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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 --
+-- --
+-- B o d y --
+-- --
+-- Copyright (C) 2006-2009, 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 body System.Generic_Array_Operations is
+
+ -- The local function Check_Unit_Last computes the index
+ -- of the last element returned by Unit_Vector or Unit_Matrix.
+ -- A separate function is needed to allow raising Constraint_Error
+ -- before declaring the function result variable. The result variable
+ -- needs to be declared first, to allow front-end inlining.
+
+ function Check_Unit_Last
+ (Index : Integer;
+ Order : Positive;
+ First : Integer) return Integer;
+ pragma Inline_Always (Check_Unit_Last);
+
+ function Square_Matrix_Length (A : Matrix) return Natural is
+ begin
+ if A'Length (1) /= A'Length (2) then
+ raise Constraint_Error with "matrix is not square";
+ end if;
+
+ return A'Length (1);
+ end Square_Matrix_Length;
+
+ ---------------------
+ -- Check_Unit_Last --
+ ---------------------
+
+ function Check_Unit_Last
+ (Index : Integer;
+ Order : Positive;
+ First : Integer) return Integer is
+ begin
+ -- Order the tests carefully to avoid overflow
+
+ if Index < First
+ or else First > Integer'Last - Order + 1
+ or else Index > First + (Order - 1)
+ then
+ raise Constraint_Error;
+ end if;
+
+ return First + (Order - 1);
+ end Check_Unit_Last;
+
+ -------------------
+ -- Inner_Product --
+ -------------------
+
+ function Inner_Product
+ (Left : Left_Vector;
+ Right : Right_Vector)
+ return Result_Scalar
+ is
+ R : Result_Scalar := Zero;
+
+ begin
+ if Left'Length /= Right'Length then
+ raise Constraint_Error with
+ "vectors are of different length in inner product";
+ end if;
+
+ for J in Left'Range loop
+ R := R + Left (J) * Right (J - Left'First + Right'First);
+ end loop;
+
+ return R;
+ end Inner_Product;
+
+ ----------------------------------
+ -- Matrix_Elementwise_Operation --
+ ----------------------------------
+
+ function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix is
+ R : Result_Matrix (X'Range (1), X'Range (2));
+
+ begin
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) := Operation (X (J, K));
+ end loop;
+ end loop;
+
+ return R;
+ end Matrix_Elementwise_Operation;
+
+ ----------------------------------
+ -- Vector_Elementwise_Operation --
+ ----------------------------------
+
+ function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector is
+ R : Result_Vector (X'Range);
+
+ begin
+ for J in R'Range loop
+ R (J) := Operation (X (J));
+ end loop;
+
+ return R;
+ end Vector_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Matrix_Matrix_Elementwise_Operation --
+ -----------------------------------------
+
+ function Matrix_Matrix_Elementwise_Operation
+ (Left : Left_Matrix;
+ Right : Right_Matrix)
+ return Result_Matrix
+ is
+ R : Result_Matrix (Left'Range (1), Left'Range (2));
+ begin
+ if Left'Length (1) /= Right'Length (1)
+ or else Left'Length (2) /= Right'Length (2)
+ then
+ raise Constraint_Error with
+ "matrices are of different dimension in elementwise operation";
+ end if;
+
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) :=
+ Operation
+ (Left (J, K),
+ Right
+ (J - R'First (1) + Right'First (1),
+ K - R'First (2) + Right'First (2)));
+ end loop;
+ end loop;
+
+ return R;
+ end Matrix_Matrix_Elementwise_Operation;
+
+ ------------------------------------------------
+ -- Matrix_Matrix_Scalar_Elementwise_Operation --
+ ------------------------------------------------
+
+ function Matrix_Matrix_Scalar_Elementwise_Operation
+ (X : X_Matrix;
+ Y : Y_Matrix;
+ Z : Z_Scalar) return Result_Matrix
+ is
+ R : Result_Matrix (X'Range (1), X'Range (2));
+
+ begin
+ if X'Length (1) /= Y'Length (1)
+ or else X'Length (2) /= Y'Length (2)
+ then
+ raise Constraint_Error with
+ "matrices are of different dimension in elementwise operation";
