| 38 |
|
* University of Notre Dame has been advised of the possibility of |
| 39 |
|
* such damages. |
| 40 |
|
*/ |
| 41 |
+ |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
| 42 |
+ |
#include "hydrodynamics/Shape.hpp" |
| 43 |
+ |
#include "hydrodynamics/Sphere.hpp" |
| 44 |
+ |
#include "hydrodynamics/Ellipsoid.hpp" |
| 45 |
+ |
#include "applications/hydrodynamics/CompositeShape.hpp" |
| 46 |
|
|
| 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" |
| 47 |
|
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 |
< |
*/ |
| 48 |
> |
|
| 49 |
> |
bool HydrodynamicsModel::calcHydroProps(Shape* shape, RealType viscosity, RealType temperature) { |
| 50 |
> |
return false; |
| 51 |
> |
} |
| 52 |
> |
|
| 53 |
> |
void HydrodynamicsModel::writeHydroProps(std::ostream& os) { |
| 54 |
|
|
| 55 |
< |
HydrodynamicsModel::HydrodynamicsModel(StuntDouble* sd, const DynamicProperty& extraParams) : sd_(sd){ |
| 56 |
< |
DynamicProperty::const_iterator iter; |
| 57 |
< |
|
| 58 |
< |
iter = extraParams.find("Viscosity"); |
| 59 |
< |
if (iter != extraParams.end()) { |
| 60 |
< |
boost::any param = iter->second; |
| 61 |
< |
viscosity_ = boost::any_cast<double>(param); |
| 62 |
< |
}else { |
| 63 |
< |
std::cout << "HydrodynamicsModel Error\n" ; |
| 64 |
< |
} |
| 65 |
< |
|
| 66 |
< |
iter = extraParams.find("Temperature"); |
| 67 |
< |
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 |
< |
} |
| 73 |
< |
} |
| 74 |
< |
|
| 75 |
< |
bool HydrodynamicsModel::calcHydrodyanmicsProps() { |
| 76 |
< |
if (!createBeads(beads_)) { |
| 77 |
< |
std::cout << "can not create beads" << std::endl; |
| 78 |
< |
return false; |
| 79 |
< |
} |
| 55 |
> |
Vector3d center; |
| 56 |
> |
Mat6x6d Xi, D; |
| 57 |
|
|
| 58 |
< |
int nbeads = beads_.size(); |
| 82 |
< |
DynamicRectMatrix<double> B(3*nbeads, 3*nbeads); |
| 83 |
< |
DynamicRectMatrix<double> C(3*nbeads, 3*nbeads); |
| 84 |
< |
Mat3x3d I; |
| 85 |
< |
I(0, 0) = 1.0; |
| 86 |
< |
I(1, 1) = 1.0; |
| 87 |
< |
I(2, 2) = 1.0; |
| 58 |
> |
os << sd_->getType() << "\t"; |
| 59 |
|
|
| 60 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 90 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 91 |
< |
Mat3x3d Tij; |
| 92 |
< |
if (i != j ) { |
| 93 |
< |
Vector3d Rij = beads_[i].pos - beads_[j].pos; |
| 94 |
< |
double rij = Rij.length(); |
| 95 |
< |
double rij2 = rij * rij; |
| 96 |
< |
double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; |
| 97 |
< |
Mat3x3d tmpMat; |
| 98 |
< |
tmpMat = outProduct(Rij, Rij) / rij2; |
| 99 |
< |
double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; |
| 100 |
< |
Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; |
| 101 |
< |
}else { |
| 102 |
< |
double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); |
| 103 |
< |
Tij(0, 0) = constant; |
| 104 |
< |
Tij(1, 1) = constant; |
| 105 |
< |
Tij(2, 2) = constant; |
| 106 |
< |
} |
| 107 |
< |
B.setSubMatrix(i*3, j*3, Tij); |
| 108 |
< |
std::cout << Tij << std::endl; |
| 109 |
< |
} |
| 110 |
< |
} |
| 60 |
> |
//center of resistance |
| 61 |
