| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | * Copyright (c) 2000-2022 Inria | ||
| 3 | * All rights reserved. | ||
| 4 | * | ||
| 5 | * Redistribution and use in source and binary forms, with or without | ||
| 6 | * modification, are permitted provided that the following conditions are met: | ||
| 7 | * | ||
| 8 | * * Redistributions of source code must retain the above copyright notice, | ||
| 9 | * this list of conditions and the following disclaimer. | ||
| 10 | * * Redistributions in binary form must reproduce the above copyright notice, | ||
| 11 | * this list of conditions and the following disclaimer in the documentation | ||
| 12 | * and/or other materials provided with the distribution. | ||
| 13 | * * Neither the name of the ALICE Project-Team nor the names of its | ||
| 14 | * contributors may be used to endorse or promote products derived from this | ||
| 15 | * software without specific prior written permission. | ||
| 16 | * | ||
| 17 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | ||
| 18 | * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | ||
| 19 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | ||
| 20 | * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE | ||
| 21 | * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | ||
| 22 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | ||
| 23 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | ||
| 24 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | ||
| 25 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | ||
| 26 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | ||
| 27 | * POSSIBILITY OF SUCH DAMAGE. | ||
| 28 | * | ||
| 29 | * Contact: Bruno Levy | ||
| 30 | * | ||
| 31 | * https://www.inria.fr/fr/bruno-levy | ||
| 32 | * | ||
| 33 | * Inria, | ||
| 34 | * Domaine de Voluceau, | ||
| 35 | * 78150 Le Chesnay - Rocquencourt | ||
| 36 | * FRANCE | ||
| 37 | * | ||
| 38 | */ | ||
| 39 | |||
| 40 | #ifndef GEOGRAM_BASIC_MATRIX | ||
| 41 | #define GEOGRAM_BASIC_MATRIX | ||
| 42 | |||
| 43 | #include <geogram/basic/common.h> | ||
| 44 | #include <geogram/basic/vecg.h> | ||
| 45 | #include <initializer_list> | ||
| 46 | |||
| 47 | /** | ||
| 48 | * \file geogram/basic/matrix.h | ||
| 49 | * \brief Generic matrix type | ||
| 50 | */ | ||
| 51 | |||
| 52 | namespace GEO { | ||
| 53 | |||
| 54 | /************************************************************************/ | ||
| 55 | |||
| 56 | |||
| 57 | /** | ||
| 58 | * \brief A matrix type | ||
| 59 | * \details Matrix implements a square matrix of dimension \p DIM. | ||
| 60 | * containing coefficients of type \p T. Type \p T is expected to be a | ||
| 61 | * numeric type. Matrix provides the classical matrix operations. | ||
| 62 | * \tparam FT type of the matrix elements | ||
| 63 | * \tparam DIM dimension of the matrix | ||
| 64 | */ | ||
| 65 | template <index_t DIM, class FT> | ||
| 66 | class Matrix { | ||
| 67 | public: | ||
| 68 | /** This matrix type */ | ||
| 69 | typedef Matrix<DIM, FT> matrix_type; | ||
| 70 | |||
| 71 | /** The type of the values */ | ||
| 72 | typedef FT value_type; | ||
| 73 | |||
| 74 | /** The dimension of the matrix */ | ||
| 75 | static constexpr index_t dim = DIM; | ||
| 76 | |||
| 77 | /** | ||
| 78 | * \brief Default constructor | ||
