




'''simple docstring'''




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

def    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      NDArray[floataa]       ,						SCREAMING_SNAKE_CASE__			:      NDArray[floataa]       ):
 '''simple docstring'''





 UpperCAmelCase__							,			UpperCAmelCase__										=    np.shape(SCREAMING_SNAKE_CASE__       )

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

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

 return x

def    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      NDArray[floataa]       ,						SCREAMING_SNAKE_CASE__			:      NDArray[floataa]       ):
 '''simple docstring'''





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

 # 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       ,						SCREAMING_SNAKE_CASE__       ):
   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_       				=      namedtuple('from_to', 'from_ to')

UpperCAmelCase_       				=      {
    '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_       				=      {
    'mm': from_to(0.001, 1_0_0_0),
    'cm': from_to(0.01, 1_0_0),
    'm': from_to(1, 1),
    'km': from_to(1_0_0_0, 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    _UpperCamelCase      (				SCREAMING_SNAKE_CASE__			:      float       ,						SCREAMING_SNAKE_CASE__			:      str       ,						SCREAMING_SNAKE_CASE__			:      str       ):
 '''simple docstring'''





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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
