Description
Map a coordinate to the upper pair min(row, column), max(row, column).
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.
Map a coordinate to the upper pair min(row, column), max(row, column).
When to use this tool
Use Matrix Packed Skewsign Alias when you need an explicit packed or band-storage coordinate mapping.
How to use the tool and how it works
- Enter 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 storageRow, storageColumn, sign, diagonal. Inspect diagonal before interpreting the associated values.
Map a coordinate to the upper pair min(row, column), max(row, column). Return sign +1 above the diagonal, -1 below, and zero on the diagonal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| row | Row | Required. Safe integer; minimum 0. |
| column | Column | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| storageRow | Storage Row | Required. Safe integer. |
| storageColumn | Storage Column | Required. Safe integer. |
| sign | Sign | Required. Safe integer. |
| diagonal | Diagonal | Required. Boolean. |
{
"input": {
"row": 3,
"column": 1
},
"output": {
"storageRow": 1,
"storageColumn": 3,
"sign": -1,
"diagonal": false
}
}Limitations and assumptions
- This assumes a real skew-symmetric matrix with an implicit zero diagonal; no matrix value or dimension is checked.
- 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 Symmetric Skew Entry Split
Return ij/2 + ji/2 as symmetric and ij/2 - ji/2 as skew.
- Matrix Skew Entry Pair Residual
Add aij and aji for the residual from skew symmetry.