Description
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.
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.
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.
When to use this tool
Use Matrix Triangular Solve Diagonal Flag when you need a triangular-entry convention or pivot diagnostic.
How to use the tool and how it works
- Enter diagonal, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read singularByTolerance, problematicIndices. Inspect singularByTolerance before interpreting the associated values.
Require a nonempty diagonal and nonnegative tolerance. Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diagonal | Diagonal | Required. Array of finite number; maximum items 256. |
| tolerance | Tolerance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| singularByTolerance | Singular By Tolerance | Required. Boolean. |
| problematicIndices | Problematic Indices | Required. Array of safe integer; maximum items 256. |
{
"input": {
"diagonal": [
2,
0,
3
],
"tolerance": 0
},
"output": {
"singularByTolerance": true,
"problematicIndices": [
1
]
}
}Limitations and assumptions
- This is an absolute diagonal threshold test, not a full conditioning analysis or a triangular solve.
- 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 Diagonal Inverse Entry
Require a nonzero diagonal value and return its reciprocal.
- Matrix Row Pivot Scale Ratio
Choose a valid pivotColumn and use the largest absolute row entry as scale.