501 lines
18 KiB
Ada
501 lines
18 KiB
Ada
------------------------------------------------------------------------------
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-- --
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-- GNAT RUN-TIME COMPONENTS --
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-- --
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-- 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 --
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-- --
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-- S p e c --
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-- --
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-- Copyright (C) 2006-2011, Free Software Foundation, Inc. --
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-- --
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-- GNAT is free software; you can redistribute it and/or modify it under --
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-- terms of the GNU General Public License as published by the Free Soft- --
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-- ware Foundation; either version 3, or (at your option) any later ver- --
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-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
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-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
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-- or FITNESS FOR A PARTICULAR PURPOSE. --
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-- --
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-- As a special exception under Section 7 of GPL version 3, you are granted --
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-- additional permissions described in the GCC Runtime Library Exception, --
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-- version 3.1, as published by the Free Software Foundation. --
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-- --
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-- You should have received a copy of the GNU General Public License and --
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-- a copy of the GCC Runtime Library Exception along with this program; --
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-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
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-- <http://www.gnu.org/licenses/>. --
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-- --
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-- GNAT was originally developed by the GNAT team at New York University. --
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-- Extensive contributions were provided by Ada Core Technologies Inc. --
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-- --
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------------------------------------------------------------------------------
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package System.Generic_Array_Operations is
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pragma Pure (Generic_Array_Operations);
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---------------------
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-- Back_Substitute --
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---------------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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with function "-" (Left, Right : Scalar) return Scalar is <>;
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with function "*" (Left, Right : Scalar) return Scalar is <>;
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with function "/" (Left, Right : Scalar) return Scalar is <>;
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with function Is_Non_Zero (X : Scalar) return Boolean is <>;
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procedure Back_Substitute (M, N : in out Matrix);
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--------------
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-- Diagonal --
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--------------
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generic
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type Scalar is private;
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type Vector is array (Integer range <>) of Scalar;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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function Diagonal (A : Matrix) return Vector;
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-----------------------
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-- Forward_Eliminate --
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-----------------------
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-- Use elementary row operations to put square matrix M in row echolon
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-- form. Identical row operations are performed on matrix N, must have the
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-- same number of rows as M.
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generic
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type Scalar is private;
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type Real is digits <>;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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with function "abs" (Right : Scalar) return Real'Base is <>;
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with function "-" (Left, Right : Scalar) return Scalar is <>;
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with function "*" (Left, Right : Scalar) return Scalar is <>;
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with function "/" (Left, Right : Scalar) return Scalar is <>;
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Zero : Scalar;
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One : Scalar;
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procedure Forward_Eliminate
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(M : in out Matrix;
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N : in out Matrix;
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Det : out Scalar);
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--------------------------
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-- Square_Matrix_Length --
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--------------------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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function Square_Matrix_Length (A : Matrix) return Natural;
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-- If A is non-square, raise Constraint_Error, else return its dimension
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----------------------------------
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-- Vector_Elementwise_Operation --
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----------------------------------
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generic
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type X_Scalar is private;
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type Result_Scalar is private;
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type X_Vector is array (Integer range <>) of X_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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with function Operation (X : X_Scalar) return Result_Scalar;
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function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector;
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----------------------------------
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-- Matrix_Elementwise_Operation --
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----------------------------------
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generic
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type X_Scalar is private;
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type Result_Scalar is private;
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type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function Operation (X : X_Scalar) return Result_Scalar;
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function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix;
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-----------------------------------------
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-- Vector_Vector_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Vector is array (Integer range <>) of Left_Scalar;
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type Right_Vector is array (Integer range <>) of Right_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Vector_Vector_Elementwise_Operation
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(Left : Left_Vector;
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Right : Right_Vector) return Result_Vector;
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------------------------------------------------
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-- Vector_Vector_Scalar_Elementwise_Operation --
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------------------------------------------------
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generic
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type X_Scalar is private;
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type Y_Scalar is private;
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type Z_Scalar is private;
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type Result_Scalar is private;
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type X_Vector is array (Integer range <>) of X_Scalar;
