------------------------------------------------------------------------------
--                                                                          --
--                         GNAT RUN-TIME COMPONENTS                         --
--                                                                          --
--                     ADA.NUMERICS.GENERIC_REAL_ARRAYS                     --
--                                                                          --
--                                 S p e c                                  --
--                                                                          --
--          Copyright (C) 2009-2020, Free Software Foundation, Inc.         --
--                                                                          --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. The copyright notice above, and the license provisions that follow --
-- apply solely to the  contents of the part following the private keyword. --
--                                                                          --
-- 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.      --
--                                                                          --
------------------------------------------------------------------------------

generic
   type Real is digits <>;
package Ada.Numerics.Generic_Real_Arrays is
   pragma Pure (Generic_Real_Arrays);

   --  Types

   type Real_Vector is array (Integer range <>) of Real'Base;
   type Real_Matrix is array (Integer range <>, Integer range <>) of Real'Base;

   --  Subprograms for Real_Vector types

   --  Real_Vector arithmetic operations

   function "+"   (Right : Real_Vector)       return Real_Vector;
   function "-"   (Right : Real_Vector)       return Real_Vector;
   function "abs" (Right : Real_Vector)       return Real_Vector;

   function "+"   (Left, Right : Real_Vector) return Real_Vector;
   function "-"   (Left, Right : Real_Vector) return Real_Vector;

   function "*"   (Left, Right : Real_Vector) return Real'Base;

   function "abs" (Right : Real_Vector)       return Real'Base;

   --  Real_Vector scaling operations

   function "*" (Left : Real'Base;   Right : Real_Vector) return Real_Vector;
   function "*" (Left : Real_Vector; Right : Real'Base)   return Real_Vector;
   function "/" (Left : Real_Vector; Right : Real'Base)   return Real_Vector;

   --  Other Real_Vector operations

   function Unit_Vector
     (Index : Integer;
      Order : Positive;
      First : Integer := 1) return Real_Vector;

   --  Subprograms for Real_Matrix types

   --  Real_Matrix arithmetic operations

   function "+"       (Right : Real_Matrix) return Real_Matrix;
   function "-"       (Right : Real_Matrix) return Real_Matrix;
   function "abs"     (Right : Real_Matrix) return Real_Matrix;
   function Transpose (X     : Real_Matrix) return Real_Matrix;

   function "+" (Left, Right : Real_Matrix) return Real_Matrix;
   function "-" (Left, Right : Real_Matrix) return Real_Matrix;
   function "*" (Left, Right : Real_Matrix) return Real_Matrix;

   function "*" (Left, Right : Real_Vector) return Real_Matrix;

   function "*" (Left : Real_Vector; Right : Real_Matrix) return Real_Vector;
   function "*" (Left : Real_Matrix; Right : Real_Vector) return Real_Vector;

   --  Real_Matrix scaling operations

   function "*" (Left : Real'Base;   Right : Real_Matrix) return Real_Matrix;
   function "*" (Left : Real_Matrix; Right : Real'Base)   return Real_Matrix;
   function "/" (Left : Real_Matrix; Right : Real'Base)   return Real_Matrix;

   --  Real_Matrix inversion and related operations

   function Solve (A : Real_Matrix; X : Real_Vector) return Real_Vector;
   function Solve (A, X : Real_Matrix) return Real_Matrix;
   function Inverse (A : Real_Matrix) return Real_Matrix;
   function Determinant (A : Real_Matrix) return Real'Base;

   --  Eigenvalues and vectors of a real symmetric matrix

   function Eigenvalues (A : Real_Matrix) return Real_Vector;

   procedure Eigensystem
     (A       : Real_Matrix;
      Values  : out Real_Vector;
      Vectors : out Real_Matrix);

   --  Other Real_Matrix operations

   function Unit_Matrix
     (Order   : Positive;
      First_1 : Integer := 1;
      First_2 : Integer := 1) return Real_Matrix;

private
   --  The following operations are either relatively simple compared to the
   --  expense of returning unconstrained arrays, or are just function wrappers
   --  calling procedures implementing the actual operation. By having the
   --  front end inline these, the expense of the unconstrained returns
   --  can be avoided.

   --  Note: We use an extended return statement in their implementation to
   --  allow the frontend to inline these functions.

   pragma Inline ("+");
   pragma Inline ("-");
   pragma Inline ("*");
   pragma Inline ("/");
   pragma Inline ("abs");
   pragma Inline (Eigenvalues);
   pragma Inline (Inverse);
   pragma Inline (Solve);
   pragma Inline (Transpose);
   pragma Inline (Unit_Matrix);
   pragma Inline (Unit_Vector);
end Ada.Numerics.Generic_Real_Arrays;
