



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






def 						_lowerCAmelCase    (					__lowerCamelCase :  NDArray[floataa]		,						__lowerCamelCase :  NDArray[floataa]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     Optional[Any]							=						np.shape(__lowerCamelCase  )

 __SCREAMING_SNAKE_CASE							:     NDArray[floataa]							=						np.zeros((rows, 1)		,						dtype=__lowerCamelCase  )
 for row in reversed(range(__lowerCamelCase  )  ):
  __SCREAMING_SNAKE_CASE							:     str							=						0
  for col in range(row + 1		,						__lowerCamelCase  ):
   total += coefficients[row, col] * x[col]

  __SCREAMING_SNAKE_CASE							:     int							=						(vector[row] - total) / coefficients[row, row]

 return x






def 						_lowerCAmelCase    (					__lowerCamelCase :  NDArray[floataa]		,						__lowerCamelCase :  NDArray[floataa]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     List[Any]							=						np.shape(__lowerCamelCase  )
 if rows != columns:
  return np.array(()		,						dtype=__lowerCamelCase  )

 # augmented matrix
 __SCREAMING_SNAKE_CASE							:     NDArray[floataa]							=						np.concatenate((coefficients, vector)		,						axis=1  )
 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						augmented_mat.astype("float64"  )

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

 __SCREAMING_SNAKE_CASE							:     Union[str, Any]							=						retroactive_resolution(
     augmented_mat[:, 0:columns]		,						augmented_mat[:, columns : columns + 1]  )

 return x


if __name__ == "__main__":
      import doctest

      doctest.testmod()








'''simple docstring'''







import logging

# standard libraries
import sys

import numpy as np
import pytest  # type: ignore

# Custom/local libraries
from matrix import matrix_operation as matop

_snake_case					: List[str]     			=					[[12, 10], [3, 9]]
_snake_case					: Any     			=					[[3, 4], [7, 4]]
_snake_case					: List[str]     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, -2], [2, 0, 2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]]
_snake_case					: Optional[Any]     			=					[1]
_snake_case					: str     			=					[2]

_snake_case					: Optional[int]     			=					logging.getLogger()
_snake_case					: Optional[Any]     			=					logging.DEBUG
_snake_case					: Tuple     			=					logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: List[Any]						,      _SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} returned integer'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_addition.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) + np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} with different matrix dims'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Optional[Any]						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} returned integer'	)
																		matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_subtraction.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) - np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} with different matrix dims'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Any						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												logger.info(F'\n\t{test_multiplication.__name__} returned integer'	)
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_multiplication.__name__} meets dim requirements'	)
												_SCREAMING_SNAKE_CASE					=			(np.matmul(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.multiply(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(
																		    F'\n\t{test_multiplication.__name__} does not meet dim requirements'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(3.5 * np.array(_SCREAMING_SNAKE_CASE	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.scalar_multiply(_SCREAMING_SNAKE_CASE						,      3.5	)
						assert theo == act



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(np.identity(5	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.identity(5	)
						assert theo == act




@pytest.mark.mat_ops
@pytest.mark.parametrize("mat"						,      [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_transpose.__name__} returned integer'	)
																		matop.transpose(_SCREAMING_SNAKE_CASE	)
						else:
												_SCREAMING_SNAKE_CASE					=			(np.transpose(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.transpose(_SCREAMING_SNAKE_CASE						,      return_map=_SCREAMING_SNAKE_CASE	)
												assert theo == act