+ end if;
+
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) :=
+ Operation
+ (X (J, K),
+ Y (J - R'First (1) + Y'First (1),
+ K - R'First (2) + Y'First (2)),
+ Z);
+ end loop;
+ end loop;
+
+ return R;
+ end Matrix_Matrix_Scalar_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Vector_Vector_Elementwise_Operation --
+ -----------------------------------------
+
+ function Vector_Vector_Elementwise_Operation
+ (Left : Left_Vector;
+ Right : Right_Vector) return Result_Vector
+ is
+ R : Result_Vector (Left'Range);
+
+ begin
+ if Left'Length /= Right'Length then
+ raise Constraint_Error with
+ "vectors are of different length in elementwise operation";
+ end if;
+
+ for J in R'Range loop
+ R (J) := Operation (Left (J), Right (J - R'First + Right'First));
+ end loop;
+
+ return R;
+ end Vector_Vector_Elementwise_Operation;
+
+ ------------------------------------------------
+ -- Vector_Vector_Scalar_Elementwise_Operation --
+ ------------------------------------------------
+
+ function Vector_Vector_Scalar_Elementwise_Operation
+ (X : X_Vector;
+ Y : Y_Vector;
+ Z : Z_Scalar) return Result_Vector
+ is
+ R : Result_Vector (X'Range);
+
+ begin
+ if X'Length /= Y'Length then
+ raise Constraint_Error with
+ "vectors are of different length in elementwise operation";
+ end if;
+
+ for J in R'Range loop
+ R (J) := Operation (X (J), Y (J - X'First + Y'First), Z);
+ end loop;
+
+ return R;
+ end Vector_Vector_Scalar_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Matrix_Scalar_Elementwise_Operation --
+ -----------------------------------------
+
+ function Matrix_Scalar_Elementwise_Operation
+ (Left : Left_Matrix;
+ Right : Right_Scalar) return Result_Matrix
+ is
+ R : Result_Matrix (Left'Range (1), Left'Range (2));
+
+ begin
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) := Operation (Left (J, K), Right);
+ end loop;
+ end loop;
+
+ return R;
+ end Matrix_Scalar_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Vector_Scalar_Elementwise_Operation --
+ -----------------------------------------
+
+ function Vector_Scalar_Elementwise_Operation
+ (Left : Left_Vector;
+ Right : Right_Scalar) return Result_Vector
+ is
+ R : Result_Vector (Left'Range);
+
+ begin
+ for J in R'Range loop
+ R (J) := Operation (Left (J), Right);
+ end loop;
+
+ return R;
+ end Vector_Scalar_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Scalar_Matrix_Elementwise_Operation --
+ -----------------------------------------
+
+ function Scalar_Matrix_Elementwise_Operation
+ (Left : Left_Scalar;
+ Right : Right_Matrix) return Result_Matrix
+ is
+ R : Result_Matrix (Right'Range (1), Right'Range (2));
+
+ begin
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) := Operation (Left, Right (J, K));
+ end loop;
+ end loop;
+
+ return R;
+ end Scalar_Matrix_Elementwise_Operation;
+
+ -----------------------------------------
+ -- Scalar_Vector_Elementwise_Operation --
+ -----------------------------------------
+
+ function Scalar_Vector_Elementwise_Operation
+ (Left : Left_Scalar;
+ Right : Right_Vector) return Result_Vector
+ is
+ R : Result_Vector (Right'Range);
+
+ begin
+ for J in R'Range loop
+ R (J) := Operation (Left, Right (J));
+ end loop;
+
+ return R;
+ end Scalar_Vector_Elementwise_Operation;
+
+ ---------------------------
+ -- Matrix_Matrix_Product --
+ ---------------------------
+
+ function Matrix_Matrix_Product
+ (Left : Left_Matrix;
+ Right : Right_Matrix) return Result_Matrix
+ is
+ R : Result_Matrix (Left'Range (1), Right'Range (2));
+
+ begin
+ if Left'Length (2) /= Right'Length (1) then
+ raise Constraint_Error with
+ "incompatible dimensions in matrix multiplication";
+ end if;
+
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ declare
+ S : Result_Scalar := Zero;
+ begin
+ for M in Left'Range (2) loop
+ S := S + Left (J, M)
+ * Right (M - Left'First (2) + Right'First (1), K);
