Description
Return column - row as signedBand and its magnitude as distanceFromDiagonal.
A matrix coordinate, a storage offset, and a block-local coordinate are different representations. Shape, stride, origin, and transpose conventions determine the correct mapping.
Return column - row as signedBand and its magnitude as distanceFromDiagonal.
When to use this tool
Use Matrix Diagonal Band Index when you need one explicit matrix-coordinate or address conversion.
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 signedBand, distanceFromDiagonal. Use the output convention below.
Return column - row as signedBand and its magnitude as distanceFromDiagonal.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 |
|---|---|---|
| signedBand | Signed Band | Required. Safe integer. |
| distanceFromDiagonal | Distance From Diagonal | Required. Safe integer. |
json
{
"input": {
"row": 2,
"column": 5
},
"output": {
"signedBand": 3,
"distanceFromDiagonal": 3
}
}Limitations and assumptions
- Positive bands are above the diagonal; matrix dimensions, bandwidth limits, and storage offsets are not supplied.
- 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
Validate the full shape, memory span, and storage convention before using the resulting index.
References
Similar or alternative tools
- Matrix: Matrix Diagonal Offset Length
For signed offset, skip max(0, -offset) rows and max(0, offset) columns.
- Matrix Symmetric Band Storage Offset
Use distance = column - row.