| 79 | * \details This initializes the matrix to the identity matrix | ||
| 80 | * \see load_identity() | ||
| 81 | */ | ||
| 82 | 508 | inline Matrix() { | |
| 83 | load_identity(); | ||
| 84 | } | ||
| 85 | |||
| 86 | /** | ||
| 87 | * \brief Constructs a matrix from an array of values. | ||
| 88 | * \param[in] vals a const pointer to the DIM*DIM values, | ||
| 89 | * coefficients of the same rows are consecutive in memory, | ||
| 90 | * i is the slowly varying index and j the quickly varying one. | ||
| 91 | */ | ||
| 92 | explicit Matrix(const FT* vals) { | ||
| 93 | for(index_t i = 0; i < DIM; i++) { | ||
| 94 | for(index_t j = 0; j < DIM; j++) { | ||
| 95 | coeff_[i][j] = *vals; | ||
| 96 | ++vals; | ||
| 97 | } | ||
| 98 | } | ||
| 99 | } | ||
| 100 | |||
| 101 | /** | ||
| 102 | * \brief Constructs a matrix from 2d array of initializers. | ||
| 103 | * \param[in] Mi a 2d array of values to be copied to the matrix. | ||
| 104 | */ | ||
| 105 | 4 | Matrix(const std::initializer_list< std::initializer_list<FT> >& Mi) { | |
| 106 | index_t i = 0; | ||
| 107 |
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20 | for(auto& it: Mi) { |
| 108 | index_t j = 0; | ||
| 109 |
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80 | for(auto& jt: it) { |
| 110 | geo_debug_assert(i < DIM); | ||
| 111 | geo_debug_assert(j < DIM); | ||
| 112 | 64 | coeff_[i][j] = jt; | |
| 113 | 64 | ++j; | |
| 114 | } | ||
| 115 | 16 | ++i; | |
| 116 | } | ||
| 117 | 4 | } | |
| 118 | |||
| 119 | |||
| 120 | /** | ||
| 121 | * \brief Gets the matrix dimension | ||
| 122 | * \return the value of \p DIM | ||
| 123 | */ | ||
| 124 | inline index_t dimension() const { | ||
| 125 | return DIM; | ||
| 126 | } | ||
| 127 | |||
| 128 | /** | ||
| 129 | * \brief Clears the matrix | ||
| 130 | * \details This resets all values to 0 (zero) | ||
| 131 | */ | ||
| 132 | inline void load_zero() { | ||
| 133 | for(index_t i = 0; i < DIM; i++) { | ||
| 134 | for(index_t j = 0; j < DIM; j++) { | ||
| 135 | coeff_[i][j] = FT(0); | ||
| 136 | } | ||
| 137 | } | ||
| 138 | } | ||
| 139 | |||
| 140 | /** | ||
| 141 | * \brief Sets the matrix to identity | ||
| 142 | * \details This sets all coefficients of this matrix to be equal to | ||
| 143 | * \p DIM x \p DIM identity matrix. | ||
| 144 | */ | ||
| 145 | inline void load_identity() { | ||
| 146 |
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| 147 |
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15240 | for(index_t j = 0; j < DIM; j++) { |
| 148 |
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21336 | coeff_[i][j] = (i == j) ? FT(1) : FT(0); |
| 149 | } | ||
| 150 | } | ||
| 151 | } | ||
| 152 | |||
| 153 | /** | ||
| 154 | * \brief Tests whether a matrix is the identity matrix. | ||
| 155 | * \retval true if the matrix is the identity matrix | ||
| 156 | * \retval false otherwise | ||
| 157 | */ | ||
| 158 | inline bool is_identity() const { | ||
| 159 | for(index_t i = 0; i < DIM; i++) { | ||
| 160 | for(index_t j = 0; j < DIM; j++) { | ||
| 161 | FT rhs = ((i == j) ? FT(1) : FT(0)); | ||
| 162 | if(coeff_[i][j] != rhs) { | ||
| 163 | return false; | ||
| 164 | } | ||
| 165 | } | ||
| 166 | } | ||
| 167 | return true; | ||
| 168 | } | ||
| 169 | |||
| 170 | /** | ||
| 171 | * \brief Gets a modifiable element | ||
