| 38 |
|
* University of Notre Dame has been advised of the possibility of |
| 39 |
|
* such damages. |
| 40 |
|
*/ |
| 41 |
+ |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
| 42 |
+ |
#include "applications/hydrodynamics/Spheric.hpp" |
| 43 |
+ |
#include "applications/hydrodynamics/Ellipsoid.hpp" |
| 44 |
+ |
#include "applications/hydrodynamics/CompositeShape.hpp" |
| 45 |
|
|
| 42 |
– |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
| 43 |
– |
#include "math/LU.hpp" |
| 44 |
– |
#include "math/DynamicRectMatrix.hpp" |
| 45 |
– |
#include "math/SquareMatrix3.hpp" |
| 46 |
– |
#include "utils/OOPSEConstant.hpp" |
| 46 |
|
namespace oopse { |
| 48 |
– |
/** |
| 49 |
– |
* Reference: |
| 50 |
– |
* Beatriz Carrasco and Jose Gracia de la Torre, Hydrodynamic Properties of Rigid Particles: |
| 51 |
– |
* Comparison of Different Modeling and Computational Procedures. |
| 52 |
– |
* Biophysical Journal, 75(6), 3044, 1999 |
| 53 |
– |
*/ |
| 47 |
|
|
| 48 |
< |
HydrodynamicsModel::HydrodynamicsModel(StuntDouble* sd, const DynamicProperty& extraParams) : sd_(sd){ |
| 49 |
< |
DynamicProperty::const_iterator iter; |
| 48 |
> |
bool HydrodynamicsModel::calcHydroProps(Spheric* spheric, double viscosity, double temperature) { |
| 49 |
> |
return false; |
| 50 |
> |
} |
| 51 |
|
|
| 52 |
< |
iter = extraParams.find("Viscosity"); |
| 53 |
< |
if (iter != extraParams.end()) { |
| 54 |
< |
boost::any param = iter->second; |
| 61 |
< |
viscosity_ = boost::any_cast<double>(param); |
| 62 |
< |
}else { |
| 63 |
< |
std::cout << "HydrodynamicsModel Error\n" ; |
| 64 |
< |
} |
| 52 |
> |
bool HydrodynamicsModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) { |
| 53 |
> |
return false; |
| 54 |
> |
} |
| 55 |
|
|
| 56 |
< |
iter = extraParams.find("Temperature"); |
| 57 |
< |
if (iter != extraParams.end()) { |
| 68 |
< |
boost::any param = iter->second; |
| 69 |
< |
temperature_ = boost::any_cast<double>(param); |
| 70 |
< |
}else { |
| 71 |
< |
std::cout << "HydrodynamicsModel Error\n" ; |
| 72 |
< |
} |
| 56 |
> |
bool HydrodynamicsModel::calcHydroProps(CompositeShape* compositexShape, double viscosity, double temperature) { |
| 57 |
> |
return false; |
| 58 |
|
} |
| 74 |
– |
|
| 75 |
– |
bool HydrodynamicsModel::calcHydrodyanmicsProps() { |
| 76 |
– |
if (!createBeads(beads_)) { |
| 77 |
– |
std::cout << "can not create beads" << std::endl; |
| 78 |
– |
return false; |
| 79 |
– |
} |
| 59 |
|
|
| 60 |
< |
//calcResistanceTensor(); |
| 61 |
< |
calcDiffusionTensor(); |
| 60 |
> |
void HydrodynamicsModel::writeHydroProps(std::ostream& os) { |
| 61 |
> |
|
| 62 |
|
|
| 63 |
< |
/* |
| 85 |
< |
int nbeads = beads_.size(); |
| 86 |
< |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
| 87 |
< |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
| 88 |
< |
Mat3x3d I; |
| 89 |
< |
I(0, 0) = 1.0; |
| 90 |
< |
I(1, 1) = 1.0; |
| 91 |
< |
I(2, 2) = 1.0; |
| 63 |
> |
os << sd_->getType() << "\t"; |
| 64 |
|
|
| 65 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 66 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 95 |
< |
Mat3x3d Tij; |
| 96 |
< |
if (i != j ) { |
| 97 |
< |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
| 98 |
< |
double rij = Rij.length(); |
| 99 |
< |
double rij2 = rij * rij; |
| 100 |
< |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
| 101 |
< |
Mat3x3d tmpMat; |
| 102 |
< |
tmpMat = outProduct(Rij, Rij) / rij2; |
| 103 |
< |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
| 104 |
< |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
| 105 |
< |
}else { |
| 106 |
< |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
| 107 |
< |
Tij(0, 0) = constant; |
| 108 |
< |
Tij(1, 1) = constant; |
| 109 |
< |
Tij(2, 2) = constant; |
| 110 |
< |
} |
| 111 |
< |
B.setSubMatrix(i*3, j*3, Tij); |
