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

--                                                                          --

--                         GNAT RUN-TIME COMPONENTS                         --

--                                                                          --

--                     ADA.NUMERICS.GENERIC_REAL_ARRAYS                     --

--                                                                          --

--                                 S p e c                                  --

--                                                                          --

--            Copyright (C) 2009, 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 always inline these, the expense of the unconstrained returns

   --  can be avoided.

   pragma Inline_Always ("+");

   pragma Inline_Always ("-");

   pragma Inline_Always ("*");

   pragma Inline_Always ("/");

   pragma Inline_Always ("abs");

   pragma Inline_Always (Eigenvalues);

   pragma Inline_Always (Inverse);

   pragma Inline_Always (Solve);

   pragma Inline_Always (Transpose);

   pragma Inline_Always (Unit_Matrix);

   pragma Inline_Always (Unit_Vector);

end Ada.Numerics.Generic_Real_Arrays;