Random Cluster-Based Row Sample Generator

Description

Draw supplied cluster IDs under explicit cluster weights and return every original row per selected cluster occurrence with conditional draw probabilities.

Sampling selects from a supplied population under rules for replacement, grouping, or eligibility. Draw probabilities, inclusion probabilities, and repeat counts describe different aspects of selection; a reproducible sample is not automatically representative of a real population.

Draw supplied cluster IDs under explicit cluster weights and return every original row per selected cluster occurrence with conditional draw probabilities.

When to use this tool

Use this generator to create reproducible cluster based row sample cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply rows, count, replacement, weighting in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read clusters, draws, returnedRowCount. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Group supplied rows by literal cluster label and sample whole clusters uniformly or proportional to their row counts. Return all rows for every draw, the current conditional selection probability, and total returned row count, removing clusters when replacement is disabled.^[1]

Input field	Meaning and units	Accepted input
rows	Rows	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 512.
rows[].id	Literal identifier used independently of display labels.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
rows[].values	Values	Required. Array of Text; maximum UTF-16 length 4096.; minimum items 0; maximum items 32.
rows[].cluster	Cluster	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
count	Count	Required. Safe integer; minimum 0; maximum 128.
replacement	Replacement	Required. Boolean.
weighting	Draw cluster IDs uniformly or proportional to their supplied row counts; include every row per cluster occurrence.	Required. Text; one of "uniform-cluster", "proportional-size".
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
clusters	Clusters	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 512.
clusters[].cluster	Cluster	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
clusters[].populationRows	Population Rows	Required. Safe integer; minimum 0.
clusters[].weight	Weight	Required. Safe integer; minimum 0.
draws	Draws	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 128.
draws[].draw	Draw	Required. Safe integer; minimum 0.
draws[].cluster	Cluster	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
draws[].conditionalProbability	Conditional Probability	Required. Finite number; minimum 0; maximum 1.
draws[].rows	Rows	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 512.
draws[].rows[].id	Literal identifier used independently of display labels.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
draws[].rows[].values	Values	Required. Array of Text; maximum UTF-16 length 4096.; minimum items 0; maximum items 32.
draws[].rows[].cluster	Cluster	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
returnedRowCount	Returned Row Count	Required. Safe integer; minimum 0; maximum 8192.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "rows": [
      {
        "id": "a",
        "cluster": "west",
        "values": [
          "12"
        ]
      },
      {
        "id": "b",
        "cluster": "west",
        "values": [
          "19"
        ]
      },
      {
        "id": "c",
        "cluster": "east",
        "values": [
          "7"
        ]
      }
    ],
    "count": 2,
    "replacement": false,
    "weighting": "uniform-cluster",
    "seed": 42
  },
  "output": {
    "clusters": [
      {
        "cluster": "west",
        "populationRows": 2,
        "weight": 1
      },
      {
        "cluster": "east",
        "populationRows": 1,
        "weight": 1
      }
    ],
    "draws": [
      {
        "draw": 0,
        "cluster": "east",
        "conditionalProbability": 0.5,
        "rows": [
          {
            "id": "c",
            "values": [
              "7"
            ],
            "cluster": "east"
          }
        ]
      },
      {
        "draw": 1,
        "cluster": "west",
        "conditionalProbability": 1,
        "rows": [
          {
            "id": "a",
            "values": [
              "12"
            ],
            "cluster": "west"
          },
          {
            "id": "b",
            "values": [
              "19"
            ],
            "cluster": "west"
          }
        ]
      }
    ],
    "returnedRowCount": 3,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Cluster sampling differs from independent row sampling. Replacement can return the same entire cluster several times, and size-weighted draw probability is not a marginal row-inclusion probability. Output expansion is bounded.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Cluster-Based Row Sample Generator — tool.io

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