Task: Gaussian elimination








VB: 
Private Function gauss_eliminate(a As Variant, b As Variant) As Variant
    Dim n As Integer: n = UBound(b)
    Dim tmp As Variant, m As Integer, mx As Variant
    For col = 1 To n
        m = col
        mx = a(m, m)
        For i = col + 1 To n
            tmp = Abs(a(i, col))
            If tmp > mx Then
                m = i
                mx = tmp
            End If
        Next i
        If col <> m Then
            For j = 1 To UBound(a, 2)
                tmp = a(col, j)
                a(col, j) = a(m, j)
                a(m, j) = tmp
            Next j
            tmp = b(col)
            b(col) = b(m)
            b(m) = tmp
        End If
        For i = col + 1 To n
            tmp = a(i, col) / a(col, col)
            For j = col + 1 To n
                a(i, j) = a(i, j) - tmp * a(col, j)
            Next j
            a(i, col) = 0
            b(i) = b(i) - tmp * b(col)
        Next i
    Next col
    Dim x() As Variant
    ReDim x(n)
    For col = n To 1 Step -1
        tmp = b(col)
        For j = n To col + 1 Step -1
            tmp = tmp - x(j) * a(col, j)
        Next j
        x(col) = tmp / a(col, col)
    Next col
    gauss_eliminate = x
End Function
Public Sub main()
    a = [{1.00, 0.00, 0.00,  0.00,  0.00,   0.00; 1.00, 0.63, 0.39,  0.25,  0.16,   0.10; 1.00, 1.26, 1.58,  1.98,  2.49,   3.13; 1.00, 1.88, 3.55,  6.70, 12.62,  23.80; 1.00, 2.51, 6.32, 15.88, 39.90, 100.28; 1.00, 3.14, 9.87, 31.01, 97.41, 306.02}]
    b = [{-0.01, 0.61, 0.91,  0.99,  0.60,   0.02}]
    Dim s() As String, x() As Variant
    ReDim s(UBound(b)), x(UBound(b))
    Debug.Print "(";
    x = gauss_eliminate(a, b)
    For i = 1 To UBound(x)
        s(i) = CStr(x(i))
    Next i
    t = Join(s, ", ")
    Debug.Print t; ")"
End Sub




Ada: with Ada.Text_IO;
with Ada.Numerics.Generic_Real_Arrays;

procedure Gaussian_Eliminations is

   type Real is new Float;

   package Real_Arrays is
      new Ada.Numerics.Generic_Real_Arrays (Real);
   use Real_Arrays;

   function Gaussian_Elimination (A : in Real_Matrix;
                                  B : in Real_Vector) return Real_Vector
   is

      procedure Swap_Row (A        : in out Real_Matrix;
                          B        : in out Real_Vector;
                          R_1, R_2 : in     Integer)
      is
         Temp : Real;
      begin
         if R_1 = R_2 then return; end if;

         
         for Col in A'Range (1) loop
            Temp := A (R_1, Col);
            A (R_1, Col) := A (R_2, Col);
            A (R_2, Col) := Temp;
         end loop;

         
         Temp    := B (R_1);
         B (R_1) := B (R_2);
         B (R_2) := Temp;
      end Swap_Row;

      AC : Real_Matrix := A;
      BC : Real_Vector := B;
      X  : Real_Vector (A'Range (1)) := BC;
      Max, Tmp : Real;
      Max_Row  : Integer;
   begin
      if
        A'Length (1) /= A'Length (2) or
        A'Length (1) /= B'Length
      then
         raise Constraint_Error with "Dimensions do not match";
      end if;

      if
        A'First (1) /= A'First (2) or
        A'First (1) /= B'First
      then
         raise Constraint_Error with "First index must be same";
      end if;

      for Dia in Ac'Range (1) loop
         Max_Row := Dia;
         Max     := Ac (Dia, Dia);

         for Row in Dia + 1 .. Ac'Last (1) loop
            Tmp := abs (Ac (Row, Dia));
            if Tmp > Max then
               Max_Row := Row;
               Max     := Tmp;
            end if;
         end loop;
         Swap_Row (Ac, Bc, Dia, Max_Row);

         for Row in Dia + 1 .. Ac'Last (1) loop
            Tmp := Ac (Row, Dia) / Ac (Dia, Dia);
            for Col in Dia + 1 .. Ac'Last (1) loop
               Ac (Row, Col) := Ac (Row, Col) - Tmp * Ac (Dia, Col);
            end loop;
            Ac (Row, Dia) := 0.0;
            Bc (Row) := Bc (Row) - Tmp * Bc (Dia);
         end loop;
      end loop;

      for Row in reverse Ac'Range (1) loop
         Tmp := Bc (Row);
         for J in reverse Row + 1 .. Ac'Last (1) loop
            Tmp := Tmp - X (J) * Ac (Row, J);
         end loop;
         X (Row) := Tmp / Ac (Row, Row);
      end loop;

      return X;
   end Gaussian_Elimination;

   procedure Put (V : in Real_Vector) is
      use Ada.Text_IO;
      package Real_IO is
         new Ada.Text_IO.Float_IO (Real);
   begin
      Put ("[ ");
      for E of V loop
         Real_IO.Put (E, Exp => 0, Aft => 6);
         Put (" ");
      end loop;
      Put (" ]");
      New_Line;
   end Put;

   A : constant Real_Matrix :=
     ((1.00, 0.00, 0.00,  0.00,  0.00, 0.00),
      (1.00, 0.63, 0.39,  0.25,  0.16, 0.10),
      (1.00, 1.26, 1.58,  1.98,  2.49, 3.13),
      (1.00, 1.88, 3.55,  6.70, 12.62, 23.80),
      (1.00, 2.51, 6.32, 15.88, 39.90, 100.28),
      (1.00, 3.14, 9.87, 31.01, 97.41, 306.02));

   B : constant Real_Vector :=
     ( -0.01, 0.61, 0.91, 0.99, 0.60, 0.02 );

   X : constant Real_Vector := Gaussian_Elimination (A, B);
begin
   Put (X);
end Gaussian_Eliminations;