






from random import shuffle

import tensorflow as tf
from numpy import array




def 				A		(					lowercase__  :  str ,		lowercase__  :  Optional[int]  )		-> str:
	UpperCamelCase__ :Any						=      int(lowercase__  )
	assert noofclusters < len(lowercase__  )

	# Find out the dimensionality
	UpperCamelCase__ :str						=      len(vectors[0]  )

	# Will help select random centroids from among the available vectors
	UpperCamelCase__ :Dict						=      list(range(len(lowercase__  )  )  )
	shuffle(lowercase__  )

	# GRAPH OF COMPUTATION
	# We initialize a new graph and set it as the default during each run
	# of this algorithm. This ensures that as this function is called
	# multiple times, the default graph doesn't keep getting crowded with
	# unused ops and Variables from previous function calls.

	UpperCamelCase__ :List[Any]						=      tf.Graph()

	with graph.as_default():
		# SESSION OF COMPUTATION

		UpperCamelCase__ :Dict						=      tf.Session()

		##CONSTRUCTING THE ELEMENTS OF COMPUTATION

		##First lets ensure we have a Variable vector for each centroid,
		##initialized to one of the vectors from the available data points
		UpperCamelCase__ :Optional[Any]						=      [
		    tf.Variable(vectors[vector_indices[i]]  ) for i in range(lowercase__  )
		]
		##These nodes will assign the centroid Variables the appropriate
		##values
		UpperCamelCase__ :Optional[Any]						=      tf.placeholder("""float64""" ,		[dim]  )
		UpperCamelCase__ :List[Any]						=      []
		for centroid in centroids:
			cent_assigns.append(tf.assign(lowercase__ ,		lowercase__  )  )

		##Variables for cluster assignments of individual vectors(initialized
		##to 0 at first)
		UpperCamelCase__ :str						=      [tf.Variable(0  ) for i in range(len(lowercase__  )  )]
		##These nodes will assign an assignment Variable the appropriate
		##value
		UpperCamelCase__ :Union[str, Any]						=      tf.placeholder("""int32"""  )
		UpperCamelCase__ :str						=      []
		for assignment in assignments:
			cluster_assigns.append(tf.assign(lowercase__ ,		lowercase__  )  )

		##Now lets construct the node that will compute the mean
		# The placeholder for the input
		UpperCamelCase__ :int						=      tf.placeholder("""float""" ,		[None, dim]  )
		# The Node/op takes the input and computes a mean along the 0th
		# dimension, i.e. the list of input vectors
		UpperCamelCase__ :List[str]						=      tf.reduce_mean(lowercase__ ,		0  )

		##Node for computing Euclidean distances
		# Placeholders for input
		UpperCamelCase__ :str						=      tf.placeholder("""float""" ,		[dim]  )
		UpperCamelCase__ :Any						=      tf.placeholder("""float""" ,		[dim]  )
		UpperCamelCase__ :List[Any]						=      tf.sqrt(tf.reduce_sum(tf.pow(tf.sub(lowercase__ ,		lowercase__  ) ,		2  )  )  )

		##This node will figure out which cluster to assign a vector to,
		##based on Euclidean distances of the vector from the centroids.
		# Placeholder for input
		UpperCamelCase__ :Dict						=      tf.placeholder("""float""" ,		[noofclusters]  )
		UpperCamelCase__ :Optional[int]						=      tf.argmin(lowercase__ ,		0  )

		##INITIALIZING STATE VARIABLES

		##This will help initialization of all Variables defined with respect
		##to the graph. The Variable-initializer should be defined after
		##all the Variables have been constructed, so that each of them
		##will be included in the initialization.
		UpperCamelCase__ :Union[str, Any]						=      tf.initialize_all_variables()