| 112 |
< |
std::cout << Tij << std::endl; |
| 113 |
< |
} |
| 114 |
< |
} |
| 65 |
> |
//center of resistance |
| 66 |
> |
os << cr_.center[0] << "\t" << cr_.center[1] << "\t" << cr_.center[2] << "\t"; |
| 67 |
|
|
| 68 |
< |
std::cout << "B=\n" |
| 69 |
< |
<< B << std::endl; |
| 70 |
< |
//invert B Matrix |
| 71 |
< |
invertMatrix(B, C); |
| 68 |
> |
//resistance tensor at center of resistance |
| 69 |
> |
//translation |
| 70 |
> |
os << cr_.Xi(0, 0) << "\t" << cr_.Xi(0, 1) << "\t" << cr_.Xi(0, 2) << "\t" |
| 71 |
> |
<< cr_.Xi(1, 0) << "\t" << cr_.Xi(1, 1) << "\t" << cr_.Xi(1, 2) << "\t" |
| 72 |
> |
<< cr_.Xi(2, 0) << "\t" << cr_.Xi(2, 1) << "\t" << cr_.Xi(2, 2) << "\t"; |
| 73 |
|
|
| 74 |
< |
std::cout << "C=\n" |
| 75 |
< |
<< C << std::endl; |
| 74 |
> |
//rotation-translation |
| 75 |
> |
os << cr_.Xi(0, 3) << "\t" << cr_.Xi(0, 4) << "\t" << cr_.Xi(0, 5) << "\t" |
| 76 |
> |
<< cr_.Xi(1, 3) << "\t" << cr_.Xi(1, 4) << "\t" << cr_.Xi(1, 5) << "\t" |
| 77 |
> |
<< cr_.Xi(2, 3) << "\t" << cr_.Xi(2, 4) << "\t" << cr_.Xi(2, 5) << "\t"; |
| 78 |
|
|
| 79 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
| 80 |
< |
std::vector<Mat3x3d> U; |
| 81 |
< |
for (int i = 0; i < nbeads; ++i) { |
| 82 |
< |
Mat3x3d currU; |
| 128 |
< |
currU.setupSkewMat(beads_[i].pos); |
| 129 |
< |
U.push_back(currU); |
| 130 |
< |
} |
| 131 |
< |
|
| 132 |
< |
//calculate Xi matrix at arbitrary origin O |
| 133 |
< |
Mat3x3d Xitt; |
| 134 |
< |
Mat3x3d Xirr; |
| 135 |
< |
Mat3x3d Xitr; |
| 79 |
> |
//translation-rotation |
| 80 |
> |
os << cr_.Xi(3, 0) << "\t" << cr_.Xi(3, 1) << "\t" << cr_.Xi(3, 2) << "\t" |
| 81 |
> |
<< cr_.Xi(4, 0) << "\t" << cr_.Xi(4, 1) << "\t" << cr_.Xi(4, 2) << "\t" |
| 82 |
> |
<< cr_.Xi(5, 0) << "\t" << cr_.Xi(5, 1) << "\t" << cr_.Xi(5, 2) << "\t"; |
| 83 |
|
|
| 84 |
< |
//calculate the total volume |
| 84 |
> |
//rotation |
| 85 |
> |
os << cr_.Xi(3, 3) << "\t" << cr_.Xi(3, 4) << "\t" << cr_.Xi(3, 5) << "\t" |
| 86 |
> |
<< cr_.Xi(4, 3) << "\t" << cr_.Xi(4, 4) << "\t" << cr_.Xi(4, 5) << "\t" |
| 87 |
> |
<< cr_.Xi(5, 3) << "\t" << cr_.Xi(5, 4) << "\t" << cr_.Xi(5, 5) << "\t"; |
| 88 |
|
|
| 139 |
– |
double volume = 0.0; |
| 140 |
– |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 141 |
– |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
| 142 |
– |
} |
| 143 |
– |
|
| 144 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 145 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 146 |
– |
Mat3x3d Cij; |
| 147 |
– |
C.getSubMatrix(i*3, j*3, Cij); |
| 148 |
– |
|
| 149 |
– |
Xitt += Cij; |
| 150 |
– |
Xitr += U[i] * Cij; |
| 151 |
– |
//Xirr += -U[i] * Cij * U[j]; |
| 152 |
– |
Xirr += -U[i] * Cij * U[j] + (0.166*6 * viscosity_ * volume) * I; |
| 153 |
– |
} |
| 154 |
– |
} |
| 89 |
|
|
| 90 |
< |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
| 91 |
< |
RectMatrix<double, 6, 6> Xi; |
| 92 |
< |
RectMatrix<double, 6, 6> Do; |
| 93 |
< |
Xi.setSubMatrix(0, 0, Xitt); |
| 94 |
< |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
| 161 |
< |
Xi.setSubMatrix(3, 0, Xitr); |
| 162 |
< |
Xi.setSubMatrix(3, 3, Xirr); |
| 163 |
< |
//invertMatrix(Xi, Do); |
| 164 |
< |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
| 165 |
< |
//Do *= kt; |
| 90 |
> |
//diffusion tensor at center of resistance |
| 91 |
> |
//translation |
| 92 |
> |
os << cr_.D(0, 0) << "\t" << cr_.D(0, 1) << "\t" << cr_.D(0, 2) << "\t" |
| 93 |
> |
<< cr_.D(1, 0) << "\t" << cr_.D(1, 1) << "\t" << cr_.D(1, 2) << "\t" |
| 94 |
> |
<< cr_.D(2, 0) << "\t" << cr_.D(2, 1) << "\t" << cr_.D(2, 2) << "\t"; |
| 95 |
|
|
| 96 |
+ |
//rotation-translation |
| 97 |
+ |
os << cr_.D(0, 3) << "\t" << cr_.D(0, 4) << "\t" << cr_.D(0, 5) << "\t" |
| 98 |
+ |
<< cr_.D(1, 3) << "\t" << cr_.D(1, 4) << "\t" << cr_.D(1, 5) << "\t" |
| 99 |
