import numpy as np
from PIL import Image
def      _lowerCAmelCase(	__A   ,       __A   ,       __A			):
  UpperCAmelCase					      =  np.array(__A			)
  if arr.shape[0] != arr.shape[1]:
    raise ValueError("The input array is not a square matrix"			)
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0

  # compute the shape of the output matrix
  UpperCAmelCase					      =  (arr.shape[0] - size) // stride + 1
  # initialize the output matrix with zeros of shape maxpool_shape
  UpperCAmelCase					      =  np.zeros((maxpool_shape, maxpool_shape)			)

  while i < arr.shape[0]:
    if i + size > arr.shape[0]:
      # if the end of the matrix is reached, break
      break
    while j < arr.shape[1]:
      # if the end of the matrix is reached, break
      if j + size > arr.shape[1]:
        break
      # compute the maximum of the pooling matrix
      UpperCAmelCase					      =  np.max(arr[i : i + size, j : j + size]			)
      # shift the pooling matrix by stride of column pixels
      j += stride
      mat_j += 1

    # shift the pooling matrix by stride of row pixels
    i += stride
    mat_i += 1

    # reset the column index to 0
    UpperCAmelCase					      =  0
    UpperCAmelCase					      =  0

  return updated_arr
def      _lowerCAmelCase(	__A   ,       __A   ,       __A			):
  UpperCAmelCase					      =  np.array(__A			)
  if arr.shape[0] != arr.shape[1]:
    raise ValueError("The input array is not a square matrix"			)
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0

  # compute the shape of the output matrix
  UpperCAmelCase					      =  (arr.shape[0] - size) // stride + 1
  # initialize the output matrix with zeros of shape avgpool_shape
  UpperCAmelCase					      =  np.zeros((avgpool_shape, avgpool_shape)			)

  while i < arr.shape[0]:
    # if the end of the matrix is reached, break
    if i + size > arr.shape[0]:
      break
    while j < arr.shape[1]:
      # if the end of the matrix is reached, break
      if j + size > arr.shape[1]:
        break
      # compute the average of the pooling matrix
      UpperCAmelCase					      =  int(np.average(arr[i : i + size, j : j + size]			)			)
      # shift the pooling matrix by stride of column pixels
      j += stride
      mat_j += 1

    # shift the pooling matrix by stride of row pixels
    i += stride
    mat_i += 1
    # reset the column index to 0
    UpperCAmelCase					      =  0
    UpperCAmelCase					      =  0

  return updated_arr


# Main Function
if __name__ == "__main__":
      from doctest import testmod

      testmod(name="avgpooling", verbose=True)

      # Loading the image
      lowerCAmelCase__       = Image.open("path_to_image")

      # Converting the image to numpy array and maxpooling, displaying the result
      # Ensure that the image is a square matrix

      Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

      # Converting the image to numpy array and averagepooling, displaying the result
      # Ensure that the image is a square matrix

      Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()






import numpy

# List of input, output pairs
lowerCAmelCase__       = (
    ((5, 2, 3), 15),
    ((6, 5, 9), 25),
    ((11, 12, 13), 41),
    ((1, 1, 1), 8),
    ((11, 12, 13), 41),
)
lowerCAmelCase__       = (((515, 22, 13), 555), ((61, 35, 49), 150))
lowerCAmelCase__       = [2, 4, 1, 5]
lowerCAmelCase__       = len(train_data)
lowerCAmelCase__       = 0.0_0_9
def      _lowerCAmelCase(	__A   ,       __A="train"			):
  return calculate_hypothesis_value(__A   ,       __A			) - output(
      __A   ,       __A			)
def      _lowerCAmelCase(	__A			):
  UpperCAmelCase					      =  0
  for i in range(len(__A			) - 1			):
    hyp_val += data_input_tuple[i] * parameter_vector[i + 1]
  hyp_val += parameter_vector[0]
  return hyp_val
def      _lowerCAmelCase(	__A   ,       __A			):
  if data_set == "train":
    return train_data[example_no][1]
  elif data_set == "test":
    return test_data[example_no][1]
  return None
def      _lowerCAmelCase(	__A   ,       __A			):
  if data_set == "train":
    return _hypothesis_value(train_data[example_no][0]			)
  elif data_set == "test":
    return _hypothesis_value(test_data[example_no][0]			)
  return None
def      _lowerCAmelCase(	__A   ,       __A=m			):
  UpperCAmelCase					      =  0
  for i in range(__A			):
    if index == -1:
      summation_value += _error(__A			)
    else:
      summation_value += _error(__A			) * train_data[i][0][index]
  return summation_value
def      _lowerCAmelCase(	__A			):
  UpperCAmelCase					      =  summation_of_cost_derivative(__A   ,       __A			) / m
  return cost_derivative_value
def      _lowerCAmelCase(	):
  global parameter_vector
  # Tune these values to set a tolerance value for predicted output
  UpperCAmelCase					      =  0.000002
  UpperCAmelCase					      =  0
  UpperCAmelCase					      =  0
  while True:
    j += 1
    UpperCAmelCase					      =  [0, 0, 0, 0]
    for i in range(0   ,       len(__A			)			):
      UpperCAmelCase					      =  get_cost_derivative(i - 1			)
      UpperCAmelCase					      =  (
          parameter_vector[i] - LEARNING_RATE * cost_derivative
      )
    if numpy.allclose(
        __A   ,       __A   ,       atol=__A   ,       rtol=__A   ,       ):
      break
    UpperCAmelCase					      =  temp_parameter_vector
  print(("Number of iterations:", j)			)
def      _lowerCAmelCase(	):
  for i in range(len(__A			)			):
    print(("Actual output value:", output(__A   ,       "test"			))			)
    print(("Hypothesis output:", calculate_hypothesis_value(__A   ,       "test"			))			)


if __name__ == "__main__":
      run_gradient_descent()
      print("\nTesting gradient descent for a linear hypothesis function.\n")
      test_gradient_descent()



