


snake_case       :					dict[str, float]        =  {
    "kilogram": 1,
    "gram": pow(10, 3),
    "milligram": pow(10, 6),
    "metric-ton": pow(10, -3),
    "long-ton": 0.00_09_84_20_73,
    "short-ton": 0.00_11_02_31_22,
    "pound": 2.20_46_24_42_02,
    "stone": 0.15_74_73_17_28,
    "ounce": 35.2_73_99_07_23,
    "carrat": 50_00,
    "atomic-mass-unit": 6.0_22_13_66_52E26,
}

snake_case       :					dict[str, float]        =  {
    "kilogram": 1,
    "gram": pow(10, -3),
    "milligram": pow(10, -6),
    "metric-ton": pow(10, 3),
    "long-ton": 10_16.0_46_08,
    "short-ton": 9_07.1_84,
    "pound": 0.45_35_92,
    "stone": 6.3_50_29,
    "ounce": 0.0_28_34_95,
    "carrat": 0.00_02,
    "atomic-mass-unit": 1.6_60_54_01_99E-27,
}
def        __lowerCamelCase		(				UpperCAmelCase_				,						UpperCAmelCase_				,						UpperCAmelCase_		):




      """simple docstring"""





      if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
            a		:Optional[Any]											= (
                F'''Invalid \'from_type\' or \'to_type\' value: {from_type!r}, {to_type!r}\n'''
                F'''Supported values are: {', '.join(UpperCAmelCase_		)}'''
            )
            raise ValueError(UpperCAmelCase_		)
      return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
     import doctest

     doctest.testmod()









import numpy as np
def        __lowerCamelCase		(				UpperCAmelCase_		:	Optional[Any]		):




      """simple docstring"""





      a							,       a		:Union[str, Any]											= a.shape
      a		:Any											= min(UpperCAmelCase_				,						UpperCAmelCase_		)
      a		:Tuple											= np.eye(UpperCAmelCase_		)
      a		:Any											= a.copy()

      for k in range(t - 1		):
            # select a column of modified matrix A':
            a		:List[str]											= r[k:, [k]]
            # construct first basis vector
            a		:List[str]											= np.zeros_like(UpperCAmelCase_		)
            a		:List[Any]											= 1.0
            # determine scaling factor
            a		:Union[str, Any]											= np.linalg.norm(UpperCAmelCase_		)
            # construct vector v for Householder reflection
            a		:List[str]											= x + np.sign(x[0]		) * alpha * ea
            v /= np.linalg.norm(UpperCAmelCase_		)

            # construct the Householder matrix
            a		:Union[str, Any]											= np.eye(m - k		) - 2.0 * v @ v.T
            # pad with ones and zeros as necessary
            a		:Tuple											= np.block([[np.eye(UpperCAmelCase_		), np.zeros((k, m - k)		)], [np.zeros((m - k, k)		), q_k]]		)

            a		:List[Any]											= q @ q_k.T
            a		:int											= q_k @ r

      return q, r


if __name__ == "__main__":
     import doctest

     doctest.testmod()





