code: def test_reduced_row_echelon(binary_matrix, result):
      r"""Test that _reduced_row_echelon returns the correct result."""
  
      # build row echelon form of the matrix
      shape = binary_matrix.shape
      for irow in range(shape[0]):
          pivot_index = 0
          if np.count_nonzero(binary_matrix[irow, :]):
              pivot_index = np.nonzero(binary_matrix[irow, :])[0][0]
  
          for jrow in range(shape[0]):
              if jrow != irow and binary_matrix[jrow, pivot_index]:
                  binary_matrix[jrow, :] = (
                      binary_matrix[jrow, :] + binary_matrix[irow, :]
                  ) % 2
  
      indices = [
          irow
          for irow in range(shape[0] - 1)
          if np.array_equal(binary_matrix[irow, :], np.zeros(shape[1]))
      ]
  
      temp_row_echelon_matrix = binary_matrix.copy()
      for row in indices[::-1]:
          temp_row_echelon_matrix = np.delete(
              temp_row_echelon_matrix, row, axis=0
          )
  
      row_echelon_matrix = np.zeros(shape, dtype=int)
      row_echelon_matrix[
          : shape[0] - len(indices), :
      ] = temp_row_echelon_matrix
  
      # build reduced row echelon form of the matrix from row echelon form
      for idx in range(len(row_echelon_matrix))[:0:-1]:
          nonzeros = np.nonzero(row_echelon_matrix[idx])[0]
          if len(nonzeros) > 0:
              redrow = (row_echelon_matrix[idx, :] % 2).reshape(1, -1)
              coeffs = (
                  (
                      -row_echelon_matrix[:idx, nonzeros[0]]
                      / row_echelon_matrix[idx, nonzeros[0]]
                  )
                  % 2
              ).reshape(1, -1)
              row_echelon_matrix[:idx, :] = (
                  row_echelon_matrix[:idx, :] + (coeffs.T * redrow) % 2
              ) % 2
  
      # get reduced row echelon form from the _reduced_row_echelon function
      rref_bin_mat = _reduced_row_echelon(binary_matrix)
  
      assert (rref_bin_mat == row_echelon_matrix).all()
      assert (rref_bin_mat == result).all()
  
imports: import functools
  import pytest
  import scipy
  import pennylane
  from pennylane import numpy
  from pennylane.pauli import pauli_sentence
  from pennylane.qchem.tapering import _kernel, _reduced_row_echelon, clifford, optimal_sector, taper_hf, taper_operation, _split_pauli_sentence, _taper_pauli_sentence
  from pennylane.operation import enable_new_opmath, disable_new_opmath
label_desc: Use image node_id 1 for calling a global function with example usage: test_reduced_row_echelon(binary_matrix, result) without return types