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   1 ------------------------------------------------------------------------------
   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 --                                 S p e c                                  --
   8 --                                                                          --
   9 --          Copyright (C) 2006-2011, 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 System.Generic_Array_Operations is
  33 pragma Pure (Generic_Array_Operations);
  34
  35    ---------------------
  36    -- Back_Substitute --
  37    ---------------------
  38
  39    generic
  40       type Scalar is private;
  41       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
  42       with function "-" (Left, Right : Scalar) return Scalar is <>;
  43       with function "*" (Left, Right : Scalar) return Scalar is <>;
  44       with function "/" (Left, Right : Scalar) return Scalar is <>;
  45       with function Is_Non_Zero (X : Scalar) return Boolean is <>;
  46    procedure Back_Substitute (M, N : in out Matrix);
  47
  48    --------------
  49    -- Diagonal --
  50    --------------
  51
  52    generic
  53       type Scalar is private;
  54       type Vector is array (Integer range <>) of Scalar;
  55       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
  56    function Diagonal (A : Matrix) return Vector;
  57
  58    -----------------------
  59    -- Forward_Eliminate --
  60    -----------------------
  61
  62    --  Use elementary row operations to put square matrix M in row echolon
  63    --  form. Identical row operations are performed on matrix N, must have the
  64    --  same number of rows as M.
  65
  66    generic
  67       type Scalar is private;
  68       type Real is digits <>;
  69       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
  70       with function "abs" (Right : Scalar) return Real'Base is <>;
  71       with function "-" (Left, Right : Scalar) return Scalar is <>;
  72       with function "*" (Left, Right : Scalar) return Scalar is <>;
  73       with function "/" (Left, Right : Scalar) return Scalar is <>;
  74       Zero : Scalar;
  75       One  : Scalar;
  76    procedure Forward_Eliminate
  77      (M   : in out Matrix;
  78       N   : in out Matrix;
  79       Det : out Scalar);
  80
  81    --------------------------
  82    -- Square_Matrix_Length --
  83    --------------------------
  84
  85    generic
  86       type Scalar is private;
  87       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
  88    function Square_Matrix_Length (A : Matrix) return Natural;
  89    --  If A is non-square, raise Constraint_Error,  else return its dimension
  90
  91    ----------------------------------
  92    -- Vector_Elementwise_Operation --
  93    ----------------------------------
  94
  95    generic
  96       type X_Scalar is private;
  97       type Result_Scalar is private;
  98       type X_Vector is array (Integer range <>) of X_Scalar;
  99       type Result_Vector is array (Integer range <>) of Result_Scalar;
 100       with function Operation (X : X_Scalar) return Result_Scalar;
 101    function Vector_Elementwise_Operation (X : X_Vector) return Result_Vector;
 102
 103    ----------------------------------
 104    -- Matrix_Elementwise_Operation --
 105    ----------------------------------
 106
 107    generic
 108       type X_Scalar is private;
 109       type Result_Scalar is private;
 110       type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
 111       type Result_Matrix is array (Integer range <>, Integer range <>)
 112         of Result_Scalar;
 113       with function Operation (X : X_Scalar) return Result_Scalar;
 114    function Matrix_Elementwise_Operation (X : X_Matrix) return Result_Matrix;
 115
 116    -----------------------------------------
 117    -- Vector_Vector_Elementwise_Operation --
 118    -----------------------------------------
 119
 120    generic
 121       type Left_Scalar is private;
 122       type Right_Scalar is private;
 123       type Result_Scalar is private;
 124       type Left_Vector is array (Integer range <>) of Left_Scalar;
 125       type Right_Vector is array (Integer range <>) of Right_Scalar;
 126       type Result_Vector is array (Integer range <>) of Result_Scalar;
 127       with function Operation
 128              (Left  : Left_Scalar;
 129               Right : Right_Scalar) return Result_Scalar;
 130    function Vector_Vector_Elementwise_Operation
 131      (Left  : Left_Vector;
 132       Right : Right_Vector) return Result_Vector;
 133
 134    ------------------------------------------------
 135    -- Vector_Vector_Scalar_Elementwise_Operation --
