Description
Validate zero-based row and column within size.
Packed matrix storage omits a triangle and maps coordinates into a linear array. Row-wise versus column-wise order and diagonal inclusion change the offset formula.
Validate zero-based row and column within size.
When to use this tool
Use Matrix: Matrix Symmetric Packed Alias Index when you need an explicit packed or band-storage coordinate mapping.
How to use the tool and how it works
- Enter size, row, column. 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.
Validate zero-based row and column within size. Map to r = max(row, column), c = min(row, column) and return r × (r + 1) / 2 + c; mirrored is true above the diagonal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| size | Size | Required. Safe integer. |
| row | Row | Required. Safe integer. |
| column | Column | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.packedLowerOffset | Packed Lower Offset | Calculated result member: number. |
| result.mirrored | Whether an upper-triangle coordinate was mapped to its lower-triangle counterpart. | Calculated result member: boolean. |
{
"input": {
"size": 4,
"row": 1,
"column": 3
},
"output": {
"result": {
"packedLowerOffset": 7,
"mirrored": true
}
}
}Limitations and assumptions
- This is row-wise packed lower storage including the diagonal; it assumes symmetry rather than checking matrix values.
- 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
Check the consuming library's storage convention against several boundary coordinates before indexing its buffer.
References
Similar or alternative tools
- Matrix: Matrix Packed Lower Index
Validate a lower-triangle coordinate.
- Matrix Lower To Upper Packed Diagonal Offset
For a zero-based diagonal index, return index × (index + 3) / 2 in row-wise lower storage and index × size - index × (index - 1) / 2 in row-wise upper storage.