| 1 |
/* |
| 2 |
* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
| 3 |
* |
| 4 |
* The University of Notre Dame grants you ("Licensee") a |
| 5 |
* non-exclusive, royalty free, license to use, modify and |
| 6 |
* redistribute this software in source and binary code form, provided |
| 7 |
* that the following conditions are met: |
| 8 |
* |
| 9 |
* 1. Redistributions of source code must retain the above copyright |
| 10 |
* notice, this list of conditions and the following disclaimer. |
| 11 |
* |
| 12 |
* 2. Redistributions in binary form must reproduce the above copyright |
| 13 |
* notice, this list of conditions and the following disclaimer in the |
| 14 |
* documentation and/or other materials provided with the |
| 15 |
* distribution. |
| 16 |
* |
| 17 |
* This software is provided "AS IS," without a warranty of any |
| 18 |
* kind. All express or implied conditions, representations and |
| 19 |
* warranties, including any implied warranty of merchantability, |
| 20 |
* fitness for a particular purpose or non-infringement, are hereby |
| 21 |
* excluded. The University of Notre Dame and its licensors shall not |
| 22 |
* be liable for any damages suffered by licensee as a result of |
| 23 |
* using, modifying or distributing the software or its |
| 24 |
* derivatives. In no event will the University of Notre Dame or its |
| 25 |
* licensors be liable for any lost revenue, profit or data, or for |
| 26 |
* direct, indirect, special, consequential, incidental or punitive |
| 27 |
* damages, however caused and regardless of the theory of liability, |
| 28 |
* arising out of the use of or inability to use software, even if the |
| 29 |
* University of Notre Dame has been advised of the possibility of |
| 30 |
* such damages. |
| 31 |
* |
| 32 |
* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your |
| 33 |
* research, please cite the appropriate papers when you publish your |
| 34 |
* work. Good starting points are: |
| 35 |
* |
| 36 |
* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
| 37 |
* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
| 38 |
* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008). |
| 39 |
* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010). |
| 40 |
* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011). |
| 41 |
*/ |
| 42 |
|
| 43 |
/** |
| 44 |
* @file RectMatrix.hpp |
| 45 |
* @author Teng Lin |
| 46 |
* @date 10/11/2004 |
| 47 |
* @version 1.0 |
| 48 |
*/ |
| 49 |
|
| 50 |
#ifndef MATH_RECTMATRIX_HPP |
| 51 |
#define MATH_RECTMATRIX_HPP |
| 52 |
#include <math.h> |
| 53 |
#include <cmath> |
| 54 |
#include "Vector.hpp" |
| 55 |
|
| 56 |
namespace OpenMD { |
| 57 |
|
| 58 |
/** |
| 59 |
* @class RectMatrix RectMatrix.hpp "math/RectMatrix.hpp" |
| 60 |
* @brief rectangular matrix class |
| 61 |
*/ |
| 62 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 63 |
class RectMatrix { |
| 64 |
public: |
| 65 |
typedef Real ElemType; |
| 66 |
typedef Real* ElemPoinerType; |
| 67 |
|
| 68 |
/** default constructor */ |
| 69 |
RectMatrix() { |
| 70 |
for (unsigned int i = 0; i < Row; i++) |
| 71 |
for (unsigned int j = 0; j < Col; j++) |
| 72 |
this->data_[i][j] = 0.0; |
| 73 |
} |
| 74 |
|
| 75 |
/** Constructs and initializes every element of this matrix to a scalar */ |
| 76 |
RectMatrix(Real s) { |
