





from random import shuffle

import tensorflow as tf
from numpy import array




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=int(lowercase__  )
   assert noofclusters < len(lowercase__  )

   # Find out the dimensionality
   UpperCAmelCase_											=len(vectors[0]  )

   # Will help select random centroids from among the available vectors
   UpperCAmelCase_											=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_											=tf.Graph()

   with graph.as_default():
      # SESSION OF COMPUTATION

      UpperCAmelCase_											=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_											=[
          tf.Variable(vectors[vector_indices[i]]  ) for i in range(lowercase__  )
      ]
      ##These nodes will assign the centroid Variables the appropriate
      ##values
      UpperCAmelCase_											=tf.placeholder("float64"  ,    [dim]  )
      UpperCAmelCase_											=[]
      for centroid in centroids:
         cent_assigns.append(tf.assign(lowercase__  ,    lowercase__  )  )

      ##Variables for cluster assignments of individual vectors(initialized
      ##to 0 at first)
      UpperCAmelCase_											=[tf.Variable(0  ) for i in range(len(lowercase__  )  )]
      ##These nodes will assign an assignment Variable the appropriate
      ##value
      UpperCAmelCase_											=tf.placeholder("int32"  )
      UpperCAmelCase_											=[]
      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_											=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_											=tf.reduce_mean(lowercase__  ,    0  )

      ##Node for computing Euclidean distances
      # Placeholders for input
      UpperCAmelCase_											=tf.placeholder("float"  ,    [dim]  )
      UpperCAmelCase_											=tf.placeholder("float"  ,    [dim]  )
      UpperCAmelCase_											=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_											=tf.placeholder("float"  ,    [noofclusters]  )
      UpperCAmelCase_											=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_											=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_											=1_0_0
      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_											=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_											=[
                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_											=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_											=[
                vectors[i]
                for i in range(len(lowercase__  )  )
                if sess.run(assignments[i]  ) == cluster_n
            ]
            # Compute new centroid location
            UpperCAmelCase_											=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_											=sess.run(lowercase__  )
      UpperCAmelCase_											=sess.run(lowercase__  )
      return centroids, assignments











import math_equivalence  # From: git+https://github.com/hendrycks/math.git

import datasets


__lowercase  :   int						      ="""\
@article{hendrycksmath2021,
  title={Measuring Mathematical Problem Solving With the MATH Dataset},
  author={Dan Hendrycks
    and Collin Burns
    and Saurav Kadavath
    and Akul Arora
    and Steven Basart
    and Eric Tang
    and Dawn Song
    and Jacob Steinhardt},
  journal={arXiv preprint arXiv:2103.03874},
  year={2021}
}
"""


__lowercase  :   List[Any]						      ="""\
This metric is used to assess performance on the Mathematics Aptitude Test of Heuristics (MATH) dataset.
It first canonicalizes the inputs (e.g., converting \"1/2\" to \"\\frac{1}{2}\") and then computes accuracy.
"""


__lowercase  :   str						      =R"""
Calculates accuracy after canonicalizing inputs.

Args:
    predictions: list of predictions to score. Each prediction
        is a string that contains natural language and LaTex.
    references: list of reference for each prediction. Each
        reference is a string that contains natural language
        and LaTex.
Returns:
    accuracy: accuracy after canonicalizing inputs
        (e.g., converting \"1/2\" to \"\\frac{1}{2}\")

Examples:
    >>> metric = datasets.load_metric(\"competition_math\")
    >>> results = metric.compute(references=[\"\\frac{1}{2}\"], predictions=[\"1/2\"])
    >>> print(results)
    {'accuracy': 1.0}
"""

@datasets.utils.file_utils.add_end_docstrings(_DESCRIPTION		,      _KWARGS_DESCRIPTION						)
class      A       (	datasets.Metric						):



      def 	lowerCAmelCase__    (	self:						Any       )						->    Optional[Any]:
         '''simple docstring'''

         return datasets.MetricInfo(
             description=_DESCRIPTION		,  citation=_CITATION		,  inputs_description=_KWARGS_DESCRIPTION		,  features=datasets.Features(
                 {
                     "predictions": datasets.Value("string"       ),
                     "references": datasets.Value("string"       ),
                 }       )		,  homepage="https://github.com/hendrycks/math"		,  codebase_urls=["https://github.com/hendrycks/math"]		,  )






      def 	lowerCAmelCase__    (	self:						Any		,  _lowerCAmelCase:						Tuple		,  _lowerCAmelCase:						Union[str, Any]       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=0.0
         for i, j in zip(_lowerCAmelCase		,  _lowerCAmelCase       ):
            n_correct += 1.0 if math_equivalence.is_equiv(_lowerCAmelCase		,  _lowerCAmelCase       ) else 0.0
         UpperCAmelCase_											=n_correct / len(_lowerCAmelCase       )
         return {
             "accuracy": accuracy,
         }




