




from __future__ import annotations
class       a__   :






						def __init__(       self		,      _A      ):




											"""simple docstring"""



											__lowerCAmelCase           =       TypeError(
											    "Matrices must be formed from a list of zero or more lists containing at "
											    "least one and the same number of values, each of which must be of type "
											    "int or float."      )
											if len(_A      ) != 0:
																__lowerCAmelCase           =       len(rows[0]      )
																if cols == 0:
																					raise error
																for row in rows:
																					if len(_A      ) != cols:
																										raise error
																					for value in row:
																										if not isinstance(_A		,      (int, float)      ):
																															raise error
																__lowerCAmelCase           =       rows
											else:
																__lowerCAmelCase           =       []






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return [[row[i] for row in self.rows] for i in range(len(self.rows[0]      )      )]






						@property
						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return len(self.rows      )






						@property
						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return len(self.rows[0]      )






						@property
						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return (self.num_rows, self.num_columns)






						@property
						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return self.order[0] == self.order[1]






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											__lowerCAmelCase           =       [
											    [0 if column_num != row_num else 1 for column_num in range(self.num_rows      )]
											    for row_num in range(self.num_rows      )
											]
											return Matrix(_A      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											if not self.is_square:
																return 0
											if self.order == (0, 0):
																return 1
											if self.order == (1, 1):
																return int(self.rows[0][0]      )
											if self.order == (2, 2):
																return int(
																    (self.rows[0][0] * self.rows[1][1])
																    - (self.rows[0][1] * self.rows[1][0])      )
											else:
																return sum(
																    self.rows[0][column] * self.cofactors().rows[0][column]
																    for column in range(self.num_columns      )      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return bool(self.determinant()      )






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A      ):




											"""simple docstring"""



											__lowerCAmelCase           =       [
											    [
											        self.rows[other_row][other_column]
											        for other_column in range(self.num_columns      )
											        if other_column != column
											    ]
											    for other_row in range(self.num_rows      )
											    if other_row != row
											]
											return Matrix(_A      ).determinant()






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A      ):




											"""simple docstring"""



											if (row + column) % 2 == 0:
																return self.get_minor(_A		,      _A      )
											return -1 * self.get_minor(_A		,      _A      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return Matrix(
											    [
											        [self.get_minor(_A		,      _A      ) for column in range(self.num_columns      )]
											        for row in range(self.num_rows      )
											    ]      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return Matrix(
											    [
											        [
											            self.minors().rows[row][column]
											            if (row + column) % 2 == 0
											            else self.minors().rows[row][column] * -1
											            for column in range(self.minors().num_columns      )
											        ]
											        for row in range(self.minors().num_rows      )
											    ]      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											__lowerCAmelCase           =       [
											    [self.cofactors().rows[column][row] for column in range(self.num_columns      )]
											    for row in range(self.num_rows      )
											]
											return Matrix(_A      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											__lowerCAmelCase           =       self.determinant()
											if not determinant:
																raise TypeError("Only matrices with a non-zero determinant have an inverse"      )
											return self.adjugate() * (1 / determinant)






						def __repr__(       self      ):




											"""simple docstring"""



											return str(self.rows      )






						def __str__(       self      ):




											"""simple docstring"""



											if self.num_rows == 0:
																return "[]"
											if self.num_rows == 1:
																return "[[" + ". ".join(str(self.rows[0]      )      ) + "]]"
											return (
											    "["
											    + "\n ".join(
											        [
											            "[" + ". ".join([str(_A      ) for value in row]      ) + ".]"
											            for row in self.rows
											        ]      )
											    + "]"
											)






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A = None      ):




											"""simple docstring"""



											__lowerCAmelCase           =       TypeError("Row must be a list containing all ints and/or floats"      )
											if not isinstance(_A		,      _A      ):
																raise type_error
											for value in row:
																if not isinstance(_A		,      (int, float)      ):
																					raise type_error
											if len(_A      ) != self.num_columns:
																raise ValueError(
																    "Row must be equal in length to the other rows in the matrix"      )
											if position is None:
																self.rows.append(_A      )
											else:
																__lowerCAmelCase           =       self.rows[0:position] + [row] + self.rows[position:]






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A = None      ):




											"""simple docstring"""



											__lowerCAmelCase           =       TypeError(
											    "Column must be a list containing all ints and/or floats"      )
											if not isinstance(_A		,      _A      ):
																raise type_error
											for value in column:
																if not isinstance(_A		,      (int, float)      ):
																					raise type_error
											if len(_A      ) != self.num_rows:
																raise ValueError(
																    "Column must be equal in length to the other columns in the matrix"      )
											if position is None:
																__lowerCAmelCase           =       [self.rows[i] + [column[i]] for i in range(self.num_rows      )]
											else:
																__lowerCAmelCase           =       [
																    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
																    for i in range(self.num_rows      )
																]






						def __eq__(       self		,      _A      ):




											"""simple docstring"""



											if not isinstance(_A		,      _A      ):
																return NotImplemented
											return self.rows == other.rows






						def __ne__(       self		,      _A      ):




											"""simple docstring"""



											return not self == other






						def __neg__(       self      ):




