Description
Form threshold = absoluteTolerance + relativeTolerance × referenceMagnitude, requiring all three nonnegative.
Row margins, entry thresholds, and small-matrix criteria summarize specific algebraic conditions. They do not automatically establish a larger matrix's conditioning or spectrum.
Form threshold = absoluteTolerance + relativeTolerance × referenceMagnitude, requiring all three nonnegative.
When to use this tool
Use Matrix: Matrix Entry Relative Threshold Mask when you need one explicitly scoped matrix bound or residual.
How to use the tool and how it works
- Enter entry, referenceMagnitude, relativeTolerance, absoluteTolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Form threshold = absoluteTolerance + relativeTolerance × referenceMagnitude, requiring all three nonnegative. Mark negligible when abs(entry) ≤ threshold.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entry | Entry | Required. Finite number. |
| referenceMagnitude | Reference Magnitude | Required. Finite number. |
| relativeTolerance | Dimensionless fractional tolerance; the applicable bound is specified above. | Required. Finite number. |
| absoluteTolerance | Absolute Tolerance | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.threshold | Threshold | Calculated result member: number. |
| result.negligible | Negligible | Calculated result member: boolean. |
{
"input": {
"entry": 0.03,
"referenceMagnitude": 2,
"relativeTolerance": 0.01,
"absoluteTolerance": 0.01
},
"output": {
"result": {
"threshold": 0.03,
"negligible": true
}
}
}Limitations and assumptions
- The reference and tolerances are caller supplied; the test is exact at the boundary and does not establish numerical insignificance for every algorithm.
- Outputs are nested inside result. 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 the complete matrix and a suitable numerical tolerance or factorization for a global property test.
References
Similar or alternative tools
- Matrix: Matrix Diagonal Dominance Row Margin
Subtract the sum of absolute off-diagonal row entries from the absolute diagonal entry.
- Matrix Triangular Solve Diagonal Flag
Return indices where abs(diagonal entry) ≤ tolerance and mark singularByTolerance if any exist.