| 172 | * \details Gets element at row \p i and column \p j in the matrix. If | ||
| 173 | * indices are out of range, the function calls abort(). | ||
| 174 | * \param[in] i row index of the element | ||
| 175 | * \param[in] j column index of the element | ||
| 176 | * \return a reference to the element at coordinates (\p i, \p j). | ||
| 177 | */ | ||
| 178 | inline FT& operator() (index_t i, index_t j) { | ||
| 179 | geo_debug_assert(i < DIM); | ||
| 180 | geo_debug_assert(j < DIM); | ||
| 181 | return coeff_[i][j]; | ||
| 182 | } | ||
| 183 | |||
| 184 | /** | ||
| 185 | * \brief Gets a non-modifiable element | ||
| 186 | * \details Gets element at row \p i and column \p j in the matrix. If | ||
| 187 | * indices are out of range, the function calls abort(). | ||
| 188 | * \param[in] i row index of the element | ||
| 189 | * \param[in] j column index of the element | ||
| 190 | * \return a const reference to the element at coordinates (\p i, \p j). | ||
| 191 | */ | ||
| 192 | inline const FT& operator() (index_t i, index_t j) const { | ||
| 193 | geo_debug_assert(i < DIM); | ||
| 194 | geo_debug_assert(j < DIM); | ||
| 195 | 258 | return coeff_[i][j]; | |
| 196 | } | ||
| 197 | |||
| 198 | /** | ||
| 199 | * \brief Adds a matrix in place | ||
| 200 | * \details This adds matrix \p m to this matrix in place. | ||
| 201 | * \param[in] m a matrix of the same dimension | ||
| 202 | * \return a reference to this matrix | ||
| 203 | */ | ||
| 204 | inline matrix_type& operator+= (const matrix_type& m) { | ||
| 205 | for(index_t i = 0; i < DIM; i++) { | ||
| 206 | for(index_t j = 0; j < DIM; j++) { | ||
| 207 | coeff_[i][j] += m.coeff_[i][j]; | ||
| 208 | } | ||
| 209 | } | ||
| 210 | return *this; | ||
| 211 | } | ||
| 212 | |||
| 213 | /** | ||
| 214 | * \brief Subtracts a matrix in place | ||
| 215 | * \details This subtracts matrix \p m from this matrix in place. | ||
| 216 | * \param[in] m a matrix of the same dimension | ||
| 217 | * \return a reference to this matrix | ||
| 218 | */ | ||
| 219 | inline matrix_type& operator-= (const matrix_type& m) { | ||
| 220 | for(index_t i = 0; i < DIM; i++) { | ||
| 221 | for(index_t j = 0; j < DIM; j++) { | ||
| 222 | coeff_[i][j] -= m.coeff_[i][j]; | ||
| 223 | } | ||
| 224 | } | ||
| 225 | return *this; | ||
| 226 | } | ||
| 227 | |||
| 228 | /** | ||
| 229 | * \brief Multiplies by a scalar in place | ||
| 230 | * \details This multiplies all the coefficients of this matrix by the | ||
| 231 | * value \p val. | ||
| 232 | * \param[in] val a scalar value of the same type than matrix elements | ||
| 233 | * \return a reference to this matrix | ||
| 234 | */ | ||
| 235 | inline matrix_type& operator*= (FT val) { | ||
| 236 | for(index_t i = 0; i < DIM; i++) { | ||
| 237 | for(index_t j = 0; j < DIM; j++) { | ||
| 238 | coeff_[i][j] *= val; | ||
| 239 | } | ||
| 240 | } | ||
| 241 | return *this; | ||
| 242 | } | ||
| 243 | |||
| 244 | /** | ||
| 245 | * \brief Divides by a scalar in place | ||
| 246 | * \details This divides all the coefficients of this matrix by the | ||
| 247 | * value \p val. | ||
| 248 | * \param[in] val a scalar value of the same type than matrix elements | ||
| 249 | * \return a reference to this matrix | ||
| 250 | */ | ||
| 251 | inline matrix_type& operator/= (FT val) { | ||
