void Vector2::RotateAround(Vector2 origin, double rotation) {
Vector2 fromMid = *this - origin;
Vector2 unitVec(1, 0);
double angleFrom0 = fromMid.AngleBetween(unitVec);
if (fromMid.y < 0) {
angleFrom0 *= -1;
}
angleFrom0 += rotation;
Vector2 endMove(cos(angleFrom0), sin(angleFrom0));
endMove *= fromMid.Magnitude();
endMove = origin + endMove;
*this = endMove;
}
Vector2 Vector2::RotateAround(Vector2 origin, float rotation) const {
if (rotation == 0) {
return *this;
}
Vector2 fromMid = *this - origin;
Vector2 unitVec(1, 0);
float angleFrom0 = fromMid.AngleBetween(unitVec);
angleFrom0 -= rotation;
Vector2 endMove(cos(angleFrom0), sin(angleFrom0));
endMove *= fromMid.Magnitude();
endMove = origin + endMove;
return endMove;
}
GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::GcmExperimentInfo(
const GpmsaComputerModelOptions& gcmOptionsObj,
bool allOutputsAreScalar,
const ExperimentStorage<S_V,S_M,D_V,D_M>& experimentStorage,
const ExperimentModel <S_V,S_M,D_V,D_M>& experimentModel,
const BaseVectorRV <P_V,P_M>& thetaPriorRv)
:
m_env (experimentStorage.env()),
m_experimentStorage (experimentStorage),
m_experimentModel (experimentModel),
m_paper_p_x (experimentStorage.scenarioSpace().dimLocal()),
m_paper_n (experimentStorage.numExperiments()),
m_paper_xs_standard (experimentStorage.xs_standard()),
m_paper_n_ys_transformed (experimentStorage.n_ys_transformed()),
m_paper_n_y (experimentStorage.n_y()),
m_paper_p_delta (experimentModel.numBasis()),
m_paper_F (experimentModel.numBasisGroups()),
m_paper_Gs (experimentModel.Gs()),
m_paper_n_space (m_env, "paper_n_", m_paper_n, NULL),
m_5lambdaYDim (MiscUintDebugMessage(1,NULL)), // "GcmExperimentInfo::consctructor(), m_5lambdaYDim")), // '1' in paper
m_5lambdaYSpace (m_env, "5lambdaY_", m_5lambdaYDim, NULL),
m_5lambdaYMins (m_env,m_5lambdaYSpace.map(),0.),
m_5lambdaYMaxs (m_env,m_5lambdaYSpace.map(),+INFINITY),
m_5lambdaYDomain ("5lambdaY_",m_5lambdaYSpace,m_5lambdaYMins,m_5lambdaYMaxs),
m_5lambdaYGammaAVec (m_env,m_5lambdaYSpace.map(),experimentModel.optionsObj().m_ov.m_a_y),
m_5lambdaYGammaBVec (m_env,m_5lambdaYSpace.map(),1./experimentModel.optionsObj().m_ov.m_b_y), // Yes, 1./...
m_5lambdaYPriorRv ("5lambdaY_",m_5lambdaYDomain,m_5lambdaYGammaAVec,m_5lambdaYGammaBVec),
m_like_previous5 (m_5lambdaYSpace.zeroVector()),
m_tmp_5lambdaYVec (m_5lambdaYSpace.zeroVector()),
m_6lambdaVDim (MiscUintDebugMessage(m_paper_F,NULL)), // "GcmExperimentInfo::consctructor(), m_6lambdaVDim")), // 'F' in paper
m_6lambdaVSpace (m_env, "6lambdaV_", m_6lambdaVDim, NULL),
m_6lambdaVMins (m_env,m_6lambdaVSpace.map(),0.),
m_6lambdaVMaxs (m_env,m_6lambdaVSpace.map(),+INFINITY),
m_6lambdaVDomain ("6lambdaV_",m_6lambdaVSpace,m_6lambdaVMins,m_6lambdaVMaxs),
m_6lambdaVGammaAVec (m_env,m_6lambdaVSpace.map(),experimentModel.optionsObj().m_ov.m_a_v),
m_6lambdaVGammaBVec (m_env,m_6lambdaVSpace.map(),1./experimentModel.optionsObj().m_ov.m_b_v), // Yes, 1./...