|
|
| 62 |
< |
std::cout << "B=\n" |
| 113 |
< |
<< B << std::endl; |
| 114 |
< |
//invert B Matrix |
| 115 |
< |
invertMatrix(B, C); |
| 62 |
> |
center = cr_->getCOR(); |
| 63 |
|
|
| 64 |
< |
std::cout << "C=\n" |
| 118 |
< |
<< C << std::endl; |
| 119 |
< |
|
| 120 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
| 121 |
< |
std::vector<Mat3x3d> U; |
| 122 |
< |
for (int i = 0; i < nbeads; ++i) { |
| 123 |
< |
Mat3x3d currU; |
| 124 |
< |
currU.setupSkewMat(beads_[i].pos); |
| 125 |
< |
U.push_back(currU); |
| 126 |
< |
} |
| 64 |
> |
os << center[0] << "\t" << center[1] << "\t" << center[2] << "\t"; |
| 65 |
|
|
| 66 |
< |
//calculate Xi matrix at arbitrary origin O |
| 67 |
< |
Mat3x3d Xitt; |
| 130 |
< |
Mat3x3d Xirr; |
| 131 |
< |
Mat3x3d Xitr; |
| 66 |
> |
//resistance tensor at center of resistance |
| 67 |
> |
//translation |
| 68 |
|
|
| 69 |
< |
//calculate the total volume |
| 69 |
> |
Xi = cr_->getXi(); |
| 70 |
|
|
| 71 |
< |
double volume = 0.0; |
| 72 |
< |
for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 73 |
< |
volume = 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); |
| 74 |
< |
} |
| 75 |
< |
|
| 76 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
| 77 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
| 78 |
< |
Mat3x3d Cij; |
| 79 |
< |
C.getSubMatrix(i*3, j*3, Cij); |
| 80 |
< |
|
| 81 |
< |
Xitt += Cij; |
| 82 |
< |
Xitr += U[i] * Cij; |
| 83 |
< |
Xirr += -U[i] * Cij * U[j]; |
| 84 |
< |
//Xirr += -U[i] * Cij * U[j] + (0.166*6 * viscosity_ * volume) * I; |
| 85 |
< |
} |
| 86 |
< |
} |
| 71 |
> |
os << Xi(0, 0) << "\t" << Xi(0, 1) << "\t" << Xi(0, 2) << "\t" |
| 72 |
> |
<< Xi(1, 0) << "\t" << Xi(1, 1) << "\t" << Xi(1, 2) << "\t" |
| 73 |
> |
<< Xi(2, 0) << "\t" << Xi(2, 1) << "\t" << Xi(2, 2) << "\t"; |
| 74 |
> |
|
| 75 |
> |
//rotation-translation |
| 76 |
> |
os << Xi(0, 3) << "\t" << Xi(0, 4) << "\t" << Xi(0, 5) << "\t" |
| 77 |
> |
<< Xi(1, 3) << "\t" << Xi(1, 4) << "\t" << Xi(1, 5) << "\t" |
| 78 |
> |
<< Xi(2, 3) << "\t" << Xi(2, 4) << "\t" << Xi(2, 5) << "\t"; |
| 79 |
> |
|
| 80 |
> |
//translation-rotation |
| 81 |
> |
os << Xi(3, 0) << "\t" << Xi(3, 1) << "\t" << Xi(3, 2) << "\t" |
| 82 |
> |
<< Xi(4, 0) << "\t" << Xi(4, 1) << "\t" << Xi(4, 2) << "\t" |
| 83 |
> |
<< Xi(5, 0) << "\t" << Xi(5, 1) << "\t" << Xi(5, 2) << "\t"; |
| 84 |
> |
|
| 85 |
> |
//rotation |
| 86 |
> |
os << Xi(3, 3) << "\t" << Xi(3, 4) << "\t" << Xi(3, 5) << "\t" |
| 87 |
> |
<< Xi(4, 3) << "\t" << Xi(4, 4) << "\t" << Xi(4, 5) << "\t" |
| 88 |
> |
<< Xi(5, 3) << "\t" << Xi(5, 4) << "\t" << Xi(5, 5) << "\t"; |
| 89 |
> |
|
| 90 |
> |
|
| 91 |
> |
//diffusion tensor at center of resistance |
| 92 |
> |
//translation |
| 93 |
|
|
| 94 |
< |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
| 153 |
< |
RectMatrix<double, 6, 6> Xi; |
| 154 |
< |
RectMatrix<double, 6, 6> Do; |
| 155 |
< |
Xi.setSubMatrix(0, 0, Xitt); |
| 156 |
< |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
| 157 |
< |
Xi.setSubMatrix(3, 0, Xitr); |
| 158 |
< |