 136    ------------------------------------------------
 137
 138    generic
 139       type X_Scalar is private;
 140       type Y_Scalar is private;
 141       type Z_Scalar is private;
 142       type Result_Scalar is private;
 143       type X_Vector is array (Integer range <>) of X_Scalar;
 144       type Y_Vector is array (Integer range <>) of Y_Scalar;
 145       type Result_Vector is array (Integer range <>) of Result_Scalar;
 146       with function Operation
 147              (X : X_Scalar;
 148               Y : Y_Scalar;
 149               Z : Z_Scalar) return Result_Scalar;
 150    function Vector_Vector_Scalar_Elementwise_Operation
 151      (X : X_Vector;
 152       Y : Y_Vector;
 153       Z : Z_Scalar) return Result_Vector;
 154
 155    -----------------------------------------
 156    -- Matrix_Matrix_Elementwise_Operation --
 157    -----------------------------------------
 158
 159    generic
 160       type Left_Scalar is private;
 161       type Right_Scalar is private;
 162       type Result_Scalar is private;
 163       type Left_Matrix is array (Integer range <>, Integer range <>)
 164         of Left_Scalar;
 165       type Right_Matrix is array (Integer range <>, Integer range <>)
 166         of Right_Scalar;
 167       type Result_Matrix is array (Integer range <>, Integer range <>)
 168         of Result_Scalar;
 169       with function Operation
 170              (Left  : Left_Scalar;
 171               Right : Right_Scalar) return Result_Scalar;
 172    function Matrix_Matrix_Elementwise_Operation
 173      (Left  : Left_Matrix;
 174       Right : Right_Matrix) return Result_Matrix;
 175
 176    ------------------------------------------------
 177    -- Matrix_Matrix_Scalar_Elementwise_Operation --
 178    ------------------------------------------------
 179
 180    generic
 181       type X_Scalar is private;
 182       type Y_Scalar is private;
 183       type Z_Scalar is private;
 184       type Result_Scalar is private;
 185       type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
 186       type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
 187       type Result_Matrix is array (Integer range <>, Integer range <>)
 188         of Result_Scalar;
 189       with function Operation
 190              (X : X_Scalar;
 191               Y : Y_Scalar;
 192               Z : Z_Scalar) return Result_Scalar;
 193    function Matrix_Matrix_Scalar_Elementwise_Operation
 194      (X : X_Matrix;
 195       Y : Y_Matrix;
 196       Z : Z_Scalar) return Result_Matrix;
 197
 198    -----------------------------------------
 199    -- Vector_Scalar_Elementwise_Operation --
 200    -----------------------------------------
 201
 202    generic
 203       type Left_Scalar is private;
 204       type Right_Scalar is private;
 205       type Result_Scalar is private;
 206       type Left_Vector is array (Integer range <>) of Left_Scalar;
 207       type Result_Vector is array (Integer range <>) of Result_Scalar;
 208       with function Operation
 209              (Left  : Left_Scalar;
 210               Right : Right_Scalar) return Result_Scalar;
 211    function Vector_Scalar_Elementwise_Operation
 212      (Left  : Left_Vector;
 213       Right : Right_Scalar) return Result_Vector;
 214
 215    -----------------------------------------
 216    -- Matrix_Scalar_Elementwise_Operation --
 217    -----------------------------------------
 218
 219    generic
 220       type Left_Scalar is private;
 221       type Right_Scalar is private;
 222       type Result_Scalar is private;
 223       type Left_Matrix is array (Integer range <>, Integer range <>)
 224         of Left_Scalar;
 225       type Result_Matrix is array (Integer range <>, Integer range <>)
 226         of Result_Scalar;
 227       with function Operation
 228              (Left  : Left_Scalar;
 229               Right : Right_Scalar) return Result_Scalar;
 230    function Matrix_Scalar_Elementwise_Operation
 231      (Left  : Left_Matrix;
 232       Right : Right_Scalar) return Result_Matrix;
 233
 234    -----------------------------------------
 235    -- Scalar_Vector_Elementwise_Operation --
 236    -----------------------------------------
 237
 238    generic
 239       type Left_Scalar is private;
 240       type Right_Scalar is private;
 241       type Result_Scalar is private;
 242       type Right_Vector is array (Integer range <>) of Right_Scalar;
 243       type Result_Vector is array (Integer range <>) of Result_Scalar;
 244       with function Operation
 245              (Left  : Left_Scalar;
 246               Right : Right_Scalar) return Result_Scalar;
 247    function Scalar_Vector_Elementwise_Operation
 248      (Left  : Left_Scalar;