		# Initialize all variables
		sess.run(lowercase__  )

		##CLUSTERING ITERATIONS

		# Now perform the Expectation-Maximization steps of K-Means clustering
		# iterations. To keep things simple, we will only do a set number of
		# iterations, instead of using a Stopping Criterion.
		UpperCamelCase__ :Dict						=      100
		for _ in range(lowercase__  ):
			##EXPECTATION STEP
			##Based on the centroid locations till last iteration, compute
			##the _expected_ centroid assignments.
			# Iterate over each vector
			for vector_n in range(len(lowercase__  )  ):
				UpperCamelCase__ :Optional[Any]						=      vectors[vector_n]
				# Compute Euclidean distance between this vector and each
				# centroid. Remember that this list cannot be named
				#'centroid_distances', since that is the input to the
				# cluster assignment node.
				UpperCamelCase__ :str						=      [
				    sess.run(lowercase__ ,		feed_dict={va: vect, va: sess.run(lowercase__  )}  )
				    for centroid in centroids
				]
				# Now use the cluster assignment node, with the distances
				# as the input
				UpperCamelCase__ :Optional[int]						=      sess.run(
				    lowercase__ ,		feed_dict={centroid_distances: distances}  )
				# Now assign the value to the appropriate state variable
				sess.run(
				    cluster_assigns[vector_n] ,		feed_dict={assignment_value: assignment}  )

			##MAXIMIZATION STEP
			# Based on the expected state computed from the Expectation Step,
			# compute the locations of the centroids so as to maximize the
			# overall objective of minimizing within-cluster Sum-of-Squares
			for cluster_n in range(lowercase__  ):
				# Collect all the vectors assigned to this cluster
				UpperCamelCase__ :Any						=      [
				    vectors[i]
				    for i in range(len(lowercase__  )  )
				    if sess.run(assignments[i]  ) == cluster_n
				]
				# Compute new centroid location
				UpperCamelCase__ :Optional[int]						=      sess.run(
				    lowercase__ ,		feed_dict={mean_input: array(lowercase__  )}  )
				# Assign value to appropriate variable
				sess.run(
				    cent_assigns[cluster_n] ,		feed_dict={centroid_value: new_location}  )

        # Return centroids and assignments
		UpperCamelCase__ :Optional[Any]						=      sess.run(lowercase__  )
		UpperCamelCase__ :Dict						=      sess.run(lowercase__  )
		return centroids, assignments







import unittest

import numpy as np






def 	UpperCamelCase	(							snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray						,snake_case__  : np.ndarray | None = None						,):




     '''simple docstring'''






     __snake_case      :Any 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)
     __snake_case      :List[str] 							=    np.shape(snake_case__	)

     if shape_a[0] != shape_b[0]:
          __snake_case      :int 							=    (
              """Expected the same number of rows for A and B. """
              f'''Instead found A of size {shape_a} and B of size {shape_b}'''
          )
          raise ValueError(snake_case__	)

     if shape_b[1] != shape_c[1]:
          __snake_case      :List[str] 							=    (
              """Expected the same number of columns for B and C. """
              f'''Instead found B of size {shape_b} and C of size {shape_c}'''
          )
          raise ValueError(snake_case__	)

     __snake_case      :Any 							=    pseudo_inv
     if a_inv is None:
          try:
               __snake_case      :Optional[Any] 							=    np.linalg.inv(snake_case__	)
          except np.linalg.LinAlgError:
               raise ValueError(
                   """Input matrix A is not invertible. Cannot compute Schur complement."""	)

     return mat_c - mat_b.T @ a_inv @ mat_b




class       snake_case__ (				unittest.TestCase):

       '''simple docstring'''



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[str] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1], [6, 3]]     )

            __snake_case      :int 							=    schur_complement(a__      ,    a__      ,    a__     )

            __snake_case      :Union[str, Any] 							=    np.block([[a, b], [b.T, c]]     )

            __snake_case      :Dict 							=    np.linalg.det(a__     )
            __snake_case      :Tuple 							=    np.linalg.det(a__     )
            __snake_case      :List[Any] 							=    np.linalg.det(a__     )

            self.assertAlmostEqual(a__      ,    det_a * det_s     )



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :Union[str, Any] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :Optional[int] 							=    np.array([[2, 1], [6, 3]]     )

            with self.assertRaises(a__     ):
                 schur_complement(a__      ,    a__      ,    a__     )



       def        __lowercase    (				self     )			->   None:






            '''simple docstring'''





            __snake_case      :Optional[Any] 							=    np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]     )
            __snake_case      :List[str] 							=    np.array([[0, 3], [3, 0], [2, 3]]     )
            __snake_case      :List[Any] 							=    np.array([[2, 1, 3], [6, 3, 5]]     )

            with self.assertRaises(a__     ):
                 schur_complement(a__      ,    a__      ,    a__     )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     unittest.main()


