Description
Use (row - column) modulo size for a first-column circulant convention, or (column - row) modulo size for a first-row convention.
A matrix coordinate, a storage offset, and a block-local coordinate are different representations. Shape, stride, origin, and transpose conventions determine the correct mapping.
Use (row - column) modulo size for a first-column circulant convention, or (column - row) modulo size for a first-row convention.
When to use this tool
Use Matrix: Matrix Circulant Source Index when you need one explicit matrix-coordinate or address conversion.
How to use the tool and how it works
- Enter size, row, column, firstVector. 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.
Use (row - column) modulo size for a first-column circulant convention, or (column - row) modulo size for a first-row convention.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| size | Size | Required. Safe integer. |
| row | Row | Required. Safe integer. |
| column | Column | Required. Safe integer. |
| firstVector | First Vector | Required. Text; one of "column", "row". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.sourceIndex | Source Index | Calculated result member: number. |
{
"input": {
"size": 5,
"row": 1,
"column": 3,
"firstVector": "column"
},
"output": {
"result": {
"sourceIndex": 3
}
}
}Limitations and assumptions
- Return indices are zero based; the defining vector is not supplied and the two circulant conventions must not be mixed.
- 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
Validate the full shape, memory span, and storage convention before using the resulting index.
References
Similar or alternative tools
- Matrix Kronecker Delta Entry
Return one when nonnegative row equals column and zero otherwise.
- Matrix Antidiagonal Index Crosswalk
For a zero-based row within square size, return column = size - 1 - row.