 249       Right : Right_Vector) return Result_Vector;
 250
 251    -----------------------------------------
 252    -- Scalar_Matrix_Elementwise_Operation --
 253    -----------------------------------------
 254
 255    generic
 256       type Left_Scalar is private;
 257       type Right_Scalar is private;
 258       type Result_Scalar is private;
 259       type Right_Matrix is array (Integer range <>, Integer range <>)
 260         of Right_Scalar;
 261       type Result_Matrix is array (Integer range <>, Integer range <>)
 262         of Result_Scalar;
 263       with function Operation
 264              (Left  : Left_Scalar;
 265               Right : Right_Scalar) return Result_Scalar;
 266    function Scalar_Matrix_Elementwise_Operation
 267      (Left  : Left_Scalar;
 268       Right : Right_Matrix) return Result_Matrix;
 269
 270    -------------------
 271    -- Inner_Product --
 272    -------------------
 273
 274    generic
 275       type Left_Scalar is private;
 276       type Right_Scalar is private;
 277       type Result_Scalar is private;
 278       type Left_Vector is array (Integer range <>) of Left_Scalar;
 279       type Right_Vector is array (Integer range <>) of Right_Scalar;
 280       Zero : Result_Scalar;
 281       with function "*"
 282              (Left  : Left_Scalar;
 283               Right : Right_Scalar) return Result_Scalar is <>;
 284       with function "+"
 285              (Left  : Result_Scalar;
 286               Right : Result_Scalar) return Result_Scalar is <>;
 287    function Inner_Product
 288      (Left  : Left_Vector;
 289       Right : Right_Vector) return Result_Scalar;
 290
 291    -------------
 292    -- L2_Norm --
 293    -------------
 294
 295    generic
 296       type X_Scalar is private;
 297       type Result_Real is digits <>;
 298       type X_Vector is array (Integer range <>) of X_Scalar;
 299       with function "abs" (Right : X_Scalar) return Result_Real is <>;
 300       with function Sqrt (X : Result_Real'Base) return Result_Real'Base is <>;
 301    function L2_Norm (X : X_Vector) return Result_Real'Base;
 302
 303    -------------------
 304    -- Outer_Product --
 305    -------------------
 306
 307    generic
 308       type Left_Scalar is private;
 309       type Right_Scalar is private;
 310       type Result_Scalar is private;
 311       type Left_Vector is array (Integer range <>) of Left_Scalar;
 312       type Right_Vector is array (Integer range <>) of Right_Scalar;
 313       type Matrix is array (Integer range <>, Integer range <>)
 314         of Result_Scalar;
 315       with function "*"
 316              (Left  : Left_Scalar;
 317               Right : Right_Scalar) return Result_Scalar is <>;
 318    function Outer_Product
 319      (Left  : Left_Vector;
 320       Right : Right_Vector) return Matrix;
 321
 322    ---------------------------
 323    -- Matrix_Vector_Product --
 324    ---------------------------
 325
 326    generic
 327       type Left_Scalar is private;
 328       type Right_Scalar is private;
 329       type Result_Scalar is private;
 330       type Matrix is array (Integer range <>, Integer range <>)
 331         of Left_Scalar;
 332       type Right_Vector is array (Integer range <>) of Right_Scalar;
 333       type Result_Vector is array (Integer range <>) of Result_Scalar;
 334       Zero : Result_Scalar;
 335       with function "*"
 336              (Left  : Left_Scalar;
 337               Right : Right_Scalar) return Result_Scalar is <>;
 338       with function "+"
 339              (Left  : Result_Scalar;
 340               Right : Result_Scalar) return Result_Scalar is <>;
 341    function Matrix_Vector_Product
 342      (Left  : Matrix;
 343       Right : Right_Vector) return Result_Vector;
 344
 345    ---------------------------
 346    -- Vector_Matrix_Product --
 347    ---------------------------
 348
 349    generic
 350       type Left_Scalar is private;
 351       type Right_Scalar is private;
 352       type Result_Scalar is private;
 353       type Left_Vector is array (Integer range <>) of Left_Scalar;
 354       type Matrix is array (Integer range <>, Integer range <>)
 355         of Right_Scalar;
 356       type Result_Vector is array (Integer range <>) of Result_Scalar;
 357       Zero : Result_Scalar;
 358       with function "*"
 359              (Left  : Left_Scalar;
 360               Right : Right_Scalar) return Result_Scalar is <>;
 361       with function "+"
 362              (Left  : Result_Scalar;
 363               Right : Result_Scalar) return Result_Scalar is <>;
 364    function Vector_Matrix_Product
 365      (Left  : Left_Vector;
 366       Right : Matrix) return Result_Vector;
 367