m_6lambdaVPriorRv ("6lambdaV_",m_6lambdaVDomain,m_6lambdaVGammaAVec,m_6lambdaVGammaBVec),
m_like_previous6 (m_6lambdaVSpace.zeroVector()),
m_tmp_6lambdaVVec (m_6lambdaVSpace.zeroVector()),
m_7rhoVDim (MiscUintDebugMessage(m_paper_F * m_paper_p_x,NULL)), // "GcmExperimentInfo::consctructor(), m_7lrhoVDim")), // 'F * p_x' in paper
m_7rhoVSpace (m_env, "7rhoV_", m_7rhoVDim, NULL),
m_7rhoVMins (m_env,m_7rhoVSpace.map(),0.),
m_7rhoVMaxs (m_env,m_7rhoVSpace.map(),1.),
m_7rhoVDomain ("7rhoV_",m_7rhoVSpace,m_7rhoVMins,m_7rhoVMaxs),
m_7rhoVBetaAVec (m_env,m_7rhoVSpace.map(),experimentModel.optionsObj().m_ov.m_a_rho_v),
m_7rhoVBetaBVec (m_env,m_7rhoVSpace.map(),experimentModel.optionsObj().m_ov.m_b_rho_v),
m_7rhoVPriorRv ("7rhoV_",m_7rhoVDomain,m_7rhoVBetaAVec,m_7rhoVBetaBVec),
m_like_previous7 (m_7rhoVSpace.zeroVector()),
m_tmp_7rhoVVec (m_7rhoVSpace.zeroVector()),
m_8thetaDim (MiscUintDebugMessage(thetaPriorRv.imageSet().vectorSpace().dimLocal(),NULL)), // "GcmExperimentInfo::consctructor(), m_8thetaDim")),
m_8thetaSpace (m_env, "8theta_", m_8thetaDim, NULL),
m_8thetaPriorRv (thetaPriorRv),
m_like_previous8 (m_8thetaSpace.zeroVector()),
m_tmp_8thetaVec (m_8thetaSpace.zeroVector()),
m_v_size (m_paper_n*m_paper_p_delta),
m_v_space (m_env, "v_", m_v_size, NULL),
m_unique_v_space (m_env, "unique_v_", m_paper_p_delta, NULL),
m_rho_v_space (m_env, "rho_v_", m_paper_p_x, NULL),
m_y_space (m_env, "n_y_", m_paper_n_y, NULL),
m_tmp_rho_v_vec (m_rho_v_space.zeroVector()),
m_Imat_v_i_spaces (m_paper_F, (VectorSpace<D_V,D_M>*) NULL), // to be deleted on destructor
m_Imat_v_is (m_paper_F, (D_M*) NULL), // to be deleted on destructor
m_Rmat_v_i_spaces (m_paper_F, (VectorSpace<D_V,D_M>*) NULL), // to be deleted on destructor
m_Rmat_v_is (m_paper_F, (D_M*) NULL), // to be deleted on destructor
m_Smat_v_i_spaces (m_paper_F, (VectorSpace<D_V,D_M>*) NULL), // to be deleted on destructor
m_Smat_v_is (m_paper_F, (D_M*) NULL), // to be deleted on destructor
m_Smat_v (m_v_space.zeroVector()),
m_Rmat_v_hat_v_asterisk_is (m_paper_p_delta, (D_M*) NULL), // to be deleted on destructor
m_Smat_v_hat_v_asterisk_is (m_paper_p_delta, (D_M*) NULL), // to be deleted on destructor
m_Smat_v_hat_v_asterisk (m_env, m_v_space.map(), m_paper_p_delta),
m_Smat_v_hat_v_asterisk_t (m_env, m_unique_v_space.map(), m_v_size),
m_PD (NULL), // to be deleted on destructor
m_Dmat_BlockDiag (NULL),
m_Dmat_BlockDiag_permut (NULL), // to be deleted on destructor
m_Wy (NULL),
m_Smat_v_asterisk_v_asterisk(m_unique_v_space.zeroVector())
{
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
*m_env.subDisplayFile() << "Entering GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": key-debug"
<< ", some entities just created (not yet populated)"
<< ", m_Smat_v.numRowsLocal() = " << m_Smat_v.numRowsLocal()
<< ", m_Smat_v.numCols() = " << m_Smat_v.numCols()
<< std::endl;
}
std::set<unsigned int> tmpSet;
tmpSet.insert(m_env.subId());
if (allOutputsAreScalar) {
// Do nothing
}
else {
m_PD = new D_M(m_v_space.zeroVector()); // to be deleted on destructor
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": key-debug"
<< ", m_PD just created (not yet populated)"
<< ", numRowsLocal() = " << m_PD->numRowsLocal()
<< ", numCols() = " << m_PD->numCols()
<< std::endl;
}
m_Dmat_BlockDiag = &experimentModel.Dmat_BlockDiag();
m_Dmat_BlockDiag_permut = new D_M(m_env,m_y_space.map(),m_v_size); // to be deleted on destructor