| 77 |
for (unsigned int i = 0; i < Row; i++) |
| 78 |
for (unsigned int j = 0; j < Col; j++) |
| 79 |
this->data_[i][j] = s; |
| 80 |
} |
| 81 |
|
| 82 |
RectMatrix(Real* array) { |
| 83 |
for (unsigned int i = 0; i < Row; i++) |
| 84 |
for (unsigned int j = 0; j < Col; j++) |
| 85 |
this->data_[i][j] = array[i * Row + j]; |
| 86 |
} |
| 87 |
|
| 88 |
/** copy constructor */ |
| 89 |
RectMatrix(const RectMatrix<Real, Row, Col>& m) { |
| 90 |
*this = m; |
| 91 |
} |
| 92 |
|
| 93 |
/** destructor*/ |
| 94 |
~RectMatrix() {} |
| 95 |
|
| 96 |
/** copy assignment operator */ |
| 97 |
RectMatrix<Real, Row, Col>& operator =(const RectMatrix<Real, Row, Col>& m) { |
| 98 |
if (this == &m) |
| 99 |
return *this; |
| 100 |
|
| 101 |
for (unsigned int i = 0; i < Row; i++) |
| 102 |
for (unsigned int j = 0; j < Col; j++) |
| 103 |
this->data_[i][j] = m.data_[i][j]; |
| 104 |
return *this; |
| 105 |
} |
| 106 |
|
| 107 |
/** |
| 108 |
* Return the reference of a single element of this matrix. |
| 109 |
* @return the reference of a single element of this matrix |
| 110 |
* @param i row index |
| 111 |
* @param j Column index |
| 112 |
*/ |
| 113 |
Real& operator()(unsigned int i, unsigned int j) { |
| 114 |
//assert( i < Row && j < Col); |
| 115 |
return this->data_[i][j]; |
| 116 |
} |
| 117 |
|
| 118 |
/** |
| 119 |
* Return the value of a single element of this matrix. |
| 120 |
* @return the value of a single element of this matrix |
| 121 |
* @param i row index |
| 122 |
* @param j Column index |
| 123 |
*/ |
| 124 |
Real operator()(unsigned int i, unsigned int j) const { |
| 125 |
|
| 126 |
return this->data_[i][j]; |
| 127 |
} |
| 128 |
|
| 129 |
/** |
| 130 |
* Copy the internal data to an array |
| 131 |
* @param array the pointer of destination array |
| 132 |
*/ |
| 133 |
void getArray(Real* array) { |
| 134 |
for (unsigned int i = 0; i < Row; i++) { |
| 135 |
for (unsigned int j = 0; j < Col; j++) { |
| 136 |
array[i * Row + j] = this->data_[i][j]; |
| 137 |
} |
| 138 |
} |
| 139 |
} |
| 140 |
|
| 141 |
|
| 142 |
/** Returns the pointer of internal array */ |
| 143 |
Real* getArrayPointer() { |
| 144 |
return &this->data_[0][0]; |
| 145 |
} |
| 146 |
|
| 147 |
/** |
| 148 |
* Returns a row of this matrix as a vector. |
| 149 |
* @return a row of this matrix as a vector |
| 150 |
* @param row the row index |
| 151 |
*/ |
| 152 |
Vector<Real, Row> getRow(unsigned int row) { |
| 153 |
Vector<Real, Row> v; |
| 154 |
|
| 155 |
for (unsigned int i = 0; i < Col; i++) |
| 156 |
v[i] = this->data_[row][i]; |
| 157 |
|
| 158 |
return v; |
| 159 |
} |
| 160 |
|
| 161 |
/** |
| 162 |
* Sets a row of this matrix |
| 163 |
* @param row the row index |
| 164 |
* @param v the vector to be set |
| 165 |
*/ |
| 166 |
void setRow(unsigned int row, const Vector<Real, Row>& v) { |
| 167 |
|
| 168 |
for (unsigned int i = 0; i < Col; i++) |
| 169 |
this->data_[row][i] = v[i]; |
| 170 |
} |
| 171 |
|
| 172 |
/** |
| 173 |
* Returns a column of this matrix as a vector. |
| 174 |
* @return a column of this matrix as a vector |
| 175 |
* @param col the column index |
| 176 |
*/ |
| 177 |
Vector<Real, Col> getColumn(unsigned int col) { |
| 178 |
Vector<Real, Col> v; |
| 179 |
|
| 180 |
for (unsigned int j = 0; j < Row; j++) |
| 181 |
v[j] = this->data_[j][col]; |
| 182 |
|
