Dynamic Time Warping Distance

DTW_Distance.adb

    function DTW_Distance(X, Y: in Data_Pairs; Window_Size: Positive) return Long_Float is
        N : Positive := X'Length;
        type Real_Array is array(X'First - Window_Size .. X'Last + Window_Size) of Long_Float;
        DTW_Current, DTW_Previous : Real_Array := (others => Long_Float'Last);
    begin
        DTW_Previous(X'First) := 0.0;

        for I in X'First .. X'Last loop
            DTW_Current(X'First) := Long_Float'Last; -- Reset current row

            for J in Integer'Max(X'First, I - Window_Size) .. Integer'Min(X'Last, I + Window_Size) loop
                declare
                    Cost : Long_Float := Abs(X(I).Value - Y(J).Value);
                    Min_Cost : Long_Float;
                    J_Previous : Integer := Integer'Max(J - 1, Y'First);
                begin
                    -- Compute minimum cost considering the DTW constraint
                    Min_Cost := Long_Float'Min( Long_Float'Min(
                        DTW_Previous(J_Previous),
                        DTW_Current(J_Previous)),
                        (if J > Y'First then DTW_Previous(J) else Long_Float'Last)
                    );

                    DTW_Current(J) := Cost + Min_Cost;
                end;
            end loop;

            -- Swap the rows
            DTW_Previous := DTW_Current;
        end loop;

        return 1.0/DTW_Current(N);
    end DTW_Distance;

reconstructed QBO driving from above