| 252 | for(index_t i = 0; i < DIM; i++) { | ||
| 253 | for(index_t j = 0; j < DIM; j++) { | ||
| 254 | coeff_[i][j] /= val; | ||
| 255 | } | ||
| 256 | } | ||
| 257 | return *this; | ||
| 258 | } | ||
| 259 | |||
| 260 | /** | ||
| 261 | * \brief Adds 2 matrices | ||
| 262 | * \details Builds a matrix by adding matrix \p m to this matrix. | ||
| 263 | * \param[in] m another matrix | ||
| 264 | * \return the matrix (\p this + \p m) | ||
| 265 | */ | ||
| 266 | inline matrix_type operator+ (const matrix_type& m) const { | ||
| 267 | matrix_type result = *this; | ||
| 268 | result += m; | ||
| 269 | return result; | ||
| 270 | } | ||
| 271 | |||
| 272 | /** | ||
| 273 | * \brief Subtracts 2 matrices | ||
| 274 | * \details Builds a matrix by subtracting matrix \p m to this matrix. | ||
| 275 | * \param[in] m another matrix | ||
| 276 | * \return the matrix (\p this + \p m) | ||
| 277 | */ | ||
| 278 | inline matrix_type operator- (const matrix_type& m) const { | ||
| 279 | matrix_type result = *this; | ||
| 280 | result -= m; | ||
| 281 | return result; | ||
| 282 | } | ||
| 283 | |||
| 284 | /** | ||
| 285 | * \brief Multiplies a matrix by a scalar | ||
| 286 | * \details Builds a matrix by multiplying all the coefficients of | ||
| 287 | * this matrix by scalar value \p val. | ||
| 288 | * \param[in] val a scalar value of the same type than matrix elements | ||
| 289 | * \return the resulting matrix | ||
| 290 | */ | ||
| 291 | inline matrix_type operator* (FT val) const { | ||
| 292 | matrix_type result = *this; | ||
| 293 | result *= val; | ||
| 294 | return result; | ||
| 295 | } | ||
| 296 | |||
| 297 | /** | ||
| 298 | * \brief Divides a matrix by a scalar | ||
| 299 | * \details Builds a matrix by dividing all the coefficients of | ||
| 300 | * this matrix by scalar value \p val. | ||
| 301 | * \param[in] val a scalar value of the same type than matrix elements | ||
| 302 | * \return the resulting matrix | ||
| 303 | */ | ||
| 304 | inline matrix_type operator/ (FT val) const { | ||
| 305 | matrix_type result = *this; | ||
| 306 | result /= val; | ||
| 307 | return result; | ||
| 308 | } | ||
| 309 | |||
| 310 | /** | ||
| 311 | * \brief Multiplies 2 matrices | ||
| 312 | * \details Builds a matrix by multiplying this matrix by matrix \p | ||
| 313 | * m. | ||
| 314 | * \param[in] m another matrix | ||
| 315 | * \return the matrix (\p this * \p m) | ||
| 316 | */ | ||
| 317 | matrix_type operator* (const matrix_type& m) const { | ||
| 318 | matrix_type result; | ||
| 319 | for(index_t i = 0; i < DIM; i++) { | ||
| 320 | for(index_t j = 0; j < DIM; j++) { | ||
| 321 | result.coeff_[i][j] = FT(0); | ||
| 322 | for(index_t k = 0; k < DIM; k++) { | ||
| 323 | result.coeff_[i][j] += coeff_[i][k] * m.coeff_[k][j]; | ||
| 324 | } | ||
| 325 | } | ||
| 326 | } | ||
| 327 | return result; | ||
| 328 | } | ||
| 329 | |||
| 330 | /** | ||
| 331 | * \brief Computes the inverse matrix | ||
| 332 | * \details Computes matrix \p M such that (\p this * \p M) = identity | ||
| 333 | * \return the inverse matrix | ||
| 334 | */ | ||
| 335 | matrix_type inverse() const { | ||
| 336 | matrix_type result; | ||
| 337 | bool invertible = compute_inverse(result); | ||
| 338 | geo_assert(invertible); | ||
| 339 | return result; | ||
| 340 | } | ||
| 341 | |||
