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root/group/trunk/OOPSE-4/src/applications/hydrodynamics/HydrodynamicsModel.cpp
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Comparing trunk/OOPSE-4/src/applications/hydrodynamics/HydrodynamicsModel.cpp (file contents):
Revision 2632 by tim, Thu Mar 16 22:50:48 2006 UTC vs.
Revision 2634 by tim, Fri Mar 17 23:20:35 2006 UTC

# Line 38 | Line 38
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;
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 <    }    
48 > bool HydrodynamicsModel::calcHydroProps(Spheric* spheric, double viscosity, double temperature) {
49 >    return false;
50   }
74 –
75 – bool HydrodynamicsModel::calcHydrodyanmicsProps() {
76 –    if (!createBeads(beads_)) {
77 –        std::cout << "can not create beads" << std::endl;
78 –        return false;
79 –    }
51  
52 <    //calcResistanceTensor();
53 <    calcDiffusionTensor();    
83 <    return true;    
52 > bool HydrodynamicsModel::calcHydroProps(Ellipsoid* ellipsoid, double viscosity, double temperature) {
53 >    return false;
54   }
55  
56 < void HydrodynamicsModel::calcResistanceTensor() {
56 > bool HydrodynamicsModel::calcHydroProps(CompositeShape* compositexShape, double viscosity, double temperature) {
57 >    return false;
58   }
59  
60 < void HydrodynamicsModel::calcDiffusionTensor() {
90 <    int nbeads = beads_.size();
91 <    DynamicRectMatrix<double> B(3*nbeads, 3*nbeads);
92 <    DynamicRectMatrix<double> C(3*nbeads, 3*nbeads);
93 <    Mat3x3d I;
94 <    I(0, 0) = 1.0;
95 <    I(1, 1) = 1.0;
96 <    I(2, 2) = 1.0;
97 <    
98 <    for (std::size_t i = 0; i < nbeads; ++i) {
99 <        for (std::size_t j = 0; j < nbeads; ++j) {
100 <            Mat3x3d Tij;
101 <            if (i != j ) {
102 <                Vector3d Rij = beads_[i].pos - beads_[j].pos;
103 <                double rij = Rij.length();
104 <                double rij2 = rij * rij;
105 <                double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2;                
106 <                Mat3x3d tmpMat;
107 <                tmpMat = outProduct(Rij, Rij) / rij2;
108 <                double constant = 8.0 * NumericConstant::PI * viscosity_ * rij;
109 <                Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant;
110 <            }else {
111 <                double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius);
112 <                Tij(0, 0) = constant;
113 <                Tij(1, 1) = constant;
114 <                Tij(2, 2) = constant;
115 <            }
116 <            B.setSubMatrix(i*3, j*3, Tij);
117 <        }
118 <    }
60 > void HydrodynamicsModel::writeHydroProps(std::ostream& os) {
61  
120 –    //invert B Matrix
121 –    invertMatrix(B, C);
122 –
123 –    //prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0)
124 –    std::vector<Mat3x3d> U;
125 –    for (int i = 0; i < nbeads; ++i) {
126 –        Mat3x3d currU;
127 –        currU.setupSkewMat(beads_[i].pos);
128 –        U.push_back(currU);
129 –    }
62      
63 <    //calculate Xi matrix at arbitrary origin O
132 <    Mat3x3d Xitt;
133 <    Mat3x3d Xirr;
134 <    Mat3x3d Xitr;
135 <
136 <    //calculate the total volume
137 <
138 <    double volume = 0.0;
139 <    for (std::vector<BeadParam>::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) {
140 <        volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3);
141 <    }
142 <        
143 <    for (std::size_t i = 0; i < nbeads; ++i) {
144 <        for (std::size_t j = 0; j < nbeads; ++j) {
145 <            Mat3x3d Cij;
146 <            C.getSubMatrix(i*3, j*3, Cij);
147 <            
148 <            Xitt += Cij;
149 <            Xitr += U[i] * Cij;
150 <            Xirr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I;            
151 <        }
152 <    }
153 <
154 <    const double convertConstant = 6.023; //convert poise.angstrom to amu/fs
155 <    Xitt *= convertConstant;
156 <    Xitr *= convertConstant;
