6 |
|
* redistribute this software in source and binary code form, provided |
7 |
|
* that the following conditions are met: |
8 |
|
* |
9 |
< |
* 1. Acknowledgement of the program authors must be made in any |
10 |
< |
* publication of scientific results based in part on use of the |
11 |
< |
* program. An acceptable form of acknowledgement is citation of |
12 |
< |
* the article in which the program was described (Matthew |
13 |
< |
* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
14 |
< |
* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
15 |
< |
* Parallel Simulation Engine for Molecular Dynamics," |
16 |
< |
* J. Comput. Chem. 26, pp. 252-271 (2005)) |
17 |
< |
* |
18 |
< |
* 2. Redistributions of source code must retain the above copyright |
9 |
> |
* 1. Redistributions of source code must retain the above copyright |
10 |
|
* notice, this list of conditions and the following disclaimer. |
11 |
|
* |
12 |
< |
* 3. Redistributions in binary form must reproduce the above copyright |
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. |
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, 24107 (2008). |
39 |
+ |
* [4] Vardeman & Gezelter, in progress (2009). |
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 |
|
|
47 |
< |
#include "applications/hydrodynamics/HydrodynamicsModel.hpp" |
48 |
< |
#include "math/LU.hpp" |
49 |
< |
#include "math/DynamicRectMatrix.hpp" |
50 |
< |
#include "math/SquareMatrix3.hpp" |
51 |
< |
#include "utils/OOPSEConstant.hpp" |
52 |
< |
namespace oopse { |
53 |
< |
/** |
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 |
> |
namespace OpenMD { |
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(beads_[i].pos, beads_[j].pos) / 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 |
< |
} |
109 |
< |
} |
60 |
> |
//center of resistance |
61 |
|
|
62 |
< |
//invert B Matrix |
63 |
< |
invertMatrix(B, C); |
64 |
< |
//prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) |
114 |
< |
std::vector<Mat3x3d> U; |
115 |
< |
for (int i = 0; i < nbeads; ++i) { |
116 |
< |
Mat3x3d currU; |
117 |
< |
currU.setupSkewMat(beads_[i].pos); |
118 |
< |
U.push_back(currU); |
119 |
< |
} |
62 |
> |
center = cr_->getCOR(); |
63 |
> |
|
64 |
> |
os << center[0] << "\t" << center[1] << "\t" << center[2] << "\t"; |
65 |
|
|
66 |
< |
//calculate Xi matrix at arbitrary origin O |
67 |
< |
Mat3x3d Xitt; |
123 |
< |
Mat3x3d Xirr; |
124 |
< |
Mat3x3d Xitr; |
125 |
< |
|
126 |
< |
for (std::size_t i = 0; i < nbeads; ++i) { |
127 |
< |
for (std::size_t j = 0; j < nbeads; ++j) { |
128 |
< |
Mat3x3d Cij; |
129 |
< |
C.getSubMatrix(i*3, j*3, Cij); |
130 |
< |
|
131 |
< |
Xitt += Cij; |
132 |
< |
Xirr += U[i] * Cij; |
133 |
< |
Xitr += U[i] * Cij * U[j]; |
134 |
< |
} |
135 |
< |
} |
66 |
> |
//resistance tensor at center of resistance |
67 |
> |
//translation |
68 |
|
|
69 |
< |
//invert Xi to get Diffusion Tensor at arbitrary origin O |
138 |
< |
RectMatrix<double, 6, 6> Xi; |
139 |
< |
RectMatrix<double, 6, 6> Do; |
140 |
< |
Xi.setSubMatrix(0, 0, Xitt); |
141 |
< |
Xi.setSubMatrix(0, 3, Xitr.transpose()); |
142 |
< |
Xi.setSubMatrix(3, 0, Xitr); |
143 |
< |
Xi.setSubMatrix(3, 3, Xirr); |
144 |
< |
//invertMatrix(Xi, Do); |
145 |
< |
double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; |
146 |
< |
//Do *= kt; |
69 |
> |
Xi = cr_->getXi(); |
70 |
|
|
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 |
< |
Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O |
150 |
< |
Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O |
151 |
< |
Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O |
94 |
> |
D = cr_->getD(); |
95 |
|
|
96 |
< |
Mat3x3d XirrInv(0.0); |
97 |