+ |
<< cr_.D(2, 3) << "\t" << cr_.D(2, 4) << "\t" << cr_.D(2, 5) << "\t"; |
| 100 |
|
|
| 101 |
< |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
| 102 |
< |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
| 103 |
< |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
| 101 |
> |
//translation-rotation |
| 102 |
> |
os << cr_.D(3, 0) << "\t" << cr_.D(3, 1) << "\t" << cr_.D(3, 2) << "\t" |
| 103 |
> |
<< cr_.D(4, 0) << "\t" << cr_.D(4, 1) << "\t" << cr_.D(4, 2) << "\t" |
| 104 |
> |
<< cr_.D(5, 0) << "\t" << cr_.D(5, 1) << "\t" << cr_.D(5, 2) << "\t"; |
| 105 |
|
|
| 106 |
< |
const static Mat3x3d zeroMat(0.0); |
| 107 |
< |
|
| 108 |
< |
Mat3x3d XittInv(0.0); |
| 109 |
< |
XittInv = Xitt.inverse(); |
| 110 |
< |
|
| 111 |
< |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
| 178 |
< |
//( a11 a12 0) |
| 179 |
< |
//( a21 a22 0) |
| 180 |
< |
//( 0 0 0) |
| 181 |
< |
Mat3x3d XirrInv; |
| 182 |
< |
XirrInv = Xirr.inverse(); |
| 106 |
> |
//rotation |
| 107 |
> |
os << cr_.D(3, 3) << "\t" << cr_.D(3, 4) << "\t" << cr_.D(3, 5) << "\t" |
| 108 |
> |
<< cr_.D(4, 3) << "\t" << cr_.D(4, 4) << "\t" << cr_.D(4, 5) << "\t" |
| 109 |
> |
<< cr_.D(5, 3) << "\t" << cr_.D(5, 4) << "\t" << cr_.D(5, 5) << "\t"; |
| 110 |
> |
|
| 111 |
> |
//--------------------------------------------------------------------- |
| 112 |
|
|
| 113 |
< |
Mat3x3d tmp; |
| 114 |
< |
Mat3x3d tmpInv; |
| 186 |
< |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
| 187 |
< |
tmpInv = tmp.inverse(); |
| 113 |
> |
//center of diffusion |
| 114 |
> |
os << cd_.center[0] << "\t" << cd_.center[1] << "\t" << cd_.center[2] << "\t"; |
| 115 |
|
|
| 116 |
< |
Dott = kt * tmpInv; |
| 117 |
< |
Dotr = -kt*XirrInv * Xitr * tmpInv* 1.0E8; |
| 116 |
> |
//resistance tensor at center of diffusion |
| 117 |
> |
//translation |
| 118 |
> |
os << cd_.Xi(0, 0) << "\t" << cd_.Xi(0, 1) << "\t" << cd_.Xi(0, 2) << "\t" |
| 119 |
> |
<< cd_.Xi(1, 0) << "\t" << cd_.Xi(1, 1) << "\t" << cd_.Xi(1, 2) << "\t" |
| 120 |
> |
<< cd_.Xi(2, 0) << "\t" << cd_.Xi(2, 1) << "\t" << cd_.Xi(2, 2) << "\t"; |
| 121 |
|
|
| 122 |
< |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
| 123 |
< |
tmpInv = tmp.inverse(); |
| 124 |
< |
|
| 125 |
< |
Dorr = kt * tmpInv*1.0E16; |
| 122 |
> |
//rotation-translation |
| 123 |
> |
os << cd_.Xi(0, 3) << "\t" << cd_.Xi(0, 4) << "\t" << cd_.Xi(0, 5) << "\t" |
| 124 |
> |
<< cd_.Xi(1, 3) << "\t" << cd_.Xi(1, 4) << "\t" << cd_.Xi(1, 5) << "\t" |
| 125 |
> |
<< cd_.Xi(2, 3) << "\t" << cd_.Xi(2, 4) << "\t" << cd_.Xi(2, 5) << "\t"; |
| 126 |
|
|
| 127 |
< |
//Do.getSubMatrix(0, 0 , Dott); |
| 128 |
< |
//Do.getSubMatrix(3, 0, Dotr); |
| 129 |
< |
//Do.getSubMatrix(3, 3, Dorr); |
| 127 |
> |
//translation-rotation |
| 128 |
> |
os << cd_.Xi(3, 0) << "\t" << cd_.Xi(3, 1) << "\t" << cd_.Xi(3, 2) << "\t" |
| 129 |
> |
<< cd_.Xi(4, 0) << "\t" << cd_.Xi(4, 1) << "\t" << cd_.Xi(4, 2) << "\t" |
| 130 |
> |
<< cd_.Xi(5, 0) << "\t" << cd_.Xi(5, 1) << "\t" << cd_.Xi(5, 2) << "\t"; |
| 131 |
|
|
| 132 |
< |
//calculate center of diffusion |
| 133 |
< |
tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); |
| 134 |
< |
tmp(0, 1) = - Dorr(0, 1); |
| 135 |
< |
tmp(0, 2) = -Dorr(0, 2); |
| 205 |
< |
tmp(1, 0) = -Dorr(0, 1); |
| 206 |
< |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
| 207 |
< |
tmp(1, 2) = -Dorr(1, 2); |
| 208 |
< |
tmp(2, 0) = -Dorr(0, 2); |
| 209 |
< |
tmp(2, 1) = -Dorr(1, 2); |
| 210 |
< |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
| 132 |
> |
//rotation |
| 133 |
> |
os << cd_.Xi(3, 3) << "\t" << cd_.Xi(3, 4) << "\t" << cd_.Xi(3, 5) << "\t" |
| 134 |
> |
<< cd_.Xi(4, 3) << "\t" << cd_.Xi(4, 4) << "\t" << cd_.Xi(4, 5) << "\t" |
| 135 |
> |
<< cd_.Xi(5, 3) << "\t" << cd_.Xi(5, 4) << "\t" << cd_.Xi(5, 5) << "\t"; |
| 136 |
|
|
