code: def _SU2_transform(matrix):
      r"""Perform a U(2) to SU(2) transformation via a global phase addition.
  
      A general element of :math:`\text{SU}_2(\mathbb{C})` has the following form:
  
      .. math::
          \text{SU}_{2} = \begin{bmatrix} \alpha & \beta \\ -\beta^{*} & \alpha^{*} \end{bmatrix},
  
      where :math:`\alpha, \beta \in \mathbb{C}` and :math:`|\alpha|^2 + |\beta|^2 = 1`.
      """
      with warnings.catch_warnings():
          warnings.simplefilter("ignore", RuntimeWarning)
          factor = qml.math.linalg.det(matrix)
  
      # We put the phase first in [0, \pi] and then convert it to [0, \pi)
      gphase = qml.math.mod(qml.math.angle(factor), 2 * math.pi) / 2
      rphase = (-1) ** qml.math.isclose(gphase, math.pi)
  
      # Get the final matrix form using the phase information
      s2_mat = (
          rphase
          * matrix
          * qml.math.exp(-1j * qml.math.cast_like(gphase, 1j))
      )
      return s2_mat, gphase if rphase == 1 else 0.0
  
file_path: pennylane/pennylane/ops/op_math/decompositions/solovay_kitaev.py
imports: import math
  import warnings
  from functools import lru_cache
  from scipy.spatial import KDTree
  import pennylane
  from pennylane.queuing import QueuingManager
  from pennylane.tape import QuantumScript
label_desc: Use image node_id 1 for calling a global function with example usage: _SU2_transform(matrix) and returns: s2_mat,  unknown