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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;

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[/] [openrisc/] [trunk/] [gnu-stable/] [gcc-4.5.1/] [gcc/] [ada/] [s-gearop.adb] - Blame information for rev 847

Line No.	Rev	Author	Line
1	281	jeremybenn	`------------------------------------------------------------------------------`
2			`-- --`
3			`-- GNAT RUN-TIME COMPONENTS --`
4			`-- --`
5			`-- 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 --`
6			`-- --`
7			`-- B o d y --`
8			`-- --`
9			`-- Copyright (C) 2006-2009, Free Software Foundation, Inc. --`
10			`-- --`
11			`-- GNAT is free software; you can redistribute it and/or modify it under --`
12			`-- terms of the GNU General Public License as published by the Free Soft- --`
13			`-- ware Foundation; either version 3, or (at your option) any later ver- --`
14			`-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --`
15			`-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --`
16			`-- or FITNESS FOR A PARTICULAR PURPOSE. --`
17			`-- --`
18			`-- As a special exception under Section 7 of GPL version 3, you are granted --`
19			`-- additional permissions described in the GCC Runtime Library Exception, --`
20			`-- version 3.1, as published by the Free Software Foundation. --`
21			`-- --`
22			`-- You should have received a copy of the GNU General Public License and --`
23			`-- a copy of the GCC Runtime Library Exception along with this program; --`
24			`-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --`
25			`-- <http://www.gnu.org/licenses/>. --`
26			`-- --`
27			`-- GNAT was originally developed by the GNAT team at New York University. --`
28			`-- Extensive contributions were provided by Ada Core Technologies Inc. --`
29			`-- --`
30			`------------------------------------------------------------------------------`
31
32			`package body System.Generic_Array_Operations is`
33
34			`-- The local function Check_Unit_Last computes the index`
35			`-- of the last element returned by Unit_Vector or Unit_Matrix.`
36			`-- A separate function is needed to allow raising Constraint_Error`
37			`-- before declaring the function result variable. The result variable`
38			`-- needs to be declared first, to allow front-end inlining.`
39
40			`function Check_Unit_Last`
41			`(Index : Integer;`
42			`Order : Positive;`
43			`First : Integer) return Integer;`
44			`pragma Inline_Always (Check_Unit_Last);`
45
46			`function Square_Matrix_Length (A : Matrix) return Natural is`
47			`begin`
48			`if A'Length (1) /= A'Length (2) then`
49			`raise Constraint_Error with "matrix is not square";`
50			`end if;`
51
52			`return A'Length (1);`
53			`end Square_Matrix_Length;`
54
55			`---------------------`
56			`-- Check_Unit_Last --`
57			`---------------------`
58
59			`function Check_Unit_Last`
60			`(Index : Integer;`
61			`Order : Positive;`
62			`First : Integer) return Integer is`
63			`begin`
64			`-- Order the tests carefully to avoid overflow`
65
66			`if Index < First`
67			`or else First > Integer'Last - Order + 1`
68			`or else Index > First + (Order - 1)`
69			`then`
70			`raise Constraint_Error;`
71			`end if;`
72
73			`return First + (Order - 1);`
74			`end Check_Unit_Last;`
75
76			`-------------------`
77			`-- Inner_Product --`
78			`-------------------`
79
80			`function Inner_Product`
81			`(Left : Left_Vector;`
82			`Right : Right_Vector)`
83			`return Result_Scalar`
84			`is`
85			`R : Result_Scalar := Zero;`
86
87			`begin`
88			`if Left'Length /= Right'Length then`
89			`raise Constraint_Error with`
90			`"vectors are of different length in inner product";`
91			`end if;`
92
93			`for J in Left'Range loop`
94			`R := R + Left (J) * Right (J - Left'First + Right'First);`
95			`end loop;`
96
97			`return R;`
98			`end Inner_Product;`
99
100			`----------------------------------`
101			`-- Matrix_Elementwise_Operation --`
102			`----------------------------------`
103
