


from __future__ import annotations

from typing import Any



class        a					:





     def __init__(    self					:				str    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				int    ,	SCREAMING_SNAKE_CASE_					:				float = 0							):
        __lowerCamelCase   ,     __lowerCamelCase:				Dict     =	row, column
        __lowerCamelCase:				Optional[Any]     =	[[default_value for c in range(SCREAMING_SNAKE_CASE_							)] for r in range(SCREAMING_SNAKE_CASE_							)]





     def __str__(    self					:				Union[str, Any]							):
        __lowerCamelCase:				str     =	F'Matrix consist of {self.row} rows and {self.column} columns\n'

        # Make string identifier
        __lowerCamelCase:				Optional[int]     =	0
        for row_vector in self.array:
           for obj in row_vector:
              __lowerCamelCase:				int     =	max(SCREAMING_SNAKE_CASE_    ,	len(str(SCREAMING_SNAKE_CASE_							)							)							)
        __lowerCamelCase:				Union[str, Any]     =	F'%{max_element_length}s'

        # Make string and return
        def single_line(SCREAMING_SNAKE_CASE_					:				list[float]							) -> str:
           nonlocal string_format_identifier
           __lowerCamelCase:				Any     =	"""["""
           line += ", ".join(string_format_identifier % (obj,) for obj in row_vector							)
           line += "]"
           return line

        s += "\n".join(single_line(SCREAMING_SNAKE_CASE_							) for row_vector in self.array							)
        return s





     def __repr__(    self					:				Union[str, Any]							):
        return str(self							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any    ,	SCREAMING_SNAKE_CASE_					:				tuple[int, int]							):
        if not (isinstance(SCREAMING_SNAKE_CASE_    ,	(list, tuple)							) and len(SCREAMING_SNAKE_CASE_							) == 2):
           return False
        elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
           return False
        else:
           return True





     def __getitem__(    self					:				Optional[int]    ,	SCREAMING_SNAKE_CASE_					:				tuple[int, int]							):
        assert self.validate_indicies(SCREAMING_SNAKE_CASE_							)
        return self.array[loc[0]][loc[1]]





     def __setitem__(    self					:				Any    ,	SCREAMING_SNAKE_CASE_					:				tuple[int, int]    ,	SCREAMING_SNAKE_CASE_					:				float							):
        assert self.validate_indicies(SCREAMING_SNAKE_CASE_							)
        __lowerCamelCase:				List[Any]     =	value





     def __add__(    self					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				Matrix							):
        assert isinstance(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							)
        assert self.row == another.row and self.column == another.column

        # Add
        __lowerCamelCase:				Any     =	Matrix(self.row    ,	self.column							)
        for r in range(self.row							):
           for c in range(self.column							):
              __lowerCamelCase:				Tuple     =	self[r, c] + another[r, c]
        return result





     def __neg__(    self					:				Any							):
        __lowerCamelCase:				List[str]     =	Matrix(self.row    ,	self.column							)
        for r in range(self.row							):
           for c in range(self.column							):
              __lowerCamelCase:				int     =	-self[r, c]
        return result





     def __sub__(    self					:				Union[str, Any]    ,	SCREAMING_SNAKE_CASE_					:				Matrix							):
        return self + (-another)





     def __mul__(    self					:				Tuple    ,	SCREAMING_SNAKE_CASE_					:				int | float | Matrix							):

        if isinstance(SCREAMING_SNAKE_CASE_    ,	(int, float)							):  # Scalar multiplication
           __lowerCamelCase:				List[str]     =	Matrix(self.row    ,	self.column							)
           for r in range(self.row							):
              for c in range(self.column							):
                 __lowerCamelCase:				List[Any]     =	self[r, c] * another
           return result
        elif isinstance(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							):  # Matrix multiplication
           assert self.column == another.row
           __lowerCamelCase:				Optional[int]     =	Matrix(self.row    ,	another.column							)
           for r in range(self.row							):
              for c in range(another.column							):
                 for i in range(self.column							):
                    result[r, c] += self[r, i] * another[i, c]
           return result
        else:
           __lowerCamelCase:				int     =	F'Unsupported type given for another ({type(SCREAMING_SNAKE_CASE_							)})'
           raise TypeError(SCREAMING_SNAKE_CASE_							)





     def  SCREAMING_SNAKE_CASE__       (    self					:				Any							):
        __lowerCamelCase:				int     =	Matrix(self.column    ,	self.row							)
        for r in range(self.row							):
           for c in range(self.column							):
              __lowerCamelCase:				List[str]     =	self[r, c]
        return result







     def  SCREAMING_SNAKE_CASE__       (    self					:				int    ,	SCREAMING_SNAKE_CASE_					:				Matrix    ,	SCREAMING_SNAKE_CASE_					:				Matrix							):
        assert isinstance(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							) and isinstance(SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_							)
        assert self.row == self.column == u.row == v.row  # u, v should be column vector
        assert u.column == v.column == 1  # u, v should be column vector

