--- trunk/src/applications/hydrodynamics/HydrodynamicsModel.cpp 2006/02/22 20:35:16 891 +++ trunk/src/applications/hydrodynamics/HydrodynamicsModel.cpp 2006/03/13 22:42:40 895 @@ -43,6 +43,7 @@ #include "math/LU.hpp" #include "math/DynamicRectMatrix.hpp" #include "math/SquareMatrix3.hpp" +#include "utils/OOPSEConstant.hpp" namespace oopse { /** * Reference: @@ -50,16 +51,45 @@ namespace oopse { * Comparison of Different Modeling and Computational Procedures. * Biophysical Journal, 75(6), 3044, 1999 */ -bool HydrodynamicsModel::calcHydrodyanmicsProps(double eta) { + +HydrodynamicsModel::HydrodynamicsModel(StuntDouble* sd, const DynamicProperty& extraParams) : sd_(sd){ + DynamicProperty::const_iterator iter; + + iter = extraParams.find("Viscosity"); + if (iter != extraParams.end()) { + boost::any param = iter->second; + viscosity_ = boost::any_cast(param); + }else { + std::cout << "HydrodynamicsModel Error\n" ; + } + + iter = extraParams.find("Temperature"); + if (iter != extraParams.end()) { + boost::any param = iter->second; + temperature_ = boost::any_cast(param); + }else { + std::cout << "HydrodynamicsModel Error\n" ; + } +} + +bool HydrodynamicsModel::calcHydrodyanmicsProps() { if (!createBeads(beads_)) { std::cout << "can not create beads" << std::endl; return false; } + + //calcResistanceTensor(); + calcDiffusionTensor(); +/* int nbeads = beads_.size(); DynamicRectMatrix B(3*nbeads, 3*nbeads); DynamicRectMatrix C(3*nbeads, 3*nbeads); Mat3x3d I; + I(0, 0) = 1.0; + I(1, 1) = 1.0; + I(2, 2) = 1.0; + for (std::size_t i = 0; i < nbeads; ++i) { for (std::size_t j = 0; j < nbeads; ++j) { Mat3x3d Tij; @@ -69,22 +99,28 @@ bool HydrodynamicsModel::calcHydrodyanmicsProps(double double rij2 = rij * rij; double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; Mat3x3d tmpMat; - tmpMat = outProduct(beads_[i].pos, beads_[j].pos) / rij2; - double constant = 8.0 * NumericConstant::PI * eta * rij; + tmpMat = outProduct(Rij, Rij) / rij2; + double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; }else { - double constant = 1.0 / (6.0 * NumericConstant::PI * eta * beads_[i].radius); + double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); Tij(0, 0) = constant; Tij(1, 1) = constant; Tij(2, 2) = constant; } B.setSubMatrix(i*3, j*3, Tij); + std::cout << Tij << std::endl; } } + std::cout << "B=\n" + << B << std::endl; //invert B Matrix invertMatrix(B, C); - + + std::cout << "C=\n" + << C << std::endl; + //prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) std::vector U; for (int i = 0; i < nbeads; ++i) { @@ -97,6 +133,13 @@ bool HydrodynamicsModel::calcHydrodyanmicsProps(double Mat3x3d Xitt; Mat3x3d Xirr; Mat3x3d Xitr; + + //calculate the total volume + + double volume = 0.0; + for (std::vector::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { + volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); + } for (std::size_t i = 0; i < nbeads; ++i) { for (std::size_t j = 0; j < nbeads; ++j) { @@ -104,8 +147,9 @@ bool HydrodynamicsModel::calcHydrodyanmicsProps(double C.getSubMatrix(i*3, j*3, Cij); Xitt += Cij; - Xirr += U[i] * Cij; - Xitr += U[i] * Cij * U[j]; + Xitr += U[i] * Cij; + //Xirr += -U[i] * Cij * U[j]; + Xirr += -U[i] * Cij * U[j] + (0.166*6 * viscosity_ * volume) * I; } } @@ -115,35 +159,65 @@ bool HydrodynamicsModel::calcHydrodyanmicsProps(double Xi.setSubMatrix(0, 0, Xitt); Xi.setSubMatrix(0, 3, Xitr.transpose()); Xi.setSubMatrix(3, 0, Xitr); - Xi.setSubMatrix(3, 3, Xitt); - invertMatrix(Xi, Do); + Xi.setSubMatrix(3, 3, Xirr); + //invertMatrix(Xi, Do); + double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; + //Do *= kt; + Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O - Do.getSubMatrix(0, 0 , Dott); - Do.getSubMatrix(3, 0, Dotr); - Do.getSubMatrix(3, 3, Dorr); + const static Mat3x3d zeroMat(0.0); + + Mat3x3d XittInv(0.0); + XittInv = Xitt.inverse(); + + //Xirr may not be inverted,if it one of the diagonal element is zero, for example + //( a11 a12 0) + //( a21 a22 0) + //( 0 0 0) + Mat3x3d XirrInv; + XirrInv = Xirr.inverse(); + + Mat3x3d tmp; + Mat3x3d tmpInv; + tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; + tmpInv = tmp.inverse(); + + Dott = kt * tmpInv; + Dotr = -kt*XirrInv * Xitr * tmpInv* 1.0E8; + + tmp = Xirr - Xitr * XittInv * Xitr.transpose(); + tmpInv = tmp.inverse(); + + Dorr = kt * tmpInv*1.0E16; + + //Do.getSubMatrix(0, 0 , Dott); + //Do.getSubMatrix(3, 0, Dotr); + //Do.getSubMatrix(3, 3, Dorr); + //calculate center of diffusion - Mat3x3d tmpMat; - tmpMat(0, 0) = Dorr(1, 1) + Dorr(2, 2); - tmpMat(0, 1) = - Dorr(0, 1); - tmpMat(0, 2) = -Dorr(0, 2); - tmpMat(1, 0) = -Dorr(0, 1); - tmpMat(1, 1) = Dorr(0, 0) + Dorr(2, 2); - tmpMat(1, 2) = -Dorr(1, 2); - tmpMat(2, 0) = -Dorr(0, 2); - tmpMat(2, 1) = -Dorr(1, 2); - tmpMat(2, 2) = Dorr(1, 1) + Dorr(0, 0); + tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); + tmp(0, 1) = - Dorr(0, 1); + tmp(0, 2) = -Dorr(0, 2); + tmp(1, 0) = -Dorr(0, 1); + tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); + tmp(1, 2) = -Dorr(1, 2); + tmp(2, 0) = -Dorr(0, 2); + tmp(2, 1) = -Dorr(1, 2); + tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); Vector3d tmpVec; tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); - - Vector3d rod = tmpMat.inverse() * tmpVec; + tmpInv = tmp.inverse(); + + Vector3d rod = tmpInv * tmpVec; + //calculate Diffusion Tensor at center of diffusion Mat3x3d Uod; Uod.setupSkewMat(rod); @@ -160,16 +234,400 @@ bool HydrodynamicsModel::calcHydrodyanmicsProps(double props_.transDiff = Ddtt; props_.transRotDiff = Ddtr; props_.rotDiff = Ddrr; - +*/ return true; +} + +void HydrodynamicsModel::calcResistanceTensor() { + + int nbeads = beads_.size(); + DynamicRectMatrix B(3*nbeads, 3*nbeads); + DynamicRectMatrix C(3*nbeads, 3*nbeads); + Mat3x3d I; + I(0, 0) = 1.0; + I(1, 1) = 1.0; + I(2, 2) = 1.0; + + for (std::size_t i = 0; i < nbeads; ++i) { + for (std::size_t j = 0; j < nbeads; ++j) { + Mat3x3d Tij; + if (i != j ) { + Vector3d Rij = beads_[i].pos - beads_[j].pos; + double rij = Rij.length(); + double rij2 = rij * rij; + double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; + Mat3x3d tmpMat; + tmpMat = outProduct(Rij, Rij) / rij2; + double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; + Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; + }else { + double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); + Tij(0, 0) = constant; + Tij(1, 1) = constant; + Tij(2, 2) = constant; + } + B.setSubMatrix(i*3, j*3, Tij); + } + } + + + //invert B Matrix + invertMatrix(B, C); + + //prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) + std::vector U; + for (int i = 0; i < nbeads; ++i) { + Mat3x3d currU; + currU.setupSkewMat(beads_[i].pos); + U.push_back(currU); + } + + //calculate Xi matrix at arbitrary origin O + Mat3x3d Xiott; + Mat3x3d Xiorr; + Mat3x3d Xiotr; + + //calculate the total volume + + double volume = 0.0; + for (std::vector::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { + volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); + } + + for (std::size_t i = 0; i < nbeads; ++i) { + for (std::size_t j = 0; j < nbeads; ++j) { + Mat3x3d Cij; + C.getSubMatrix(i*3, j*3, Cij); + + Xiott += Cij; + Xiotr += U[i] * Cij; + //Xiorr += -U[i] * Cij * U[j]; + Xiorr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; + } + } + + Mat3x3d tmp; + Mat3x3d tmpInv; + Vector3d tmpVec; + tmp(0, 0) = Xiott(1, 1) + Xiott(2, 2); + tmp(0, 1) = - Xiott(0, 1); + tmp(0, 2) = -Xiott(0, 2); + tmp(1, 0) = -Xiott(0, 1); + tmp(1, 1) = Xiott(0, 0) + Xiott(2, 2); + tmp(1, 2) = -Xiott(1, 2); + tmp(2, 0) = -Xiott(0, 2); + tmp(2, 1) = -Xiott(1, 2); + tmp(2, 2) = Xiott(1, 1) + Xiott(0, 0); + tmpVec[0] = Xiotr(2, 1) - Xiotr(1, 2); + tmpVec[1] = Xiotr(0, 2) - Xiotr(2, 0); + tmpVec[2] = Xiotr(1, 0) - Xiotr(0, 1); + tmpInv = tmp.inverse(); + Vector3d ror = tmpInv * tmpVec; //center of resistance + Mat3x3d Uor; + Uor.setupSkewMat(ror); + + Mat3x3d Xirtt; + Mat3x3d Xirrr; + Mat3x3d Xirtr; + + Xirtt = Xiott; + Xirtr = (Xiotr - Uor * Xiott) * 1E-8; + Xirrr = Xiorr - Uor * Xiott * Uor + Xiotr * Uor - Uor * Xiotr.transpose() * 1E-16; +/* + SquareMatrix Xir6x6; + SquareMatrix Dr6x6; + + Xir6x6.setSubMatrix(0, 0, Xirtt); + Xir6x6.setSubMatrix(0, 3, Xirtr.transpose()); + Xir6x6.setSubMatrix(3, 0, Xirtr); + Xir6x6.setSubMatrix(3, 3, Xirrr); + + invertMatrix(Xir6x6, Dr6x6); + Mat3x3d Drtt; + Mat3x3d Drtr; + Mat3x3d Drrr; + Dr6x6.getSubMatrix(0, 0, Drtt); + Dr6x6.getSubMatrix(3, 0, Drtr); + Dr6x6.getSubMatrix(3, 3, Drrr); + double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; + Drtt *= kt; + Drtr *= kt*1E8; + Drrr *= kt*1E16; +*/ + + const static Mat3x3d zeroMat(0.0); + + + + Mat3x3d XirttInv(0.0); + XirttInv = Xirtt.inverse(); + + //Xirr may not be inverted,if it one of the diagonal element is zero, for example + //( a11 a12 0) + //( a21 a22 0) + //( 0 0 0) + Mat3x3d XirrrInv; + XirrrInv = Xirrr.inverse(); + tmp = Xirtt - Xirtr.transpose() * XirrrInv * Xirtr; + tmpInv = tmp.inverse(); + + Mat3x3d Drtt; + Mat3x3d Drtr; + Mat3x3d Drrr; + double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; + Drtt = kt * tmpInv; + Drtr = -kt*XirrrInv * Xirtr * tmpInv* 1.0E8; + + tmp = Xirrr - Xirtr * XirttInv * Xirtr.transpose(); + tmpInv = tmp.inverse(); + + Drrr = kt * tmpInv*1.0E16; + + std::cout << "-----------------------------------------\n"; + std::cout << "center of resistance :" << std::endl; + std::cout << ror << std::endl; + std::cout << "resistant tensor at center of resistance" << std::endl; + std::cout << "translation:" << std::endl; + std::cout << Xirtt << std::endl; + std::cout << "translation-rotation:" << std::endl; + std::cout << Xirtr << std::endl; + std::cout << "rotation:" << std::endl; + std::cout << Xirrr << std::endl; + std::cout << "diffusion tensor at center of resistance" << std::endl; + std::cout << "translation:" << std::endl; + std::cout << Drtt << std::endl; + std::cout << "translation-rotation:" << std::endl; + std::cout << Drtr << std::endl; + std::cout << "rotation:" << std::endl; + std::cout << Drrr << std::endl; + std::cout << "-----------------------------------------\n"; + } +void HydrodynamicsModel::calcDiffusionTensor() { + int nbeads = beads_.size(); + DynamicRectMatrix B(3*nbeads, 3*nbeads); + DynamicRectMatrix C(3*nbeads, 3*nbeads); + Mat3x3d I; + I(0, 0) = 1.0; + I(1, 1) = 1.0; + I(2, 2) = 1.0; + + for (std::size_t i = 0; i < nbeads; ++i) { + for (std::size_t j = 0; j < nbeads; ++j) { + Mat3x3d Tij; + if (i != j ) { + Vector3d Rij = beads_[i].pos - beads_[j].pos; + double rij = Rij.length(); + double rij2 = rij * rij; + double sumSigma2OverRij2 = ((beads_[i].radius*beads_[i].radius) + (beads_[i].radius*beads_[i].radius)) / rij2; + Mat3x3d tmpMat; + tmpMat = outProduct(Rij, Rij) / rij2; + double constant = 8.0 * NumericConstant::PI * viscosity_ * rij; + Tij = ((1.0 + sumSigma2OverRij2/3.0) * I + (1.0 - sumSigma2OverRij2) * tmpMat ) / constant; + }else { + double constant = 1.0 / (6.0 * NumericConstant::PI * viscosity_ * beads_[i].radius); + Tij(0, 0) = constant; + Tij(1, 1) = constant; + Tij(2, 2) = constant; + } + B.setSubMatrix(i*3, j*3, Tij); + } + } + + //invert B Matrix + invertMatrix(B, C); + + //prepare U Matrix relative to arbitrary origin O(0.0, 0.0, 0.0) + std::vector U; + for (int i = 0; i < nbeads; ++i) { + Mat3x3d currU; + currU.setupSkewMat(beads_[i].pos); + U.push_back(currU); + } + + //calculate Xi matrix at arbitrary origin O + Mat3x3d Xitt; + Mat3x3d Xirr; + Mat3x3d Xitr; + + //calculate the total volume + + double volume = 0.0; + for (std::vector::iterator iter = beads_.begin(); iter != beads_.end(); ++iter) { + volume += 4.0/3.0 * NumericConstant::PI * pow((*iter).radius,3); + } + + for (std::size_t i = 0; i < nbeads; ++i) { + for (std::size_t j = 0; j < nbeads; ++j) { + Mat3x3d Cij; + C.getSubMatrix(i*3, j*3, Cij); + + Xitt += Cij; + Xitr += U[i] * Cij; + //Xirr += -U[i] * Cij * U[j]; + Xirr += -U[i] * Cij * U[j] + (6 * viscosity_ * volume) * I; + } + } + + //invert Xi to get Diffusion Tensor at arbitrary origin O + RectMatrix Xi; + RectMatrix Do; + Xi.setSubMatrix(0, 0, Xitt); + Xi.setSubMatrix(0, 3, Xitr.transpose()); + Xi.setSubMatrix(3, 0, Xitr); + Xi.setSubMatrix(3, 3, Xirr); + //invertMatrix(Xi, Do); + //double kt = OOPSEConstant::kB * temperature_ * 1.66E-2; + + //1 poise = 0.1 N.S/m^2 = 1.661E-3 amu/ (Angstrom*fs) + double kt = OOPSEConstant::kB * temperature_ * 1.66E-3; + + Mat3x3d Dott; //translational diffusion tensor at arbitrary origin O + Mat3x3d Dorr; //rotational diffusion tensor at arbitrary origin O + Mat3x3d Dotr; //translation-rotation couplingl diffusion tensor at arbitrary origin O + + const static Mat3x3d zeroMat(0.0); + + Mat3x3d XittInv(0.0); + XittInv = Xitt.inverse(); + + //Xirr may not be inverted,if it one of the diagonal element is zero, for example + //( a11 a12 0) + //( a21 a22 0) + //( 0 0 0) + Mat3x3d XirrInv; + XirrInv = Xirr.inverse(); + + Mat3x3d tmp; + Mat3x3d tmpInv; + tmp = Xitt - Xitr.transpose() * XirrInv * Xitr; + tmpInv = tmp.inverse(); + + //Dott = kt * tmpInv; //unit in A^2/fs + Dott = tmpInv; + //Dotr = -kt*XirrInv * Xitr * tmpInv*1E8; + //Dotr = -kt*XirrInv * Xitr * tmpInv; + Dotr = -XirrInv* Xitr * tmpInv; + + tmp = Xirr - Xitr * XittInv * Xitr.transpose(); + tmpInv = tmp.inverse(); + + //Dorr = kt * tmpInv*1E16; + //Dorr = kt * tmpInv; + Dorr = tmpInv; + //calculate center of diffusion + tmp(0, 0) = Dorr(1, 1) + Dorr(2, 2); + tmp(0, 1) = - Dorr(0, 1); + tmp(0, 2) = -Dorr(0, 2); + tmp(1, 0) = -Dorr(0, 1); + tmp(1, 1) = Dorr(0, 0) + Dorr(2, 2); + tmp(1, 2) = -Dorr(1, 2); + tmp(2, 0) = -Dorr(0, 2); + tmp(2, 1) = -Dorr(1, 2); + tmp(2, 2) = Dorr(1, 1) + Dorr(0, 0); + + Vector3d tmpVec; + tmpVec[0] = Dotr(1, 2) - Dotr(2, 1); + tmpVec[1] = Dotr(2, 0) - Dotr(0, 2); + tmpVec[2] = Dotr(0, 1) - Dotr(1, 0); + + tmpInv = tmp.inverse(); + + Vector3d rod = tmpInv * tmpVec; + + //calculate Diffusion Tensor at center of diffusion + Mat3x3d Uod; + Uod.setupSkewMat(rod); + + Mat3x3d Ddtt; //translational diffusion tensor at diffusion center + Mat3x3d Ddtr; //rotational diffusion tensor at diffusion center + Mat3x3d Ddrr; //translation-rotation couplingl diffusion tensor at diffusion tensor + + Ddtt = Dott - Uod * Dorr * Uod + Dotr.transpose() * Uod - Uod * Dotr; + Ddrr = Dorr; + Ddtr = Dotr + Dorr * Uod; + + props_.diffCenter = rod; + props_.Ddtt = Ddtt; + props_.Ddtr = Ddtr; + props_.Ddrr = Ddrr; + + SquareMatrix Dd; + Dd.setSubMatrix(0, 0, Ddtt); + Dd.setSubMatrix(0, 3, Ddtr.transpose()); + Dd.setSubMatrix(3, 0, Ddtr); + Dd.setSubMatrix(3, 3, Ddrr); + SquareMatrix Xid; + invertMatrix(Dd, Xid); + + Ddtt *= kt; + Ddtr *= kt; + Ddrr *= kt; + Xid /= 1.66E-3; + + Xid.getSubMatrix(0, 0, props_.Xidtt); + Xid.getSubMatrix(0, 3, props_.Xidrt); + Xid.getSubMatrix(3, 0, props_.Xidtr); + Xid.getSubMatrix(3, 