code: def ward(y):
      """
      Perform Ward's linkage on a condensed distance matrix.
  
      See `linkage` for more information on the return structure
      and algorithm.
  
      The following are common calling conventions:
  
      1. ``Z = ward(y)``
         Performs Ward's linkage on the condensed distance matrix ``y``.
  
      2. ``Z = ward(X)``
         Performs Ward's linkage on the observation matrix ``X`` using
         Euclidean distance as the distance metric.
  
      Parameters
      ----------
      y : ndarray
          A condensed distance matrix. A condensed
          distance matrix is a flat array containing the upper
          triangular of the distance matrix. This is the form that
          ``pdist`` returns.  Alternatively, a collection of
          m observation vectors in n dimensions may be passed as
          an m by n array.
  
      Returns
      -------
      Z : ndarray
          The hierarchical clustering encoded as a linkage matrix. See
          `linkage` for more information on the return structure and
          algorithm.
  
      See Also
      --------
      linkage : for advanced creation of hierarchical clusterings.
      scipy.spatial.distance.pdist : pairwise distance metrics
  
      Examples
      --------
      >>> from scipy.cluster.hierarchy import ward, fcluster
      >>> from scipy.spatial.distance import pdist
  
      First, we need a toy dataset to play with::
  
          x x    x x
          x        x
  
          x        x
          x x    x 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]]
  
      Then, we get a condensed distance matrix from this dataset:
  
      >>> y = pdist(X)
  
      Finally, we can perform the clustering:
  
      >>> Z = ward(y)
      >>> Z
      array([[ 0.        ,  1.        ,  1.        ,  2.        ],
             [ 3.        ,  4.        ,  1.        ,  2.        ],
             [ 6.        ,  7.        ,  1.        ,  2.        ],
             [ 9.        , 10.        ,  1.        ,  2.        ],
             [ 2.        , 12.        ,  1.29099445,  3.        ],
             [ 5.        , 13.        ,  1.29099445,  3.        ],
             [ 8.        , 14.        ,  1.29099445,  3.        ],
             [11.        , 15.        ,  1.29099445,  3.        ],
             [16.        , 17.        ,  5.77350269,  6.        ],
             [18.        , 19.        ,  5.77350269,  6.        ],
             [20.        , 21.        ,  8.16496581, 12.        ]])
  
      The linkage matrix ``Z`` represents a dendrogram - see
      `scipy.cluster.hierarchy.linkage` for a detailed explanation of its
      contents.
  
      We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster
      each initial point would belong given a distance threshold:
  
      >>> fcluster(Z, 0.9, criterion='distance')
      array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
      >>> fcluster(Z, 1.1, criterion='distance')
      array([1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8], dtype=int32)
      >>> fcluster(Z, 3, criterion='distance')
      array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
      >>> fcluster(Z, 9, criterion='distance')
      array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)
  
      Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a
      plot of the dendrogram.
  
      """
      return linkage(y, method="ward", metric="euclidean")
  
imports: import warnings
  import bisect
  from collections import deque
  import numpy
  from .None import _hierarchy, _optimal_leaf_ordering
  import scipy.spatial.distance
  from scipy._lib._disjoint_set import DisjointSet
label_desc: Use image node_id 11 for calling a global function with example usage: ward(y) and returns: linkage