 368    ---------------------------
 369    -- Matrix_Matrix_Product --
 370    ---------------------------
 371
 372    generic
 373       type Left_Scalar is private;
 374       type Right_Scalar is private;
 375       type Result_Scalar is private;
 376       type Left_Matrix is array (Integer range <>, Integer range <>)
 377         of Left_Scalar;
 378       type Right_Matrix is array (Integer range <>, Integer range <>)
 379         of Right_Scalar;
 380       type Result_Matrix is array (Integer range <>, Integer range <>)
 381         of Result_Scalar;
 382       Zero : Result_Scalar;
 383       with function "*"
 384              (Left  : Left_Scalar;
 385               Right : Right_Scalar) return Result_Scalar is <>;
 386       with function "+"
 387              (Left  : Result_Scalar;
 388               Right : Result_Scalar) return Result_Scalar is <>;
 389    function Matrix_Matrix_Product
 390      (Left  : Left_Matrix;
 391       Right : Right_Matrix) return Result_Matrix;
 392
 393    ----------------------------
 394    -- Matrix_Vector_Solution --
 395    ----------------------------
 396
 397    generic
 398       type Scalar is private;
 399       type Vector is array (Integer range <>) of Scalar;
 400       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
 401       with procedure Back_Substitute (M, N : in out Matrix) is <>;
 402       with procedure Forward_Eliminate
 403              (M   : in out Matrix;
 404               N   : in out Matrix;
 405               Det : out Scalar) is <>;
 406    function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector;
 407
 408    ----------------------------
 409    -- Matrix_Matrix_Solution --
 410    ----------------------------
 411
 412    generic
 413       type Scalar is private;
 414       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
 415       with procedure Back_Substitute (M, N : in out Matrix) is <>;
 416       with procedure Forward_Eliminate
 417              (M   : in out Matrix;
 418               N   : in out Matrix;
 419               Det : out Scalar) is <>;
 420    function Matrix_Matrix_Solution (A : Matrix; X : Matrix) return Matrix;
 421
 422    ----------
 423    -- Sqrt --
 424    ----------
 425
 426    generic
 427       type Real is digits <>;
 428    function Sqrt (X : Real'Base) return Real'Base;
 429
 430    -----------------
 431    -- Swap_Column --
 432    -----------------
 433
 434    generic
 435       type Scalar is private;
 436       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
 437    procedure Swap_Column (A : in out Matrix; Left, Right : Integer);
 438
 439    ---------------
 440    -- Transpose --
 441    ---------------
 442
 443    generic
 444       type Scalar is private;
 445       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
 446    procedure Transpose (A : Matrix; R : out Matrix);
 447
 448    -------------------------------
 449    -- Update_Vector_With_Vector --
 450    -------------------------------
 451
 452    generic
 453       type X_Scalar is private;
 454       type Y_Scalar is private;
 455       type X_Vector is array (Integer range <>) of X_Scalar;
 456       type Y_Vector is array (Integer range <>) of Y_Scalar;
 457       with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
 458    procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector);
 459
 460    -------------------------------
 461    -- Update_Matrix_With_Matrix --
 462    -------------------------------
 463
 464    generic
 465       type X_Scalar is private;
 466       type Y_Scalar is private;
 467       type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar;
 468       type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar;
 469       with procedure Update (X : in out X_Scalar; Y : Y_Scalar);
 470    procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix);
 471
 472    -----------------
 473    -- Unit_Matrix --
 474    -----------------
 475
 476    generic
 477       type Scalar is private;
 478       type Matrix is array (Integer range <>, Integer range <>) of Scalar;
 479       Zero : Scalar;
 480       One  : Scalar;
 481    function Unit_Matrix
 482      (Order   : Positive;
 483       First_1 : Integer := 1;
 484       First_2 : Integer := 1) return Matrix;
 485
 486    -----------------
 487    -- Unit_Vector --
 488    -----------------
 489
 490    generic
 491       type Scalar is private;
 492       type Vector is array (Integer range <>) of Scalar;
 493       Zero : Scalar;
 494       One  : Scalar;
 495    function Unit_Vector
 496      (Index : Integer;
 497       Order : Positive;
 498       First : Integer := 1) return Vector;
 499
 500 end System.Generic_Array_Operations;