3, props_.Xidrr); + + /* + std::cout << "center of diffusion :" << std::endl; + std::cout << rod << std::endl; + std::cout << "diffusion tensor at center of diffusion" << std::endl; + std::cout << "translation:" << std::endl; + std::cout << Ddtt << std::endl; + std::cout << "translation-rotation:" << std::endl; + std::cout << Ddtr << std::endl; + std::cout << "rotation:" << std::endl; + std::cout << Ddrr << std::endl; + */ + +} + void HydrodynamicsModel::writeBeads(std::ostream& os) { + std::vector::iterator iter; + os << beads_.size() << std::endl; + os << "Generated by Hydro" << std::endl; + for (iter = beads_.begin(); iter != beads_.end(); ++iter) { + os << iter->atomName << "\t" << iter->pos[0] << "\t" << iter->pos[1] << "\t" << iter->pos[2] << std::endl; + } } void HydrodynamicsModel::writeDiffCenterAndDiffTensor(std::ostream& os) { + os << sd_->getType() << "\t"; + os << props_.diffCenter[0] << "\t" << props_.diffCenter[1] << "\t" << props_.diffCenter[2] << "\t"; + + os << props_.Ddtt(0, 0) << "\t" << props_.Ddtt(0, 1) << "\t" << props_.Ddtt(0, 2) << "\t" + << props_.Ddtt(1, 0) << "\t" << props_.Ddtt(1, 1) << "\t" << props_.Ddtt(1, 2) << "\t" + << props_.Ddtt(2, 0) << "\t" << props_.Ddtt(2, 1) << "\t" << props_.Ddtt(2, 2) << "\t"; + + os << props_.Ddtr(0, 0) << "\t" << props_.Ddtr(0, 1) << "\t" << props_.Ddtr(0, 2) << "\t" + << props_.Ddtr(1, 0) << "\t" << props_.Ddtr(1, 1) << "\t" << props_.Ddtr(1, 2) << "\t" + << props_.Ddtr(2, 0) << "\t" << props_.Ddtr(2, 1) << "\t" << props_.Ddtr(2, 2) << "\t"; + + os << props_.Ddrr(0, 0) << "\t" << props_.Ddrr(0, 1) << "\t" << props_.Ddrr(0, 2) << "\t" + << props_.Ddrr(1, 0) << "\t" << props_.Ddrr(1, 1) << "\t" << props_.Ddrr(1, 2) << "\t" + << props_.Ddrr(2, 0) << "\t" << props_.Ddrr(2, 1) << "\t" << props_.Ddrr(2, 2) <<"\t"; + + os << props_.Xidtt(0, 0) << "\t" << props_.Xidtt(0, 1) << "\t" << props_.Xidtt(0, 2) << "\t" + << props_.Xidtt(1, 0) << "\t" << props_.Xidtt(1, 1) << "\t" << props_.Xidtt(1, 2) << "\t" + << props_.Xidtt(2, 0) << "\t" << props_.Xidtt(2, 1) << "\t" << props_.Xidtt(2, 2) << "\t"; + + os << props_.Xidrt(0, 0) << "\t" << props_.Xidrt(0, 1) << "\t" << props_.Xidrt(0, 2) << "\t" + << props_.Xidrt(1, 0) << "\t" << props_.Xidrt(1, 1) << "\t" << props_.Xidrt(1, 2) << "\t" + << props_.Xidrt(2, 0) << "\t" << props_.Xidrt(2, 1) << "\t" << props_.Xidrt(2, 2) << "\t"; + + os << props_.Xidtr(0, 0) << "\t" << props_.Xidtr(0, 1) << "\t" << props_.Xidtr(0, 2) << "\t" + << props_.Xidtr(1, 0) << "\t" << props_.Xidtr(1, 1) << "\t" << props_.Xidtr(1, 2) << "\t" + << props_.Xidtr(2, 0) << "\t" << props_.Xidtr(2, 1) << "\t" << props_.Xidtr(2, 2) << "\t"; + + os << props_.Xidrr(0, 0) << "\t" << props_.Xidrr(0, 1) << "\t" << props_.Xidrr(0, 2) << "\t" + << props_.Xidrr(1, 0) << "\t" << props_.Xidrr(1, 1) << "\t" << props_.Xidrr(1, 2) << "\t" + << props_.Xidrr(2, 0) << "\t" << props_.Xidrr(2, 1) << "\t" << props_.Xidrr(2, 2) << std::endl; + } }