| 212 |
– |
Vector3d tmpVec; |
| 213 |
– |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
| 214 |
– |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
| 215 |
– |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
| 137 |
|
|
| 138 |
< |
tmpInv = tmp.inverse(); |
| 139 |
< |
|
| 140 |
< |
Vector3d rod = tmpInv * tmpVec; |
| 138 |
> |
//diffusion tensor at center of diffusion |
| 139 |
> |
//translation |
| 140 |
> |
os << cd_.D(0, 0) << "\t" << cd_.D(0, 1) << "\t" << cd_.D(0, 2) << "\t" |
| 141 |
> |
<< cd_.D(1, 0) << "\t" << cd_.D(1, 1) << "\t" << cd_.D(1, 2) << "\t" |
| 142 |
> |
<< cd_.D(2, 0) << "\t" << cd_.D(2, 1) << "\t" << cd_.D(2, 2) << "\t"; |
| 143 |
|
|
| 144 |
< |
//calculate Diffusion Tensor at center of diffusion |
| 145 |
< |
Mat3x3d Uod; |
| 146 |
< |
Uod.setupSkewMat(rod); |
| 147 |
< |
|
| 225 |
< |
Mat3x3d Ddtt; //translational diffusion tensor at diffusion center |
| 226 |
< |
Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center |
| 227 |
< |
Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor |
| 228 |
< |
|
| 229 |
< |
Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; |
| 230 |
< |
Ddrr = Dorr; |
| 231 |
< |
Ddtr = Dotr + Dorr * Uod; |
| 232 |
< |
|
| 233 |
< |
props_.diffCenter = rod; |
| 234 |
< |
props_.transDiff = Ddtt; |
| 235 |
< |
props_.transRotDiff = Ddtr; |
| 236 |
< |
props_.rotDiff = Ddrr; |
| 237 |
< |
*/ |
| 238 |
< |
return true; |
| 239 |
< |
} |
| 144 |
> |
//rotation-translation |
| 145 |
> |
os << cd_.D(0, 3) << "\t" << cd_.D(0, 4) << "\t" << cd_.D(0, 5) << "\t" |
| 146 |
> |
<< cd_.D(1, 3) << "\t" << cd_.D(1, 4) << "\t" << cd_.D(1, 5) << "\t" |
| 147 |
> |
<< cd_.D(2, 3) << "\t" << cd_.D(2, 4) << "\t" << cd_.D(2, 5) << "\t"; |
| 148 |
|
|
| 149 |
< |
void HydrodynamicsModel::calcResistanceTensor() { |
| 150 |
< |
|
| 151 |
< |
int nbeads = beads_.size(); |
| 152 |
< |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
| 245 |
< |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
| 246 |
< |
Mat3x3d I; |
| 247 |
< |
I(0, 0) = 1.0; |
| 248 |
< |
I(1, 1) = 1.0; |
| 249 |
< |
I(2, 2) = 1.0; |
| 250 |
< |
|
| 251 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 252 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 253 |
< |
Mat3x3d Tij; |
| 254 |
< |
if (i != j ) { |
| 255 |
< |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
| 256 |
< |
double rij = Rij.length(); |
| 257 |
< |
double rij2 = rij * rij; |
| 258 |
< |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
| 259 |
< |
Mat3x3d tmpMat; |
| 260 |
< |
tmpMat = outProduct(Rij, Rij) / rij2; |
| 261 |
< |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
| 262 |
< |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
| 263 |
< |
}else { |
| 264 |
< |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
| 265 |
< |
Tij(0, 0) = constant; |
| 266 |
< |
Tij(1, 1) = constant; |
| 267 |
< |
Tij(2, 2) = constant; |
| 268 |
< |
} |
| 269 |
< |
B.setSubMatrix(i*3, j*3, Tij); |
| 270 |
< |
} |
| 271 |
< |
} |
| 149 |
> |
//translation-rotation |
| 150 |
> |
os << cd_.D(3, 0) << "\t" << cd_.D(3, 1) << "\t" << cd_.D(3, 2) << "\t" |
| 151 |
> |
<< cd_.D(4, 0) << "\t" << cd_.D(4, 1) << "\t" << cd_.D(4, 2) << "\t" |
| 152 |
> |
<< cd_.D(5, 0) << "\t" << cd_.D(5, 1) << "\t" << cd_.D(5, 2) << "\t"; |
| 153 |
|
|
| 154 |
< |
|
| 155 |
< |
//invert B Matrix |
| 156 |
< |
invertMatrix(B, C); |
| 157 |
< |
|
| 277 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
| 278 |
< |
std::vector<Mat3x3d> U; |
| 279 |
< |
for (int i = 0; i < nbeads; ++i) { |
| 280 |
< |
Mat3x3d currU; |
| 281 |
< |
currU.setupSkewMat(beads_[i].pos); |
| 282 |
< |
U.push_back(currU); |
| 283 |
< |
} |
| 284 |
< |
|
| 285 |
< |
//calculate Xi matrix at arbitrary origin O |
| 286 |
< |
Mat3x3d Xiott; |
| 287 |
< |
Mat3x3d Xiorr; |