| 342 | |||
| 343 | /** | ||
| 344 | * \brief Computes the inverse matrix | ||
| 345 | * \details Computes matrix \p M such that (\p this * \p M) = identity | ||
| 346 | * \param[out] result the inverse matrix | ||
| 347 | * \param[in] min_val minimum absolute value of pivot. If lower than | ||
| 348 | * that, the matrix is considered to be non-invertible. | ||
| 349 | * \return true if the matrix is invertible | ||
| 350 | * \retval false otherwise | ||
| 351 | */ | ||
| 352 | bool compute_inverse( | ||
| 353 | matrix_type& result, value_type min_val = value_type(0) | ||
| 354 | ) const { | ||
| 355 | FT val=FT(0.0), val2=FT(0.0); | ||
| 356 | matrix_type tmp = (*this); | ||
| 357 | |||
| 358 | result.load_identity(); | ||
| 359 | |||
| 360 | for(index_t i = 0; i != DIM; i++) { | ||
| 361 | val = tmp(i, i); /* find pivot */ | ||
| 362 | index_t ind = i; | ||
| 363 | for(index_t j = i + 1; j != DIM; j++) { | ||
| 364 | if(fabs(tmp(j, i)) > fabs(val)) { | ||
| 365 | ind = j; | ||
| 366 | val = tmp(j, i); | ||
| 367 | } | ||
| 368 | } | ||
| 369 | |||
| 370 | if(ind != i) { | ||
| 371 | for(index_t j = 0; j != DIM; j++) { | ||
| 372 | val2 = result(i, j); | ||
| 373 | result(i, j) = result(ind, j); | ||
| 374 | result(ind, j) = val2; /* swap columns */ | ||
| 375 | val2 = tmp(i, j); | ||
| 376 | tmp(i, j) = tmp(ind, j); | ||
| 377 | tmp(ind, j) = val2; | ||
| 378 | } | ||
| 379 | } | ||
| 380 | |||
| 381 | if(abs(val) <= min_val) { | ||
| 382 | return false; | ||
| 383 | } | ||
| 384 | |||
| 385 | for(index_t j = 0; j != DIM; j++) { | ||
| 386 | tmp(i, j) /= val; | ||
| 387 | result(i, j) /= val; | ||
| 388 | } | ||
| 389 | |||
| 390 | for(index_t j = 0; j != DIM; j++) { | ||
| 391 | if(j == i) { | ||
| 392 | continue; /* eliminate column */ | ||
| 393 | } | ||
| 394 | val = tmp(j, i); | ||
| 395 | for(index_t k = 0; k != DIM; k++) { | ||
| 396 | tmp(j, k) -= tmp(i, k) * val; | ||
| 397 | result(j, k) -= result(i, k) * val; | ||
| 398 | } | ||
| 399 | } | ||
| 400 | } | ||
| 401 | |||
| 402 | return true; | ||
| 403 | } | ||
| 404 | |||
| 405 | /** | ||
| 406 | * \brief Computes the transposed matrix | ||
| 407 | * \return the transposed matrix | ||
| 408 | */ | ||
| 409 | matrix_type transpose() const { | ||
| 410 | matrix_type result; | ||
| 411 | for(index_t i = 0; i < DIM; i++) { | ||
| 412 | for(index_t j = 0; j < DIM; j++) { | ||
| 413 | result(i, j) = (* this)(j, i); | ||
| 414 | } | ||
| 415 | } | ||
| 416 | return result; | ||
| 417 | } | ||
| 418 | |||
| 419 | /** For interfacing with Fortran, OpenGL etc... */ | ||
| 420 | |||
| 421 | /** | ||
| 422 | * \brief Gets non-modifiable matrix data | ||
| 423 | * \return a const pointer to the first element of the matrix | ||
| 424 | */ | ||
| 425 | inline const FT* data() const { | ||
| 426 | return &(coeff_[0][0]); | ||
| 427 | } | ||
| 428 | |||
| 429 | /** For interfacing with Fortran, OpenGL etc... */ | ||
| 430 | |||
| 431 | /** | ||
| 432 | * \brief Gets modifiable matrix data | ||
| 433 | * \return a pointer to the first element of the matrix | ||
| 434 | */ | ||
| 435 | inline FT* data() { | ||
| 436 | return &(coeff_[0][0]); | ||
| 437 | } | ||
| 438 | |||
| 439 | /** | ||
| 440 | * \brief Gets the lower triangle of the matrix | ||
| 441 | * \details Gets all the coefficients of the matrix under the | ||
