code: def _bisect_compute_a(u: np.ndarray):
      """
      Given the U matrix, compute the A matrix such that
      At x A x At x A x = U
      where At is the adjoint of A
      and x is the Pauli X matrix.
      """
      x = np.real(u[0, 1])
      z = u[1, 1]
      zr = np.real(z)
      zi = np.imag(z)
      if np.isclose(zr, -1):
          # special case [[-1, 0], [0, -1]]
          # would cause divide by 0 with the other formula, so we use hardcoded solution
          return np.array([[1, -1], [1, 1]]) * 2**-0.5
      ar = np.sqrt((np.sqrt((zr + 1) / 2) + 1) / 2)
      mul = 1 / (2 * np.sqrt((zr + 1) * (np.sqrt((zr + 1) / 2) + 1)))
      ai = zi * mul
      br = x * mul
      bi = 0
      return _param_su2(ar, ai, br, bi)
  
file_path: pennylane/pennylane/ops/op_math/controlled_decompositions.py
imports: from copy import copy
  import numpy
  import numpy.linalg
  import pennylane
  from pennylane.operation import Operator
  from pennylane.wires import Wires
  from pennylane import math
label_desc: Use image node_id 4 for calling a global function with example usage: _bisect_compute_a(u) and returns: _param_su2, unknown