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------------------------------------------------------------------------------

--                                                                          --

--                         GNAT RUN-TIME COMPONENTS                         --

--                                                                          --

--       S Y S T E M . G E N E R I C _ A R R A Y _ O P E R A T I O N S      --

--                                                                          --

--                                 S p e c                                  --

--                                                                          --

--          Copyright (C) 2006-2011, Free Software Foundation, Inc.         --

--                                                                          --

-- GNAT is free software;  you can  redistribute it  and/or modify it under --

-- terms of the  GNU General Public License as published  by the Free Soft- --

-- ware  Foundation;  either version 3,  or (at your option) any later ver- --

-- sion.  GNAT is distributed in the hope that it will be useful, but WITH- --

-- OUT ANY WARRANTY;  without even the  implied warranty of MERCHANTABILITY --

-- or FITNESS FOR A PARTICULAR PURPOSE.                                     --

--                                                                          --

-- As a special exception under Section 7 of GPL version 3, you are granted --

-- additional permissions described in the GCC Runtime Library Exception,   --

-- version 3.1, as published by the Free Software Foundation.               --

--                                                                          --

-- You should have received a copy of the GNU General Public License and    --

-- a copy of the GCC Runtime Library Exception along with this program;     --

-- see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see    --

-- <http://www.gnu.org/licenses/>.                                          --

--                                                                          --

-- GNAT was originally developed  by the GNAT team at  New York University. --

-- Extensive contributions were provided by Ada Core Technologies Inc.      --

--                                                                          --

------------------------------------------------------------------------------

package System.Generic_Array_Operations is

pragma Pure (Generic_Array_Operations);

   ---------------------

   -- Back_Substitute --

   ---------------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

      with function "-" (Left, Right : Scalar) return Scalar is <>;

      with function "*" (Left, Right : Scalar) return Scalar is <>;

      with function "/" (Left, Right : Scalar) return Scalar is <>;

      with function Is_Non_Zero (X : Scalar) return Boolean is <>;

   procedure Back_Substitute (M, N : in out Matrix);

   --------------

   -- Diagonal --

   --------------

   generic

      type Scalar is private;

      type Vector is array (Integer range <>) of Scalar;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

   function Diagonal (A : Matrix) return Vector;

   -----------------------

   -- Forward_Eliminate --

   -----------------------

   --  Use elementary row operations to put square matrix M in row echolon

   --  form. Identical row operations are performed on matrix N, must have the

   --  same number of rows as M.

   generic

      type Scalar is private;

      type Real is digits <>;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

      with function "abs" (Right : Scalar) return Real'Base is <>;

      with function "-" (Left, Right : Scalar) return Scalar is <>;

      with function "*" (Left, Right : Scalar) return Scalar is <>;

      with function "/" (Left, Right : Scalar) return Scalar is <>;

      Zero : Scalar;

      One  : Scalar;

   procedure Forward_Eliminate

     (M   : in out Matrix;

      N   : in out Matrix;

      Det : out Scalar);

   --------------------------

   -- Square_Matrix_Length --

   --------------------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

   function Square_Matrix_Length (A : Matrix) return Natural;

   --  If A is non-square, raise Constraint_Error,  else return its dimension

   ----------------------------------

   -- Vector_Elementwise_Operation --

   ----------------------------------

   generic

      type X_Scalar is private;

      type Result_Scalar is private;

      type X_Vector is array (Integer range <>) of X_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      with function Operation (X : X_Scalar) return Result_Scalar;

   function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector;

   ----------------------------------

   -- Matrix_Elementwise_Operation --

   ----------------------------------

   generic

      type X_Scalar is private;

      type Result_Scalar is private;

      type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function Operation (X : X_Scalar) return Result_Scalar;

   function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix;

   -----------------------------------------

   -- Vector_Vector_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Vector is array (Integer range <>) of Left_Scalar;

      type Right_Vector is array (Integer range <>) of Right_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Vector_Vector_Elementwise_Operation

     (Left  : Left_Vector;

      Right : Right_Vector) return Result_Vector;