157 <    Xirr *= convertConstant;
158 <
159 <    double kt = OOPSEConstant::kB * temperature_;
160 <
161 <    Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O
162 <    Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O
163 <    Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O
164 <
165 <    const static Mat3x3d zeroMat(0.0);
63 >    os << sd_->getType() << "\t";
64      
65 <    Mat3x3d XittInv(0.0);
66 <    XittInv = Xitt.inverse();
169 <    
170 <    Mat3x3d XirrInv;
171 <    XirrInv = Xirr.inverse();
65 >    //center of resistance
66 >    os << cr_.center[0] <<  "\t" << cr_.center[1] <<  "\t" << cr_.center[2] <<  "\t";
67  
68 <    Mat3x3d tmp;
69 <    Mat3x3d tmpInv;
70 <    tmp = Xitt - Xitr.transpose() * XirrInv * Xitr;
71 <    tmpInv = tmp.inverse();
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 <    Dott = tmpInv;
75 <    Dotr = -XirrInv * Xitr * tmpInv;
76 <    
77 <    tmp = Xirr - Xitr * XittInv * Xitr.transpose();    
182 <    tmpInv = tmp.inverse();
183 <    
184 <    Dorr = tmpInv;
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 <    //calculate center of diffusion
80 <    tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2);
81 <    tmp(0, 1) = - Dorr(0, 1);
82 <    tmp(0, 2) = -Dorr(0, 2);
190 <    tmp(1, 0) = -Dorr(0, 1);
191 <    tmp(1, 1) = Dorr(0, 0)  + Dorr(2, 2);
192 <    tmp(1, 2) = -Dorr(1, 2);
193 <    tmp(2, 0) = -Dorr(0, 2);
194 <    tmp(2, 1) = -Dorr(1, 2);
195 <    tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0);
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 <    Vector3d tmpVec;
85 <    tmpVec[0] = Dotr(1, 2) - Dotr(2, 1);
86 <    tmpVec[1] = Dotr(2, 0) - Dotr(0, 2);
87 <    tmpVec[2] = Dotr(0, 1) - Dotr(1, 0);
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  
202 –    tmpInv = tmp.inverse();
203 –    
204 –    Vector3d rod = tmpInv * tmpVec;
89  
90 <    //calculate Diffusion Tensor at center of diffusion
91 <    Mat3x3d Uod;
92 <    Uod.setupSkewMat(rod);
93 <    
94 <    Mat3x3d Ddtt; //translational diffusion tensor at diffusion center
211 <    Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center
212 <    Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor
213 <    
214 <    Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr;
215 <    Ddrr = Dorr;
216 <    Ddtr = Dotr + Dorr * Uod;
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 <    SquareMatrix<double, 6> Dd;
97 <    Dd.setSubMatrix(0, 0, Ddtt);
98 <    Dd.setSubMatrix(0, 3, Ddtr.transpose());
99 <    Dd.setSubMatrix(3, 0, Ddtr);
222 <    Dd.setSubMatrix(3, 3, Ddrr);    
223 <    SquareMatrix<double, 6> Xid;
224 <    Ddtt *= kt;
225 <    Ddtr *=kt;
226 <    Ddrr *= kt;
227 <    invertMatrix(Dd, Xid);
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 +    //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 +    //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 <    //Xidtt in units of kcal*fs*mol^-1*Ang^-2
114 <    //Xid /= OOPSEConstant::energyConvert;
233 <    Xid *= OOPSEConstant::kb * temperature_;
234 <    props_.diffCenter = rod;
235 <    props_.Ddtt = Ddtt;
236 <    props_.Ddtr = Ddtr;
237 <    props_.Ddrr = Ddrr;
238 <    Xid.getSubMatrix(0, 0, props_.Xidtt);
239 <    Xid.getSubMatrix(0, 3, props_.Xidrt);
240 <    Xid.getSubMatrix(3, 0, props_.Xidtr);
241 <    Xid.getSubMatrix(3, 3, props_.Xidrr);
113 >    //center of diffusion
114 >    os << cd_.center[0] <<  "\t" << cd_.center[1] <<  "\t" << cd_.center[2] <<  "\t";
115  
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 <    std::cout << "viscosity = " << viscosity_ << std::endl;
123 <    std::cout << "temperature = " << temperature_ << std::endl;
124 <    std::cout << "center of diffusion :" << std::endl;
125 <    std::cout << rod << std::endl;
248 <    std::cout << "diffusion tensor at center of diffusion " << std::endl;
249 <    std::cout << "translation(A^2/fs) :" << std::endl;
250 <    std::cout << Ddtt << std::endl;
251 <    std::cout << "translation-rotation(A^3/fs):" << std::endl;
