






"""simple docstring"""


from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  seed(1					)
  return [gauss(__UpperCamelCase						,			__UpperCamelCase					) for _ in range(__UpperCamelCase					)]



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  return [k for k in range(__UpperCamelCase					) for _ in range(instance_count[k]					)]



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  return sum(__UpperCamelCase					) / instance_count



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  return instance_count / total_count



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  __A		     =					[]  # An empty list to store all squared differences
  # iterate over number of elements in items
  for i in range(len(__UpperCamelCase					)					):
    # for loop iterates over number of elements in inner layer of items
    for j in range(len(items[i]					)					):
      # appending squared differences to 'squared_diff' list
      squared_diff.append((items[i][j] - means[i]) ** 2					)

    # one divided by (the number of all instances - number of classes) multiplied by
    # sum of all squared differences
  __A		     =					len(__UpperCamelCase					)  # Number of classes in dataset
  return 1 / (total_count - n_classes) * sum(__UpperCamelCase					)



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  __A		     =					[]
  # for loop iterates over number of elements in list
  for i in range(len(__UpperCamelCase					)					):
    # for loop iterates over number of inner items of each element
    for j in range(len(x_items[i]					)					):
      __A		     =					[]  # to store all discriminant values of each item as a list
      # for loop iterates over number of classes we have in our dataset
      for k in range(len(__UpperCamelCase					)					):
        # appending values of discriminants for each class to 'temp' list
        temp.append(
            x_items[i][j] * (means[k] / variance)
            - (means[k] ** 2 / (2 * variance))
            + log(probabilities[k]					)					)
      # appending discriminant values of each item to 'results' list
      results.append(__UpperCamelCase					)

  return [result.index(max(__UpperCamelCase					)					) for result in results]



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase					):




  """simple docstring"""







  __A		     =					sum(1 for i, j in zip(__UpperCamelCase						,			__UpperCamelCase					) if i == j					)
  # percentage of accuracy equals to number of correct predictions divided by number
  # of all data and multiplied by 100
  return (correct / len(__UpperCamelCase					)) * 1_0_0


lowercase_								=	TypeVar('num')



def    lowerCAmelCase							(       __UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase = lambda __UpperCamelCase					: True						,			__UpperCamelCase = None						,			):




  """simple docstring"""







  while True:
    try:
      __A		     =					input_type(input(__UpperCamelCase					).strip() or default					)
      if condition(__UpperCamelCase					):
        return user_input
      else:
        print(f'{user_input}: {err_msg}'					)
        continue
    except ValueError:
      print(
          f'{user_input}: Incorrect input type, expected {input_type.__name__!r}'					)



def    lowerCAmelCase							(       ):




  """simple docstring"""







  while True:
    print(''' Linear Discriminant Analysis '''.center(5_0						,			'''*'''					)					)
    print('''*''' * 5_0						,			'''\n'''					)
    print('''First of all we should specify the number of classes that'''					)
    print('''we want to generate as training dataset'''					)
    # Trying to get number of classes
    __A		     =					valid_input(
        input_type=__UpperCamelCase						,			condition=lambda __UpperCamelCase					: x > 0						,			input_msg='''Enter the number of classes (Data Groupings): '''						,			err_msg='''Number of classes should be positive!'''						,			)

    print('''-''' * 1_0_0					)

    # Trying to get the value of standard deviation
    __A		     =					valid_input(
        input_type=__UpperCamelCase						,			condition=lambda __UpperCamelCase					: x >= 0						,			input_msg=(
            '''Enter the value of standard deviation'''
            '''(Default value is 1.0 for all classes): '''
        )						,			err_msg='''Standard deviation should not be negative!'''						,			default='''1.0'''						,			)

    print('''-''' * 1_0_0					)

    # Trying to get number of instances in classes and theirs means to generate
    # dataset
    __A		     =					[]  # An empty list to store instance counts of classes in dataset
    for i in range(__UpperCamelCase					):
      __A		     =					valid_input(
          input_type=__UpperCamelCase						,			condition=lambda __UpperCamelCase					: x > 0						,			input_msg=(f'Enter The number of instances for class_{i+1}: ')						,			err_msg='''Number of instances should be positive!'''						,			)
      counts.append(__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    # An empty list to store values of user-entered means of classes
    __A		     =					[]
    for a in range(__UpperCamelCase					):
      __A		     =					valid_input(
          input_type=__UpperCamelCase						,			input_msg=(f'Enter the value of mean for class_{a+1}: ')						,			err_msg='''This is an invalid value.'''						,			)
      user_means.append(__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    print('''Standard deviation: '''						,			__UpperCamelCase					)
    # print out the number of instances in classes in separated line
    for i, count in enumerate(__UpperCamelCase						,			1					):
      print(f'Number of instances in class_{i} is: {count}'					)
    print('''-''' * 1_0_0					)

