"""simple docstring"""







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


def 					a__ (						UpperCAmelCase__    :     NDArray[floataa]						,     UpperCAmelCase__    :     NDArray[floataa]							)->		NDArray[floataa]:
						UpperCAmelCase__		, UpperCAmelCase__   		=						np.shape(_A							)

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

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

						return x


def 					a__ (						UpperCAmelCase__    :     NDArray[floataa]						,     UpperCAmelCase__    :     NDArray[floataa]							)->		NDArray[floataa]:
						UpperCAmelCase__		, UpperCAmelCase__   		=						np.shape(_A							)
						if rows != columns:
												return np.array(()						,     dtype=_A							)

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

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

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

						return x


if __name__ == "__main__":
						import doctest

						doctest.testmod()


"""simple docstring"""







from collections import namedtuple

UpperCamelCase_    :    Any											=						namedtuple("""from_to""", """from_ to""")

UpperCamelCase_    :    Union[str, Any]											=						{
    """millimeter""": """mm""",
    """centimeter""": """cm""",
    """meter""": """m""",
    """kilometer""": """km""",
    """inch""": """in""",
    """inche""": """in""",  # Trailing 's' has been stripped off
    """feet""": """ft""",
    """foot""": """ft""",
    """yard""": """yd""",
    """mile""": """mi""",
}

UpperCamelCase_    :    str											=						{
    """mm""": from_to(0.001, 1000),
    """cm""": from_to(0.01, 100),
    """m""": from_to(1, 1),
    """km""": from_to(1000, 0.001),
    """in""": from_to(0.0254, 39.3701),
    """ft""": from_to(0.3048, 3.2_8084),
    """yd""": from_to(0.9144, 1.0_9361),
    """mi""": from_to(1609.34, 0.0_0062_1371),
}


def 					a__ (						UpperCAmelCase__    :     float						,     UpperCAmelCase__    :     str						,     UpperCAmelCase__    :     str     )->		float:
						UpperCAmelCase__   		=						from_type.lower().rstrip("""s"""     )
						UpperCAmelCase__   		=						TYPE_CONVERSION.get(UpperCAmelCase__						,     UpperCAmelCase__     )
						UpperCAmelCase__   		=						to_type.lower().rstrip("""s"""     )
						UpperCAmelCase__   		=						TYPE_CONVERSION.get(UpperCAmelCase__						,     UpperCAmelCase__     )
						if new_from not in METRIC_CONVERSION:
												UpperCAmelCase__   		=						(
												    f'Invalid \'from_type\' value: {from_type!r}.\n'
												    f'Conversion abbreviations are: {", ".join(UpperCAmelCase__     )}'
												)
												raise ValueError(UpperCAmelCase__     )
						if new_to not in METRIC_CONVERSION:
												UpperCAmelCase__   		=						(
												    f'Invalid \'to_type\' value: {to_type!r}.\n'
												    f'Conversion abbreviations are: {", ".join(UpperCAmelCase__     )}'
												)
												raise ValueError(UpperCAmelCase__     )
						return value * METRIC_CONVERSION[new_from].from_ * METRIC_CONVERSION[new_to].to


if __name__ == "__main__":
						import doctest

						doctest.testmod()