252 <    std::cout << Ddtr << std::endl;
253 <    std::cout << "rotation(A^4/fs):" << std::endl;
254 <    std::cout << Ddrr << std::endl;
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 <    std::cout << "resistance tensor at center of diffusion " << std::endl;
128 <    std::cout << "translation(kcal*fs*mol^-1*Ang^-2) :" << std::endl;
129 <    std::cout << props_.Xidtt << std::endl;
130 <    std::cout << "rotation-translation (kcal*fs*mol^-1*Ang^-3):" << std::endl;
260 <    std::cout << props_.Xidrt << std::endl;
261 <    std::cout << "translation-rotation(kcal*fs*mol^-1*Ang^-3):" << std::endl;
262 <    std::cout << props_.Xidtr << std::endl;
263 <    std::cout << "rotation(kcal*fs*mol^-1*Ang^-4):" << std::endl;
264 <    std::cout << props_.Xidrr << std::endl;
265 <    
266 <      
267 < }
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 < void HydrodynamicsModel::writeBeads(std::ostream& os) {
133 <    std::vector<BeadParam>::iterator iter;
134 <    os << beads_.size() << std::endl;
135 <    os << "Generated by Hydro" << std::endl;
273 <    for (iter = beads_.begin(); iter != beads_.end(); ++iter) {
274 <        os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl;
275 <    }
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  
277 – }
137  
138 < void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) {
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 <    os << sd_->getType() << "\t";
145 <    os << props_.diffCenter[0] << "\t" << props_.diffCenter[1] << "\t" << props_.diffCenter[2] << "\t";
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 <    os << props_.Ddtt(0, 0) << "\t" << props_.Ddtt(0, 1) << "\t" << props_.Ddtt(0, 2) << "\t"
150 <        << props_.Ddtt(1, 0) << "\t" << props_.Ddtt(1, 1) << "\t" << props_.Ddtt(1, 2) << "\t"
151 <        << props_.Ddtt(2, 0) << "\t" << props_.Ddtt(2, 1) << "\t" << props_.Ddtt(2, 2) << "\t";
152 <    
288 <    os << props_.Ddtr(0, 0) << "\t" << props_.Ddtr(0, 1) << "\t" << props_.Ddtr(0, 2) << "\t"
289 <        << props_.Ddtr(1, 0) << "\t" << props_.Ddtr(1, 1) << "\t" << props_.Ddtr(1, 2) << "\t"
290 <        << props_.Ddtr(2, 0) << "\t" << props_.Ddtr(2, 1) << "\t" << props_.Ddtr(2, 2) << "\t";
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 <    os << props_.Ddrr(0, 0) << "\t" << props_.Ddrr(0, 1) << "\t" << props_.Ddrr(0, 2) << "\t"
155 <        << props_.Ddrr(1, 0) << "\t" << props_.Ddrr(1, 1) << "\t" << props_.Ddrr(1, 2) << "\t"
156 <        << props_.Ddrr(2, 0) << "\t" << props_.Ddrr(2, 1) << "\t" << props_.Ddrr(2, 2) <<"\t";        
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  
296 –    os << props_.Xidtt(0, 0) << "\t" << props_.Xidtt(0, 1) << "\t" << props_.Xidtt(0, 2) << "\t"
297 –        << props_.Xidtt(1, 0) << "\t" << props_.Xidtt(1, 1) << "\t" << props_.Xidtt(1, 2) << "\t"
298 –        << props_.Xidtt(2, 0) << "\t" << props_.Xidtt(2, 1) << "\t" << props_.Xidtt(2, 2) << "\t";
159  
300 –    os << props_.Xidrt(0, 0) << "\t" << props_.Xidrt(0, 1) << "\t" << props_.Xidrt(0, 2) << "\t"
301 –        << props_.Xidrt(1, 0) << "\t" << props_.Xidrt(1, 1) << "\t" << props_.Xidrt(1, 2) << "\t"
302 –        << props_.Xidrt(2, 0) << "\t" << props_.Xidrt(2, 1) << "\t" << props_.Xidrt(2, 2) << "\t";
303 –    
304 –    os << props_.Xidtr(0, 0) << "\t" << props_.Xidtr(0, 1) << "\t" << props_.Xidtr(0, 2) << "\t"
305 –        << props_.Xidtr(1, 0) << "\t" << props_.Xidtr(1, 1) << "\t" << props_.Xidtr(1, 2) << "\t"
306 –        << props_.Xidtr(2, 0) << "\t" << props_.Xidtr(2, 1) << "\t" << props_.Xidtr(2, 2) << "\t";
307 –
308 –    os << props_.Xidrr(0, 0) << "\t" << props_.Xidrr(0, 1) << "\t" << props_.Xidrr(0, 2) << "\t"
309 –        << props_.Xidrr(1, 0) << "\t" << props_.Xidrr(1, 1) << "\t" << props_.Xidrr(1, 2) << "\t"
310 –        << props_.Xidrr(2, 0) << "\t" << props_.Xidrr(2, 1) << "\t" << props_.Xidrr(2, 2) << std::endl;
311 –    
160   }
161  
162   }

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