| 442 | * diagonal (included) to array \p store, Array \p store must be large | ||
| 443 | * enough to contain (DIM * (DIM+1))/2 values. | ||
| 444 | * \param[in] store an array of at least (DIM * (DIM+1))/2 values | ||
| 445 | */ | ||
| 446 | void get_lower_triangle(FT* store) const { | ||
| 447 | for(index_t i = 0; i < DIM; i++) { | ||
| 448 | for(index_t j = 0; j <= i; j++) { | ||
| 449 | *store++ = coeff_[i][j]; | ||
| 450 | } | ||
| 451 | } | ||
| 452 | } | ||
| 453 | |||
| 454 | private: | ||
| 455 | FT coeff_[DIM][DIM]; | ||
| 456 | }; | ||
| 457 | |||
| 458 | /************************************************************************/ | ||
| 459 | |||
| 460 | /** | ||
| 461 | * \brief Writes a matrix to a stream | ||
| 462 | * \details This writes the coefficients of matrix \p m separated by a | ||
| 463 | * space character to the output stream \p output. | ||
| 464 | * \param[in] output the output stream | ||
| 465 | * \param[in] m the matrix to write | ||
| 466 | * \return a reference to the output stream \p output | ||
| 467 | * \relates Matrix | ||
| 468 | */ | ||
| 469 | template <index_t DIM, class FT> | ||
| 470 | inline std::ostream& operator<< ( | ||
| 471 | std::ostream& output, const Matrix<DIM, FT>& m | ||
| 472 | ) { | ||
| 473 | const char* sep = ""; | ||
| 474 | for(index_t i = 0; i < DIM; i++) { | ||
| 475 | for(index_t j = 0; j < DIM; j++) { | ||
| 476 | output << sep << m(i, j); | ||
| 477 | sep = " "; | ||
| 478 | } | ||
| 479 | } | ||
| 480 | return output; | ||
| 481 | } | ||
| 482 | |||
| 483 | /** | ||
| 484 | * \brief Reads a matrix from a stream | ||
| 485 | * \details This reads \p DIM * \p DIM coefficients from the input stream | ||
| 486 | * \p input and stores them in matrix \p m | ||
| 487 | * \param[in] input the input stream | ||
| 488 | * \param[out] m the matrix to read | ||
| 489 | * \return a reference to the input stream \p input | ||
| 490 | * \relates Matrix | ||
| 491 | */ | ||
| 492 | template <index_t DIM, class FT> | ||
| 493 | inline std::istream& operator>> ( | ||
| 494 | std::istream& input, Matrix<DIM, FT>& m | ||
| 495 | ) { | ||
| 496 | for(index_t i = 0; i < DIM; i++) { | ||
| 497 | for(index_t j = 0; j < DIM; j++) { | ||
| 498 | input >> m(i, j); | ||
| 499 | } | ||
| 500 | } | ||
| 501 | return input; | ||
| 502 | } | ||
| 503 | |||
| 504 | /************************************************************************/ | ||
| 505 | |||
| 506 | /** | ||
| 507 | * \brief Multiplies a matrix by a vector | ||
| 508 | * \details Multiplies matrix \p M by vector \p x and stores the result in | ||
| 509 | * vector y. Vectors \p x and \p y are given as arrays of elements and | ||
| 510 | * must at least contain \p DIM elements, otherwise the result is | ||
| 511 | * undefined. | ||
| 512 | * \param[in] M a \p DIM x \p DIM matrix | ||
| 513 | * \param[in] x the input vector | ||
| 514 | * \param[in] y the result of the multiplication | ||
| 515 | * \tparam FT the type of the matrix elements | ||
| 516 | * \tparam DIM the dimension of the matrix | ||
| 517 | * \relates Matrix | ||
| 518 | */ | ||
| 519 | template <index_t DIM, class FT> inline | ||
| 520 | void mult(const Matrix<DIM, FT>& M, const FT* x, FT* y) { | ||
| 521 | for(index_t i = 0; i < DIM; i++) { | ||
| 522 | y[i] = 0; | ||
