Pairwise Comparison Sign Matrix

Return the exact pairwise comparison sign matrix for finite numeric values; zero retains ties rather than forcing an order.

Description

Return the exact pairwise comparison sign matrix for finite numeric values; zero retains ties rather than forcing an order.

A pairwise comparison matrix records all relative order signs, including ties and diagonal equality.

When to use this tool

Return the exact pairwise comparison sign matrix for finite numeric values; zero retains ties rather than forcing an order.

Prepare the supplied values fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter values. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.matrix. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

For every row value a and column value b, return -1 if a is smaller, +1 if larger and zero if equal.^[1]

Input field	Meaning and representation	Accepted input
values	values.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.matrix	The matrix list in the ordering and representation described above.

json

{
  "input": {
    "values": [
      2,
      1,
      2
    ]
  },
  "output": {
    "result": {
      "matrix": [
        [
          0,
          1,
          0
        ],
        [
          -1,
          0,
          -1
        ],
        [
          0,
          1,
          0
        ]
      ]
    }
  }
}

Limitations and assumptions

This is an exact numeric comparison table, without subtraction magnitude, rank assignment or tolerance.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Choose the tie policy and whether you need values, original indexes, sorted positions or one-based ranks. Use a complete sort verifier when a local stability or adjacent-comparison check is insufficient.

References

Tool behavior and example: Pairwise Comparison Sign Matrix — tool.io

Similar or alternative tools

Bottom K Cutoff Tie Partitioner
Partition a numeric bottom-K cutoff into strict selections and all tied candidates, reporting how many ties are needed without arbitrarily breaking them.
Competition Rank Tie Table
Assign one-based ascending competition numeric ranks; exact numeric ties are preserved according to the stated policy.