| 288 |
< |
Mat3x3d Xiotr; |
| 289 |
< |
|
| 290 |
< |
//calculate the total volume |
| 291 |
< |
|
| 292 |
< |
double volume = 0.0; |
| 293 |
< |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 294 |
< |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
| 295 |
< |
} |
| 296 |
< |
|
| 297 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 298 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 299 |
< |
Mat3x3d Cij; |
| 300 |
< |
C.getSubMatrix(i*3, j*3, Cij); |
| 301 |
< |
|
| 302 |
< |
Xiott += Cij; |
| 303 |
< |
Xiotr += U[i] * Cij; |
| 304 |
< |
//Xiorr += -U[i] * Cij * U[j]; |
| 305 |
< |
Xiorr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; |
| 306 |
< |
} |
| 307 |
< |
} |
| 308 |
< |
|
| 309 |
< |
Mat3x3d tmp; |
| 310 |
< |
Mat3x3d tmpInv; |
| 311 |
< |
Vector3d tmpVec; |
| 312 |
< |
tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2); |
| 313 |
< |
tmp(0, 1) = - Xiott(0, 1); |
| 314 |
< |
tmp(0, 2) = -Xiott(0, 2); |
| 315 |
< |
tmp(1, 0) = -Xiott(0, 1); |
| 316 |
< |
tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2); |
| 317 |
< |
tmp(1, 2) = -Xiott(1, 2); |
| 318 |
< |
tmp(2, 0) = -Xiott(0, 2); |
| 319 |
< |
tmp(2, 1) = -Xiott(1, 2); |
| 320 |
< |
tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0); |
| 321 |
< |
tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2); |
| 322 |
< |
tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0); |
| 323 |
< |
tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1); |
| 324 |
< |
tmpInv = tmp.inverse(); |
| 325 |
< |
Vector3d ror = tmpInv * tmpVec; //center of resistance |
| 326 |
< |
Mat3x3d Uor; |
| 327 |
< |
Uor.setupSkewMat(ror); |
| 328 |
< |
|
| 329 |
< |
Mat3x3d Xirtt; |
| 330 |
< |
Mat3x3d Xirrr; |
| 331 |
< |
Mat3x3d Xirtr; |
| 154 |
> |
//rotation |
| 155 |
> |
os << cd_.D(3, 3) << "\t" << cd_.D(3, 4) << "\t" << cd_.D(3, 5) << "\t" |
| 156 |
> |
<< cd_.D(4, 3) << "\t" << cd_.D(4, 4) << "\t" << cd_.D(4, 5) << "\t" |
| 157 |
> |
<< cd_.D(5, 3) << "\t" << cd_.D(5, 4) << "\t" << cd_.D(5, 5) << "\n"; |
| 158 |
|
|
| 333 |
– |
Xirtt = Xiott; |
| 334 |
– |
Xirtr = (Xiotr - Uor * Xiott) * 1E-8; |
| 335 |
– |
Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose() * 1E-16; |
| 336 |
– |
/* |
| 337 |
– |
SquareMatrix<double,6> Xir6x6; |
| 338 |
– |
SquareMatrix<double,6> Dr6x6; |
| 159 |
|
|
| 340 |
– |
Xir6x6.setSubMatrix(0, 0, Xirtt); |
| 341 |
– |
Xir6x6.setSubMatrix(0, 3, Xirtr.transpose()); |
| 342 |
– |
Xir6x6.setSubMatrix(3, 0, Xirtr); |
| 343 |
– |
Xir6x6.setSubMatrix(3, 3, Xirrr); |
| 344 |
– |
|
| 345 |
– |
invertMatrix(Xir6x6, Dr6x6); |
| 346 |
– |
Mat3x3d Drtt; |
| 347 |
– |
Mat3x3d Drtr; |
| 348 |
– |
Mat3x3d Drrr; |
| 349 |
– |
Dr6x6.getSubMatrix(0, 0, Drtt); |
| 350 |
– |
Dr6x6.getSubMatrix(3, 0, Drtr); |
| 351 |
– |
Dr6x6.getSubMatrix(3, 3, Drrr); |
| 352 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
| 353 |
– |
Drtt *= kt; |
| 354 |
– |
Drtr *= kt*1E8; |
| 355 |
– |
Drrr *= kt*1E16; |
| 356 |
– |
*/ |
| 357 |
– |
|
| 358 |
– |
const static Mat3x3d zeroMat(0.0); |
| 359 |
– |
|
| 360 |
– |
|
| 361 |
– |
|
| 362 |
– |
Mat3x3d XirttInv(0.0); |
| 363 |
– |
XirttInv = Xirtt.inverse(); |
| 364 |
– |
|
| 365 |
– |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
| 366 |
– |
//( a11 a12 0) |
| 367 |
– |
//( a21 a22 0) |
| 368 |
– |
//( 0 0 0) |
| 369 |
– |
Mat3x3d XirrrInv; |
| 370 |
– |
XirrrInv = Xirrr.inverse(); |
| 371 |
– |
tmp = Xirtt - Xirtr.transpose() * XirrrInv * Xirtr; |
| 372 |
– |
tmpInv = tmp.inverse(); |
| 373 |
– |
|
| 374 |
– |
Mat3x3d Drtt; |
| 375 |
– |
Mat3x3d Drtr; |
| 376 |
– |
Mat3x3d Drrr; |
| 377 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
| 378 |
– |
Drtt = kt * tmpInv; |
| 379 |
– |
Drtr = -kt*XirrrInv * Xirtr * tmpInv* 1.0E8; |
| 380 |
– |
|
| 381 |
– |
