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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Acknowledgement of the program authors must be made in any |
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< |
* publication of scientific results based in part on use of the |
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* program. An acceptable form of acknowledgement is citation of |
| 12 |
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* the article in which the program was described (Matthew |
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* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
| 15 |
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* Parallel Simulation Engine for Molecular Dynamics," |
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< |
* J. Comput. Chem. 26, pp. 252-271 (2005)) |
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< |
* |
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* 2. Redistributions of source code must retain the above copyright |
| 9 |
> |
* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
| 11 |
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* |
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* 3. Redistributions in binary form must reproduce the above copyright |
| 12 |
> |
* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
| 14 |
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* documentation and/or other materials provided with the |
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* distribution. |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
| 30 |
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* such damages. |
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+ |
* |
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+ |
* 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 |
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* |
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+ |
* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). |
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+ |
* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). |
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+ |
* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). |
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* [4] Vardeman & Gezelter, in progress (2009). |
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*/ |
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|
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/** |
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#include "SquareMatrix.hpp" |
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#include "Vector3.hpp" |
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#include "utils/NumericConstant.hpp" |
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namespace oopse { |
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namespace OpenMD { |
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|
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template<typename Real> |
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class SquareMatrix3 : public SquareMatrix<Real, 3> { |
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* @return the euler angles in a vector |
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* @exception invalid rotation matrix |
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* We use so-called "x-convention", which is the most common definition. |
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* In this convention, the rotation given by Euler angles (phi, theta, psi), where the first |
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* rotation is by an angle phi about the z-axis, the second is by an angle |
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* theta (0 <= theta <= 180)about the x-axis, and thethird is by an angle psi about the |
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* z-axis (again). |
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> |
* In this convention, the rotation given by Euler angles (phi, theta, |
| 248 |
> |
* psi), where the first rotation is by an angle phi about the z-axis, |
| 249 |
> |
* the second is by an angle theta (0 <= theta <= 180) about the x-axis, |
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> |
* and the third is by an angle psi about the z-axis (again). |
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*/ |
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Vector3<Real> toEulerAngles() { |
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Vector3<Real> myEuler; |
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ctheta = this->data_[2][2]; |
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stheta = sqrt(1.0 - ctheta * ctheta); |
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|
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// when sin(theta) is close to 0, we need to consider singularity |
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// In this case, we can assign an arbitary value to phi (or psi), and then determine |
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// the psi (or phi) or vice-versa. We'll assume that phi always gets the rotation, and psi is 0 |
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// in cases of singularity. |
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> |
// when sin(theta) is close to 0, we need to consider |
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> |
// singularity In this case, we can assign an arbitary value to |
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> |
// phi (or psi), and then determine the psi (or phi) or |
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> |
// vice-versa. We'll assume that phi always gets the rotation, |
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// and psi is 0 in cases of singularity. |
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|
// we use atan2 instead of atan, since atan2 will give us -Pi to Pi. |
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// Since 0 <= theta <= 180, sin(theta) will be always non-negative. Therefore, it never |
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// change the sign of both of the parameters passed to atan2. |
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> |
// Since 0 <= theta <= 180, sin(theta) will be always |
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> |
// non-negative. Therefore, it will never change the sign of both of |
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> |
// the parameters passed to atan2. |
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|
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< |
if (fabs(stheta) <= oopse::epsilon){ |
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> |
if (fabs(stheta) < 1e-6){ |
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psi = 0.0; |
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phi = atan2(-this->data_[1][0], this->data_[0][0]); |
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} |
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|
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//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
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if (phi < 0) |
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phi += M_PI; |
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> |
phi += 2.0 * M_PI; |
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|
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if (psi < 0) |
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psi += M_PI; |
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psi += 2.0 * M_PI; |
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|
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myEuler[0] = phi; |
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myEuler[1] = theta; |
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SquareMatrix3<Real> inverse() const { |
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SquareMatrix3<Real> m; |
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RealType det = determinant(); |
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< |
if (fabs(det) <= oopse::epsilon) { |
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> |
if (fabs(det) <= OpenMD::epsilon) { |
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//"The method was called on a matrix with |determinant| <= 1e-6.", |
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//"This is a runtime or a programming error in your application."); |
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std::vector<int> zeroDiagElementIndex; |
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for (int i =0; i < 3; ++i) { |
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< |
if (fabs(this->data_[i][i]) <= oopse::epsilon) { |
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> |
if (fabs(this->data_[i][i]) <= OpenMD::epsilon) { |
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zeroDiagElementIndex.push_back(i); |
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} |
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} |
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|
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/* |
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for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) { |
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< |
if (this->data_[*iter][0] > oopse::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] || |
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< |
this->data_[0][*iter] > oopse::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) { |
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> |
if (this->data_[*iter][0] > OpenMD::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] || |
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> |
this->data_[0][*iter] > OpenMD::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) { |
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std::cout << "can not inverse matrix" << std::endl; |
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} |
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} |
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Vector3<Real> v_maxI, v_k, v_j; |
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|
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// diagonalize using Jacobi |
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< |
jacobi(a, w, v); |
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> |
SquareMatrix3<Real>::jacobi(a, w, v); |
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// if all the eigenvalues are the same, return identity matrix |
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if (w[0] == w[1] && w[0] == w[2] ) { |
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v = SquareMatrix3<Real>::identity(); |
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typedef SquareMatrix3<RealType> Mat3x3d; |
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typedef SquareMatrix3<RealType> RotMat3x3d; |
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|
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< |
} //namespace oopse |
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> |
} //namespace OpenMD |
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#endif // MATH_SQUAREMATRIX_HPP |
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|
