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scipy.cluster.hierarchy.

# maxinconsts

scipy.cluster.hierarchy.maxinconsts(Z, R)

  Return the maximum inconsistency coefficient for each non-singleton cluster and its children.

  Parameters:
    Z ndarray

      The hierarchical clustering encoded as a matrix. See `linkage` for more information.

    R ndarray

      The inconsistency matrix.

  Returns:
    MI ndarray

      A monotonic `(n-1)`-sized numpy array of doubles.

  See also

  `linkage`

    for a description of what a linkage matrix is.

  `inconsistent`

    for the creation of a inconsistency matrix.

  Notes

  Array API Standard Support

  `maxinconsts` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ⛔
  PyTorch | ✅ | ⛔
  JAX | ✅ | ⛔
  Dask | ⚠️ merges chunks | n/a

  See Support for the array API standard for more information.

  Examples

      >>> from scipy.cluster.hierarchy import median, inconsistent, maxinconsts
      >>> from scipy.spatial.distance import pdist

  Given a data set `X`, we can apply a clustering method to obtain a linkage matrix `Z`. `scipy.cluster.hierarchy.inconsistent` can be also used to obtain the inconsistency matrix `R` associated to this clustering process:

      >>> X = [[0, 0], [0, 1], [1, 0],
      ...      [0, 4], [0, 3], [1, 4],
      ...      [4, 0], [3, 0], [4, 1],
      ...      [4, 4], [3, 4], [4, 3]]

      >>> Z = median(pdist(X))
      >>> R = inconsistent(Z)
      >>> Z
      array([[ 0.        ,  1.        ,  1.        ,  2.        ],
             [ 3.        ,  4.        ,  1.        ,  2.        ],
             [ 9.        , 10.        ,  1.        ,  2.        ],
             [ 6.        ,  7.        ,  1.        ,  2.        ],
             [ 2.        , 12.        ,  1.11803399,  3.        ],
             [ 5.        , 13.        ,  1.11803399,  3.        ],
             [ 8.        , 15.        ,  1.11803399,  3.        ],
             [11.        , 14.        ,  1.11803399,  3.        ],
             [18.        , 19.        ,  3.        ,  6.        ],
             [16.        , 17.        ,  3.5       ,  6.        ],
             [20.        , 21.        ,  3.25      , 12.        ]])
      >>> R
      array([[1.        , 0.        , 1.        , 0.        ],
             [1.        , 0.        , 1.        , 0.        ],
             [1.        , 0.        , 1.        , 0.        ],
             [1.        , 0.        , 1.        , 0.        ],
             [1.05901699, 0.08346263, 2.        , 0.70710678],
             [1.05901699, 0.08346263, 2.        , 0.70710678],
             [1.05901699, 0.08346263, 2.        , 0.70710678],
             [1.05901699, 0.08346263, 2.        , 0.70710678],
             [1.74535599, 1.08655358, 3.        , 1.15470054],
             [1.91202266, 1.37522872, 3.        , 1.15470054],
             [3.25      , 0.25      , 3.        , 0.        ]])

  Here, `scipy.cluster.hierarchy.maxinconsts` can be used to compute the maximum value of the inconsistency statistic (the last column of `R`) for each non-singleton cluster and its children:

      >>> maxinconsts(Z, R)
      array([0.        , 0.        , 0.        , 0.        , 0.70710678,
             0.70710678, 0.70710678, 0.70710678, 1.15470054, 1.15470054,
             1.15470054])