tmp = Xirrr - Xirtr * XirttInv * Xirtr.transpose(); |
| 382 |
– |
tmpInv = tmp.inverse(); |
| 383 |
– |
|
| 384 |
– |
Drrr = kt * tmpInv*1.0E16; |
| 385 |
– |
|
| 386 |
– |
std::cout << "-----------------------------------------\n"; |
| 387 |
– |
std::cout << "center of resistance :" << std::endl; |
| 388 |
– |
std::cout << ror << std::endl; |
| 389 |
– |
std::cout << "resistant tensor at center of resistance" << std::endl; |
| 390 |
– |
std::cout << "translation:" << std::endl; |
| 391 |
– |
std::cout << Xirtt << std::endl; |
| 392 |
– |
std::cout << "translation-rotation:" << std::endl; |
| 393 |
– |
std::cout << Xirtr << std::endl; |
| 394 |
– |
std::cout << "rotation:" << std::endl; |
| 395 |
– |
std::cout << Xirrr << std::endl; |
| 396 |
– |
std::cout << "diffusion tensor at center of resistance" << std::endl; |
| 397 |
– |
std::cout << "translation:" << std::endl; |
| 398 |
– |
std::cout << Drtt << std::endl; |
| 399 |
– |
std::cout << "translation-rotation:" << std::endl; |
| 400 |
– |
std::cout << Drtr << std::endl; |
| 401 |
– |
std::cout << "rotation:" << std::endl; |
| 402 |
– |
std::cout << Drrr << std::endl; |
| 403 |
– |
std::cout << "-----------------------------------------\n"; |
| 404 |
– |
|
| 160 |
|
} |
| 161 |
|
|
| 407 |
– |
void HydrodynamicsModel::calcDiffusionTensor() { |
| 408 |
– |
int nbeads = beads_.size(); |
| 409 |
– |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
| 410 |
– |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
| 411 |
– |
Mat3x3d I; |
| 412 |
– |
I(0, 0) = 1.0; |
| 413 |
– |
I(1, 1) = 1.0; |
| 414 |
– |
I(2, 2) = 1.0; |
| 415 |
– |
|
| 416 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 417 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 418 |
– |
Mat3x3d Tij; |
| 419 |
– |
if (i != j ) { |
| 420 |
– |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
| 421 |
– |
double rij = Rij.length(); |
| 422 |
– |
double rij2 = rij * rij; |
| 423 |
– |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
| 424 |
– |
Mat3x3d tmpMat; |
| 425 |
– |
tmpMat = outProduct(Rij, Rij) / rij2; |
| 426 |
– |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
| 427 |
– |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
| 428 |
– |
}else { |
| 429 |
– |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
| 430 |
– |
Tij(0, 0) = constant; |
| 431 |
– |
Tij(1, 1) = constant; |
| 432 |
– |
Tij(2, 2) = constant; |
| 433 |
– |
} |
| 434 |
– |
B.setSubMatrix(i*3, j*3, Tij); |
| 435 |
– |
} |
| 436 |
– |
} |
| 437 |
– |
|
| 438 |
– |
//invert B Matrix |
| 439 |
– |
invertMatrix(B, C); |
| 440 |
– |
|
| 441 |
– |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
| 442 |
– |
std::vector<Mat3x3d> U; |
| 443 |
– |
for (int i = 0; i < nbeads; ++i) { |
| 444 |
– |
Mat3x3d currU; |
| 445 |
– |
currU.setupSkewMat(beads_[i].pos); |
| 446 |
– |
U.push_back(currU); |
| 447 |
– |
} |
| 448 |
– |
|
| 449 |
– |
//calculate Xi matrix at arbitrary origin O |
| 450 |
– |
Mat3x3d Xitt; |
| 451 |
– |
Mat3x3d Xirr; |
| 452 |
– |
Mat3x3d Xitr; |
| 453 |
– |
|
| 454 |
– |
//calculate the total volume |
| 455 |
– |
|
| 456 |
– |
double volume = 0.0; |
| 457 |
– |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 458 |
– |
volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
| 459 |
– |
} |
| 460 |
– |
|
| 461 |
– |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 462 |
– |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 463 |
– |
Mat3x3d Cij; |
| 464 |
– |
C.getSubMatrix(i*3, j*3, Cij); |
| 465 |
– |
|
| 466 |
– |
Xitt += Cij; |
| 467 |
– |
Xitr += U[i] * Cij; |
| 468 |
– |
//Xirr += -U[i] * Cij * U[j]; |
| 469 |
– |
Xirr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; |
| 470 |
– |
} |
| 471 |
– |
} |
| 472 |
– |
|
| 473 |
– |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
| 474 |
– |