        # Calculate
        __lowerCamelCase:				Optional[Any]     =	v.transpose()
        __lowerCamelCase:				Any     =	(v_t * self * u)[0, 0] + 1
        if numerator_factor == 0:
           return None  # It's not invertable
        return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":



   def     __lowerCAmelCase						(							)       ->							None:
      # a^(-1)
      __lowerCamelCase:				int     =	Matrix(3						,      3						,      0 )
      for i in range(3 ):
         __lowerCamelCase:				List[Any]     =	1
      print(f'a^(-1) is {ainv}' )
      # u, v
      __lowerCamelCase:				List[str]     =	Matrix(3						,      1						,      0 )
      __lowerCamelCase   ,     __lowerCamelCase   ,     __lowerCamelCase:				Optional[Any]     =	1, 2, -3
      __lowerCamelCase:				Dict     =	Matrix(3						,      1						,      0 )
      __lowerCamelCase   ,     __lowerCamelCase   ,     __lowerCamelCase:				Union[str, Any]     =	4, -2, 5
      print(f'u is {u}' )
      print(f'v is {v}' )
      print(f'uv^T is {u * v.transpose()}' )
      # Sherman Morrison
      print(f'(a + uv^T)^(-1) is {ainv.sherman_morrison(snake_case						,      snake_case )}' )



   def     __lowerCAmelCase						(							)       ->							None:
      import doctest

      doctest.testmod()







   testa()






from sklearn.metrics import fa_score

import datasets


_A		:				Any									=       '''
The F1 score is the harmonic mean of the precision and recall. It can be computed with the equation:
F1 = 2 * (precision * recall) / (precision + recall)
'''


_A		:				Dict									=       '''
Args:
    predictions (`list` of `int`): Predicted labels.
    references (`list` of `int`): Ground truth labels.
    labels (`list` of `int`): The set of labels to include when `average` is not set to `\'binary\'`, and the order of the labels if `average` is `None`. Labels present in the data can be excluded, for example to calculate a multiclass average ignoring a majority negative class. Labels not present in the data will result in 0 components in a macro average. For multilabel targets, labels are column indices. By default, all labels in `predictions` and `references` are used in sorted order. Defaults to None.
    pos_label (`int`): The class to be considered the positive class, in the case where `average` is set to `binary`. Defaults to 1.
    average (`string`): This parameter is required for multiclass/multilabel targets. If set to `None`, the scores for each class are returned. Otherwise, this determines the type of averaging performed on the data. Defaults to `\'binary\'`.

        - \'binary\': Only report results for the class specified by `pos_label`. This is applicable only if the classes found in `predictions` and `references` are binary.
        - \'micro\': Calculate metrics globally by counting the total true positives, false negatives and false positives.
        - \'macro\': Calculate metrics for each label, and find their unweighted mean. This does not take label imbalance into account.
        - \'weighted\': Calculate metrics for each label, and find their average weighted by support (the number of true instances for each label). This alters `\'macro\'` to account for label imbalance. This option can result in an F-score that is not between precision and recall.
        - \'samples\': Calculate metrics for each instance, and find their average (only meaningful for multilabel classification).
    sample_weight (`list` of `float`): Sample weights Defaults to None.

Returns:
    f1 (`float` or `array` of `float`): F1 score or list of f1 scores, depending on the value passed to `average`. Minimum possible value is 0. Maximum possible value is 1. Higher f1 scores are better.

Examples:

    Example 1-A simple binary example
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0])
        >>> print(results)
        {\'f1\': 0.5}

    Example 2-The same simple binary example as in Example 1, but with `pos_label` set to `0`.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], pos_label=0)
        >>> print(round(results[\'f1\'], 2))
        0.67

    Example 3-The same simple binary example as in Example 1, but with `sample_weight` included.
        >>> f1_metric = datasets.load_metric("f1")
        >>> results = f1_metric.compute(references=[0, 1, 0, 1, 0], predictions=[0, 0, 1, 1, 0], sample_weight=[0.9, 0.5, 3.9, 1.2, 0.3])
        >>> print(round(results[\'f1\'], 2))
        0.35

    Example 4-A multiclass example, with different values for the `average` input.
        >>> predictions = [0, 2, 1, 0, 0, 1]
        >>> references = [0, 1, 2, 0, 1, 2]
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="macro")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="micro")
        >>> print(round(results[\'f1\'], 2))
        0.33
        >>> results = f1_metric.compute(predictions=predictions, references=references, average="weighted")
        >>> print(round(results[\'f1\'], 2))
        0.27
        >>> results = f1_metric.compute(predictions=predictions, references=references, average=None)
        >>> print(results)
        {\'f1\': array([0.8, 0. , 0. ])}
'''


_A		:				Union[str, Any]									=       '''
@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}
}
'''



@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION     ,_KWARGS_DESCRIPTION   )
class        a					(			datasets.Metric   ):





     def  SCREAMING_SNAKE_CASE__       (    self					:				Union[str, Any]							):
        return datasets.MetricInfo(
            description=_DESCRIPTION    ,	citation=_CITATION    ,	inputs_description=_KWARGS_DESCRIPTION    ,	features=datasets.Features(
                {
                    """predictions""": datasets.Sequence(datasets.Value("""int32"""							)							),
                    """references""": datasets.Sequence(datasets.Value("""int32"""							)							),
                }
                if self.config_name == """multilabel"""
                else {
                    """predictions""": datasets.Value("""int32"""							),
                    """references""": datasets.Value("""int32"""							),
                }							)    ,	reference_urls=["""https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html"""]    ,	)







     def  SCREAMING_SNAKE_CASE__       (    self					:				int    ,	SCREAMING_SNAKE_CASE_					:				Optional[Any]    ,	SCREAMING_SNAKE_CASE_					:				str    ,	SCREAMING_SNAKE_CASE_					:				str=None    ,	SCREAMING_SNAKE_CASE_					:				str=1    ,	SCREAMING_SNAKE_CASE_					:				List[str]="binary"    ,	SCREAMING_SNAKE_CASE_					:				List[str]=None							):
        __lowerCamelCase:				str     =	fa_score(
            SCREAMING_SNAKE_CASE_    ,	SCREAMING_SNAKE_CASE_    ,	labels=SCREAMING_SNAKE_CASE_    ,	pos_label=SCREAMING_SNAKE_CASE_    ,	average=SCREAMING_SNAKE_CASE_    ,	sample_weight=SCREAMING_SNAKE_CASE_							)
        return {"f1": float(SCREAMING_SNAKE_CASE_							) if score.size == 1 else score}