Xi.setSubMatrix(3, 3, Xirr); |
| 159 |
< |
//invertMatrix(Xi, Do); |
| 160 |
< |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
| 161 |
< |
//Do *= kt; |
| 94 |
> |
D = cr_->getD(); |
| 95 |
|
|
| 96 |
< |
|
| 97 |
< |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
| 98 |
< |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
| 166 |
< |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
| 167 |
< |
|
| 168 |
< |
const static Mat3x3d zeroMat(0.0); |
| 96 |
> |
os << D(0, 0) << "\t" << D(0, 1) << "\t" << D(0, 2) << "\t" |
| 97 |
> |
<< D(1, 0) << "\t" << D(1, 1) << "\t" << D(1, 2) << "\t" |
| 98 |
> |
<< D(2, 0) << "\t" << D(2, 1) << "\t" << D(2, 2) << "\t"; |
| 99 |
|
|
| 100 |
< |
Mat3x3d XittInv(0.0); |
| 101 |
< |
XittInv = Xitt.inverse(); |
| 100 |
> |
//rotation-translation |
| 101 |
> |
os << D(0, 3) << "\t" << D(0, 4) << "\t" << D(0, 5) << "\t" |
| 102 |
> |
<< D(1, 3) << "\t" << D(1, 4) << "\t" << D(1, 5) << "\t" |
| 103 |
> |
<< D(2, 3) << "\t" << D(2, 4) << "\t" << D(2, 5) << "\t"; |
| 104 |
|
|
| 105 |
< |
//Xirr may not be inverted,if it one of the diagonal element is zero, for example |
| 106 |
< |
//( a11 a12 0) |
| 107 |
< |
//( a21 a22 0) |
| 108 |
< |
//( 0 0 0) |
| 109 |
< |
Mat3x3d XirrInv; |
| 110 |
< |
XirrInv = Xirr.inverse(); |
| 105 |
> |
//translation-rotation |
| 106 |
> |
os << D(3, 0) << "\t" << D(3, 1) << "\t" << D(3, 2) << "\t" |
| 107 |
> |
<< D(4, 0) << "\t" << D(4, 1) << "\t" << D(4, 2) << "\t" |
| 108 |
> |
<< D(5, 0) << "\t" << D(5, 1) << "\t" << D(5, 2) << "\t"; |
| 109 |
> |
|
| 110 |
> |
//rotation |
| 111 |
> |
os << D(3, 3) << "\t" << D(3, 4) << "\t" << D(3, 5) << "\t" |
| 112 |
> |
<< D(4, 3) << "\t" << D(4, 4) << "\t" << D(4, 5) << "\t" |
| 113 |
> |
<< D(5, 3) << "\t" << D(5, 4) << "\t" << D(5, 5) << "\t"; |
| 114 |
> |
|
| 115 |
> |
//--------------------------------------------------------------------- |
| 116 |
> |
|
| 117 |
> |
//center of diffusion |
| 118 |
|
|
| 119 |
< |
Mat3x3d tmp; |
| 181 |
< |
Mat3x3d tmpInv; |
| 182 |
< |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
| 183 |
< |
tmpInv = tmp.inverse(); |
| 119 |
> |
center = cd_->getCOR(); |
| 120 |
|
|
| 121 |
< |
Dott = kt * tmpInv; |
| 186 |
< |
Dotr = -kt*XirrInv * Xitr * tmpInv* 1.0E8; |
| 187 |
< |
|
| 188 |
< |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
| 189 |
< |
tmpInv = tmp.inverse(); |
| 121 |
> |
os << center[0] << "\t" << center[1] << "\t" << center[2] << "\t"; |
| 122 |
|
|
| 123 |
< |
Dorr = kt * tmpInv*1.0E16; |
| 123 |
> |
//resistance tensor at center of diffusion |
| 124 |
> |
//translation |
| 125 |
|
|
| 126 |
< |
//Do.getSubMatrix(0, 0 , Dott); |
| 194 |
< |
//Do.getSubMatrix(3, 0, Dotr); |
| 195 |
< |
//Do.getSubMatrix(3, 3, Dorr); |
| 126 |
> |
Xi = cd_->getXi(); |
| 127 |
|
|
| 128 |
< |
//calculate center of diffusion |
| 129 |
< |
tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); |
| 130 |
< |
tmp(0, 1) = - Dorr(0, 1); |
| 200 |
< |
tmp(0, 2) = -Dorr(0, 2); |
| 201 |
< |
tmp(1, 0) = -Dorr(0, 1); |
| 202 |