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type Y_Vector is array (Integer range <>) of Y_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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with function Operation
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(X : X_Scalar;
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Y : Y_Scalar;
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Z : Z_Scalar) return Result_Scalar;
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function Vector_Vector_Scalar_Elementwise_Operation
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(X : X_Vector;
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Y : Y_Vector;
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Z : Z_Scalar) return Result_Vector;
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-----------------------------------------
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-- Matrix_Matrix_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Matrix is array (Integer range <>, Integer range <>)
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of Left_Scalar;
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type Right_Matrix is array (Integer range <>, Integer range <>)
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of Right_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Matrix_Matrix_Elementwise_Operation
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(Left : Left_Matrix;
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Right : Right_Matrix) return Result_Matrix;
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------------------------------------------------
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-- Matrix_Matrix_Scalar_Elementwise_Operation --
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------------------------------------------------
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generic
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type X_Scalar is private;
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type Y_Scalar is private;
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type Z_Scalar is private;
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type Result_Scalar is private;
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type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function Operation
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(X : X_Scalar;
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Y : Y_Scalar;
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Z : Z_Scalar) return Result_Scalar;
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function Matrix_Matrix_Scalar_Elementwise_Operation
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(X : X_Matrix;
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Y : Y_Matrix;
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Z : Z_Scalar) return Result_Matrix;
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-----------------------------------------
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-- Vector_Scalar_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Vector is array (Integer range <>) of Left_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Vector_Scalar_Elementwise_Operation
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(Left : Left_Vector;
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Right : Right_Scalar) return Result_Vector;
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-----------------------------------------
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-- Matrix_Scalar_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Matrix is array (Integer range <>, Integer range <>)
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of Left_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Matrix_Scalar_Elementwise_Operation
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(Left : Left_Matrix;
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Right : Right_Scalar) return Result_Matrix;
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-----------------------------------------
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-- Scalar_Vector_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Right_Vector is array (Integer range <>) of Right_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Scalar_Vector_Elementwise_Operation
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(Left : Left_Scalar;
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Right : Right_Vector) return Result_Vector;
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-----------------------------------------
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-- Scalar_Matrix_Elementwise_Operation --
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-----------------------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Right_Matrix is array (Integer range <>, Integer range <>)
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of Right_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function Operation
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar;
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function Scalar_Matrix_Elementwise_Operation
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(Left : Left_Scalar;
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Right : Right_Matrix) return Result_Matrix;
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-------------------
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-- Inner_Product --
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-------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Vector is array (Integer range <>) of Left_Scalar;
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type Right_Vector is array (Integer range <>) of Right_Scalar;
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Zero : Result_Scalar;
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with function "*"
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar is <>;
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with function "+"
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(Left : Result_Scalar;
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Right : Result_Scalar) return Result_Scalar is <>;
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function Inner_Product
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(Left : Left_Vector;
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Right : Right_Vector) return Result_Scalar;
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-------------
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-- L2_Norm --
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-------------
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generic
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type X_Scalar is private;
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type Result_Real is digits <>;
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type X_Vector is array (Integer range <>) of X_Scalar;
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with function "abs" (Right : X_Scalar) return Result_Real is <>;
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with function Sqrt (X : Result_Real'Base) return Result_Real'Base is <>;
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function L2_Norm (X : X_Vector) return Result_Real'Base;
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-------------------
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-- Outer_Product --
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-------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Vector is array (Integer range <>) of Left_Scalar;
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type Right_Vector is array (Integer range <>) of Right_Scalar;
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type Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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with function "*"
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar is <>;
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function Outer_Product
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(Left : Left_Vector;
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Right : Right_Vector) return Matrix;
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---------------------------
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-- Matrix_Vector_Product --
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---------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>)
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of Left_Scalar;
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type Right_Vector is array (Integer range <>) of Right_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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Zero : Result_Scalar;
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with function "*"
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar is <>;
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with function "+"
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(Left : Result_Scalar;
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Right : Result_Scalar) return Result_Scalar is <>;
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function Matrix_Vector_Product
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(Left : Matrix;
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Right : Right_Vector) return Result_Vector;
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---------------------------
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-- Vector_Matrix_Product --
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---------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Vector is array (Integer range <>) of Left_Scalar;