| 183 |
return v; |
| 184 |
} |
| 185 |
|
| 186 |
/** |
| 187 |
* Sets a column of this matrix |
| 188 |
* @param col the column index |
| 189 |
* @param v the vector to be set |
| 190 |
*/ |
| 191 |
void setColumn(unsigned int col, const Vector<Real, Col>& v){ |
| 192 |
|
| 193 |
for (unsigned int j = 0; j < Row; j++) |
| 194 |
this->data_[j][col] = v[j]; |
| 195 |
} |
| 196 |
|
| 197 |
/** |
| 198 |
* swap two rows of this matrix |
| 199 |
* @param i the first row |
| 200 |
* @param j the second row |
| 201 |
*/ |
| 202 |
void swapRow(unsigned int i, unsigned int j){ |
| 203 |
assert(i < Row && j < Row); |
| 204 |
|
| 205 |
for (unsigned int k = 0; k < Col; k++) |
| 206 |
std::swap(this->data_[i][k], this->data_[j][k]); |
| 207 |
} |
| 208 |
|
| 209 |
/** |
| 210 |
* swap two Columns of this matrix |
| 211 |
* @param i the first Column |
| 212 |
* @param j the second Column |
| 213 |
*/ |
| 214 |
void swapColumn(unsigned int i, unsigned int j){ |
| 215 |
assert(i < Col && j < Col); |
| 216 |
|
| 217 |
for (unsigned int k = 0; k < Row; k++) |
| 218 |
std::swap(this->data_[k][i], this->data_[k][j]); |
| 219 |
} |
| 220 |
|
| 221 |
/** |
| 222 |
* Tests if this matrix is identical to matrix m |
| 223 |
* @return true if this matrix is equal to the matrix m, return false otherwise |
| 224 |
* @param m matrix to be compared |
| 225 |
* |
| 226 |
* @todo replace operator == by template function equal |
| 227 |
*/ |
| 228 |
bool operator ==(const RectMatrix<Real, Row, Col>& m) { |
| 229 |
for (unsigned int i = 0; i < Row; i++) |
| 230 |
for (unsigned int j = 0; j < Col; j++) |
| 231 |
if (!equal(this->data_[i][j], m.data_[i][j])) |
| 232 |
return false; |
| 233 |
|
| 234 |
return true; |
| 235 |
} |
| 236 |
|
| 237 |
/** |
| 238 |
* Tests if this matrix is not equal to matrix m |
| 239 |
* @return true if this matrix is not equal to the matrix m, return false otherwise |
| 240 |
* @param m matrix to be compared |
| 241 |
*/ |
| 242 |
bool operator !=(const RectMatrix<Real, Row, Col>& m) { |
| 243 |
return !(*this == m); |
| 244 |
} |
| 245 |
|
| 246 |
/** Negates the value of this matrix in place. */ |
| 247 |
inline void negate() { |
| 248 |
for (unsigned int i = 0; i < Row; i++) |
| 249 |
for (unsigned int j = 0; j < Col; j++) |
| 250 |
this->data_[i][j] = -this->data_[i][j]; |
| 251 |
} |
| 252 |
|
| 253 |
/** |
| 254 |
* Sets the value of this matrix to the negation of matrix m. |
| 255 |
* @param m the source matrix |
| 256 |
*/ |
| 257 |
inline void negate(const RectMatrix<Real, Row, Col>& m) { |
| 258 |
for (unsigned int i = 0; i < Row; i++) |
| 259 |
for (unsigned int j = 0; j < Col; j++) |
| 260 |
this->data_[i][j] = -m.data_[i][j]; |
| 261 |
} |
| 262 |
|
| 263 |
/** |
| 264 |
* Sets the value of this matrix to the sum of itself and m (*this += m). |
| 265 |
* @param m the other matrix |
| 266 |
*/ |
| 267 |
inline void add( const RectMatrix<Real, Row, Col>& m ) { |
| 268 |
for (unsigned int i = 0; i < Row; i++) |
| 269 |
for (unsigned int j = 0; j < Col; j++) |
| 270 |
this->data_[i][j] += m.data_[i][j]; |
| 271 |
} |
| 272 |
|
| 273 |
/** |
| 274 |
* Sets the value of this matrix to the sum of m1 and m2 (*this = m1 + m2). |
| 275 |
* @param m1 the first matrix |
| 276 |
* @param m2 the second matrix |
| 277 |
*/ |
| 278 |
