Battleship Curve Fit Checker

Check each type-frequency column in a supplied ordering for nondecreasing-then-nonincreasing battleship shape under caller tolerance; monotone and plateau series are accepted, not proof of chronology.

Description

Battleship-shaped frequency sequences rise and then fall across an ordering.

Battleship-shaped frequency sequences rise and then fall across an ordering. Tolerance can treat small differences as ties, while monotone or plateau sequences still satisfy a no-return-to-rise test.^[1]

When to use Battleship Curve Fit Checker

Use this tool to check each type-frequency column in a supplied ordering for nondecreasing-then-nonincreasing battleship shape under caller tolerance; monotone and plateau series are accepted, not proof of chronology.

Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.

How to use Battleship Curve Fit Checker and understand its results

Prepare the artifact, site or survey measurements and any independently established calibration or model choices. Keep paired observations aligned and confirm units and coordinate conventions.
Enter orderedTypeFrequencies, callerTolerance using the field table and calculation rules, then run the tool.
Read unimodalColumnFlags, directionReversalCounts. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
orderedTypeFrequencies	Ordered type frequencies	list of list of number	Required
callerTolerance	Caller tolerance	number	Required

Enter a nonempty rectangular matrix of nonnegative ordered type frequencies and a nonnegative tolerance. For each column, ignore changes within tolerance, count changes between nonzero rise/fall directions and flag whether any rise follows a decline. Return binary unimodality flags and direction-reversal counts.

ignore |adjacent change|≤tolerance; reject any rise after a decline

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
unimodalColumnFlags	Unimodal column flags	list of number
directionReversalCounts	Direction reversal counts	list of number

json

{
  "input": {
    "orderedTypeFrequencies": [
      [
        0,
        1
      ],
      [
        2,
        2
      ],
      [
        1,
        3
      ],
      [
        2,
        2
      ]
    ],
    "callerTolerance": 0
  },
  "output": {
    "unimodalColumnFlags": [
      0,
      1
    ],
    "directionReversalCounts": [
      2,
      1
    ]
  }
}

Limitations and assumptions

Monotone columns and plateaus are accepted. The tool tests the supplied ordering without finding a better one or proving chronological validity. It does not require percentages to sum to 100.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Seriation Frequency Ordering Tool: Produce deterministic type-frequency centroid seriation on a supplied type axis, input order breaking ties; not an optimal unimodal or independently dated ordering. For a complementary task, use Type Frequency Percent Per Phase: Normalize classified ceramic types within each phase and report excluded unclassified coverage on original denominators; not pooled across phases or a forced chronological classifier.

References

Battleship Curve Fit Checker — tool.io

Similar or alternative tools

Seriation Frequency Ordering Tool
Produce deterministic type-frequency centroid seriation on a supplied type axis, input order breaking ties; not an optimal unimodal or independently dated ordering.
Type Frequency Percent Per Phase
Normalize classified ceramic types within each phase and report excluded unclassified coverage on original denominators; not pooled across phases or a forced chronological classifier.