+ end loop;
+
+ R (J, K) := S;
+ end;
+ end loop;
+ end loop;
+
+ return R;
+ end Matrix_Matrix_Product;
+
+ ---------------------------
+ -- Matrix_Vector_Product --
+ ---------------------------
+
+ function Matrix_Vector_Product
+ (Left : Matrix;
+ Right : Right_Vector) return Result_Vector
+ is
+ R : Result_Vector (Left'Range (1));
+
+ begin
+ if Left'Length (2) /= Right'Length then
+ raise Constraint_Error with
+ "incompatible dimensions in matrix-vector multiplication";
+ end if;
+
+ for J in Left'Range (1) loop
+ declare
+ S : Result_Scalar := Zero;
+ begin
+ for K in Left'Range (2) loop
+ S := S + Left (J, K) * Right (K - Left'First (2) + Right'First);
+ end loop;
+
+ R (J) := S;
+ end;
+ end loop;
+
+ return R;
+ end Matrix_Vector_Product;
+
+ -------------------
+ -- Outer_Product --
+ -------------------
+
+ function Outer_Product
+ (Left : Left_Vector;
+ Right : Right_Vector) return Matrix
+ is
+ R : Matrix (Left'Range, Right'Range);
+
+ begin
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) := Left (J) * Right (K);
+ end loop;
+ end loop;
+
+ return R;
+ end Outer_Product;
+
+ ---------------
+ -- Transpose --
+ ---------------
+
+ procedure Transpose (A : Matrix; R : out Matrix) is
+ begin
+ for J in R'Range (1) loop
+ for K in R'Range (2) loop
+ R (J, K) := A (K - R'First (2) + A'First (1),
+ J - R'First (1) + A'First (2));
+ end loop;
+ end loop;
+ end Transpose;
+
+ -------------------------------
+ -- Update_Matrix_With_Matrix --
+ -------------------------------
+
+ procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix) is
+ begin
+ if X'Length (1) /= Y'Length (1)
+ or else X'Length (2) /= Y'Length (2)
+ then
+ raise Constraint_Error with
+ "matrices are of different dimension in update operation";
+ end if;
+
+ for J in X'Range (1) loop
+ for K in X'Range (2) loop
+ Update (X (J, K), Y (J - X'First (1) + Y'First (1),
+ K - X'First (2) + Y'First (2)));
+ end loop;
+ end loop;
+ end Update_Matrix_With_Matrix;
+
+ -------------------------------
+ -- Update_Vector_With_Vector --
+ -------------------------------
+
+ procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector) is
+ begin
+ if X'Length /= Y'Length then
+ raise Constraint_Error with
+ "vectors are of different length in update operation";
+ end if;
+
+ for J in X'Range loop
+ Update (X (J), Y (J - X'First + Y'First));
+ end loop;
+ end Update_Vector_With_Vector;
+
+ -----------------
+ -- Unit_Matrix --
+ -----------------
+
+ function Unit_Matrix
+ (Order : Positive;
+ First_1 : Integer := 1;
+ First_2 : Integer := 1) return Matrix
+ is
+ R : Matrix (First_1 .. Check_Unit_Last (First_1, Order, First_1),
+ First_2 .. Check_Unit_Last (First_2, Order, First_2));
+
+ begin
+ R := (others => (others => Zero));
+
+ for J in 0 .. Order - 1 loop
+ R (First_1 + J, First_2 + J) := One;
+ end loop;
+
+ return R;
+ end Unit_Matrix;
+
+ -----------------
+ -- Unit_Vector --
+ -----------------
+
+ function Unit_Vector
+ (Index : Integer;
+ Order : Positive;
+ First : Integer := 1) return Vector
+ is
+ R : Vector (First .. Check_Unit_Last (Index, Order, First));
+ begin
+ R := (others => Zero);
+ R (Index) := One;
+ return R;
+ end Unit_Vector;
+
+ ---------------------------
+ -- Vector_Matrix_Product --
+ ---------------------------
+
+ function Vector_Matrix_Product
+ (Left : Left_Vector;
+ Right : Matrix) return Result_Vector
+ is
+ R : Result_Vector (Right'Range (2));
+
+ begin
+ if Left'Length /= Right'Length (2) then
+ raise Constraint_Error with
+ "incompatible dimensions in vector-matrix multiplication";
+ end if;
+
+ for J in Right'Range (2) loop
+ declare
+ S : Result_Scalar := Zero;
+
+ begin
+ for K in Right'Range (1) loop
+ S := S + Left (J - Right'First (1) + Left'First) * Right (K, J);
+ end loop;
+
+ R (J) := S;
+ end;
+ end loop;
+
+ return R;
+ end Vector_Matrix_Product;
+
+end System.Generic_Array_Operations;