code: import numpy as np
  
  
  def plug_in(symbol_values):
  
      req_symbols = ["S", "e", "d"]
      data = {}
      if all(s in symbol_values for s in req_symbols):
          e = symbol_values["e"]
          S = symbol_values["S"]
          d = symbol_values["d"]
  
          data["k"] = np.abs(d[2][2] / np.sqrt(e[2][2] * S[2][2]))
  
      return data
  
  
  DESCRIPTION = """
  Model calculating the electromechanical coupling factor,
  which is the efficiency of converting eletrical energy
  to acoustic energy in a piezoeletric transducer or filter
  """
  
  test_data = [{
      "inputs": {
          "S": [[0.007482236755310126, -0.002827041595205337, -0.002827041595205337, 0.0, 0.0, 0.0],
                [-0.002827041595205337, 0.007482236755310125, -0.002827041595205337, 0.0, 0.0, 0.0],
                [-0.0028270415952053366, -0.002827041595205337, 0.007482236755310125, 0.0, 0.0, 0.0],
                [0.0, 0.0, 0.0, 0.010309278350515464, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.010309278350515464, 0.0],
                [0.0, 0.0, 0.0, 0.0, 0.0, 0.010309278350515464]],
          "e": [[18.65, 0.00, 0.00], [-0.00, 18.65, 0.00], [-0.00, 0.00, 7.88]],
          "d": [[-0.0412497, -0.28686697, 0.06342802], [0.05065159, 0.26064878, -0.04828778],
                [0.08828203, 0.5660897, -0.11520665], [-0.16218673, -0.92468949, 0.2109461],
                [0.02485558, 0.03232004, -0.02421919], [0.06636329, 0.46541895, -0.09526407]]
      },
      "outputs": {
          "k": 0.47445902984
      }
  }]
  
  config = {
      "name": "electromechanical_coupling",
      "connections": [{
          "inputs": ["e", "S", "d"],
          "outputs": ["k"]
      }],
      "categories": ["mechanical", "electrical"],
      "variable_symbol_map": {
          "S": "compliance_tensor_voigt",
          "e": "dielectric_tensor",
          "d": "piezoelectric_tensor_converse",
          "k": "electromechanical_coupling"
      },
      "description": DESCRIPTION,
      "implemented_by": ["shyamd"],
      "references": [],
      "plug_in": plug_in,
      "test_data": test_data
  }
  
apis: numpy.sqrt