RectMatrix<double, 6, 6> Xi; |
| 475 |
– |
RectMatrix<double, 6, 6> Do; |
| 476 |
– |
Xi.setSubMatrix(0, 0, Xitt); |
| 477 |
– |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
| 478 |
– |
Xi.setSubMatrix(3, 0, Xitr); |
| 479 |
– |
Xi.setSubMatrix(3, 3, Xirr); |
| 480 |
– |
//invertMatrix(Xi, Do); |
| 481 |
– |
//double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
| 482 |
– |
|
| 483 |
– |
//1 poise = 0.1 N.S/m^2 = 1.661E-3 amu/ (Angstrom*fs) |
| 484 |
– |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-3; |
| 485 |
– |
|
| 486 |
– |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
| 487 |
– |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
| 488 |
– |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
| 489 |
– |
|
| 490 |
– |
const static Mat3x3d zeroMat(0.0); |
| 491 |
– |
|
| 492 |
– |
Mat3x3d XittInv(0.0); |
| 493 |
– |
XittInv = Xitt.inverse(); |
| 494 |
– |
|
| 495 |
– |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
| 496 |
– |
//( a11 a12 0) |
| 497 |
– |
//( a21 a22 0) |
| 498 |
– |
//( 0 0 0) |
| 499 |
– |
Mat3x3d XirrInv; |
| 500 |
– |
XirrInv = Xirr.inverse(); |
| 501 |
– |
|
| 502 |
– |
Mat3x3d tmp; |
| 503 |
– |
Mat3x3d tmpInv; |
| 504 |
– |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
| 505 |
– |
tmpInv = tmp.inverse(); |
| 506 |
– |
|
| 507 |
– |
//Dott = kt * tmpInv; //unit in A^2/fs |
| 508 |
– |
Dott = tmpInv; |
| 509 |
– |
//Dotr = -kt*XirrInv * Xitr * tmpInv*1E8; |
| 510 |
– |
//Dotr = -kt*XirrInv * Xitr * tmpInv; |
| 511 |
– |
Dotr = -XirrInv* Xitr * tmpInv; |
| 512 |
– |
|
| 513 |
– |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
| 514 |
– |
tmpInv = tmp.inverse(); |
| 515 |
– |
|
| 516 |
– |
//Dorr = kt * tmpInv*1E16; |
| 517 |
– |
//Dorr = kt * tmpInv; |
| 518 |
– |
Dorr = tmpInv; |
| 519 |
– |
//calculate center of diffusion |
| 520 |
– |
tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); |
| 521 |
– |
tmp(0, 1) = - Dorr(0, 1); |
| 522 |
– |
tmp(0, 2) = -Dorr(0, 2); |
| 523 |
– |
tmp(1, 0) = -Dorr(0, 1); |
| 524 |
– |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
| 525 |
– |
tmp(1, 2) = -Dorr(1, 2); |
| 526 |
– |
tmp(2, 0) = -Dorr(0, 2); |
| 527 |
– |
tmp(2, 1) = -Dorr(1, 2); |
| 528 |
– |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
| 529 |
– |
|
| 530 |
– |
Vector3d tmpVec; |
| 531 |
– |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
| 532 |
– |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
| 533 |
– |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
| 534 |
– |
|
| 535 |
– |
tmpInv = tmp.inverse(); |
| 536 |
– |
|
| 537 |
– |
Vector3d rod = tmpInv * tmpVec; |
| 538 |
– |
|
| 539 |
– |
//calculate Diffusion Tensor at center of diffusion |
| 540 |
– |
Mat3x3d Uod; |
| 541 |
– |
Uod.setupSkewMat(rod); |
| 542 |
– |
|
| 543 |
– |
Mat3x3d Ddtt; //translational diffusion tensor at diffusion center |
| 544 |
– |
Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center |
| 545 |
– |
Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor |
| 546 |
– |
|
| 547 |
– |
Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; |
| 548 |
– |
Ddrr = Dorr; |
| 549 |
– |
Ddtr = Dotr + Dorr * Uod; |
| 550 |
– |
|
| 551 |
– |
props_.diffCenter = rod; |
| 552 |
– |
props_.Ddtt = Ddtt; |
| 553 |
– |
props_.Ddtr = Ddtr; |
| 554 |
– |
props_.Ddrr = Ddrr; |
| 555 |
– |
|
| 556 |
– |
SquareMatrix<double, 6> Dd; |
| 557 |
– |
Dd.setSubMatrix(0, 0, Ddtt); |
| 558 |
– |
Dd.setSubMatrix(0, 3, Ddtr.transpose()); |
| 559 |
– |
Dd.setSubMatrix(3, 0, Ddtr); |
| 560 |
– |
Dd.setSubMatrix(3, 3, Ddrr); |
| 561 |
– |
SquareMatrix<double, 6> Xid; |
| 562 |
– |
invertMatrix(Dd, Xid); |
| 563 |
– |
|
| 564 |
– |
Ddtt *= kt; |
| 565 |
– |
Ddtr *= kt; |
| 566 |
– |
Ddrr *= kt; |
| 567 |
– |
Xid /= 1.66E-3; |
| 568 |
– |
|
| 569 |
– |
