





from __future__ import annotations

from typing import Any
class        SCREAMING_SNAKE_CASE     :


   def __init__(					self    :       List[str]    ,  a    :       int    ,  a    :       int    ,  a    :       float = 0 )->     None:





     """simple docstring"""







     lowercase__    ,					lowercase__			    =						row, column
     lowercase__			    =						[[default_value for c in range(a )] for r in range(a )]


   def __str__(					self    :       int )->     str:





     """simple docstring"""







     lowercase__			    =						f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

     # Make string identifier
     lowercase__			    =						0
     for row_vector in self.array:
       for obj in row_vector:
         lowercase__			    =						max(a    ,  len(str(a ) ) )
     lowercase__			    =						f"""%{max_element_length}s"""

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

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


   def __repr__(					self    :       List[str] )->     str:





     """simple docstring"""







     return str(self )


   def  SCREAMING_SNAKE_CASE_							(					self    :       Dict    ,  a    :       tuple[int, int] )->     bool:





     """simple docstring"""







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


   def __getitem__(					self    :       List[Any]    ,  a    :       tuple[int, int] )->     Any:





     """simple docstring"""







     assert self.validate_indicies(a )
     return self.array[loc[0]][loc[1]]


   def __setitem__(					self    :       int    ,  a    :       tuple[int, int]    ,  a    :       float )->     None:





     """simple docstring"""







     assert self.validate_indicies(a )
     lowercase__			    =						value


   def __add__(					self    :       List[Any]    ,  a    :       Matrix )->     Matrix:





     """simple docstring"""







     assert isinstance(a    ,  a )
     assert self.row == another.row and self.column == another.column

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


   def __neg__(					self    :       str )->     Matrix:





     """simple docstring"""







     lowercase__			    =						Matrix(self.row    ,  self.column )
     for r in range(self.row ):
       for c in range(self.column ):
         lowercase__			    =						-self[r, c]
     return result


   def __sub__(					self    :       int    ,  a    :       Matrix )->     Matrix:





     """simple docstring"""







     return self + (-another)


   def __mul__(					self    :       Any    ,  a    :       int | float | Matrix )->     Matrix:





     """simple docstring"""







     if isinstance(a    ,  (int, float) ):  # Scalar multiplication
       lowercase__			    =						Matrix(self.row    ,  self.column )
       for r in range(self.row ):
         for c in range(self.column ):
           lowercase__			    =						self[r, c] * another
       return result
     elif isinstance(a    ,  a ):  # Matrix multiplication
       assert self.column == another.row
       lowercase__			    =						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:
       lowercase__			    =						f"""Unsupported type given for another ({type(a )})"""
       raise TypeError(a )


   def  SCREAMING_SNAKE_CASE_							(					self    :       Union[str, Any] )->     Matrix:





     """simple docstring"""







     lowercase__			    =						Matrix(self.column    ,  self.row )
     for r in range(self.row ):
       for c in range(self.column ):
         lowercase__			    =						self[r, c]
     return result


   def  SCREAMING_SNAKE_CASE_							(					self    :       int    ,  a    :       Matrix    ,  a    :       Matrix )->     Any:





     """simple docstring"""







     assert isinstance(a    ,  a ) and isinstance(a    ,  a )
     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
     lowercase__			    =						v.transpose()
     lowercase__			    =						(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     __UpperCamelCase						()       ->     None:
        # a^(-1)
        lowercase__			    =						Matrix(3	,		3	,		0	)
        for i in range(3	):
          lowercase__			    =						1
        print(F"""a^(-1) is {ainv}"""	)
        # u, v
        lowercase__			    =						Matrix(3	,		1	,		0	)
        lowercase__    ,					lowercase__    ,					lowercase__			    =						1, 2, -3
        lowercase__			    =						Matrix(3	,		1	,		0	)
        lowercase__    ,					lowercase__    ,					lowercase__			    =						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(_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE	)}"""	)




      def     __UpperCamelCase						()       ->     None:
        import doctest

        doctest.testmod()


      testa()









from scipy.stats import spearmanr

import datasets


lowercase_					     =	"""
The Spearman rank-order correlation coefficient is a measure of the
relationship between two datasets. Like other correlation coefficients,
this one varies between -1 and +1 with 0 implying no correlation.
Positive correlations imply that as data in dataset x increases, so
does data in dataset y. Negative correlations imply that as x increases,
y decreases. Correlations of -1 or +1 imply an exact monotonic relationship.