inline void add( const RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2 ) { |
| 279 |
for (unsigned int i = 0; i < Row; i++) |
| 280 |
for (unsigned int j = 0; j < Col; j++) |
| 281 |
this->data_[i][j] = m1.data_[i][j] + m2.data_[i][j]; |
| 282 |
} |
| 283 |
|
| 284 |
/** |
| 285 |
* Sets the value of this matrix to the difference of itself and m (*this -= m). |
| 286 |
* @param m the other matrix |
| 287 |
*/ |
| 288 |
inline void sub( const RectMatrix<Real, Row, Col>& m ) { |
| 289 |
for (unsigned int i = 0; i < Row; i++) |
| 290 |
for (unsigned int j = 0; j < Col; j++) |
| 291 |
this->data_[i][j] -= m.data_[i][j]; |
| 292 |
} |
| 293 |
|
| 294 |
/** |
| 295 |
* Sets the value of this matrix to the difference of matrix m1 and m2 (*this = m1 - m2). |
| 296 |
* @param m1 the first matrix |
| 297 |
* @param m2 the second matrix |
| 298 |
*/ |
| 299 |
inline void sub( const RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2){ |
| 300 |
for (unsigned int i = 0; i < Row; i++) |
| 301 |
for (unsigned int j = 0; j < Col; j++) |
| 302 |
this->data_[i][j] = m1.data_[i][j] - m2.data_[i][j]; |
| 303 |
} |
| 304 |
|
| 305 |
/** |
| 306 |
* Sets the value of this matrix to the scalar multiplication of itself (*this *= s). |
| 307 |
* @param s the scalar value |
| 308 |
*/ |
| 309 |
inline void mul( Real s ) { |
| 310 |
for (unsigned int i = 0; i < Row; i++) |
| 311 |
for (unsigned int j = 0; j < Col; j++) |
| 312 |
this->data_[i][j] *= s; |
| 313 |
} |
| 314 |
|
| 315 |
/** |
| 316 |
* Sets the value of this matrix to the scalar multiplication of matrix m (*this = s * m). |
| 317 |
* @param s the scalar value |
| 318 |
* @param m the matrix |
| 319 |
*/ |
| 320 |
inline void mul( Real s, const RectMatrix<Real, Row, Col>& m ) { |
| 321 |
for (unsigned int i = 0; i < Row; i++) |
| 322 |
for (unsigned int j = 0; j < Col; j++) |
| 323 |
this->data_[i][j] = s * m.data_[i][j]; |
| 324 |
} |
| 325 |
|
| 326 |
/** |
| 327 |
* Sets the value of this matrix to the scalar division of itself (*this /= s ). |
| 328 |
* @param s the scalar value |
| 329 |
*/ |
| 330 |
inline void div( Real s) { |
| 331 |
for (unsigned int i = 0; i < Row; i++) |
| 332 |
for (unsigned int j = 0; j < Col; j++) |
| 333 |
this->data_[i][j] /= s; |
| 334 |
} |
| 335 |
|
| 336 |
/** |
| 337 |
* Sets the value of this matrix to the scalar division of matrix m (*this = m /s). |
| 338 |
* @param s the scalar value |
| 339 |
* @param m the matrix |
| 340 |
*/ |
| 341 |
inline void div( Real s, const RectMatrix<Real, Row, Col>& m ) { |
| 342 |
for (unsigned int i = 0; i < Row; i++) |
| 343 |
for (unsigned int j = 0; j < Col; j++) |
| 344 |
this->data_[i][j] = m.data_[i][j] / s; |
| 345 |
} |
| 346 |
|
| 347 |
/** |
| 348 |
* Multiples a scalar into every element of this matrix. |
| 349 |
* @param s the scalar value |
| 350 |
*/ |
| 351 |
RectMatrix<Real, Row, Col>& operator *=(const Real s) { |
| 352 |
this->mul(s); |
| 353 |
return *this; |
| 354 |
} |
| 355 |
|
| 356 |
/** |
| 357 |
* Divides every element of this matrix by a scalar. |
| 358 |
* @param s the scalar value |
| 359 |
*/ |
| 360 |
RectMatrix<Real, Row, Col>& operator /=(const Real s) { |
| 361 |
this->div(s); |
| 362 |
return *this; |
| 363 |
} |
| 364 |
|
| 365 |
/** |
| 366 |
* Sets the value of this matrix to the sum of the other matrix and itself (*this += m). |
