| 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, 24107 (2008). |
| 39 |
< |
* [4] Vardeman & Gezelter, in progress (2009). |
| 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 |
|
/** |
| 507 |
|
} |
| 508 |
|
|
| 509 |
|
/** |
| 510 |
< |
* Return the multiplication of a matrix and a vector (m * v). |
| 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 |
| 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 |
|
} |
| 555 |
|
return result; |
| 556 |
|
} |
| 557 |
|
|
| 558 |
+ |
|
| 559 |
+ |
/** |
| 560 |
+ |
* Returns the vector (cross) product of two matrices. This |
| 561 |
+ |
* operation is defined in: |
| 562 |
+ |
* |
| 563 |
+ |
* W. Smith, "Point Multipoles in the Ewald Summation (Revisited)," |
| 564 |
+ |
* CCP5 Newsletter No 46., pp. 18-30. |
| 565 |
+ |
* |
| 566 |
+ |
* Equation 21 defines: |
| 567 |
+ |
* V_alpha = \sum_\beta [ A_{\alpha+1,\beta} * B_{\alpha+2,\beta} |
| 568 |
+ |
-A_{\alpha+2,\beta} * B_{\alpha+2,\beta} ] |
| 569 |
+ |
* where \alpha+1 and \alpha+2 are regarded as cyclic permuations of the |
| 570 |
+ |
* matrix indices (i.e. for a 3x3 matrix, when \alpha = 2, \alpha + 1 = 3, |
| 571 |
+ |
* and \alpha + 2 = 1). |
| 572 |
+ |
* |
| 573 |
+ |
* @param t1 first matrix |
| 574 |
+ |
* @param t2 second matrix |
| 575 |
+ |
* @return the cross product (vector product) of t1 and t2 |
| 576 |
+ |
*/ |
| 577 |
+ |
template<typename Real, unsigned int Row, unsigned int Col> |
| 578 |
+ |
inline Vector<Real, Row> cross( const RectMatrix<Real, Row, Col>& t1, const RectMatrix<Real, Row, Col>& t2 ) { |
| 579 |
+ |
Vector<Real, Row> result; |
| 580 |
+ |
unsigned int i1; |
| 581 |
+ |
unsigned int i2; |
| 582 |
+ |
|
| 583 |
+ |
for (unsigned int i = 0; i < Row; i++) { |
| 584 |
+ |
i1 = (i+1)%Row; |
| 585 |
+ |
i2 = (i+2)%Row; |
| 586 |
+ |
|
| 587 |
+ |
for (unsigned int j =0; j < Col; j++) { |
| 588 |
+ |
result[i] = t1(i1,j) * t2(i2,j) - t1(i2,j) * t2(i1,j); |
| 589 |
+ |
} |
| 590 |
+ |
} |
| 591 |
+ |
|
| 592 |
+ |
return result; |
| 593 |
+ |
} |
| 594 |
+ |
|
| 595 |
+ |
|
| 596 |
|
/** |
| 597 |
|
* Write to an output stream |
| 598 |
|
*/ |
