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) 2006-2021, 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 32package System.Generic_Array_Operations is 33pragma 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 Zero : Scalar; 400 type Vector is array (Integer range <>) of Scalar; 401 type Matrix is array (Integer range <>, Integer range <>) of Scalar; 402 with procedure Back_Substitute (M, N : in out Matrix) is <>; 403 with procedure Forward_Eliminate 404 (M : in out Matrix; 405 N : in out Matrix; 406 Det : out Scalar) is <>; 407 function Matrix_Vector_Solution (A : Matrix; X : Vector) return Vector; 408 409 ---------------------------- 410 -- Matrix_Matrix_Solution -- 411 ---------------------------- 412 413 generic 414 type Scalar is private; 415 Zero : Scalar; 416 type Matrix is array (Integer range <>, Integer range <>) of Scalar; 417 with procedure Back_Substitute (M, N : in out Matrix) is <>; 418 with procedure Forward_Eliminate 419 (M : in out Matrix; 420 N : in out Matrix; 421 Det : out Scalar) is <>; 422 function Matrix_Matrix_Solution (A : Matrix; X : Matrix) return Matrix; 423 424 ---------- 425 -- Sqrt -- 426 ---------- 427 428 generic 429 type Real is digits <>; 430 function Sqrt (X : Real'Base) return Real'Base; 431 432 ----------------- 433 -- Swap_Column -- 434 ----------------- 435 436 generic 437 type Scalar is private; 438 type Matrix is array (Integer range <>, Integer range <>) of Scalar; 439 procedure Swap_Column (A : in out Matrix; Left, Right : Integer); 440 441 --------------- 442 -- Transpose -- 443 --------------- 444 445 generic 446 type Scalar is private; 447 type Matrix is array (Integer range <>, Integer range <>) of Scalar; 448 procedure Transpose (A : Matrix; R : out Matrix); 449 450 ------------------------------- 451 -- Update_Vector_With_Vector -- 452 ------------------------------- 453 454 generic 455 type X_Scalar is private; 456 type Y_Scalar is private; 457 type X_Vector is array (Integer range <>) of X_Scalar; 458 type Y_Vector is array (Integer range <>) of Y_Scalar; 459 with procedure Update (X : in out X_Scalar; Y : Y_Scalar); 460 procedure Update_Vector_With_Vector (X : in out X_Vector; Y : Y_Vector); 461 462 ------------------------------- 463 -- Update_Matrix_With_Matrix -- 464 ------------------------------- 465 466 generic 467 type X_Scalar is private; 468 type Y_Scalar is private; 469 type X_Matrix is array (Integer range <>, Integer range <>) of X_Scalar; 470 type Y_Matrix is array (Integer range <>, Integer range <>) of Y_Scalar; 471 with procedure Update (X : in out X_Scalar; Y : Y_Scalar); 472 procedure Update_Matrix_With_Matrix (X : in out X_Matrix; Y : Y_Matrix); 473 474 ----------------- 475 -- Unit_Matrix -- 476 ----------------- 477 478 generic 479 type Scalar is private; 480 type Matrix is array (Integer range <>, Integer range <>) of Scalar; 481 Zero : Scalar; 482 One : Scalar; 483 function Unit_Matrix 484 (Order : Positive; 485 First_1 : Integer := 1; 486 First_2 : Integer := 1) return Matrix; 487 488 ----------------- 489 -- Unit_Vector -- 490 ----------------- 491 492 generic 493 type Scalar is private; 494 type Vector is array (Integer range <>) of Scalar; 495 Zero : Scalar; 496 One : Scalar; 497 function Unit_Vector 498 (Index : Integer; 499 Order : Positive; 500 First : Integer := 1) return Vector; 501 502end System.Generic_Array_Operations; 503