Xid.getSubMatrix(0, 0, props_.Xidtt); |
| 570 |
– |
Xid.getSubMatrix(0, 3, props_.Xidrt); |
| 571 |
– |
Xid.getSubMatrix(3, 0, props_.Xidtr); |
| 572 |
– |
Xid.getSubMatrix(3, 3, props_.Xidrr); |
| 573 |
– |
|
| 574 |
– |
/* |
| 575 |
– |
std::cout << "center of diffusion :" << std::endl; |
| 576 |
– |
std::cout << rod << std::endl; |
| 577 |
– |
std::cout << "diffusion tensor at center of diffusion" << std::endl; |
| 578 |
– |
std::cout << "translation:" << std::endl; |
| 579 |
– |
std::cout << Ddtt << std::endl; |
| 580 |
– |
std::cout << "translation-rotation:" << std::endl; |
| 581 |
– |
std::cout << Ddtr << std::endl; |
| 582 |
– |
std::cout << "rotation:" << std::endl; |
| 583 |
– |
std::cout << Ddrr << std::endl; |
| 584 |
– |
*/ |
| 585 |
– |
|
| 162 |
|
} |
| 587 |
– |
|
| 588 |
– |
void HydrodynamicsModel::writeBeads(std::ostream& os) { |
| 589 |
– |
std::vector<BeadParam>::iterator iter; |
| 590 |
– |
os << beads_.size() << std::endl; |
| 591 |
– |
os << "Generated by Hydro" << std::endl; |
| 592 |
– |
for (iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 593 |
– |
os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl; |
| 594 |
– |
} |
| 595 |
– |
|
| 596 |
– |
} |
| 597 |
– |
|
| 598 |
– |
void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) { |
| 599 |
– |
|
| 600 |
– |
os << sd_->getType() << "\t"; |
| 601 |
– |
os << props_.diffCenter[0] << "\t" << props_.diffCenter[1] << "\t" << props_.diffCenter[2] << "\t"; |
| 602 |
– |
|
| 603 |
– |
os << props_.Ddtt(0, 0) << "\t" << props_.Ddtt(0, 1) << "\t" << props_.Ddtt(0, 2) << "\t" |
| 604 |
– |
<< props_.Ddtt(1, 0) << "\t" << props_.Ddtt(1, 1) << "\t" << props_.Ddtt(1, 2) << "\t" |
| 605 |
– |
<< props_.Ddtt(2, 0) << "\t" << props_.Ddtt(2, 1) << "\t" << props_.Ddtt(2, 2) << "\t"; |
| 606 |
– |
|
| 607 |
– |
os << props_.Ddtr(0, 0) << "\t" << props_.Ddtr(0, 1) << "\t" << props_.Ddtr(0, 2) << "\t" |
| 608 |
– |
<< props_.Ddtr(1, 0) << "\t" << props_.Ddtr(1, 1) << "\t" << props_.Ddtr(1, 2) << "\t" |
| 609 |
– |
<< props_.Ddtr(2, 0) << "\t" << props_.Ddtr(2, 1) << "\t" << props_.Ddtr(2, 2) << "\t"; |
| 610 |
– |
|
| 611 |
– |
os << props_.Ddrr(0, 0) << "\t" << props_.Ddrr(0, 1) << "\t" << props_.Ddrr(0, 2) << "\t" |
| 612 |
– |
<< props_.Ddrr(1, 0) << "\t" << props_.Ddrr(1, 1) << "\t" << props_.Ddrr(1, 2) << "\t" |
| 613 |
– |
<< props_.Ddrr(2, 0) << "\t" << props_.Ddrr(2, 1) << "\t" << props_.Ddrr(2, 2) <<"\t"; |
| 614 |
– |
|
| 615 |
– |
os << props_.Xidtt(0, 0) << "\t" << props_.Xidtt(0, 1) << "\t" << props_.Xidtt(0, 2) << "\t" |
| 616 |
– |
<< props_.Xidtt(1, 0) << "\t" << props_.Xidtt(1, 1) << "\t" << props_.Xidtt(1, 2) << "\t" |
| 617 |
– |
<< props_.Xidtt(2, 0) << "\t" << props_.Xidtt(2, 1) << "\t" << props_.Xidtt(2, 2) << "\t"; |
| 618 |
– |
|
| 619 |
– |
os << props_.Xidrt(0, 0) << "\t" << props_.Xidrt(0, 1) << "\t" << props_.Xidrt(0, 2) << "\t" |
| 620 |
– |
<< props_.Xidrt(1, 0) << "\t" << props_.Xidrt(1, 1) << "\t" << props_.Xidrt(1, 2) << "\t" |
| 621 |
– |
<< props_.Xidrt(2, 0) << "\t" << props_.Xidrt(2, 1) << "\t" << props_.Xidrt(2, 2) << "\t"; |
| 622 |
– |
|
| 623 |
– |
os << props_.Xidtr(0, 0) << "\t" << props_.Xidtr(0, 1) << "\t" << props_.Xidtr(0, 2) << "\t" |
| 624 |
– |
<< props_.Xidtr(1, 0) << "\t" << props_.Xidtr(1, 1) << "\t" << props_.Xidtr(1, 2) << "\t" |
| 625 |
– |
<< props_.Xidtr(2, 0) << "\t" << props_.Xidtr(2, 1) << "\t" << props_.Xidtr(2, 2) << "\t"; |
| 626 |
– |
|
| 627 |
– |
os << props_.Xidrr(0, 0) << "\t" << props_.Xidrr(0, 1) << "\t" << props_.Xidrr(0, 2) << "\t" |
| 628 |
– |
<< props_.Xidrr(1, 0) << "\t" << props_.Xidrr(1, 1) << "\t" << props_.Xidrr(1, 2) << "\t" |
| 629 |
– |
<< props_.Xidrr(2, 0) << "\t" << props_.Xidrr(2, 1) << "\t" << props_.Xidrr(2, 2) << std::endl; |
| 630 |
– |
|
| 631 |
– |
} |
| 632 |
– |
|
| 633 |
– |
} |