| 367 |
* @param m the other matrix |
| 368 |
*/ |
| 369 |
RectMatrix<Real, Row, Col>& operator += (const RectMatrix<Real, Row, Col>& m) { |
| 370 |
add(m); |
| 371 |
return *this; |
| 372 |
} |
| 373 |
|
| 374 |
/** |
| 375 |
* Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m) |
| 376 |
* @param m the other matrix |
| 377 |
*/ |
| 378 |
RectMatrix<Real, Row, Col>& operator -= (const RectMatrix<Real, Row, Col>& m){ |
| 379 |
sub(m); |
| 380 |
return *this; |
| 381 |
} |
| 382 |
|
| 383 |
/** Return the transpose of this matrix */ |
| 384 |
RectMatrix<Real, Col, Row> transpose() const{ |
| 385 |
RectMatrix<Real, Col, Row> result; |
| 386 |
|
| 387 |
for (unsigned int i = 0; i < Row; i++) |
| 388 |
for (unsigned int j = 0; j < Col; j++) |
| 389 |
result(j, i) = this->data_[i][j]; |
| 390 |
|
| 391 |
return result; |
| 392 |
} |
| 393 |
|
| 394 |
template<class MatrixType> |
| 395 |
void setSubMatrix(unsigned int beginRow, unsigned int beginCol, const MatrixType& m) { |
| 396 |
assert(beginRow + m.getNRow() -1 <= getNRow()); |
| 397 |
assert(beginCol + m.getNCol() -1 <= getNCol()); |
| 398 |
|
| 399 |
for (unsigned int i = 0; i < m.getNRow(); ++i) |
| 400 |
for (unsigned int j = 0; j < m.getNCol(); ++j) |
| 401 |
this->data_[beginRow+i][beginCol+j] = m(i, j); |
| 402 |
} |
| 403 |
|
| 404 |
template<class MatrixType> |
| 405 |
void getSubMatrix(unsigned int beginRow, unsigned int beginCol, MatrixType& m) { |
| 406 |
assert(beginRow + m.getNRow() -1 <= getNRow()); |
| 407 |
assert(beginCol + m.getNCol() - 1 <= getNCol()); |
| 408 |
|
| 409 |
for (unsigned int i = 0; i < m.getNRow(); ++i) |
| 410 |
for (unsigned int j = 0; j < m.getNCol(); ++j) |
| 411 |
m(i, j) = this->data_[beginRow+i][beginCol+j]; |
| 412 |
} |
| 413 |
|
| 414 |
unsigned int getNRow() const {return Row;} |
| 415 |
unsigned int getNCol() const {return Col;} |
| 416 |
|
| 417 |
protected: |
| 418 |
Real data_[Row][Col]; |
| 419 |
}; |
| 420 |
|
| 421 |
/** Negate the value of every element of this matrix. */ |
| 422 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 423 |
inline RectMatrix<Real, Row, Col> operator -(const RectMatrix<Real, Row, Col>& m) { |
| 424 |
RectMatrix<Real, Row, Col> result(m); |
| 425 |
|
| 426 |
result.negate(); |
| 427 |
|
| 428 |
return result; |
| 429 |
} |
| 430 |
|
| 431 |
/** |
| 432 |
* Return the sum of two matrixes (m1 + m2). |
| 433 |
* @return the sum of two matrixes |
| 434 |
* @param m1 the first matrix |
| 435 |
* @param m2 the second matrix |
| 436 |
*/ |
| 437 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 438 |
inline RectMatrix<Real, Row, Col> operator + (const RectMatrix<Real, Row, Col>& m1,const RectMatrix<Real, Row, Col>& m2) { |
| 439 |
RectMatrix<Real, Row, Col> result; |
| 440 |
|
| 441 |
result.add(m1, m2); |
| 442 |
|
| 443 |
return result; |
| 444 |
} |
| 445 |
|
| 446 |
/** |
| 447 |
* Return the difference of two matrixes (m1 - m2). |
| 448 |
* @return the sum of two matrixes |
| 449 |
* @param m1 the first matrix |
| 450 |
* @param m2 the second matrix |
| 451 |
*/ |
| 452 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 453 |
inline RectMatrix<Real, Row, Col> operator - (const RectMatrix<Real, Row, Col>& m1, const RectMatrix<Real, Row, Col>& m2) { |
| 454 |
RectMatrix<Real, Row, Col> result; |
| 455 |