| 523 | for(index_t j = 0; j < DIM; j++) { | ||
| 524 | y[i] += M(i, j) * x[j]; | ||
| 525 | } | ||
| 526 | } | ||
| 527 | } | ||
| 528 | |||
| 529 | /************************************************************************/ | ||
| 530 | |||
| 531 | /** | ||
| 532 | * \brief Computes a matrix vector product. | ||
| 533 | * \param[in] M the matrix | ||
| 534 | * \param[in] x the vector | ||
| 535 | * \return \p M times \p x | ||
| 536 | * \note This function copies the resulting vector, thus it is not | ||
| 537 | * very efficient and should be only used when prototyping. | ||
| 538 | */ | ||
| 539 | template <index_t DIM, class FT> inline | ||
| 540 | 60625 | vecng<DIM,FT> operator*( | |
| 541 | const Matrix<DIM, FT>& M, const vecng<DIM,FT>& x | ||
| 542 | ) { | ||
| 543 | vecng<DIM,FT> y; | ||
| 544 |
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303125 | for(index_t i = 0; i < DIM; i++) { |
| 545 | 242500 | y[i] = 0; | |
| 546 |
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1212500 | for(index_t j = 0; j < DIM; j++) { |
| 547 | 970000 | y[i] += M(i, j) * x[j]; | |
| 548 | } | ||
| 549 | } | ||
| 550 | 60625 | return y; | |
| 551 | } | ||
| 552 | |||
| 553 | /************************************************************************/ | ||
| 554 | |||
| 555 | /** | ||
| 556 | * \brief Computes a matrix vector product. | ||
| 557 | * \param[in] x the vector considered as a row vector | ||
| 558 | * \param[in] M the matrix | ||
| 559 | * \return \p x times \p M | ||
| 560 | * \note This function copies the resulting vector, thus it is not | ||
| 561 | * very efficient and should be only used when prototyping. | ||
| 562 | */ | ||
| 563 | template <index_t DIM, class FT> inline | ||
| 564 | vecng<DIM,FT> operator*( | ||
| 565 | const vecng<DIM,FT>& x, const Matrix<DIM, FT>& M | ||
| 566 | ) { | ||
| 567 | vecng<DIM,FT> y; | ||
| 568 | for(index_t i = 0; i < DIM; i++) { | ||
| 569 | y[i] = 0; | ||
| 570 | for(index_t j = 0; j < DIM; j++) { | ||
| 571 | y[i] += M(j, i) * x[j]; | ||
| 572 | } | ||
| 573 | } | ||
| 574 | return y; | ||
| 575 | } | ||
| 576 | |||
| 577 | |||
| 578 | /************************************************************************/ | ||
| 579 | |||
| 580 | #ifndef GOMGEN | ||
| 581 | |||
| 582 | /** | ||
| 583 | * \brief Computes a matrix vector product. | ||
| 584 | * \param[in] M the matrix | ||
| 585 | * \param[in] x the vector | ||
| 586 | * \return \p M times \p x | ||
| 587 | * \note This function copies the resulting vector, thus it is not | ||
| 588 | * very efficient and should be only used when prototyping. | ||
| 589 | */ | ||
| 590 | template <index_t DIM, class FT> | ||
| 591 | [[deprecated("use operator*(matrix, vector) instead")]] | ||
| 592 | inline vecng<DIM,FT> mult( | ||
| 593 | const Matrix<DIM, FT>& M, const vecng<DIM,FT>& x | ||
| 594 | ) { | ||
| 595 | vecng<DIM,FT> y; | ||
| 596 | for(index_t i = 0; i < DIM; i++) { | ||
| 597 | y[i] = 0; | ||
| 598 | for(index_t j = 0; j < DIM; j++) { | ||
| 599 | y[i] += M(i, j) * x[j]; | ||
| 600 | } | ||
| 601 | } | ||
| 602 | return y; | ||
| 603 | } | ||
| 604 | |||
| 605 | #endif | ||
| 606 | |||
| 607 | /************************************************************************/ | ||
| 608 | |||
| 609 | } | ||
| 610 | |||
| 611 | #endif | ||
| 612 |