104			`function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix is`
105			`R : Result_Matrix (X'Range (1), X'Range (2));`
106
107			`begin`
108			`for J in R'Range (1) loop`
109			`for K in R'Range (2) loop`
110			`R (J, K) := Operation (X (J, K));`
111			`end loop;`
112			`end loop;`
113
114			`return R;`
115			`end Matrix_Elementwise_Operation;`
116
117			`----------------------------------`
118			`-- Vector_Elementwise_Operation --`
119			`----------------------------------`
120
121			`function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector is`
122			`R : Result_Vector (X'Range);`
123
124			`begin`
125			`for J in R'Range loop`
126			`R (J) := Operation (X (J));`
127			`end loop;`
128
129			`return R;`
130			`end Vector_Elementwise_Operation;`
131
132			`-----------------------------------------`
133			`-- Matrix_Matrix_Elementwise_Operation --`
134			`-----------------------------------------`
135
136			`function Matrix_Matrix_Elementwise_Operation`
137			`(Left : Left_Matrix;`
138			`Right : Right_Matrix)`
139			`return Result_Matrix`
140			`is`
141			`R : Result_Matrix (Left'Range (1), Left'Range (2));`
142			`begin`
143			`if Left'Length (1) /= Right'Length (1)`
144			`or else Left'Length (2) /= Right'Length (2)`
145			`then`
146			`raise Constraint_Error with`
147			`"matrices are of different dimension in elementwise operation";`
148			`end if;`
149
150			`for J in R'Range (1) loop`
151			`for K in R'Range (2) loop`
152			`R (J, K) :=`
153			`Operation`
154			`(Left (J, K),`
155			`Right`
156			`(J - R'First (1) + Right'First (1),`
157			`K - R'First (2) + Right'First (2)));`
158			`end loop;`
159			`end loop;`
160
161			`return R;`
162			`end Matrix_Matrix_Elementwise_Operation;`
163
164			`------------------------------------------------`
165			`-- Matrix_Matrix_Scalar_Elementwise_Operation --`
166			`------------------------------------------------`
167
168			`function Matrix_Matrix_Scalar_Elementwise_Operation`
169			`(X : X_Matrix;`
170			`Y : Y_Matrix;`
171			`Z : Z_Scalar) return Result_Matrix`
172			`is`
173			`R : Result_Matrix (X'Range (1), X'Range (2));`
174
175			`begin`
176			`if X'Length (1) /= Y'Length (1)`
177			`or else X'Length (2) /= Y'Length (2)`
178			`then`
179			`raise Constraint_Error with`
180			`"matrices are of different dimension in elementwise operation";`
181			`end if;`
182
183			`for J in R'Range (1) loop`
184			`for K in R'Range (2) loop`
185			`R (J, K) :=`
186			`Operation`
187			`(X (J, K),`
188			`Y (J - R'First (1) + Y'First (1),`
189			`K - R'First (2) + Y'First (2)),`
190			`Z);`
191			`end loop;`
192			`end loop;`
193
194			`return R;`
195			`end Matrix_Matrix_Scalar_Elementwise_Operation;`
196
197			`-----------------------------------------`
198			`-- Vector_Vector_Elementwise_Operation --`
199			`-----------------------------------------`
200
201			`function Vector_Vector_Elementwise_Operation`
202			`(Left : Left_Vector;`
203			`Right : Right_Vector) return Result_Vector`
204			`is`
205			`R : Result_Vector (Left'Range);`
206
207			`begin`
208			`if Left'Length /= Right'Length then`
209			`raise Constraint_Error with`
210			`"vectors are of different length in elementwise operation";`
211			`end if;`
212
213			`for J in R'Range loop`
214			`R (J) := Operation (Left (J), Right (J - R'First + Right'First));`
215			`end loop;`
216
217			`return R;`
218			`end Vector_Vector_Elementwise_Operation;`
219
220			`------------------------------------------------`
221			`-- Vector_Vector_Scalar_Elementwise_Operation --`
222			`------------------------------------------------`
223
224			`function Vector_Vector_Scalar_Elementwise_Operation`
225			`(X : X_Vector;`
226			`Y : Y_Vector;`
227			`Z : Z_Scalar) return Result_Vector`
228			`is`
229			`R : Result_Vector (X'Range);`
230
231			`begin`
232			`if X'Length /= Y'Length then`
233			`raise Constraint_Error with`
234			`"vectors are of different length in elementwise operation";`
235			`end if;`
236
237			`for J in R'Range loop`