|
| 456 |
result.sub(m1, m2); |
| 457 |
|
| 458 |
return result; |
| 459 |
} |
| 460 |
|
| 461 |
/** |
| 462 |
* Return the multiplication of scalra and matrix (m * s). |
| 463 |
* @return the multiplication of a scalra and a matrix |
| 464 |
* @param m the matrix |
| 465 |
* @param s the scalar |
| 466 |
*/ |
| 467 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 468 |
inline RectMatrix<Real, Row, Col> operator *(const RectMatrix<Real, Row, Col>& m, Real s) { |
| 469 |
RectMatrix<Real, Row, Col> result; |
| 470 |
|
| 471 |
result.mul(s, m); |
| 472 |
|
| 473 |
return result; |
| 474 |
} |
| 475 |
|
| 476 |
/** |
| 477 |
* Return the multiplication of a scalra and a matrix (s * m). |
| 478 |
* @return the multiplication of a scalra and a matrix |
| 479 |
* @param s the scalar |
| 480 |
* @param m the matrix |
| 481 |
*/ |
| 482 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 483 |
inline RectMatrix<Real, Row, Col> operator *(Real s, const RectMatrix<Real, Row, Col>& m) { |
| 484 |
RectMatrix<Real, Row, Col> result; |
| 485 |
|
| 486 |
result.mul(s, m); |
| 487 |
|
| 488 |
return result; |
| 489 |
} |
| 490 |
|
| 491 |
/** |
| 492 |
* Return the multiplication of two matrixes (m1 * m2). |
| 493 |
* @return the multiplication of two matrixes |
| 494 |
* @param m1 the first matrix |
| 495 |
* @param m2 the second matrix |
| 496 |
*/ |
| 497 |
template<typename Real, unsigned int Row, unsigned int Col, unsigned int SameDim> |
| 498 |
inline RectMatrix<Real, Row, Col> operator *(const RectMatrix<Real, Row, SameDim>& m1, const RectMatrix<Real, SameDim, Col>& m2) { |
| 499 |
RectMatrix<Real, Row, Col> result; |
| 500 |
|
| 501 |
for (unsigned int i = 0; i < Row; i++) |
| 502 |
for (unsigned int j = 0; j < Col; j++) |
| 503 |
for (unsigned int k = 0; k < SameDim; k++) |
| 504 |
result(i, j) += m1(i, k) * m2(k, j); |
| 505 |
|
| 506 |
return result; |
| 507 |
} |
| 508 |
|
| 509 |
/** |
| 510 |
* Returns the multiplication of a matrix and a vector (m * v). |
| 511 |
* @return the multiplication of a matrix and a vector |
| 512 |
* @param m the matrix |
| 513 |
* @param v the vector |
| 514 |
*/ |
| 515 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 516 |
inline Vector<Real, Row> operator *(const RectMatrix<Real, Row, Col>& m, const Vector<Real, Col>& v) { |
| 517 |
Vector<Real, Row> result; |
| 518 |
|
| 519 |
for (unsigned int i = 0; i < Row ; i++) |
| 520 |
for (unsigned int j = 0; j < Col ; j++) |
| 521 |
result[i] += m(i, j) * v[j]; |
| 522 |
|
| 523 |
return result; |
| 524 |
} |
| 525 |
|
| 526 |
/** |
| 527 |
* Returns the multiplication of a vector transpose and a matrix (v^T * m). |
| 528 |
* @return the multiplication of a vector transpose and a matrix |
| 529 |
* @param v the vector |
| 530 |
* @param m the matrix |
| 531 |
*/ |
| 532 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 533 |
inline Vector<Real, Col> operator *(const Vector<Real, Row>& v, const RectMatrix<Real, Row, Col>& m) { |
| 534 |
Vector<Real, Row> result; |
| 535 |
|
| 536 |
for (unsigned int i = 0; i < Col ; i++) |
| 537 |
for (unsigned int j = 0; j < Row ; j++) |
| 538 |
result[i] += v[j] * m(j, i); |
| 539 |
|
| 540 |
return result; |
| 541 |
} |
| 542 |
|
| 543 |
/** |
| 544 |
* Return the scalar division of matrix (m / s). |
| 545 |
