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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;
|