238			`R (J) := Operation (X (J), Y (J - X'First + Y'First), Z);`
239			`end loop;`
240
241			`return R;`
242			`end Vector_Vector_Scalar_Elementwise_Operation;`
243
244			`-----------------------------------------`
245			`-- Matrix_Scalar_Elementwise_Operation --`
246			`-----------------------------------------`
247
248			`function Matrix_Scalar_Elementwise_Operation`
249			`(Left : Left_Matrix;`
250			`Right : Right_Scalar) return Result_Matrix`
251			`is`
252			`R : Result_Matrix (Left'Range (1), Left'Range (2));`
253
254			`begin`
255			`for J in R'Range (1) loop`
256			`for K in R'Range (2) loop`
257			`R (J, K) := Operation (Left (J, K), Right);`
258			`end loop;`
259			`end loop;`
260
261			`return R;`
262			`end Matrix_Scalar_Elementwise_Operation;`
263
264			`-----------------------------------------`
265			`-- Vector_Scalar_Elementwise_Operation --`
266			`-----------------------------------------`
267
268			`function Vector_Scalar_Elementwise_Operation`
269			`(Left : Left_Vector;`
270			`Right : Right_Scalar) return Result_Vector`
271			`is`
272			`R : Result_Vector (Left'Range);`
273
274			`begin`
275			`for J in R'Range loop`
276			`R (J) := Operation (Left (J), Right);`
277			`end loop;`
278
279			`return R;`
280			`end Vector_Scalar_Elementwise_Operation;`
281
282			`-----------------------------------------`
283			`-- Scalar_Matrix_Elementwise_Operation --`
284			`-----------------------------------------`
285
286			`function Scalar_Matrix_Elementwise_Operation`
287			`(Left : Left_Scalar;`
288			`Right : Right_Matrix) return Result_Matrix`
289			`is`
290			`R : Result_Matrix (Right'Range (1), Right'Range (2));`
291
292			`begin`
293			`for J in R'Range (1) loop`
294			`for K in R'Range (2) loop`
295			`R (J, K) := Operation (Left, Right (J, K));`
296			`end loop;`
297			`end loop;`
298
299			`return R;`
300			`end Scalar_Matrix_Elementwise_Operation;`
301
302			`-----------------------------------------`
303			`-- Scalar_Vector_Elementwise_Operation --`
304			`-----------------------------------------`
305
306			`function Scalar_Vector_Elementwise_Operation`
307			`(Left : Left_Scalar;`
308			`Right : Right_Vector) return Result_Vector`
309			`is`
310			`R : Result_Vector (Right'Range);`
311
312			`begin`
313			`for J in R'Range loop`
314			`R (J) := Operation (Left, Right (J));`
315			`end loop;`
316
317			`return R;`
318			`end Scalar_Vector_Elementwise_Operation;`
319
320			`---------------------------`
321			`-- Matrix_Matrix_Product --`
322			`---------------------------`
323
324			`function Matrix_Matrix_Product`
325			`(Left : Left_Matrix;`
326			`Right : Right_Matrix) return Result_Matrix`
327			`is`
328			`R : Result_Matrix (Left'Range (1), Right'Range (2));`
329
330			`begin`
331			`if Left'Length (2) /= Right'Length (1) then`
332			`raise Constraint_Error with`
333			`"incompatible dimensions in matrix multiplication";`
334			`end if;`
335
336			`for J in R'Range (1) loop`
337			`for K in R'Range (2) loop`
338			`declare`
339			`S : Result_Scalar := Zero;`
340			`begin`
341			`for M in Left'Range (2) loop`
342			`S := S + Left (J, M)`
343			`* Right (M - Left'First (2) + Right'First (1), K);`
344			`end loop;`
345
346			`R (J, K) := S;`
347			`end;`
348			`end loop;`
349			`end loop;`
350
351			`return R;`
352			`end Matrix_Matrix_Product;`
353
354			`---------------------------`
355			`-- Matrix_Vector_Product --`
356			`---------------------------`
357
358			`function Matrix_Vector_Product`
359			`(Left : Matrix;`
360			`Right : Right_Vector) return Result_Vector`
361			`is`
362			`R : Result_Vector (Left'Range (1));`
363
364			`begin`
365			`if Left'Length (2) /= Right'Length then`
366			`raise Constraint_Error with`
367			`"incompatible dimensions in matrix-vector multiplication";`
368			`end if;`
369
370			`for J in Left'Range (1) loop`
371			`declare`
372			`S : Result_Scalar := Zero;`
373			`begin`
374			`for K in Left'Range (2) loop`
375			`S := S + Left (J, K) * Right (K - Left'First (2) + Right'First);`