Unlike the Pearson correlation, the Spearman correlation does not
assume that both datasets are normally distributed.

The p-value roughly indicates the probability of an uncorrelated system
producing datasets that have a Spearman correlation at least as extreme
as the one computed from these datasets. The p-values are not entirely
reliable but are probably reasonable for datasets larger than 500 or so.
"""

lowercase_					     =	"""
Args:
    predictions (`List[float]`): Predicted labels, as returned by a model.
    references (`List[float]`): Ground truth labels.
    return_pvalue (`bool`): If `True`, returns the p-value. If `False`, returns
            only the spearmanr score. Defaults to `False`.
Returns:
    spearmanr (`float`): Spearman correlation coefficient.
    p-value (`float`): p-value. **Note**: is only returned if `return_pvalue=True` is input.
Examples:
    Example 1:
        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")
        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5], predictions=[10, 9, 2.5, 6, 4])
        >>> print(results)
        {'spearmanr': -0.7}

    Example 2:
        >>> spearmanr_metric = datasets.load_metric(\"spearmanr\")
        >>> results = spearmanr_metric.compute(references=[1, 2, 3, 4, 5],
        ...                                     predictions=[10, 9, 2.5, 6, 4],
        ...                                     return_pvalue=True)
        >>> print(results['spearmanr'])
        -0.7
        >>> print(round(results['spearmanr_pvalue'], 2))
        0.19
"""

lowercase_					     =	R"""\
@book{kokoska2000crc,
  title={CRC standard probability and statistics tables and formulae},
  author={Kokoska, Stephen and Zwillinger, Daniel},
  year={2000},
  publisher={Crc Press}
}
@article{2020SciPy-NMeth,
  author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and
            Haberland, Matt and Reddy, Tyler and Cournapeau, David and
            Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and
            Bright, Jonathan and {van der Walt}, St{\'e}fan J. and
            Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and
            Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and
            Kern, Robert and Larson, Eric and Carey, C J and
            Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and
            {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and
            Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and
            Harris, Charles R. and Archibald, Anne M. and
            Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and
            {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},
  title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific
            Computing in Python}},
  journal = {Nature Methods},
  year    = {2020},
  volume  = {17},
  pages   = {261--272},
  adsurl  = {https://rdcu.be/b08Wh},
  doi     = {10.1038/s41592-019-0686-2},
}
"""
@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION    ,			_KWARGS_DESCRIPTION   )
class        SCREAMING_SNAKE_CASE     (datasets.Metric   ):


   def  SCREAMING_SNAKE_CASE_							(					self    :       Union[str, Any] )->     Tuple:





     """simple docstring"""







     return datasets.MetricInfo(
         description=_DESCRIPTION    ,  citation=_CITATION    ,  inputs_description=_KWARGS_DESCRIPTION    ,  features=datasets.Features(
             {
                 'predictions': datasets.Value('float' ),
                 'references': datasets.Value('float' ),
             } )    ,  reference_urls=['https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html']    ,  )


   def  SCREAMING_SNAKE_CASE_							(					self    :       int    ,  a    :       str    ,  a    :       Any    ,  a    :       str=False )->     Optional[int]:





     """simple docstring"""







     lowercase__			    =						spearmanr(a    ,  a )
     if return_pvalue:
       return {"spearmanr": results[0], "spearmanr_pvalue": results[1]}
     else:
       return {"spearmanr": results[0]}


