

"""simple docstring"""


from __future__ import annotations

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



def   _A					(	_a	:						NDArray[floataa]     ,   _a	:						NDArray[floataa]     ,   _a	:						list[int]     ,   _a	:						int     ,   ):



      """simple docstring"""






      A  ,			A				  =		coefficient_matrix.shape
      A  ,			A				  =		constant_matrix.shape

      if rowsa != colsa:
            A				  =		f'Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}'
            raise ValueError(_a				)

      if colsa != 1:
            A				  =		f'Constant matrix must be nx1 but received {rowsa}x{colsa}'
            raise ValueError(_a				)

      if rowsa != rowsa:
            A				  =		(
                """Coefficient and constant matrices dimensions must be nxn and nx1 but """
                f'received {rowsa}x{colsa} and {rowsa}x{colsa}'
            )
            raise ValueError(_a				)

      if len(_a				) != rowsa:
            A				  =		(
                """Number of initial values must be equal to number of rows in coefficient """
                f'matrix but received {len(_a				)} and {rowsa}'
            )
            raise ValueError(_a				)

      if iterations <= 0:
            raise ValueError("""Iterations must be at least 1"""				)

      A				  =		np.concatenate(
          (coefficient_matrix, constant_matrix)     ,   axis=1				)

      A  ,			A				  =		table.shape

      strictly_diagonally_dominant(_a				)

      # Iterates the whole matrix for given number of times
      for _ in range(_a				):
            A				  =		[]
            for row in range(_a				):
                  A				  =		0
                  for col in range(_a				):
                        if col == row:
                              A				  =		table[row][col]
                        elif col == cols - 1:
                              A				  =		table[row][col]
                        else:
                              temp += (-1) * table[row][col] * init_val[col]
                  A				  =		(temp + val) / denom
                  new_val.append(_a				)
            A				  =		new_val

      return [float(_a				) for i in new_val]



def   _A					(	_a	:						NDArray[floataa]				):



      """simple docstring"""






      A  ,			A				  =		table.shape

      A				  =		True

      for i in range(0     ,   _a				):
            A				  =		0
            for j in range(0     ,   cols - 1				):
                  if i == j:
                        continue
                  else:
                        total += table[i][j]

            if table[i][i] <= total:
                  raise ValueError("""Coefficient matrix is not strictly diagonally dominant"""				)

      return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
  import doctest

  doctest.testmod()







"""simple docstring"""


import qiskit



def   _A					(	_a	:						int     ,   _a	:						int				):



      """simple docstring"""






      A				  =		qiskit.Aer.get_backend("""aer_simulator"""				)

      # Create a Quantum Circuit acting on the q register
      A				  =		qiskit.QuantumCircuit(_a     ,   _a				)

      # Apply X (NOT) Gate to Qubits 0 & 1
      circuit.x(0				)
      circuit.x(1				)

      # Map the quantum measurement to the classical bits
      circuit.measure([0, 1]     ,   [0, 1]				)

      # Execute the circuit on the qasm simulator
      A				  =		qiskit.execute(_a     ,   _a     ,   shots=1_0_0_0				)

      # Return the histogram data of the results of the experiment.
      return job.result().get_counts(_a				)


if __name__ == "__main__":
  UpperCAmelCase													=single_qubit_measure(2, 2)
  print(f"""Total count for various states are: {counts}""")