   ------------------------------------------------

   -- Vector_Vector_Scalar_Elementwise_Operation --

   ------------------------------------------------

   generic

      type X_Scalar is private;

      type Y_Scalar is private;

      type Z_Scalar is private;

      type Result_Scalar is private;

      type X_Vector is array (Integer range <>) of X_Scalar;

      type Y_Vector is array (Integer range <>) of Y_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      with function Operation

             (X : X_Scalar;

              Y : Y_Scalar;

              Z : Z_Scalar) return Result_Scalar;

   function Vector_Vector_Scalar_Elementwise_Operation

     (X : X_Vector;

      Y : Y_Vector;

      Z : Z_Scalar) return Result_Vector;

   -----------------------------------------

   -- Matrix_Matrix_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Matrix is array (Integer range <>, Integer range <>)

        of Left_Scalar;

      type Right_Matrix is array (Integer range <>, Integer range <>)

        of Right_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Matrix_Matrix_Elementwise_Operation

     (Left  : Left_Matrix;

      Right : Right_Matrix) return Result_Matrix;

   ------------------------------------------------

   -- Matrix_Matrix_Scalar_Elementwise_Operation --

   ------------------------------------------------

   generic

      type X_Scalar is private;

      type Y_Scalar is private;

      type Z_Scalar is private;

      type Result_Scalar is private;

      type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;

      type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function Operation

             (X : X_Scalar;

              Y : Y_Scalar;

              Z : Z_Scalar) return Result_Scalar;

   function Matrix_Matrix_Scalar_Elementwise_Operation

     (X : X_Matrix;

      Y : Y_Matrix;

      Z : Z_Scalar) return Result_Matrix;

   -----------------------------------------

   -- Vector_Scalar_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Vector is array (Integer range <>) of Left_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Vector_Scalar_Elementwise_Operation

     (Left  : Left_Vector;

      Right : Right_Scalar) return Result_Vector;

   -----------------------------------------

   -- Matrix_Scalar_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Matrix is array (Integer range <>, Integer range <>)

        of Left_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Matrix_Scalar_Elementwise_Operation

     (Left  : Left_Matrix;

      Right : Right_Scalar) return Result_Matrix;

   -----------------------------------------

   -- Scalar_Vector_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Right_Vector is array (Integer range <>) of Right_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Scalar_Vector_Elementwise_Operation

     (Left  : Left_Scalar;

      Right : Right_Vector) return Result_Vector;

   -----------------------------------------

   -- Scalar_Matrix_Elementwise_Operation --

   -----------------------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Right_Matrix is array (Integer range <>, Integer range <>)

        of Right_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function Operation

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar;

   function Scalar_Matrix_Elementwise_Operation

     (Left  : Left_Scalar;

      Right : Right_Matrix) return Result_Matrix;

   -------------------

   -- Inner_Product --

   -------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Vector is array (Integer range <>) of Left_Scalar;

      type Right_Vector is array (Integer range <>) of Right_Scalar;

      Zero : Result_Scalar;

      with function "*"

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar is <>;

      with function "+"

             (Left  : Result_Scalar;

              Right : Result_Scalar) return Result_Scalar is <>;

   function Inner_Product

     (Left  : Left_Vector;

      Right : Right_Vector) return Result_Scalar;

   -------------

   -- L2_Norm --

   -------------

   generic

      type X_Scalar is private;

      type Result_Real is digits <>;

      type X_Vector is array (Integer range <>) of X_Scalar;

      with function "abs" (Right : X_Scalar) return Result_Real is <>;

      with function Sqrt (X : Result_Real'Base) return Result_Real'Base is <>;

   function L2_Norm (X : X_Vector) return Result_Real'Base;

   -------------------

   -- Outer_Product --

   -------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Vector is array (Integer range <>) of Left_Scalar;

      type Right_Vector is array (Integer range <>) of Right_Scalar;

      type Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      with function "*"

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar is <>;

   function Outer_Product

     (Left  : Left_Vector;

      Right : Right_Vector) return Matrix;

   ---------------------------

   -- Matrix_Vector_Product --

   ---------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>)

        of Left_Scalar;

      type Right_Vector is array (Integer range <>) of Right_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      Zero : Result_Scalar;

      with function "*"

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar is <>;

      with function "+"

             (Left  : Result_Scalar;