< |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
| 203 |
< |
tmp(1, 2) = -Dorr(1, 2); |
| 204 |
< |
tmp(2, 0) = -Dorr(0, 2); |
| 205 |
< |
tmp(2, 1) = -Dorr(1, 2); |
| 206 |
< |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
| 207 |
< |
|
| 208 |
< |
Vector3d tmpVec; |
| 209 |
< |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
| 210 |
< |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
| 211 |
< |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
| 212 |
< |
|
| 213 |
< |
tmpInv = tmp.inverse(); |
| 128 |
> |
os << Xi(0, 0) << "\t" << Xi(0, 1) << "\t" << Xi(0, 2) << "\t" |
| 129 |
> |
<< Xi(1, 0) << "\t" << Xi(1, 1) << "\t" << Xi(1, 2) << "\t" |
| 130 |
> |
<< Xi(2, 0) << "\t" << Xi(2, 1) << "\t" << Xi(2, 2) << "\t"; |
| 131 |
|
|
| 132 |
< |
Vector3d rod = tmpInv * tmpVec; |
| 133 |
< |
|
| 134 |
< |
//calculate Diffusion Tensor at center of diffusion |
| 135 |
< |
Mat3x3d Uod; |
| 219 |
< |
Uod.setupSkewMat(rod); |
| 132 |
> |
//rotation-translation |
| 133 |
> |
os << Xi(0, 3) << "\t" << Xi(0, 4) << "\t" << Xi(0, 5) << "\t" |
| 134 |
> |
<< Xi(1, 3) << "\t" << Xi(1, 4) << "\t" << Xi(1, 5) << "\t" |
| 135 |
> |
<< Xi(2, 3) << "\t" << Xi(2, 4) << "\t" << Xi(2, 5) << "\t"; |
| 136 |
|
|
| 137 |
< |
Mat3x3d Ddtt; //translational diffusion tensor at diffusion center |
| 138 |
< |
Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center |
| 139 |
< |
Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor |
| 137 |
> |
//translation-rotation |
| 138 |
> |
os << Xi(3, 0) << "\t" << Xi(3, 1) << "\t" << Xi(3, 2) << "\t" |
| 139 |
> |
<< Xi(4, 0) << "\t" << Xi(4, 1) << "\t" << Xi(4, 2) << "\t" |
| 140 |
> |
<< Xi(5, 0) << "\t" << Xi(5, 1) << "\t" << Xi(5, 2) << "\t"; |
| 141 |
|
|
| 142 |
< |
Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; |
| 143 |
< |
Ddrr = Dorr; |
| 144 |
< |
Ddtr = Dotr + Dorr * Uod; |
| 142 |
> |
//rotation |
| 143 |
> |
os << Xi(3, 3) << "\t" << Xi(3, 4) << "\t" << Xi(3, 5) << "\t" |
| 144 |
> |
<< Xi(4, 3) << "\t" << Xi(4, 4) << "\t" << Xi(4, 5) << "\t" |
| 145 |
> |
<< Xi(5, 3) << "\t" << Xi(5, 4) << "\t" << Xi(5, 5) << "\t"; |
| 146 |
|
|
| 147 |
< |
props_.diffCenter = rod; |
| 148 |
< |
props_.transDiff = Ddtt; |
| 149 |
< |
props_.transRotDiff = Ddtr; |
| 232 |
< |
props_.rotDiff = Ddrr; |
| 147 |
> |
|
| 148 |
> |
//diffusion tensor at center of diffusion |
| 149 |
> |
//translation |
| 150 |
|
|
| 151 |
< |
return true; |
| 235 |
< |
} |
| 151 |
> |
D = cd_->getD(); |
| 152 |
|
|
| 153 |
< |
void HydrodynamicsModel::writeBeads(std::ostream& os) { |
| 154 |
< |
std::vector<BeadParam>::iterator iter; |
| 155 |
< |
os << beads_.size() << std::endl; |
| 240 |
< |
os << "Generated by Hydro" << std::endl; |
| 241 |
< |
for (iter = beads_.begin(); iter != beads_.end(); ++iter) { |
| 242 |
< |
os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl; |
| 243 |
< |
} |
| 244 |
< |
|
| 245 |
< |
} |
| 246 |
< |
|
| 247 |
< |
void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) { |
| 248 |
< |
os << "//viscosity = " << viscosity_ << std::endl; |
| 249 |
< |
