




import numpy as np
from numpy import floataa
from numpy.typing import NDArray



def 	UpperCAmelCase_    (	__UpperCamelCase,				__UpperCamelCase	):
    SCREAMING_SNAKE_CASE__			,		SCREAMING_SNAKE_CASE__								=np.shape(__UpperCamelCase	)

    SCREAMING_SNAKE_CASE__								=np.zeros((rows, 1),				dtype=__UpperCamelCase	)
    for row in reversed(range(__UpperCamelCase	)	):
        SCREAMING_SNAKE_CASE__								=0
        for col in range(row + 1,				__UpperCamelCase	):
            total += coefficients[row, col] * x[col]

        SCREAMING_SNAKE_CASE__								=(vector[row] - total) / coefficients[row, row]

    return x



def 	UpperCAmelCase_    (	__UpperCamelCase,				__UpperCamelCase	):
    SCREAMING_SNAKE_CASE__			,		SCREAMING_SNAKE_CASE__								=np.shape(__UpperCamelCase	)
    if rows != columns:
        return np.array((),				dtype=__UpperCamelCase	)

    # augmented matrix
    SCREAMING_SNAKE_CASE__								=np.concatenate((coefficients, vector),				axis=1	)
    SCREAMING_SNAKE_CASE__								=augmented_mat.astype("""float64"""	)

    # scale the matrix leaving it triangular
    for row in range(rows - 1	):
        SCREAMING_SNAKE_CASE__								=augmented_mat[row, row]
        for col in range(row + 1,				__UpperCamelCase	):
            SCREAMING_SNAKE_CASE__								=augmented_mat[col, row] / pivot
            augmented_mat[col, :] -= factor * augmented_mat[row, :]

    SCREAMING_SNAKE_CASE__								=retroactive_resolution(
        augmented_mat[:, 0:columns],				augmented_mat[:, columns : columns + 1]	)

    return x


if __name__ == "__main__":
    import doctest

    doctest.testmod()












import unittest
from dataclasses import dataclass
from typing import Optional

from transformers.utils import ModelOutput
@dataclass
class       __a					( __lowerCamelCase     ):


     """simple docstring"""


     _A				:    float
     _A				:    Optional[float]									=  None
     _A				:    Optional[float]									=  None






class       __a					( unittest.TestCase     ):


     """simple docstring"""


     def   __A				(	self			: Dict						)		->   Optional[int]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         self.assertEqual(x.a				,3_0						)
         self.assertIsNone(x.b						)
         self.assertIsNone(x.c						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.d




     def   __A				(	self			: Tuple						)		->   Dict:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(x[0]				,3_0						)
         self.assertEqual(x[1]				,1_0						)
         self.assertEqual(x[:2]				,(3_0, 1_0)						)
         self.assertEqual(x[:]				,(3_0, 1_0)						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(x[0]				,3_0						)
         self.assertEqual(x[1]				,1_0						)
         self.assertEqual(x[:2]				,(3_0, 1_0)						)
         self.assertEqual(x[:]				,(3_0, 1_0)						)




     def   __A				(	self			: List[str]						)		->   Dict:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(x["""a"""]				,3_0						)
         self.assertEqual(x["""b"""]				,1_0						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x["""c"""]

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(x["""a"""]				,3_0						)
         self.assertEqual(x["""c"""]				,1_0						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x["""b"""]




     def   __A				(	self			: Optional[int]						)		->   List[str]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         self.assertEqual(list(x.keys()						)				,["""a"""]						)
         self.assertEqual(list(x.values()						)				,[3_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a"""]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,b=1_0						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(list(x.values()						)				,[3_0, 1_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0), ("""b""", 1_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a""", """b"""]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0				,c=1_0						)
         self.assertEqual(list(x.keys()						)				,["""a""", """c"""]						)
         self.assertEqual(list(x.values()						)				,[3_0, 1_0]						)
         self.assertEqual(list(x.items()						)				,[("""a""", 3_0), ("""c""", 1_0)]						)
         self.assertEqual(list(_UpperCamelCase						)				,["""a""", """c"""]						)

         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.update({"""d""": 2_0}						)
         with self.assertRaises(_UpperCamelCase						):
             del x["a"]
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.pop("""a"""						)
         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=x.setdefault("""d"""				,3_2						)




     def   __A				(	self			: int						)		->   List[Any]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         SCREAMING_SNAKE_CASE__								=1_0
         self.assertEqual(x.a				,1_0						)
         self.assertEqual(x["""a"""]				,1_0						)




     def   __A				(	self			: Union[str, Any]						)		->   Optional[Any]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=3_0						)
         SCREAMING_SNAKE_CASE__								=1_0
         self.assertEqual(x.a				,1_0						)
         self.assertEqual(x["""a"""]				,1_0						)




     def   __A				(	self			: Dict						)		->   List[str]:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest({"""a""": 3_0, """b""": 1_0}						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(x.a				,3_0						)
         self.assertEqual(x.b				,1_0						)




     def   __A				(	self			: Optional[int]						)		->   int:


         '''simple docstring'''





         SCREAMING_SNAKE_CASE__								=ModelOutputTest([("""a""", 3_0), ("""b""", 1_0)]						)
         self.assertEqual(list(x.keys()						)				,["""a""", """b"""]						)
         self.assertEqual(x.a				,3_0						)
         self.assertEqual(x.b				,1_0						)

         with self.assertRaises(_UpperCamelCase						):
             SCREAMING_SNAKE_CASE__								=ModelOutputTest([("""a""", 3_0), (1_0, 1_0)]						)

         SCREAMING_SNAKE_CASE__								=ModelOutputTest(a=(3_0, 3_0)						)
         self.assertEqual(list(x.keys()						)				,["""a"""]						)
         self.assertEqual(x.a				,(3_0, 3_0)						)






