Update all documents setting a value equal to value of an array where index taken from another value (MongoDB)

I am trying to execute a mongo Shell command on a 80k documents Collection in MongoDB.

Here is a sample doc:

{ 
   "weights":[ 
      { 
         "amount":100,
         "description":"grams",
         "grams":100
      },
      { 
         "amount":1,
         "description":"cup",
         "grams":258
      },
      { 
         "amount":1,
         "description":"tbsp",
         "grams":16
      },
      { 
         "amount":1,
         "description":"tsp",
         "grams":5.38
      }
   ],
   "default_units":2,
   "nutrition":{ 
      "calories":598,
      "carbs":22.31,
      "fats":51.36,
      "proteins":22.21,
   },
   "serving_calories":95,
   "serving_carbs":3,
   "serving_fats":8,
   "serving_proteins":2,
}

What I want to do is go over each Doc in the collection and update the "serving_calories" field to be as follows:

serving_calories = doc.nutrition.calories * (doc.weights[doc.default_units].grams / 100);

So executing this properly would make serving_calories = 598 * (16 / 100) = ‭95.68‬

I wasn't able to find the right commands to be able to do the array index as needed from another value. What is the right mongo command to execute?