os << "//temperature = " << temperature_<< std::endl; |
| 250 |
< |
std::vector<BeadParam>::iterator iter; |
| 251 |
< |
os << sd_->getType() << "\n"; |
| 252 |
< |
|
| 253 |
< |
os << "//diffusion center" << std::endl; |
| 254 |
< |
os << props_.diffCenter << std::endl; |
| 255 |
< |
|
| 256 |
< |
os << "//translational diffusion tensor" << std::endl; |
| 257 |
< |
os << props_.transDiff << std::endl; |
| 258 |
< |
|
| 259 |
< |
os << "//translation-rotation coupling diffusion tensor" << std::endl; |
| 260 |
< |
os << props_.transRotDiff << std::endl; |
| 261 |
< |
|
| 262 |
< |
os << "//rotational diffusion tensor" << std::endl; |
| 263 |
< |
os << props_.rotDiff << std::endl; |
| 153 |
> |
os << D(0, 0) << "\t" << D(0, 1) << "\t" << D(0, 2) << "\t" |
| 154 |
> |
<< D(1, 0) << "\t" << D(1, 1) << "\t" << D(1, 2) << "\t" |
| 155 |
> |
<< D(2, 0) << "\t" << D(2, 1) << "\t" << D(2, 2) << "\t"; |
| 156 |
|
|
| 157 |
< |
/* |
| 158 |
< |
os << props_.diffCenter[0] << "\t" << props_.diffCenter[1] << "\t" << props_.diffCenter[2] << "\n" |
| 159 |
< |
|
| 160 |
< |
os << props_.transDiff(0, 0) << "\t" << props_.transDiff(0, 1) << "\t" << props_.transDiff(0, 2) << "\t" |
| 269 |
< |
<< props_.transDiff(1, 0) << "\t" << props_.transDiff(1, 1) << "\t" << props_.transDiff(1, 2) << "\t" |
| 270 |
< |
<< props_.transDiff(2, 0) << "\t" << props_.transDiff(2, 1) << "\t" << props_.transDiff(2, 2) << "\n"; |
| 157 |
> |
//rotation-translation |
| 158 |
> |
os << D(0, 3) << "\t" << D(0, 4) << "\t" << D(0, 5) << "\t" |
| 159 |
> |
<< D(1, 3) << "\t" << D(1, 4) << "\t" << D(1, 5) << "\t" |
| 160 |
> |
<< D(2, 3) << "\t" << D(2, 4) << "\t" << D(2, 5) << "\t"; |
| 161 |
|
|
| 162 |
< |
os << props_.transRotDiff(0, 0) << "\t" << props_.transRotDiff(0, 1) << "\t" << props_.transRotDiff(0, 2) << "\t" |
| 163 |
< |
<< props_.transRotDiff(1, 0) << "\t" << props_.transRotDiff(1, 1) << "\t" << props_.transRotDiff(1, 2) << "\t" |
| 164 |
< |
<< props_.transRotDiff(2, 0) << "\t" << props_.transRotDiff(2, 1) << "\t" << props_.transRotDiff(2, 2) << "\t" |
| 165 |
< |
|
| 166 |
< |
os << props_.rotDiff(0, 0) << "\t" << props_.rotDiff(0, 1) << "\t" << props_.rotDiff(0, 2) << "\t" |
| 167 |
< |
<< props_.rotDiff(1, 0) << "\t" << props_.rotDiff(1, 1) << "\t" << props_.rotDiff(1, 2) << "\t" |
| 168 |
< |
<< props_.rotDiff(2, 0) << "\t" << props_.rotDiff(2, 1) << "\t" << props_.rotDiff(2, 2) << ";" |
| 169 |
< |
<< std::endl; |
| 170 |
< |
*/ |
| 162 |
> |
//translation-rotation |
| 163 |
> |
os << D(3, 0) << "\t" << D(3, 1) << "\t" << D(3, 2) << "\t" |
| 164 |
> |
<< D(4, 0) << "\t" << D(4, 1) << "\t" << D(4, 2) << "\t" |
| 165 |
> |
<< D(5, 0) << "\t" << D(5, 1) << "\t" << D(5, 2) << "\t"; |
| 166 |
> |
|
| 167 |
> |
//rotation |
| 168 |
> |
os << D(3, 3) << "\t" << D(3, 4) << "\t" << D(3, 5) << "\t" |
| 169 |
> |
<< D(4, 3) << "\t" << D(4, 4) << "\t" << D(4, 5) << "\t" |
| 170 |
> |
<< D(5, 3) << "\t" << D(5, 4) << "\t" << D(5, 5) << "\n"; |
| 171 |
> |
|
| 172 |
> |
} |
| 173 |
> |
|
| 174 |
|
} |
| 282 |
– |
|
| 283 |
– |
} |