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type Matrix is array (Integer range <>, Integer range <>)
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of Right_Scalar;
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type Result_Vector is array (Integer range <>) of Result_Scalar;
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Zero : Result_Scalar;
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with function "*"
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar is <>;
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with function "+"
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(Left : Result_Scalar;
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Right : Result_Scalar) return Result_Scalar is <>;
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function Vector_Matrix_Product
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(Left : Left_Vector;
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Right : Matrix) return Result_Vector;
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---------------------------
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-- Matrix_Matrix_Product --
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---------------------------
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generic
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type Left_Scalar is private;
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type Right_Scalar is private;
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type Result_Scalar is private;
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type Left_Matrix is array (Integer range <>, Integer range <>)
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of Left_Scalar;
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type Right_Matrix is array (Integer range <>, Integer range <>)
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of Right_Scalar;
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type Result_Matrix is array (Integer range <>, Integer range <>)
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of Result_Scalar;
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Zero : Result_Scalar;
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with function "*"
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(Left : Left_Scalar;
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Right : Right_Scalar) return Result_Scalar is <>;
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with function "+"
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(Left : Result_Scalar;
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Right : Result_Scalar) return Result_Scalar is <>;
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function Matrix_Matrix_Product
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(Left : Left_Matrix;
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Right : Right_Matrix) return Result_Matrix;
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----------------------------
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-- Matrix_Vector_Solution --
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----------------------------
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generic
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type Scalar is private;
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type Vector is array (Integer range <>) of Scalar;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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with procedure Back_Substitute (M, N : in out Matrix) is <>;
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with procedure Forward_Eliminate
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(M : in out Matrix;
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N : in out Matrix;
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Det : out Scalar) is <>;
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function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector;
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----------------------------
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-- Matrix_Matrix_Solution --
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----------------------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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with procedure Back_Substitute (M, N : in out Matrix) is <>;
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with procedure Forward_Eliminate
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(M : in out Matrix;
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N : in out Matrix;
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Det : out Scalar) is <>;
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function Matrix_Matrix_Solution (A : Matrix; X : Matrix) return Matrix;
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----------
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-- Sqrt --
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----------
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generic
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type Real is digits <>;
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function Sqrt (X : Real'Base) return Real'Base;
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-----------------
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-- Swap_Column --
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-----------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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procedure Swap_Column (A : in out Matrix; Left, Right : Integer);
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---------------
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-- Transpose --
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---------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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procedure Transpose (A : Matrix; R : out Matrix);
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-------------------------------
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-- Update_Vector_With_Vector --
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-------------------------------
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generic
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type X_Scalar is private;
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type Y_Scalar is private;
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type X_Vector is array (Integer range <>) of X_Scalar;
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type Y_Vector is array (Integer range <>) of Y_Scalar;
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with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
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procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector);
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-------------------------------
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-- Update_Matrix_With_Matrix --
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-------------------------------
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generic
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type X_Scalar is private;
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type Y_Scalar is private;
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type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
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type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
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with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
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procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix);
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-----------------
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-- Unit_Matrix --
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-----------------
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generic
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type Scalar is private;
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type Matrix is array (Integer range <>, Integer range <>) of Scalar;
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Zero : Scalar;
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One : Scalar;
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function Unit_Matrix
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(Order : Positive;
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First_1 : Integer := 1;
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First_2 : Integer := 1) return Matrix;
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-----------------
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-- Unit_Vector --
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-----------------
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generic
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type Scalar is private;
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type Vector is array (Integer range <>) of Scalar;
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Zero : Scalar;
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One : Scalar;
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function Unit_Vector
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(Index : Integer;
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Order : Positive;
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First : Integer := 1) return Vector;
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end System.Generic_Array_Operations;
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