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scipy.cluster.hierarchy.

# correspond

scipy.cluster.hierarchy.correspond(Z, Y)

  Check for correspondence between linkage and condensed distance matrices.

  They must have the same number of original observations for the check to succeed.

  This function is useful as a sanity check in algorithms that make extensive use of linkage and distance matrices that must correspond to the same set of original observations.

  Parameters:
    Z array_like

      The linkage matrix to check for correspondence.

    Y array_like

      The condensed distance matrix to check for correspondence.

  Returns:
    b bool

      A boolean indicating whether the linkage matrix and distance matrix could possibly correspond to one another.

  See also

  `linkage`

    for a description of what a linkage matrix is.

  Notes

  Array API Standard Support

  `correspond` 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 | ✅ | n/a

  See Support for the array API standard for more information.

  Examples

      >>> from scipy.cluster.hierarchy import ward, correspond
      >>> from scipy.spatial.distance import pdist

  This method can be used to check if a given linkage matrix `Z` has been obtained from the application of a cluster method over a dataset `X`:

      >>> 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]]
      >>> X_condensed = pdist(X)
      >>> Z = ward(X_condensed)

  Here, we can compare `Z` and `X` (in condensed form):

      >>> correspond(Z, X_condensed)
      True