376			`end loop;`
377
378			`R (J) := S;`
379			`end;`
380			`end loop;`
381
382			`return R;`
383			`end Matrix_Vector_Product;`
384
385			`-------------------`
386			`-- Outer_Product --`
387			`-------------------`
388
389			`function Outer_Product`
390			`(Left : Left_Vector;`
391			`Right : Right_Vector) return Matrix`
392			`is`
393			`R : Matrix (Left'Range, Right'Range);`
394
395			`begin`
396			`for J in R'Range (1) loop`
397			`for K in R'Range (2) loop`
398			`R (J, K) := Left (J) * Right (K);`
399			`end loop;`
400			`end loop;`
401
402			`return R;`
403			`end Outer_Product;`
404
405			`---------------`
406			`-- Transpose --`
407			`---------------`
408
409			`procedure Transpose (A : Matrix; R : out Matrix) is`
410			`begin`
411			`for J in R'Range (1) loop`
412			`for K in R'Range (2) loop`
413			`R (J, K) := A (K - R'First (2) + A'First (1),`
414			`J - R'First (1) + A'First (2));`
415			`end loop;`
416			`end loop;`
417			`end Transpose;`
418
419			`-------------------------------`
420			`-- Update_Matrix_With_Matrix --`
421			`-------------------------------`
422
423			`procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix) is`
424			`begin`
425			`if X'Length (1) /= Y'Length (1)`
426			`or else X'Length (2) /= Y'Length (2)`
427			`then`
428			`raise Constraint_Error with`
429			`"matrices are of different dimension in update operation";`
430			`end if;`
431
432			`for J in X'Range (1) loop`
433			`for K in X'Range (2) loop`
434			`Update (X (J, K), Y (J - X'First (1) + Y'First (1),`
435			`K - X'First (2) + Y'First (2)));`
436			`end loop;`
437			`end loop;`
438			`end Update_Matrix_With_Matrix;`
439
440			`-------------------------------`
441			`-- Update_Vector_With_Vector --`
442			`-------------------------------`
443
444			`procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector) is`
445			`begin`
446			`if X'Length /= Y'Length then`
447			`raise Constraint_Error with`
448			`"vectors are of different length in update operation";`
449			`end if;`
450
451			`for J in X'Range loop`
452			`Update (X (J), Y (J - X'First + Y'First));`
453			`end loop;`
454			`end Update_Vector_With_Vector;`
455
456			`-----------------`
457			`-- Unit_Matrix --`
458			`-----------------`
459
460			`function Unit_Matrix`
461			`(Order : Positive;`
462			`First_1 : Integer := 1;`
463			`First_2 : Integer := 1) return Matrix`
464			`is`
465			`R : Matrix (First_1 .. Check_Unit_Last (First_1, Order, First_1),`
466			`First_2 .. Check_Unit_Last (First_2, Order, First_2));`
467
468			`begin`
469			`R := (others => (others => Zero));`
470
471			`for J in 0 .. Order - 1 loop`
472			`R (First_1 + J, First_2 + J) := One;`
473			`end loop;`
474
475			`return R;`
476			`end Unit_Matrix;`
477
478			`-----------------`
479			`-- Unit_Vector --`
480			`-----------------`
481
482			`function Unit_Vector`
483			`(Index : Integer;`
484			`Order : Positive;`
485			`First : Integer := 1) return Vector`
486			`is`
487			`R : Vector (First .. Check_Unit_Last (Index, Order, First));`
488			`begin`
489			`R := (others => Zero);`
490			`R (Index) := One;`
491			`return R;`
492			`end Unit_Vector;`
493
494			`---------------------------`
495			`-- Vector_Matrix_Product --`
496			`---------------------------`
497
498			`function Vector_Matrix_Product`
499			`(Left : Left_Vector;`
500			`Right : Matrix) return Result_Vector`
501			`is`
502			`R : Result_Vector (Right'Range (2));`
503
504			`begin`
505			`if Left'Length /= Right'Length (2) then`
506			`raise Constraint_Error with`
507			`"incompatible dimensions in vector-matrix multiplication";`
508			`end if;`
509
510			`for J in Right'Range (2) loop`
511			`declare`
512			`S : Result_Scalar := Zero;`
513
514			`begin`
515			`for K in Right'Range (1) loop`
516			`S := S + Left (J - Right'First (1) + Left'First) * Right (K, J);`
517			`end loop;`
518
519			`R (J) := S;`
520			`end;`
521			`end loop;`
522
523			`return R;`
524			`end Vector_Matrix_Product;`
525
526			`end System.Generic_Array_Operations;`