Description
Select observed COO diagonal coordinate occurrences, preserving duplicates and zero values in rectangular matrices.
A sparse matrix can be stored as coordinate triplets or as pointer/index/value arrays. Stored entries are not necessarily distinct numerical nonzeros: duplicates and explicit zeros can matter to representation checks. Row and column coordinates here are zero-based, and omitted entries are handled only as stated for the particular operation.
Select observed COO diagonal coordinate occurrences, preserving duplicates and zero values in rectangular matrices.
When to use this tool
Use this tool to select observed COO diagonal coordinate occurrences, preserving duplicates and zero values in rectangular matrices.
How to use the tool and how it works
- Enter tripletsJson, rows, columns using the field definitions below. For JSON text, serialize the explicit records in the shown shape.
- Run the operation. Correct input errors before interpreting an output.
- Read result.triplets. Use the ordering, boundary rules and absence conditions described below.
Keep only triplets whose row equals column, preserving input order, duplicates and zero values.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| tripletsJson | JSON array of records with zero-based row, column and finite value fields. | Text, at most 8,192 UTF-16 code units; the operation’s grammar also applies. |
| rows | Declared row count; coordinate operations use 0–128, dense budgets allow larger integers. | A finite safe integer within the operation’s stated bounds. |
| columns | Declared column count; coordinate operations use 0–128, dense budgets allow larger integers. | A finite safe integer within the operation’s stated bounds. |
These are the decoded structures used in the example’s JSON text fields. Supply the corresponding serialized JSON strings as input.
{
"tripletsJson": [
{
"row": 0,
"column": 1,
"value": 2
},
{
"row": 0,
"column": 1,
"value": 3
},
{
"row": 1,
"column": 0,
"value": 0
}
]
}| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.triplets | Stored {row, column, value} records under the operation’s stated ordering and duplicate policy. |
{
"input": {
"tripletsJson": "[{\"row\":0,\"column\":1,\"value\":2},{\"row\":0,\"column\":1,\"value\":3},{\"row\":1,\"column\":0,\"value\":0}]",
"rows": 2,
"columns": 2
},
"output": {
"result": {
"triplets": []
}
}
}Limitations and assumptions
- This selects stored diagonal records rather than constructing a complete diagonal vector.
- Triplets are JSON records with row, column and value. Coordinate shapes are ordinarily bounded to 128 per axis; compressed major dimensions are limited to 127 for pointer-list capacity. The dense-budget operation has separate larger shape limits and returns exact counts as decimal text.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Distinguish stored-record counts, coordinate-pattern checks and arithmetic matrix properties. Combine duplicates or prune zeros explicitly when required, and use a matrix library for numerical linear algebra.
References
Similar or alternative tools
- Sparse Diagonal Coverage Check
Audit COO diagonal observation coverage separately from explicitly observed zero diagonal values; no assumption of implicit zeros as supplied evidence.
- Sparse Coordinate Triangle Selector
Select explicit upper or lower COO triangular coordinate observations with a caller diagonal policy; no implied symmetric values.