              Right : Result_Scalar) return Result_Scalar is <>;

   function Matrix_Vector_Product

     (Left  : Matrix;

      Right : Right_Vector) return Result_Vector;

   ---------------------------

   -- Vector_Matrix_Product --

   ---------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Vector is array (Integer range <>) of Left_Scalar;

      type Matrix is array (Integer range <>, Integer range <>)

        of Right_Scalar;

      type Result_Vector is array (Integer range <>) of Result_Scalar;

      Zero : Result_Scalar;

      with function "*"

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar is <>;

      with function "+"

             (Left  : Result_Scalar;

              Right : Result_Scalar) return Result_Scalar is <>;

   function Vector_Matrix_Product

     (Left  : Left_Vector;

      Right : Matrix) return Result_Vector;

   ---------------------------

   -- Matrix_Matrix_Product --

   ---------------------------

   generic

      type Left_Scalar is private;

      type Right_Scalar is private;

      type Result_Scalar is private;

      type Left_Matrix is array (Integer range <>, Integer range <>)

        of Left_Scalar;

      type Right_Matrix is array (Integer range <>, Integer range <>)

        of Right_Scalar;

      type Result_Matrix is array (Integer range <>, Integer range <>)

        of Result_Scalar;

      Zero : Result_Scalar;

      with function "*"

             (Left  : Left_Scalar;

              Right : Right_Scalar) return Result_Scalar is <>;

      with function "+"

             (Left  : Result_Scalar;

              Right : Result_Scalar) return Result_Scalar is <>;

   function Matrix_Matrix_Product

     (Left  : Left_Matrix;

      Right : Right_Matrix) return Result_Matrix;

   ----------------------------

   -- Matrix_Vector_Solution --

   ----------------------------

   generic

      type Scalar is private;

      type Vector is array (Integer range <>) of Scalar;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

      with procedure Back_Substitute (M, N : in out Matrix) is <>;

      with procedure Forward_Eliminate

             (M   : in out Matrix;

              N   : in out Matrix;

              Det : out Scalar) is <>;

   function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector;

   ----------------------------

   -- Matrix_Matrix_Solution --

   ----------------------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

      with procedure Back_Substitute (M, N : in out Matrix) is <>;

      with procedure Forward_Eliminate

             (M   : in out Matrix;

              N   : in out Matrix;

              Det : out Scalar) is <>;

   function Matrix_Matrix_Solution (A : Matrix; X : Matrix) return Matrix;

   ----------

   -- Sqrt --

   ----------

   generic

      type Real is digits <>;

   function Sqrt (X : Real'Base) return Real'Base;

   -----------------

   -- Swap_Column --

   -----------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

   procedure Swap_Column (A : in out Matrix; Left, Right : Integer);

   ---------------

   -- Transpose --

   ---------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

   procedure Transpose (A : Matrix; R : out Matrix);

   -------------------------------

   -- Update_Vector_With_Vector --

   -------------------------------

   generic

      type X_Scalar is private;

      type Y_Scalar is private;

      type X_Vector is array (Integer range <>) of X_Scalar;

      type Y_Vector is array (Integer range <>) of Y_Scalar;

      with procedure Update (X : in out X_Scalar; Y : Y_Scalar);

   procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector);

   -------------------------------

   -- Update_Matrix_With_Matrix --

   -------------------------------

   generic

      type X_Scalar is private;

      type Y_Scalar is private;

      type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;

      type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;

      with procedure Update (X : in out X_Scalar; Y : Y_Scalar);

   procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix);

   -----------------

   -- Unit_Matrix --

   -----------------

   generic

      type Scalar is private;

      type Matrix is array (Integer range <>, Integer range <>) of Scalar;

      Zero : Scalar;

      One  : Scalar;

   function Unit_Matrix

     (Order   : Positive;

      First_1 : Integer := 1;

      First_2 : Integer := 1) return Matrix;

   -----------------

   -- Unit_Vector --

   -----------------

   generic

      type Scalar is private;

      type Vector is array (Integer range <>) of Scalar;

      Zero : Scalar;

      One  : Scalar;

   function Unit_Vector

     (Index : Integer;

      Order : Positive;

      First : Integer := 1) return Vector;

end System.Generic_Array_Operations;