow": false
}
}Limitations and assumptions
- This is a scaled pivot ratio, not a tolerance-based pivot decision or a complete elimination strategy.
- 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 stable triangular solver and a condition estimate for a complete numerical solution.
References
Similar or alternative tools
- Matrix Triangular Solve Diagonal Flag
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.
- Matrix: Matrix Diagonal Dominance Row Margin
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry.