Bernhard Rosenkraenzer | c83ebe5 | 2012-09-18 21:38:03 +0159 | [diff] [blame] | 1 | ------------------------------------------------------------------------------ |
| 2 | -- -- |
| 3 | -- GNAT COMPILER COMPONENTS -- |
| 4 | -- -- |
| 5 | -- ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS -- |
| 6 | -- -- |
| 7 | -- B o d y -- |
| 8 | -- -- |
Bernhard Rosenkraenzer | ee2ec6d | 2012-10-10 01:40:27 +0159 | [diff] [blame^] | 9 | -- Copyright (C) 2006-2012, Free Software Foundation, Inc. -- |
Bernhard Rosenkraenzer | c83ebe5 | 2012-09-18 21:38:03 +0159 | [diff] [blame] | 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 | with System.Generic_Array_Operations; use System.Generic_Array_Operations; |
| 33 | with Ada.Numerics; use Ada.Numerics; |
| 34 | |
| 35 | package body Ada.Numerics.Generic_Complex_Arrays is |
| 36 | |
| 37 | -- Operations that are defined in terms of operations on the type Real, |
| 38 | -- such as addition, subtraction and scaling, are computed in the canonical |
| 39 | -- way looping over all elements. |
| 40 | |
| 41 | package Ops renames System.Generic_Array_Operations; |
| 42 | |
| 43 | subtype Real is Real_Arrays.Real; |
| 44 | -- Work around visibility bug ??? |
| 45 | |
| 46 | function Is_Non_Zero (X : Complex) return Boolean is (X /= (0.0, 0.0)); |
| 47 | -- Needed by Back_Substitute |
| 48 | |
| 49 | procedure Back_Substitute is new Ops.Back_Substitute |
| 50 | (Scalar => Complex, |
| 51 | Matrix => Complex_Matrix, |
| 52 | Is_Non_Zero => Is_Non_Zero); |
| 53 | |
| 54 | procedure Forward_Eliminate is new Ops.Forward_Eliminate |
| 55 | (Scalar => Complex, |
| 56 | Real => Real'Base, |
| 57 | Matrix => Complex_Matrix, |
| 58 | Zero => (0.0, 0.0), |
| 59 | One => (1.0, 0.0)); |
| 60 | |
| 61 | procedure Transpose is new Ops.Transpose |
| 62 | (Scalar => Complex, |
| 63 | Matrix => Complex_Matrix); |
| 64 | |
| 65 | -- Helper function that raises a Constraint_Error is the argument is |
| 66 | -- not a square matrix, and otherwise returns its length. |
| 67 | |
| 68 | function Length is new Square_Matrix_Length (Complex, Complex_Matrix); |
| 69 | |
| 70 | -- Instant a generic square root implementation here, in order to avoid |
| 71 | -- instantiating a complete copy of Generic_Elementary_Functions. |
| 72 | -- Speed of the square root is not a big concern here. |
| 73 | |
| 74 | function Sqrt is new Ops.Sqrt (Real'Base); |
| 75 | |
| 76 | -- Instantiating the following subprograms directly would lead to |
| 77 | -- name clashes, so use a local package. |
| 78 | |
| 79 | package Instantiations is |
| 80 | |
| 81 | --------- |
| 82 | -- "*" -- |
| 83 | --------- |
| 84 | |
| 85 | function "*" is new Vector_Scalar_Elementwise_Operation |
| 86 | (Left_Scalar => Complex, |
| 87 | Right_Scalar => Complex, |
| 88 | Result_Scalar => Complex, |
| 89 | Left_Vector => Complex_Vector, |
| 90 | Result_Vector => Complex_Vector, |
| 91 | Operation => "*"); |
| 92 | |
| 93 | function "*" is new Vector_Scalar_Elementwise_Operation |
| 94 | (Left_Scalar => Complex, |
| 95 | Right_Scalar => Real'Base, |
| 96 | Result_Scalar => Complex, |
| 97 | Left_Vector => Complex_Vector, |
| 98 | Result_Vector => Complex_Vector, |
| 99 | Operation => "*"); |
| 100 | |
| 101 | function "*" is new Scalar_Vector_Elementwise_Operation |
| 102 | (Left_Scalar => Complex, |
| 103 | Right_Scalar => Complex, |
| 104 | Result_Scalar => Complex, |
| 105 | Right_Vector => Complex_Vector, |
| 106 | Result_Vector => Complex_Vector, |
| 107 | Operation => "*"); |
| 108 | |
| 109 | function "*" is new Scalar_Vector_Elementwise_Operation |
| 110 | (Left_Scalar => Real'Base, |
| 111 | Right_Scalar => Complex, |
| 112 | Result_Scalar => Complex, |
| 113 | Right_Vector => Complex_Vector, |
| 114 | Result_Vector => Complex_Vector, |
| 115 | Operation => "*"); |
| 116 | |
| 117 | function "*" is new Inner_Product |
| 118 | (Left_Scalar => Complex, |
| 119 | Right_Scalar => Real'Base, |
| 120 | Result_Scalar => Complex, |
| 121 | Left_Vector => Complex_Vector, |
| 122 | Right_Vector => Real_Vector, |
| 123 | Zero => (0.0, 0.0)); |
| 124 | |
| 125 | function "*" is new Inner_Product |
| 126 | (Left_Scalar => Real'Base, |
| 127 | Right_Scalar => Complex, |
| 128 | Result_Scalar => Complex, |
| 129 | Left_Vector => Real_Vector, |
| 130 | Right_Vector => Complex_Vector, |
| 131 | Zero => (0.0, 0.0)); |
| 132 | |
| 133 | function "*" is new Inner_Product |
| 134 | (Left_Scalar => Complex, |
| 135 | Right_Scalar => Complex, |
| 136 | Result_Scalar => Complex, |
| 137 | Left_Vector => Complex_Vector, |
| 138 | Right_Vector => Complex_Vector, |
| 139 | Zero => (0.0, 0.0)); |
| 140 | |
| 141 | function "*" is new Outer_Product |
| 142 | (Left_Scalar => Complex, |
| 143 | Right_Scalar => Complex, |
| 144 | Result_Scalar => Complex, |
| 145 | Left_Vector => Complex_Vector, |
| 146 | Right_Vector => Complex_Vector, |
| 147 | Matrix => Complex_Matrix); |
| 148 | |
| 149 | function "*" is new Outer_Product |
| 150 | (Left_Scalar => Real'Base, |
| 151 | Right_Scalar => Complex, |
| 152 | Result_Scalar => Complex, |
| 153 | Left_Vector => Real_Vector, |
| 154 | Right_Vector => Complex_Vector, |
| 155 | Matrix => Complex_Matrix); |
| 156 | |
| 157 | function "*" is new Outer_Product |
| 158 | (Left_Scalar => Complex, |
| 159 | Right_Scalar => Real'Base, |
| 160 | Result_Scalar => Complex, |
| 161 | Left_Vector => Complex_Vector, |
| 162 | Right_Vector => Real_Vector, |
| 163 | Matrix => Complex_Matrix); |
| 164 | |
| 165 | function "*" is new Matrix_Scalar_Elementwise_Operation |
| 166 | (Left_Scalar => Complex, |
| 167 | Right_Scalar => Complex, |
| 168 | Result_Scalar => Complex, |
| 169 | Left_Matrix => Complex_Matrix, |
| 170 | Result_Matrix => Complex_Matrix, |
| 171 | Operation => "*"); |
| 172 | |
| 173 | function "*" is new Matrix_Scalar_Elementwise_Operation |
| 174 | (Left_Scalar => Complex, |
| 175 | Right_Scalar => Real'Base, |
| 176 | Result_Scalar => Complex, |
| 177 | Left_Matrix => Complex_Matrix, |
| 178 | Result_Matrix => Complex_Matrix, |
| 179 | Operation => "*"); |
| 180 | |
| 181 | function "*" is new Scalar_Matrix_Elementwise_Operation |
| 182 | (Left_Scalar => Complex, |
| 183 | Right_Scalar => Complex, |
| 184 | Result_Scalar => Complex, |
| 185 | Right_Matrix => Complex_Matrix, |
| 186 | Result_Matrix => Complex_Matrix, |
| 187 | Operation => "*"); |
| 188 | |
| 189 | function "*" is new Scalar_Matrix_Elementwise_Operation |
| 190 | (Left_Scalar => Real'Base, |
| 191 | Right_Scalar => Complex, |
| 192 | Result_Scalar => Complex, |
| 193 | Right_Matrix => Complex_Matrix, |
| 194 | Result_Matrix => Complex_Matrix, |
| 195 | Operation => "*"); |
| 196 | |
| 197 | function "*" is new Matrix_Vector_Product |
| 198 | (Left_Scalar => Real'Base, |
| 199 | Right_Scalar => Complex, |
| 200 | Result_Scalar => Complex, |
| 201 | Matrix => Real_Matrix, |
| 202 | Right_Vector => Complex_Vector, |
| 203 | Result_Vector => Complex_Vector, |
| 204 | Zero => (0.0, 0.0)); |
| 205 | |
| 206 | function "*" is new Matrix_Vector_Product |
| 207 | (Left_Scalar => Complex, |
| 208 | Right_Scalar => Real'Base, |
| 209 | Result_Scalar => Complex, |
| 210 | Matrix => Complex_Matrix, |
| 211 | Right_Vector => Real_Vector, |
| 212 | Result_Vector => Complex_Vector, |
| 213 | Zero => (0.0, 0.0)); |
| 214 | |
| 215 | function "*" is new Matrix_Vector_Product |
| 216 | (Left_Scalar => Complex, |
| 217 | Right_Scalar => Complex, |
| 218 | Result_Scalar => Complex, |
| 219 | Matrix => Complex_Matrix, |
| 220 | Right_Vector => Complex_Vector, |
| 221 | Result_Vector => Complex_Vector, |
| 222 | Zero => (0.0, 0.0)); |
| 223 | |
| 224 | function "*" is new Vector_Matrix_Product |
| 225 | (Left_Scalar => Real'Base, |
| 226 | Right_Scalar => Complex, |
| 227 | Result_Scalar => Complex, |
| 228 | Left_Vector => Real_Vector, |
| 229 | Matrix => Complex_Matrix, |
| 230 | Result_Vector => Complex_Vector, |
| 231 | Zero => (0.0, 0.0)); |
| 232 | |
| 233 | function "*" is new Vector_Matrix_Product |
| 234 | (Left_Scalar => Complex, |
| 235 | Right_Scalar => Real'Base, |
| 236 | Result_Scalar => Complex, |
| 237 | Left_Vector => Complex_Vector, |
| 238 | Matrix => Real_Matrix, |
| 239 | Result_Vector => Complex_Vector, |
| 240 | Zero => (0.0, 0.0)); |
| 241 | |
| 242 | function "*" is new Vector_Matrix_Product |
| 243 | (Left_Scalar => Complex, |
| 244 | Right_Scalar => Complex, |
| 245 | Result_Scalar => Complex, |
| 246 | Left_Vector => Complex_Vector, |
| 247 | Matrix => Complex_Matrix, |
| 248 | Result_Vector => Complex_Vector, |
| 249 | Zero => (0.0, 0.0)); |
| 250 | |
| 251 | function "*" is new Matrix_Matrix_Product |
| 252 | (Left_Scalar => Complex, |
| 253 | Right_Scalar => Complex, |
| 254 | Result_Scalar => Complex, |
| 255 | Left_Matrix => Complex_Matrix, |
| 256 | Right_Matrix => Complex_Matrix, |
| 257 | Result_Matrix => Complex_Matrix, |
| 258 | Zero => (0.0, 0.0)); |
| 259 | |
| 260 | function "*" is new Matrix_Matrix_Product |
| 261 | (Left_Scalar => Real'Base, |
| 262 | Right_Scalar => Complex, |
| 263 | Result_Scalar => Complex, |
| 264 | Left_Matrix => Real_Matrix, |
| 265 | Right_Matrix => Complex_Matrix, |
| 266 | Result_Matrix => Complex_Matrix, |
| 267 | Zero => (0.0, 0.0)); |
| 268 | |
| 269 | function "*" is new Matrix_Matrix_Product |
| 270 | (Left_Scalar => Complex, |
| 271 | Right_Scalar => Real'Base, |
| 272 | Result_Scalar => Complex, |
| 273 | Left_Matrix => Complex_Matrix, |
| 274 | Right_Matrix => Real_Matrix, |
| 275 | Result_Matrix => Complex_Matrix, |
| 276 | Zero => (0.0, 0.0)); |
| 277 | |
| 278 | --------- |
| 279 | -- "+" -- |
| 280 | --------- |
| 281 | |
| 282 | function "+" is new Vector_Elementwise_Operation |
| 283 | (X_Scalar => Complex, |
| 284 | Result_Scalar => Complex, |
| 285 | X_Vector => Complex_Vector, |
| 286 | Result_Vector => Complex_Vector, |
| 287 | Operation => "+"); |
| 288 | |
| 289 | function "+" is new Vector_Vector_Elementwise_Operation |
| 290 | (Left_Scalar => Complex, |
| 291 | Right_Scalar => Complex, |
| 292 | Result_Scalar => Complex, |
| 293 | Left_Vector => Complex_Vector, |
| 294 | Right_Vector => Complex_Vector, |
| 295 | Result_Vector => Complex_Vector, |
| 296 | Operation => "+"); |
| 297 | |
| 298 | function "+" is new Vector_Vector_Elementwise_Operation |
| 299 | (Left_Scalar => Real'Base, |
| 300 | Right_Scalar => Complex, |
| 301 | Result_Scalar => Complex, |
| 302 | Left_Vector => Real_Vector, |
| 303 | Right_Vector => Complex_Vector, |
| 304 | Result_Vector => Complex_Vector, |
| 305 | Operation => "+"); |
| 306 | |
| 307 | function "+" is new Vector_Vector_Elementwise_Operation |
| 308 | (Left_Scalar => Complex, |
| 309 | Right_Scalar => Real'Base, |
| 310 | Result_Scalar => Complex, |
| 311 | Left_Vector => Complex_Vector, |
| 312 | Right_Vector => Real_Vector, |
| 313 | Result_Vector => Complex_Vector, |
| 314 | Operation => "+"); |
| 315 | |
| 316 | function "+" is new Matrix_Elementwise_Operation |
| 317 | (X_Scalar => Complex, |
| 318 | Result_Scalar => Complex, |
| 319 | X_Matrix => Complex_Matrix, |
| 320 | Result_Matrix => Complex_Matrix, |
| 321 | Operation => "+"); |
| 322 | |
| 323 | function "+" is new Matrix_Matrix_Elementwise_Operation |
| 324 | (Left_Scalar => Complex, |
| 325 | Right_Scalar => Complex, |
| 326 | Result_Scalar => Complex, |
| 327 | Left_Matrix => Complex_Matrix, |
| 328 | Right_Matrix => Complex_Matrix, |
| 329 | Result_Matrix => Complex_Matrix, |
| 330 | Operation => "+"); |
| 331 | |
| 332 | function "+" is new Matrix_Matrix_Elementwise_Operation |
| 333 | (Left_Scalar => Real'Base, |
| 334 | Right_Scalar => Complex, |
| 335 | Result_Scalar => Complex, |
| 336 | Left_Matrix => Real_Matrix, |
| 337 | Right_Matrix => Complex_Matrix, |
| 338 | Result_Matrix => Complex_Matrix, |
| 339 | Operation => "+"); |
| 340 | |
| 341 | function "+" is new Matrix_Matrix_Elementwise_Operation |
| 342 | (Left_Scalar => Complex, |
| 343 | Right_Scalar => Real'Base, |
| 344 | Result_Scalar => Complex, |
| 345 | Left_Matrix => Complex_Matrix, |
| 346 | Right_Matrix => Real_Matrix, |
| 347 | Result_Matrix => Complex_Matrix, |
| 348 | Operation => "+"); |
| 349 | |
| 350 | --------- |
| 351 | -- "-" -- |
| 352 | --------- |
| 353 | |
| 354 | function "-" is new Vector_Elementwise_Operation |
| 355 | (X_Scalar => Complex, |
| 356 | Result_Scalar => Complex, |
| 357 | X_Vector => Complex_Vector, |
| 358 | Result_Vector => Complex_Vector, |
| 359 | Operation => "-"); |
| 360 | |
| 361 | function "-" is new Vector_Vector_Elementwise_Operation |
| 362 | (Left_Scalar => Complex, |
| 363 | Right_Scalar => Complex, |
| 364 | Result_Scalar => Complex, |
| 365 | Left_Vector => Complex_Vector, |
| 366 | Right_Vector => Complex_Vector, |
| 367 | Result_Vector => Complex_Vector, |
| 368 | Operation => "-"); |
| 369 | |
| 370 | function "-" is new Vector_Vector_Elementwise_Operation |
| 371 | (Left_Scalar => Real'Base, |
| 372 | Right_Scalar => Complex, |
| 373 | Result_Scalar => Complex, |
| 374 | Left_Vector => Real_Vector, |
| 375 | Right_Vector => Complex_Vector, |
| 376 | Result_Vector => Complex_Vector, |
| 377 | Operation => "-"); |
| 378 | |
| 379 | function "-" is new Vector_Vector_Elementwise_Operation |
| 380 | (Left_Scalar => Complex, |
| 381 | Right_Scalar => Real'Base, |
| 382 | Result_Scalar => Complex, |
| 383 | Left_Vector => Complex_Vector, |
| 384 | Right_Vector => Real_Vector, |
| 385 | Result_Vector => Complex_Vector, |
| 386 | Operation => "-"); |
| 387 | |
| 388 | function "-" is new Matrix_Elementwise_Operation |
| 389 | (X_Scalar => Complex, |
| 390 | Result_Scalar => Complex, |
| 391 | X_Matrix => Complex_Matrix, |
| 392 | Result_Matrix => Complex_Matrix, |
| 393 | Operation => "-"); |
| 394 | |
| 395 | function "-" is new Matrix_Matrix_Elementwise_Operation |
| 396 | (Left_Scalar => Complex, |
| 397 | Right_Scalar => Complex, |
| 398 | Result_Scalar => Complex, |
| 399 | Left_Matrix => Complex_Matrix, |
| 400 | Right_Matrix => Complex_Matrix, |
| 401 | Result_Matrix => Complex_Matrix, |
| 402 | Operation => "-"); |
| 403 | |
| 404 | function "-" is new Matrix_Matrix_Elementwise_Operation |
| 405 | (Left_Scalar => Real'Base, |
| 406 | Right_Scalar => Complex, |
| 407 | Result_Scalar => Complex, |
| 408 | Left_Matrix => Real_Matrix, |
| 409 | Right_Matrix => Complex_Matrix, |
| 410 | Result_Matrix => Complex_Matrix, |
| 411 | Operation => "-"); |
| 412 | |
| 413 | function "-" is new Matrix_Matrix_Elementwise_Operation |
| 414 | (Left_Scalar => Complex, |
| 415 | Right_Scalar => Real'Base, |
| 416 | Result_Scalar => Complex, |
| 417 | Left_Matrix => Complex_Matrix, |
| 418 | Right_Matrix => Real_Matrix, |
| 419 | Result_Matrix => Complex_Matrix, |
| 420 | Operation => "-"); |
| 421 | |
| 422 | --------- |
| 423 | -- "/" -- |
| 424 | --------- |
| 425 | |
| 426 | function "/" is new Vector_Scalar_Elementwise_Operation |
| 427 | (Left_Scalar => Complex, |
| 428 | Right_Scalar => Complex, |
| 429 | Result_Scalar => Complex, |
| 430 | Left_Vector => Complex_Vector, |
| 431 | Result_Vector => Complex_Vector, |
| 432 | Operation => "/"); |
| 433 | |
| 434 | function "/" is new Vector_Scalar_Elementwise_Operation |
| 435 | (Left_Scalar => Complex, |
| 436 | Right_Scalar => Real'Base, |
| 437 | Result_Scalar => Complex, |
| 438 | Left_Vector => Complex_Vector, |
| 439 | Result_Vector => Complex_Vector, |
| 440 | Operation => "/"); |
| 441 | |
| 442 | function "/" is new Matrix_Scalar_Elementwise_Operation |
| 443 | (Left_Scalar => Complex, |
| 444 | Right_Scalar => Complex, |
| 445 | Result_Scalar => Complex, |
| 446 | Left_Matrix => Complex_Matrix, |
| 447 | Result_Matrix => Complex_Matrix, |
| 448 | Operation => "/"); |
| 449 | |
| 450 | function "/" is new Matrix_Scalar_Elementwise_Operation |
| 451 | (Left_Scalar => Complex, |
| 452 | Right_Scalar => Real'Base, |
| 453 | Result_Scalar => Complex, |
| 454 | Left_Matrix => Complex_Matrix, |
| 455 | Result_Matrix => Complex_Matrix, |
| 456 | Operation => "/"); |
| 457 | |
| 458 | ----------- |
| 459 | -- "abs" -- |
| 460 | ----------- |
| 461 | |
| 462 | function "abs" is new L2_Norm |
| 463 | (X_Scalar => Complex, |
| 464 | Result_Real => Real'Base, |
| 465 | X_Vector => Complex_Vector); |
| 466 | |
| 467 | -------------- |
| 468 | -- Argument -- |
| 469 | -------------- |
| 470 | |
| 471 | function Argument is new Vector_Elementwise_Operation |
| 472 | (X_Scalar => Complex, |
| 473 | Result_Scalar => Real'Base, |
| 474 | X_Vector => Complex_Vector, |
| 475 | Result_Vector => Real_Vector, |
| 476 | Operation => Argument); |
| 477 | |
| 478 | function Argument is new Vector_Scalar_Elementwise_Operation |
| 479 | (Left_Scalar => Complex, |
| 480 | Right_Scalar => Real'Base, |
| 481 | Result_Scalar => Real'Base, |
| 482 | Left_Vector => Complex_Vector, |
| 483 | Result_Vector => Real_Vector, |
| 484 | Operation => Argument); |
| 485 | |
| 486 | function Argument is new Matrix_Elementwise_Operation |
| 487 | (X_Scalar => Complex, |
| 488 | Result_Scalar => Real'Base, |
| 489 | X_Matrix => Complex_Matrix, |
| 490 | Result_Matrix => Real_Matrix, |
| 491 | Operation => Argument); |
| 492 | |
| 493 | function Argument is new Matrix_Scalar_Elementwise_Operation |
| 494 | (Left_Scalar => Complex, |
| 495 | Right_Scalar => Real'Base, |
| 496 | Result_Scalar => Real'Base, |
| 497 | Left_Matrix => Complex_Matrix, |
| 498 | Result_Matrix => Real_Matrix, |
| 499 | Operation => Argument); |
| 500 | |
| 501 | ---------------------------- |
| 502 | -- Compose_From_Cartesian -- |
| 503 | ---------------------------- |
| 504 | |
| 505 | function Compose_From_Cartesian is new Vector_Elementwise_Operation |
| 506 | (X_Scalar => Real'Base, |
| 507 | Result_Scalar => Complex, |
| 508 | X_Vector => Real_Vector, |
| 509 | Result_Vector => Complex_Vector, |
| 510 | Operation => Compose_From_Cartesian); |
| 511 | |
| 512 | function Compose_From_Cartesian is |
| 513 | new Vector_Vector_Elementwise_Operation |
| 514 | (Left_Scalar => Real'Base, |
| 515 | Right_Scalar => Real'Base, |
| 516 | Result_Scalar => Complex, |
| 517 | Left_Vector => Real_Vector, |
| 518 | Right_Vector => Real_Vector, |
| 519 | Result_Vector => Complex_Vector, |
| 520 | Operation => Compose_From_Cartesian); |
| 521 | |
| 522 | function Compose_From_Cartesian is new Matrix_Elementwise_Operation |
| 523 | (X_Scalar => Real'Base, |
| 524 | Result_Scalar => Complex, |
| 525 | X_Matrix => Real_Matrix, |
| 526 | Result_Matrix => Complex_Matrix, |
| 527 | Operation => Compose_From_Cartesian); |
| 528 | |
| 529 | function Compose_From_Cartesian is |
| 530 | new Matrix_Matrix_Elementwise_Operation |
| 531 | (Left_Scalar => Real'Base, |
| 532 | Right_Scalar => Real'Base, |
| 533 | Result_Scalar => Complex, |
| 534 | Left_Matrix => Real_Matrix, |
| 535 | Right_Matrix => Real_Matrix, |
| 536 | Result_Matrix => Complex_Matrix, |
| 537 | Operation => Compose_From_Cartesian); |
| 538 | |
| 539 | ------------------------ |
| 540 | -- Compose_From_Polar -- |
| 541 | ------------------------ |
| 542 | |
| 543 | function Compose_From_Polar is |
| 544 | new Vector_Vector_Elementwise_Operation |
| 545 | (Left_Scalar => Real'Base, |
| 546 | Right_Scalar => Real'Base, |
| 547 | Result_Scalar => Complex, |
| 548 | Left_Vector => Real_Vector, |
| 549 | Right_Vector => Real_Vector, |
| 550 | Result_Vector => Complex_Vector, |
| 551 | Operation => Compose_From_Polar); |
| 552 | |
| 553 | function Compose_From_Polar is |
| 554 | new Vector_Vector_Scalar_Elementwise_Operation |
| 555 | (X_Scalar => Real'Base, |
| 556 | Y_Scalar => Real'Base, |
| 557 | Z_Scalar => Real'Base, |
| 558 | Result_Scalar => Complex, |
| 559 | X_Vector => Real_Vector, |
| 560 | Y_Vector => Real_Vector, |
| 561 | Result_Vector => Complex_Vector, |
| 562 | Operation => Compose_From_Polar); |
| 563 | |
| 564 | function Compose_From_Polar is |
| 565 | new Matrix_Matrix_Elementwise_Operation |
| 566 | (Left_Scalar => Real'Base, |
| 567 | Right_Scalar => Real'Base, |
| 568 | Result_Scalar => Complex, |
| 569 | Left_Matrix => Real_Matrix, |
| 570 | Right_Matrix => Real_Matrix, |
| 571 | Result_Matrix => Complex_Matrix, |
| 572 | Operation => Compose_From_Polar); |
| 573 | |
| 574 | function Compose_From_Polar is |
| 575 | new Matrix_Matrix_Scalar_Elementwise_Operation |
| 576 | (X_Scalar => Real'Base, |
| 577 | Y_Scalar => Real'Base, |
| 578 | Z_Scalar => Real'Base, |
| 579 | Result_Scalar => Complex, |
| 580 | X_Matrix => Real_Matrix, |
| 581 | Y_Matrix => Real_Matrix, |
| 582 | Result_Matrix => Complex_Matrix, |
| 583 | Operation => Compose_From_Polar); |
| 584 | |
| 585 | --------------- |
| 586 | -- Conjugate -- |
| 587 | --------------- |
| 588 | |
| 589 | function Conjugate is new Vector_Elementwise_Operation |
| 590 | (X_Scalar => Complex, |
| 591 | Result_Scalar => Complex, |
| 592 | X_Vector => Complex_Vector, |
| 593 | Result_Vector => Complex_Vector, |
| 594 | Operation => Conjugate); |
| 595 | |
| 596 | function Conjugate is new Matrix_Elementwise_Operation |
| 597 | (X_Scalar => Complex, |
| 598 | Result_Scalar => Complex, |
| 599 | X_Matrix => Complex_Matrix, |
| 600 | Result_Matrix => Complex_Matrix, |
| 601 | Operation => Conjugate); |
| 602 | |
| 603 | -------- |
| 604 | -- Im -- |
| 605 | -------- |
| 606 | |
| 607 | function Im is new Vector_Elementwise_Operation |
| 608 | (X_Scalar => Complex, |
| 609 | Result_Scalar => Real'Base, |
| 610 | X_Vector => Complex_Vector, |
| 611 | Result_Vector => Real_Vector, |
| 612 | Operation => Im); |
| 613 | |
| 614 | function Im is new Matrix_Elementwise_Operation |
| 615 | (X_Scalar => Complex, |
| 616 | Result_Scalar => Real'Base, |
| 617 | X_Matrix => Complex_Matrix, |
| 618 | Result_Matrix => Real_Matrix, |
| 619 | Operation => Im); |
| 620 | |
| 621 | ------------- |
| 622 | -- Modulus -- |
| 623 | ------------- |
| 624 | |
| 625 | function Modulus is new Vector_Elementwise_Operation |
| 626 | (X_Scalar => Complex, |
| 627 | Result_Scalar => Real'Base, |
| 628 | X_Vector => Complex_Vector, |
| 629 | Result_Vector => Real_Vector, |
| 630 | Operation => Modulus); |
| 631 | |
| 632 | function Modulus is new Matrix_Elementwise_Operation |
| 633 | (X_Scalar => Complex, |
| 634 | Result_Scalar => Real'Base, |
| 635 | X_Matrix => Complex_Matrix, |
| 636 | Result_Matrix => Real_Matrix, |
| 637 | Operation => Modulus); |
| 638 | |
| 639 | -------- |
| 640 | -- Re -- |
| 641 | -------- |
| 642 | |
| 643 | function Re is new Vector_Elementwise_Operation |
| 644 | (X_Scalar => Complex, |
| 645 | Result_Scalar => Real'Base, |
| 646 | X_Vector => Complex_Vector, |
| 647 | Result_Vector => Real_Vector, |
| 648 | Operation => Re); |
| 649 | |
| 650 | function Re is new Matrix_Elementwise_Operation |
| 651 | (X_Scalar => Complex, |
| 652 | Result_Scalar => Real'Base, |
| 653 | X_Matrix => Complex_Matrix, |
| 654 | Result_Matrix => Real_Matrix, |
| 655 | Operation => Re); |
| 656 | |
| 657 | ------------ |
| 658 | -- Set_Im -- |
| 659 | ------------ |
| 660 | |
| 661 | procedure Set_Im is new Update_Vector_With_Vector |
| 662 | (X_Scalar => Complex, |
| 663 | Y_Scalar => Real'Base, |
| 664 | X_Vector => Complex_Vector, |
| 665 | Y_Vector => Real_Vector, |
| 666 | Update => Set_Im); |
| 667 | |
| 668 | procedure Set_Im is new Update_Matrix_With_Matrix |
| 669 | (X_Scalar => Complex, |
| 670 | Y_Scalar => Real'Base, |
| 671 | X_Matrix => Complex_Matrix, |
| 672 | Y_Matrix => Real_Matrix, |
| 673 | Update => Set_Im); |
| 674 | |
| 675 | ------------ |
| 676 | -- Set_Re -- |
| 677 | ------------ |
| 678 | |
| 679 | procedure Set_Re is new Update_Vector_With_Vector |
| 680 | (X_Scalar => Complex, |
| 681 | Y_Scalar => Real'Base, |
| 682 | X_Vector => Complex_Vector, |
| 683 | Y_Vector => Real_Vector, |
| 684 | Update => Set_Re); |
| 685 | |
| 686 | procedure Set_Re is new Update_Matrix_With_Matrix |
| 687 | (X_Scalar => Complex, |
| 688 | Y_Scalar => Real'Base, |
| 689 | X_Matrix => Complex_Matrix, |
| 690 | Y_Matrix => Real_Matrix, |
| 691 | Update => Set_Re); |
| 692 | |
| 693 | ----------- |
| 694 | -- Solve -- |
| 695 | ----------- |
| 696 | |
| 697 | function Solve is |
| 698 | new Matrix_Vector_Solution (Complex, Complex_Vector, Complex_Matrix); |
| 699 | |
| 700 | function Solve is |
| 701 | new Matrix_Matrix_Solution (Complex, Complex_Matrix); |
| 702 | |
| 703 | ----------------- |
| 704 | -- Unit_Matrix -- |
| 705 | ----------------- |
| 706 | |
| 707 | function Unit_Matrix is new System.Generic_Array_Operations.Unit_Matrix |
| 708 | (Scalar => Complex, |
| 709 | Matrix => Complex_Matrix, |
| 710 | Zero => (0.0, 0.0), |
| 711 | One => (1.0, 0.0)); |
| 712 | |
| 713 | function Unit_Vector is new System.Generic_Array_Operations.Unit_Vector |
| 714 | (Scalar => Complex, |
| 715 | Vector => Complex_Vector, |
| 716 | Zero => (0.0, 0.0), |
| 717 | One => (1.0, 0.0)); |
| 718 | end Instantiations; |
| 719 | |
| 720 | --------- |
| 721 | -- "*" -- |
| 722 | --------- |
| 723 | |
| 724 | function "*" |
| 725 | (Left : Complex_Vector; |
| 726 | Right : Complex_Vector) return Complex |
| 727 | renames Instantiations."*"; |
| 728 | |
| 729 | function "*" |
| 730 | (Left : Real_Vector; |
| 731 | Right : Complex_Vector) return Complex |
| 732 | renames Instantiations."*"; |
| 733 | |
| 734 | function "*" |
| 735 | (Left : Complex_Vector; |
| 736 | Right : Real_Vector) return Complex |
| 737 | renames Instantiations."*"; |
| 738 | |
| 739 | function "*" |
| 740 | (Left : Complex; |
| 741 | Right : Complex_Vector) return Complex_Vector |
| 742 | renames Instantiations."*"; |
| 743 | |
| 744 | function "*" |
| 745 | (Left : Complex_Vector; |
| 746 | Right : Complex) return Complex_Vector |
| 747 | renames Instantiations."*"; |
| 748 | |
| 749 | function "*" |
| 750 | (Left : Real'Base; |
| 751 | Right : Complex_Vector) return Complex_Vector |
| 752 | renames Instantiations."*"; |
| 753 | |
| 754 | function "*" |
| 755 | (Left : Complex_Vector; |
| 756 | Right : Real'Base) return Complex_Vector |
| 757 | renames Instantiations."*"; |
| 758 | |
| 759 | function "*" |
| 760 | (Left : Complex_Matrix; |
| 761 | Right : Complex_Matrix) return Complex_Matrix |
| 762 | renames Instantiations."*"; |
| 763 | |
| 764 | function "*" |
| 765 | (Left : Complex_Vector; |
| 766 | Right : Complex_Vector) return Complex_Matrix |
| 767 | renames Instantiations."*"; |
| 768 | |
| 769 | function "*" |
| 770 | (Left : Complex_Vector; |
| 771 | Right : Complex_Matrix) return Complex_Vector |
| 772 | renames Instantiations."*"; |
| 773 | |
| 774 | function "*" |
| 775 | (Left : Complex_Matrix; |
| 776 | Right : Complex_Vector) return Complex_Vector |
| 777 | renames Instantiations."*"; |
| 778 | |
| 779 | function "*" |
| 780 | (Left : Real_Matrix; |
| 781 | Right : Complex_Matrix) return Complex_Matrix |
| 782 | renames Instantiations."*"; |
| 783 | |
| 784 | function "*" |
| 785 | (Left : Complex_Matrix; |
| 786 | Right : Real_Matrix) return Complex_Matrix |
| 787 | renames Instantiations."*"; |
| 788 | |
| 789 | function "*" |
| 790 | (Left : Real_Vector; |
| 791 | Right : Complex_Vector) return Complex_Matrix |
| 792 | renames Instantiations."*"; |
| 793 | |
| 794 | function "*" |
| 795 | (Left : Complex_Vector; |
| 796 | Right : Real_Vector) return Complex_Matrix |
| 797 | renames Instantiations."*"; |
| 798 | |
| 799 | function "*" |
| 800 | (Left : Real_Vector; |
| 801 | Right : Complex_Matrix) return Complex_Vector |
| 802 | renames Instantiations."*"; |
| 803 | |
| 804 | function "*" |
| 805 | (Left : Complex_Vector; |
| 806 | Right : Real_Matrix) return Complex_Vector |
| 807 | renames Instantiations."*"; |
| 808 | |
| 809 | function "*" |
| 810 | (Left : Real_Matrix; |
| 811 | Right : Complex_Vector) return Complex_Vector |
| 812 | renames Instantiations."*"; |
| 813 | |
| 814 | function "*" |
| 815 | (Left : Complex_Matrix; |
| 816 | Right : Real_Vector) return Complex_Vector |
| 817 | renames Instantiations."*"; |
| 818 | |
| 819 | function "*" |
| 820 | (Left : Complex; |
| 821 | Right : Complex_Matrix) return Complex_Matrix |
| 822 | renames Instantiations."*"; |
| 823 | |
| 824 | function "*" |
| 825 | (Left : Complex_Matrix; |
| 826 | Right : Complex) return Complex_Matrix |
| 827 | renames Instantiations."*"; |
| 828 | |
| 829 | function "*" |
| 830 | (Left : Real'Base; |
| 831 | Right : Complex_Matrix) return Complex_Matrix |
| 832 | renames Instantiations."*"; |
| 833 | |
| 834 | function "*" |
| 835 | (Left : Complex_Matrix; |
| 836 | Right : Real'Base) return Complex_Matrix |
| 837 | renames Instantiations."*"; |
| 838 | |
| 839 | --------- |
| 840 | -- "+" -- |
| 841 | --------- |
| 842 | |
| 843 | function "+" (Right : Complex_Vector) return Complex_Vector |
| 844 | renames Instantiations."+"; |
| 845 | |
| 846 | function "+" |
| 847 | (Left : Complex_Vector; |
| 848 | Right : Complex_Vector) return Complex_Vector |
| 849 | renames Instantiations."+"; |
| 850 | |
| 851 | function "+" |
| 852 | (Left : Real_Vector; |
| 853 | Right : Complex_Vector) return Complex_Vector |
| 854 | renames Instantiations."+"; |
| 855 | |
| 856 | function "+" |
| 857 | (Left : Complex_Vector; |
| 858 | Right : Real_Vector) return Complex_Vector |
| 859 | renames Instantiations."+"; |
| 860 | |
| 861 | function "+" (Right : Complex_Matrix) return Complex_Matrix |
| 862 | renames Instantiations."+"; |
| 863 | |
| 864 | function "+" |
| 865 | (Left : Complex_Matrix; |
| 866 | Right : Complex_Matrix) return Complex_Matrix |
| 867 | renames Instantiations."+"; |
| 868 | |
| 869 | function "+" |
| 870 | (Left : Real_Matrix; |
| 871 | Right : Complex_Matrix) return Complex_Matrix |
| 872 | renames Instantiations."+"; |
| 873 | |
| 874 | function "+" |
| 875 | (Left : Complex_Matrix; |
| 876 | Right : Real_Matrix) return Complex_Matrix |
| 877 | renames Instantiations."+"; |
| 878 | |
| 879 | --------- |
| 880 | -- "-" -- |
| 881 | --------- |
| 882 | |
| 883 | function "-" |
| 884 | (Right : Complex_Vector) return Complex_Vector |
| 885 | renames Instantiations."-"; |
| 886 | |
| 887 | function "-" |
| 888 | (Left : Complex_Vector; |
| 889 | Right : Complex_Vector) return Complex_Vector |
| 890 | renames Instantiations."-"; |
| 891 | |
| 892 | function "-" |
| 893 | (Left : Real_Vector; |
| 894 | Right : Complex_Vector) return Complex_Vector |
| 895 | renames Instantiations."-"; |
| 896 | |
| 897 | function "-" |
| 898 | (Left : Complex_Vector; |
| 899 | Right : Real_Vector) return Complex_Vector |
| 900 | renames Instantiations."-"; |
| 901 | |
| 902 | function "-" (Right : Complex_Matrix) return Complex_Matrix |
| 903 | renames Instantiations."-"; |
| 904 | |
| 905 | function "-" |
| 906 | (Left : Complex_Matrix; |
| 907 | Right : Complex_Matrix) return Complex_Matrix |
| 908 | renames Instantiations."-"; |
| 909 | |
| 910 | function "-" |
| 911 | (Left : Real_Matrix; |
| 912 | Right : Complex_Matrix) return Complex_Matrix |
| 913 | renames Instantiations."-"; |
| 914 | |
| 915 | function "-" |
| 916 | (Left : Complex_Matrix; |
| 917 | Right : Real_Matrix) return Complex_Matrix |
| 918 | renames Instantiations."-"; |
| 919 | |
| 920 | --------- |
| 921 | -- "/" -- |
| 922 | --------- |
| 923 | |
| 924 | function "/" |
| 925 | (Left : Complex_Vector; |
| 926 | Right : Complex) return Complex_Vector |
| 927 | renames Instantiations."/"; |
| 928 | |
| 929 | function "/" |
| 930 | (Left : Complex_Vector; |
| 931 | Right : Real'Base) return Complex_Vector |
| 932 | renames Instantiations."/"; |
| 933 | |
| 934 | function "/" |
| 935 | (Left : Complex_Matrix; |
| 936 | Right : Complex) return Complex_Matrix |
| 937 | renames Instantiations."/"; |
| 938 | |
| 939 | function "/" |
| 940 | (Left : Complex_Matrix; |
| 941 | Right : Real'Base) return Complex_Matrix |
| 942 | renames Instantiations."/"; |
| 943 | |
| 944 | ----------- |
| 945 | -- "abs" -- |
| 946 | ----------- |
| 947 | |
| 948 | function "abs" (Right : Complex_Vector) return Real'Base |
| 949 | renames Instantiations."abs"; |
| 950 | |
| 951 | -------------- |
| 952 | -- Argument -- |
| 953 | -------------- |
| 954 | |
| 955 | function Argument (X : Complex_Vector) return Real_Vector |
| 956 | renames Instantiations.Argument; |
| 957 | |
| 958 | function Argument |
| 959 | (X : Complex_Vector; |
| 960 | Cycle : Real'Base) return Real_Vector |
| 961 | renames Instantiations.Argument; |
| 962 | |
| 963 | function Argument (X : Complex_Matrix) return Real_Matrix |
| 964 | renames Instantiations.Argument; |
| 965 | |
| 966 | function Argument |
| 967 | (X : Complex_Matrix; |
| 968 | Cycle : Real'Base) return Real_Matrix |
| 969 | renames Instantiations.Argument; |
| 970 | |
| 971 | ---------------------------- |
| 972 | -- Compose_From_Cartesian -- |
| 973 | ---------------------------- |
| 974 | |
| 975 | function Compose_From_Cartesian (Re : Real_Vector) return Complex_Vector |
| 976 | renames Instantiations.Compose_From_Cartesian; |
| 977 | |
| 978 | function Compose_From_Cartesian |
| 979 | (Re : Real_Vector; |
| 980 | Im : Real_Vector) return Complex_Vector |
| 981 | renames Instantiations.Compose_From_Cartesian; |
| 982 | |
| 983 | function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix |
| 984 | renames Instantiations.Compose_From_Cartesian; |
| 985 | |
| 986 | function Compose_From_Cartesian |
| 987 | (Re : Real_Matrix; |
| 988 | Im : Real_Matrix) return Complex_Matrix |
| 989 | renames Instantiations.Compose_From_Cartesian; |
| 990 | |
| 991 | ------------------------ |
| 992 | -- Compose_From_Polar -- |
| 993 | ------------------------ |
| 994 | |
| 995 | function Compose_From_Polar |
| 996 | (Modulus : Real_Vector; |
| 997 | Argument : Real_Vector) return Complex_Vector |
| 998 | renames Instantiations.Compose_From_Polar; |
| 999 | |
| 1000 | function Compose_From_Polar |
| 1001 | (Modulus : Real_Vector; |
| 1002 | Argument : Real_Vector; |
| 1003 | Cycle : Real'Base) return Complex_Vector |
| 1004 | renames Instantiations.Compose_From_Polar; |
| 1005 | |
| 1006 | function Compose_From_Polar |
| 1007 | (Modulus : Real_Matrix; |
| 1008 | Argument : Real_Matrix) return Complex_Matrix |
| 1009 | renames Instantiations.Compose_From_Polar; |
| 1010 | |
| 1011 | function Compose_From_Polar |
| 1012 | (Modulus : Real_Matrix; |
| 1013 | Argument : Real_Matrix; |
| 1014 | Cycle : Real'Base) return Complex_Matrix |
| 1015 | renames Instantiations.Compose_From_Polar; |
| 1016 | |
| 1017 | --------------- |
| 1018 | -- Conjugate -- |
| 1019 | --------------- |
| 1020 | |
| 1021 | function Conjugate (X : Complex_Vector) return Complex_Vector |
| 1022 | renames Instantiations.Conjugate; |
| 1023 | |
| 1024 | function Conjugate (X : Complex_Matrix) return Complex_Matrix |
| 1025 | renames Instantiations.Conjugate; |
| 1026 | |
| 1027 | ----------------- |
| 1028 | -- Determinant -- |
| 1029 | ----------------- |
| 1030 | |
| 1031 | function Determinant (A : Complex_Matrix) return Complex is |
| 1032 | M : Complex_Matrix := A; |
| 1033 | B : Complex_Matrix (A'Range (1), 1 .. 0); |
| 1034 | R : Complex; |
| 1035 | begin |
| 1036 | Forward_Eliminate (M, B, R); |
| 1037 | return R; |
| 1038 | end Determinant; |
| 1039 | |
| 1040 | ----------------- |
| 1041 | -- Eigensystem -- |
| 1042 | ----------------- |
| 1043 | |
| 1044 | procedure Eigensystem |
| 1045 | (A : Complex_Matrix; |
| 1046 | Values : out Real_Vector; |
| 1047 | Vectors : out Complex_Matrix) |
| 1048 | is |
| 1049 | N : constant Natural := Length (A); |
| 1050 | |
| 1051 | -- For a Hermitian matrix C, we convert the eigenvalue problem to a |
| 1052 | -- real symmetric one: if C = A + i * B, then the (N, N) complex |
| 1053 | -- eigenvalue problem: |
| 1054 | -- (A + i * B) * (u + i * v) = Lambda * (u + i * v) |
| 1055 | -- |
| 1056 | -- is equivalent to the (2 * N, 2 * N) real eigenvalue problem: |
| 1057 | -- [ A, B ] [ u ] = Lambda * [ u ] |
| 1058 | -- [ -B, A ] [ v ] [ v ] |
| 1059 | -- |
| 1060 | -- Note that the (2 * N, 2 * N) matrix above is symmetric, as |
| 1061 | -- Transpose (A) = A and Transpose (B) = -B if C is Hermitian. |
| 1062 | |
| 1063 | -- We solve this eigensystem using the real-valued algorithms. The final |
| 1064 | -- result will have every eigenvalue twice, so in the sorted output we |
| 1065 | -- just pick every second value, with associated eigenvector u + i * v. |
| 1066 | |
| 1067 | M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N); |
| 1068 | Vals : Real_Vector (1 .. 2 * N); |
| 1069 | Vecs : Real_Matrix (1 .. 2 * N, 1 .. 2 * N); |
| 1070 | |
| 1071 | begin |
| 1072 | for J in 1 .. N loop |
| 1073 | for K in 1 .. N loop |
| 1074 | declare |
| 1075 | C : constant Complex := |
Bernhard Rosenkraenzer | ee2ec6d | 2012-10-10 01:40:27 +0159 | [diff] [blame^] | 1076 | (A (A'First (1) + (J - 1), A'First (2) + (K - 1))); |
Bernhard Rosenkraenzer | c83ebe5 | 2012-09-18 21:38:03 +0159 | [diff] [blame] | 1077 | begin |
| 1078 | M (J, K) := Re (C); |
| 1079 | M (J + N, K + N) := Re (C); |
| 1080 | M (J + N, K) := Im (C); |
| 1081 | M (J, K + N) := -Im (C); |
| 1082 | end; |
| 1083 | end loop; |
| 1084 | end loop; |
| 1085 | |
| 1086 | Eigensystem (M, Vals, Vecs); |
| 1087 | |
| 1088 | for J in 1 .. N loop |
| 1089 | declare |
| 1090 | Col : constant Integer := Values'First + (J - 1); |
| 1091 | begin |
| 1092 | Values (Col) := Vals (2 * J); |
| 1093 | |
| 1094 | for K in 1 .. N loop |
| 1095 | declare |
| 1096 | Row : constant Integer := Vectors'First (2) + (K - 1); |
| 1097 | begin |
| 1098 | Vectors (Row, Col) |
| 1099 | := (Vecs (J * 2, Col), Vecs (J * 2, Col + N)); |
| 1100 | end; |
| 1101 | end loop; |
| 1102 | end; |
| 1103 | end loop; |
| 1104 | end Eigensystem; |
| 1105 | |
| 1106 | ----------------- |
| 1107 | -- Eigenvalues -- |
| 1108 | ----------------- |
| 1109 | |
| 1110 | function Eigenvalues (A : Complex_Matrix) return Real_Vector is |
| 1111 | -- See Eigensystem for a description of the algorithm |
| 1112 | |
| 1113 | N : constant Natural := Length (A); |
| 1114 | R : Real_Vector (A'Range (1)); |
| 1115 | |
| 1116 | M : Real_Matrix (1 .. 2 * N, 1 .. 2 * N); |
| 1117 | Vals : Real_Vector (1 .. 2 * N); |
| 1118 | begin |
| 1119 | for J in 1 .. N loop |
| 1120 | for K in 1 .. N loop |
| 1121 | declare |
| 1122 | C : constant Complex := |
Bernhard Rosenkraenzer | ee2ec6d | 2012-10-10 01:40:27 +0159 | [diff] [blame^] | 1123 | (A (A'First (1) + (J - 1), A'First (2) + (K - 1))); |
Bernhard Rosenkraenzer | c83ebe5 | 2012-09-18 21:38:03 +0159 | [diff] [blame] | 1124 | begin |
| 1125 | M (J, K) := Re (C); |
| 1126 | M (J + N, K + N) := Re (C); |
| 1127 | M (J + N, K) := Im (C); |
| 1128 | M (J, K + N) := -Im (C); |
| 1129 | end; |
| 1130 | end loop; |
| 1131 | end loop; |
| 1132 | |
| 1133 | Vals := Eigenvalues (M); |
| 1134 | |
| 1135 | for J in 1 .. N loop |
| 1136 | R (A'First (1) + (J - 1)) := Vals (2 * J); |
| 1137 | end loop; |
| 1138 | |
| 1139 | return R; |
| 1140 | end Eigenvalues; |
| 1141 | |
| 1142 | -------- |
| 1143 | -- Im -- |
| 1144 | -------- |
| 1145 | |
| 1146 | function Im (X : Complex_Vector) return Real_Vector |
| 1147 | renames Instantiations.Im; |
| 1148 | |
| 1149 | function Im (X : Complex_Matrix) return Real_Matrix |
| 1150 | renames Instantiations.Im; |
| 1151 | |
| 1152 | ------------- |
| 1153 | -- Inverse -- |
| 1154 | ------------- |
| 1155 | |
| 1156 | function Inverse (A : Complex_Matrix) return Complex_Matrix is |
| 1157 | (Solve (A, Unit_Matrix (Length (A)))); |
| 1158 | |
| 1159 | ------------- |
| 1160 | -- Modulus -- |
| 1161 | ------------- |
| 1162 | |
| 1163 | function Modulus (X : Complex_Vector) return Real_Vector |
| 1164 | renames Instantiations.Modulus; |
| 1165 | |
| 1166 | function Modulus (X : Complex_Matrix) return Real_Matrix |
| 1167 | renames Instantiations.Modulus; |
| 1168 | |
| 1169 | -------- |
| 1170 | -- Re -- |
| 1171 | -------- |
| 1172 | |
| 1173 | function Re (X : Complex_Vector) return Real_Vector |
| 1174 | renames Instantiations.Re; |
| 1175 | |
| 1176 | function Re (X : Complex_Matrix) return Real_Matrix |
| 1177 | renames Instantiations.Re; |
| 1178 | |
| 1179 | ------------ |
| 1180 | -- Set_Im -- |
| 1181 | ------------ |
| 1182 | |
| 1183 | procedure Set_Im |
| 1184 | (X : in out Complex_Matrix; |
| 1185 | Im : Real_Matrix) |
| 1186 | renames Instantiations.Set_Im; |
| 1187 | |
| 1188 | procedure Set_Im |
| 1189 | (X : in out Complex_Vector; |
| 1190 | Im : Real_Vector) |
| 1191 | renames Instantiations.Set_Im; |
| 1192 | |
| 1193 | ------------ |
| 1194 | -- Set_Re -- |
| 1195 | ------------ |
| 1196 | |
| 1197 | procedure Set_Re |
| 1198 | (X : in out Complex_Matrix; |
| 1199 | Re : Real_Matrix) |
| 1200 | renames Instantiations.Set_Re; |
| 1201 | |
| 1202 | procedure Set_Re |
| 1203 | (X : in out Complex_Vector; |
| 1204 | Re : Real_Vector) |
| 1205 | renames Instantiations.Set_Re; |
| 1206 | |
| 1207 | ----------- |
| 1208 | -- Solve -- |
| 1209 | ----------- |
| 1210 | |
| 1211 | function Solve |
| 1212 | (A : Complex_Matrix; |
| 1213 | X : Complex_Vector) return Complex_Vector |
| 1214 | renames Instantiations.Solve; |
| 1215 | |
| 1216 | function Solve |
| 1217 | (A : Complex_Matrix; |
| 1218 | X : Complex_Matrix) return Complex_Matrix |
| 1219 | renames Instantiations.Solve; |
| 1220 | |
| 1221 | --------------- |
| 1222 | -- Transpose -- |
| 1223 | --------------- |
| 1224 | |
| 1225 | function Transpose |
| 1226 | (X : Complex_Matrix) return Complex_Matrix |
| 1227 | is |
| 1228 | R : Complex_Matrix (X'Range (2), X'Range (1)); |
| 1229 | begin |
| 1230 | Transpose (X, R); |
| 1231 | return R; |
| 1232 | end Transpose; |
| 1233 | |
| 1234 | ----------------- |
| 1235 | -- Unit_Matrix -- |
| 1236 | ----------------- |
| 1237 | |
| 1238 | function Unit_Matrix |
| 1239 | (Order : Positive; |
| 1240 | First_1 : Integer := 1; |
| 1241 | First_2 : Integer := 1) return Complex_Matrix |
| 1242 | renames Instantiations.Unit_Matrix; |
| 1243 | |
| 1244 | ----------------- |
| 1245 | -- Unit_Vector -- |
| 1246 | ----------------- |
| 1247 | |
| 1248 | function Unit_Vector |
| 1249 | (Index : Integer; |
| 1250 | Order : Positive; |
| 1251 | First : Integer := 1) return Complex_Vector |
| 1252 | renames Instantiations.Unit_Vector; |
| 1253 | |
| 1254 | end Ada.Numerics.Generic_Complex_Arrays; |