    # print out mean values of classes separated line
    for i, user_mean in enumerate(__UpperCamelCase						,			1					):
      print(f'Mean of class_{i} is: {user_mean}'					)
    print('''-''' * 1_0_0					)

    # Generating training dataset drawn from gaussian distribution
    __A		     =					[
        gaussian_distribution(user_means[j]						,			__UpperCamelCase						,			counts[j]					)
        for j in range(__UpperCamelCase					)
    ]
    print('''Generated Normal Distribution: \n'''						,			__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    # Generating Ys to detecting corresponding classes
    __A		     =					y_generator(__UpperCamelCase						,			__UpperCamelCase					)
    print('''Generated Corresponding Ys: \n'''						,			__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    # Calculating the value of actual mean for each class
    __A		     =					[calculate_mean(counts[k]						,			x[k]					) for k in range(__UpperCamelCase					)]
    # for loop iterates over number of elements in 'actual_means' list and print
    # out them in separated line
    for i, actual_mean in enumerate(__UpperCamelCase						,			1					):
      print(f'Actual(Real) mean of class_{i} is: {actual_mean}'					)
    print('''-''' * 1_0_0					)

    # Calculating the value of probabilities for each class
    __A		     =					[
        calculate_probabilities(counts[i]						,			sum(__UpperCamelCase					)					) for i in range(__UpperCamelCase					)
    ]

    # for loop iterates over number of elements in 'probabilities' list and print
    # out them in separated line
    for i, probability in enumerate(__UpperCamelCase						,			1					):
      print(f'Probability of class_{i} is: {probability}'					)
    print('''-''' * 1_0_0					)

    # Calculating the values of variance for each class
    __A		     =					calculate_variance(__UpperCamelCase						,			__UpperCamelCase						,			sum(__UpperCamelCase					)					)
    print('''Variance: '''						,			__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    # Predicting Y values
    # storing predicted Y values in 'pre_indexes' variable
    __A		     =					predict_y_values(__UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase						,			__UpperCamelCase					)
    print('''-''' * 1_0_0					)

    # Calculating Accuracy of the model
    print(f'Accuracy: {accuracy(__UpperCamelCase						,			__UpperCamelCase					)}'					)
    print('''-''' * 1_0_0					)
    print(''' DONE '''.center(1_0_0						,			'''+'''					)					)

    if input('''Press any key to restart or \'q\' for quit: '''					).strip().lower() == "q":
      print('''\n''' + '''GoodBye!'''.center(1_0_0						,			'''-'''					) + '''\n'''					)
      break
    system('''cls''' if name == '''nt''' else '''clear'''					)  # noqa: S605


if __name__ == "__main__":
       main()





"""simple docstring"""


from ...configuration_utils import PretrainedConfig
from ...utils import logging


__UpperCamelCase										=     logging.get_logger(__name__)

__UpperCamelCase										=     {
    '''uw-madison/nystromformer-512''': '''https://huggingface.co/uw-madison/nystromformer-512/resolve/main/config.json''',
    # See all Nystromformer models at https://huggingface.co/models?filter=nystromformer
}




class 					UpperCamelCase   (							lowerCAmelCase__  ):
       SCREAMING_SNAKE_CASE_						      = "nystromformer"







       def __init__(					self,				lowerCAmelCase__=3_0000,				lowerCAmelCase__=768,				lowerCAmelCase__=12,				lowerCAmelCase__=12,				lowerCAmelCase__=3072,				lowerCAmelCase__="gelu_new",				lowerCAmelCase__=0.1,				lowerCAmelCase__=0.1,				lowerCAmelCase__=510,				lowerCAmelCase__=2,				lowerCAmelCase__=64,				lowerCAmelCase__=64,				lowerCAmelCase__=65,				lowerCAmelCase__=False,				lowerCAmelCase__=0.02,				lowerCAmelCase__=1e-5,				lowerCAmelCase__=1,				lowerCAmelCase__=0,				lowerCAmelCase__=2,				**lowerCAmelCase__,				) -> Optional[Any]:
            snake_case_   			=   vocab_size
            snake_case_   			=   max_position_embeddings
            snake_case_   			=   hidden_size
            snake_case_   			=   num_hidden_layers
            snake_case_   			=   num_attention_heads
            snake_case_   			=   intermediate_size
            snake_case_   			=   hidden_act
            snake_case_   			=   hidden_dropout_prob
            snake_case_   			=   attention_probs_dropout_prob
            snake_case_   			=   initializer_range
            snake_case_   			=   type_vocab_size
            snake_case_   			=   segment_means_seq_len
            snake_case_   			=   num_landmarks
            snake_case_   			=   conv_kernel_size
            snake_case_   			=   inv_coeff_init_option
            snake_case_   			=   layer_norm_eps
            super().__init__(pad_token_id=lowerCAmelCase__,				bos_token_id=lowerCAmelCase__,				eos_token_id=lowerCAmelCase__,				**lowerCAmelCase__)