* @return the scalar division of matrix |
| 546 |
* @param m the matrix |
| 547 |
* @param s the scalar |
| 548 |
*/ |
| 549 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 550 |
inline RectMatrix<Real, Row, Col> operator /(const RectMatrix<Real, Row, Col>& m, Real s) { |
| 551 |
RectMatrix<Real, Row, Col> result; |
| 552 |
|
| 553 |
result.div(s, m); |
| 554 |
|
| 555 |
return result; |
| 556 |
} |
| 557 |
|
| 558 |
|
| 559 |
/** |
| 560 |
* Returns the tensor contraction (double dot product) of two rank 2 |
| 561 |
* tensors (or Matrices) |
| 562 |
* |
| 563 |
* \f[ \mathbf{A} \colon \! \mathbf{B} = \sum_\alpha \sum_\beta \mathbf{A}_{\alpha \beta} B_{\alpha \beta} \f] |
| 564 |
* |
| 565 |
* @param t1 first tensor |
| 566 |
* @param t2 second tensor |
| 567 |
* @return the tensor contraction (double dot product) of t1 and t2 |
| 568 |
*/ |
| 569 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 570 |
inline Real doubleDot( const RectMatrix<Real, Row, Col>& t1, |
| 571 |
const RectMatrix<Real, Row, Col>& t2 ) { |
| 572 |
Real tmp; |
| 573 |
tmp = 0; |
| 574 |
|
| 575 |
for (unsigned int i = 0; i < Row; i++) |
| 576 |
for (unsigned int j =0; j < Col; j++) |
| 577 |
tmp += t1(i,j) * t2(i,j); |
| 578 |
|
| 579 |
return tmp; |
| 580 |
} |
| 581 |
|
| 582 |
|
| 583 |
|
| 584 |
/** |
| 585 |
* Returns the vector (cross) product of two matrices. This |
| 586 |
* operation is defined in: |
| 587 |
* |
| 588 |
* W. Smith, "Point Multipoles in the Ewald Summation (Revisited)," |
| 589 |
* CCP5 Newsletter No 46., pp. 18-30. |
| 590 |
* |
| 591 |
* Equation 21 defines: |
| 592 |
* \f[ |
| 593 |
* V_alpha = \sum_\beta \left[ A_{\alpha+1,\beta} * B_{\alpha+2,\beta} |
| 594 |
-A_{\alpha+2,\beta} * B_{\alpha+2,\beta} \right] |
| 595 |
* \f] |
| 596 |
|
| 597 |
* where \f[\alpha+1\f] and \f[\alpha+2\f] are regarded as cyclic |
| 598 |
* permuations of the matrix indices (i.e. for a 3x3 matrix, when |
| 599 |
* \f[\alpha = 2\f], \f[\alpha + 1 = 3 \f], and \f[\alpha + 2 = 1 \f] ). |
| 600 |
* |
| 601 |
* @param t1 first matrix |
| 602 |
* @param t2 second matrix |
| 603 |
* @return the cross product (vector product) of t1 and t2 |
| 604 |
*/ |
| 605 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 606 |
inline Vector<Real, Row> mCross( const RectMatrix<Real, Row, Col>& t1, |
| 607 |
const RectMatrix<Real, Row, Col>& t2 ) { |
| 608 |
Vector<Real, Row> result; |
| 609 |
unsigned int i1; |
| 610 |
unsigned int i2; |
| 611 |
|
| 612 |
for (unsigned int i = 0; i < Row; i++) { |
| 613 |
i1 = (i+1)%Row; |
| 614 |
i2 = (i+2)%Row; |
| 615 |
for (unsigned int j = 0; j < Col; j++) { |
| 616 |
result[i] += t1(i1,j) * t2(i2,j) - t1(i2,j) * t2(i1,j); |
| 617 |
} |
| 618 |
} |
| 619 |
return result; |
| 620 |
} |
| 621 |
|
| 622 |
|
| 623 |
/** |
| 624 |
* Write to an output stream |
| 625 |
*/ |
| 626 |
template<typename Real, unsigned int Row, unsigned int Col> |
| 627 |
std::ostream &operator<< ( std::ostream& o, const RectMatrix<Real, Row, Col>& m) { |
| 628 |
for (unsigned int i = 0; i < Row ; i++) { |
| 629 |
o << "("; |
| 630 |
for (unsigned int j = 0; j < Col ; j++) { |
| 631 |
o << m(i, j); |
| 632 |
if (j != Col -1) |
| 633 |
o << "\t"; |
| 634 |
} |
| 635 |
o << ")" << std::endl; |
| 636 |
} |
| 637 |
return o; |
| 638 |
} |
| 639 |
} |
| 640 |
#endif //MATH_RECTMATRIX_HPP |