											"""simple docstring"""



											return self * -1






						def __add__(       self		,      _A      ):




											"""simple docstring"""



											if self.order != other.order:
																raise ValueError("Addition requires matrices of the same order"      )
											return Matrix(
											    [
											        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns      )]
											        for i in range(self.num_rows      )
											    ]      )






						def __sub__(       self		,      _A      ):




											"""simple docstring"""



											if self.order != other.order:
																raise ValueError("Subtraction requires matrices of the same order"      )
											return Matrix(
											    [
											        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns      )]
											        for i in range(self.num_rows      )
											    ]      )






						def __mul__(       self		,      _A      ):




											"""simple docstring"""



											if isinstance(_A		,      (int, float)      ):
																return Matrix(
																    [[int(element * other      ) for element in row] for row in self.rows]      )
											elif isinstance(_A		,      _A      ):
																if self.num_columns != other.num_rows:
																					raise ValueError(
																					    "The number of columns in the first matrix must "
																					    "be equal to the number of rows in the second"      )
																return Matrix(
																    [
																        [Matrix.dot_product(_A		,      _A      ) for column in other.columns()]
																        for row in self.rows
																    ]      )
											else:
																raise TypeError(
																    "A Matrix can only be multiplied by an int, float, or another matrix"      )






						def __pow__(       self		,      _A      ):




											"""simple docstring"""



											if not isinstance(_A		,      _A      ):
																raise TypeError("A Matrix can only be raised to the power of an int"      )
											if not self.is_square:
																raise ValueError("Only square matrices can be raised to a power"      )
											if other == 0:
																return self.identity()
											if other < 0:
																if self.is_invertable():
																					return self.inverse() ** (-other)
																raise ValueError(
																    "Only invertable matrices can be raised to a negative power"      )
											__lowerCAmelCase           =       self
											for _ in range(other - 1      ):
																result *= self
											return result






						@classmethod
						def     __SCREAMING_SNAKE_CASE(       cls		,      _A		,      _A      ):




											"""simple docstring"""



											return sum(row[i] * column[i] for i in range(len(_A      )      )      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()










from sklearn.metrics import mean_squared_error

import datasets


UpperCamelCase__         =      """\
@article{scikit-learn,
 title={Scikit-learn: Machine Learning in {P}ython},
 author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.
         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.
         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and
         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
 journal={Journal of Machine Learning Research},
 volume={12},
 pages={2825--2830},
 year={2011}
}
"""

UpperCamelCase__         =      """\
Mean Squared Error(MSE) is the average of the square of difference between the predicted
and actual values.
"""


UpperCamelCase__         =      """
Args:
    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Estimated target values.
    references: array-like of shape (n_samples,) or (n_samples, n_outputs)
        Ground truth (correct) target values.
    sample_weight: array-like of shape (n_samples,), default=None
        Sample weights.
    multioutput: {\"raw_values\", \"uniform_average\"} or array-like of shape (n_outputs,), default=\"uniform_average\"
        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.

        \"raw_values\" : Returns a full set of errors in case of multioutput input.

        \"uniform_average\" : Errors of all outputs are averaged with uniform weight.

    squared : bool, default=True
        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.

Returns:
    mse : mean squared error.
Examples:

    >>> mse_metric = datasets.load_metric(\"mse\")
    >>> predictions = [2.5, 0.0, 2, 8]
    >>> references = [3, -0.5, 2, 7]
    >>> results = mse_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mse': 0.375}
    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)
    >>> print(rmse_result)
    {'mse': 0.6123724356957945}

    If you're using multi-dimensional lists, then set the config as follows :

    >>> mse_metric = datasets.load_metric(\"mse\", \"multilist\")
    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]
    >>> references = [[0, 2], [-1, 2], [8, -5]]
    >>> results = mse_metric.compute(predictions=predictions, references=references)
    >>> print(results)
    {'mse': 0.7083333333333334}
    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput='raw_values')
    >>> print(results) # doctest: +NORMALIZE_WHITESPACE
    {'mse': array([0.41666667, 1. ])}
"""
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION			,    _KWARGS_DESCRIPTION				)
class       a__   ( datasets.Metric				):






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											return datasets.MetricInfo(
											    description=_DESCRIPTION		,      citation=_CITATION		,      inputs_description=_KWARGS_DESCRIPTION		,      features=datasets.Features(self._get_feature_types()      )		,      reference_urls=[
											        "https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html"
											    ]		,      )






						def     __SCREAMING_SNAKE_CASE(       self      ):




											"""simple docstring"""



											if self.config_name == "multilist":
																return {
																    "predictions": datasets.Sequence(datasets.Value("float"      )      ),
																    "references": datasets.Sequence(datasets.Value("float"      )      ),
																}
											else:
																return {
																    "predictions": datasets.Value("float"      ),
																    "references": datasets.Value("float"      ),
																}






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A		,      _A=None		,      _A="uniform_average"		,      _A=True      ):




											"""simple docstring"""



											__lowerCAmelCase           =	mean_squared_error(
											    _A		,      _A		,      sample_weight=_A		,      multioutput=_A		,      squared=_A      )

											return {"mse": mse}




