ip_distance.gsql

CREATE FUNCTION gds.vector.ip_distance(list<double> list1, list<double> list2) RETURNS(float) {

  /*
  First Author: Jue Yuan
  First Commit Date:  Nov 27, 2024 

  Recent Author: Jue Yuan
  Recent Commit Date: Nov 27, 2024 

  Maturity:
      alpha

  Description:
      Calculates the inner product (dot product) between two vectors represented as lists of double values.
      The inner product is a key measure in linear algebra, indicating the magnitude of the projection of one vector onto another.
      This function provides a similarity measure commonly used in machine learning and data analysis.

  Parameters:
      list<double> list1:
          The first vector as a list of double values.
      list<double> list2:
          The second vector as a list of double values.

  Returns:
      float:
          The inner product (dot product) of the two input vectors.

  Exceptions:
      list_size_mismatch (90000):
          Raised when the input vectors are not of equal size.

  Logic Overview:
      Input Validation:
          Ensures both vectors have the same length.
      Inner Product Calculation:
          Computes the sum of the element-wise products of the two vectors.

  Formula:
      Inner Product = (x1 x y1) + (x2 x y2) + ... + (xn x yn)
      Where xi and yi are elements of list1 and list2, respectively.

  Use Case:
      This function is widely used in:
          Calculating similarity in machine learning models (e.g., recommendation systems).
          Performing vector projections in linear algebra.
          Evaluating similarity between embeddings in natural language processing (NLP).
  */

  EXCEPTION list_size_mismatch (90000);
  ListAccum<double> @@myList1 = list1;
  ListAccum<double> @@myList2 = list2;

  IF (@@myList1.size() != @@myList2.size()) THEN
    RAISE list_size_mismatch ("Two lists provided for gds.vector.euclidean_distance have different sizes.");
  END;

  RETURN inner_product(@@myList1, @@myList2);
}