< |
Mat3x3d XirrCopy; |
98 |
< |
XirrCopy = Xirr; |
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 |
< |
Mat3x3d XittCopy; |
102 |
< |
XittCopy = Xitt; |
103 |
< |
invertMatrix(XittCopy, XittInv); |
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 |
> |
//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; |
163 |
< |
Mat3x3d tmpInv; |
164 |
< |
tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; |
119 |
> |
center = cd_->getCOR(); |
120 |
|
|
121 |
< |
const static Mat3x3d zeroMat(0.0); |
167 |
< |
if (!invertMatrix(tmp, tmpInv)) { |
168 |
< |
tmpInv = zeroMat; |
169 |
< |
} |
170 |
< |
|
171 |
< |
Dott = kt * tmpInv; |
172 |
< |
Dotr = -kt*XirrInv * Xitr * tmpInv; |
173 |
< |
|
174 |
< |
tmp = Xirr - Xitr * XittInv * Xitr.transpose(); |
121 |
> |
os << center[0] << "\t" << center[1] << "\t" << center[2] << "\t"; |
122 |
|
|
123 |
< |
if(!invertMatrix(tmp, tmpInv)) { |
124 |
< |
tmpInv = zeroMat; |
178 |
< |
} |
179 |
< |
Dorr = kt * tmpInv; |
123 |
> |
//resistance tensor at center of diffusion |
124 |
> |
//translation |
125 |
|
|
126 |
< |
//Do.getSubMatrix(0, 0 , Dott); |
182 |
< |
//Do.getSubMatrix(3, 0, Dotr); |
183 |
< |
//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); |
188 |
< |
tmp(0, 2) = -Dorr(0, 2); |
189 |
< |
tmp(1, 0) = -Dorr(0, 1); |
190 |
< |
tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); |
191 |
< |
tmp(1, 2) = -Dorr(1, 2); |
192 |
< |
tmp(2, 0) = -Dorr(0, 2); |
193 |
< |
tmp(2, 1) = -Dorr(1, 2); |
194 |
< |
tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); |
195 |
< |
|
196 |
< |
Vector3d tmpVec; |
197 |
< |
tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); |
198 |
< |
tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); |
199 |
< |
tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); |
200 |
< |
|
201 |
< |
if(!invertMatrix(tmp, tmpInv)) { |
202 |
< |
tmpInv = zeroMat; |
203 |
< |
} |
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; |
209 |
< |
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; |
222 |
< |
props_.rotDiff = Ddrr; |
147 |
> |
|
148 |
> |
//diffusion tensor at center of diffusion |
149 |
> |
//translation |
150 |
|
|
151 |
< |
return true; |
225 |
< |
} |
151 |
> |
D = cd_->getD(); |
152 |
|
|
153 |
< |
void HydrodynamicsModel::writeBeads(std::ostream& os) { |
154 |
< |
std::vector<BeadParam>::iterator iter; |
155 |
< |
os << beads_.size() << std::endl; |
230 |
< |
os << "Generated by Hydro" << std::endl; |
231 |
< |
for (iter = beads_.begin(); iter != beads_.end(); ++iter) { |
232 |
< |
os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl; |
233 |
< |
} |
234 |
< |
|
235 |
< |
} |
236 |
< |
|
237 |
< |
void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) { |
238 |
< |
os << "//viscosity = " << viscosity_ << std::endl; |
239 |
< |
os << "//temperature = " << temperature_<< std::endl; |
240 |
< |
std::vector<BeadParam>::iterator iter; |
241 |
< |
os << sd_->getType() << "\n"; |
242 |
< |
|
243 |
< |
os << "//diffusion center" << std::endl; |
244 |
< |
os << props_.diffCenter << std::endl; |
245 |
< |
|
246 |
< |
os << "//translational diffusion tensor" << std::endl; |
247 |
< |
os << props_.transDiff << std::endl; |
248 |
< |
|
249 |
< |
os << "//translational diffusion tensor" << std::endl; |
250 |
< |
os << props_.transRotDiff << std::endl; |
251 |
< |
|
252 |
< |
os << "//rotational diffusion tensor" << std::endl; |
253 |
< |
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" |
259 |
< |
<< props_.transDiff(1, 0) << "\t" << props_.transDiff(1, 1) << "\t" << props_.transDiff(1, 2) << "\t" |
260 |
< |
<< 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 |
|
} |
272 |
– |
|
273 |
– |
} |