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": key-debug"
<< ", m_Dmat_BlockDiag just created (not yet populated)"
<< ", numRowsLocal() = " << m_Dmat_BlockDiag->numRowsLocal()
<< ", numCols() = " << m_Dmat_BlockDiag->numCols()
<< std::endl;
}
m_Wy = &experimentStorage.Wy();
//********************************************************************************
// Print information
//********************************************************************************
if (gcmOptionsObj.m_ov.m_dataOutputAllowedSet.find(m_env.subId()) != gcmOptionsObj.m_ov.m_dataOutputAllowedSet.end()) {
m_Wy->subWriteContents("Wy",
"mat_Wy",
"m",
tmpSet);
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 99)) {
D_M Wy_filtered(*m_Wy);
Wy_filtered.setPrintHorizontally(false);
Wy_filtered.filterSmallValues(1.e-6);
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": Wy_filtered.numRowsLocal() = " << Wy_filtered.numRowsLocal()
<< ", Wy_filtered.numCols() = " << Wy_filtered.numCols()
<< ", Wy_filtered contents =\n" << Wy_filtered
<< std::endl;
}
//********************************************************************************
// Form 'P_D' matrix
//********************************************************************************
for (unsigned int i = 0; i < m_paper_p_delta; ++i) {
for (unsigned int j = 0; j < m_paper_n; ++j) {
unsigned int row = j + (m_paper_n*i);
unsigned int col = (j*m_paper_p_delta)+i;
(*m_PD)(row,col) = 1.;
}
}
if (m_env.checkingLevel() >= 1) {
// Check transpose operation
D_M PDt(m_PD->transpose());
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ", tests on m_PD"
<< ": m_PD->numRowsLocal() = " << m_PD->numRowsLocal()
<< ", m_PD->numCols() = " << m_PD->numCols()
<< ": PDt.numRowsLocal() = " << PDt.numRowsLocal()
<< ", PDt.numCols() = " << PDt.numCols()
<< std::endl;
}
D_M matShouldBeI1( *m_PD * PDt );
D_M matI1 (m_v_space.zeroVector());
for (unsigned int i = 0; i < matI1.numRowsLocal(); ++i) {
matI1(i,i) = 1.;
}
matShouldBeI1 -= matI1;
double auxNorm1 = matShouldBeI1.normFrob();
D_M matShouldBeI2( PDt * *m_PD );
D_M matI2 (m_v_space.zeroVector());
for (unsigned int i = 0; i < matI2.numRowsLocal(); ++i) {
matI2(i,i) = 1.;
}
matShouldBeI2 -= matI2;
double auxNorm2 = matShouldBeI2.normFrob();
if (m_env.subDisplayFile()) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M,Q_V,Q_M>::constructor()"
<< ", tests on m_PD"
<< ": matShouldBeI1.numRowsLocal() = " << matShouldBeI1.numRowsLocal()
<< ", ||matI1||_2^2 = " << matI1.normFrob() * matI1.normFrob()
<< ", ||matShouldBeI1 - matI1||_2^2 = " << auxNorm1 * auxNorm1
<< "; matShouldBeI2.numRowsLocal() = " << matShouldBeI2.numRowsLocal()
<< ", ||matI2||_2^2 = " << matI2.normFrob() * matI2.normFrob()
<< ", ||matShouldBeI2 - matI2||_2^2 = " << auxNorm2 * auxNorm2
<< std::endl;
}
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": finished forming 'P_D'"
<< std::endl;
}
//********************************************************************************
// Compute 'Dmat_BlockDiag_permut' matrix
//********************************************************************************
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": m_Dmat_BlockDiag->numRowsLocal() = " << m_Dmat_BlockDiag->numRowsLocal()
<< ", m_Dmat_BlockDiag->numCols() = " << m_Dmat_BlockDiag->numCols()
<< ", m_PD->numRowsLocal() = " << m_PD->numRowsLocal()
<< ", m_PD->numCols() = " << m_PD->numCols()
<< std::endl;
}
*m_Dmat_BlockDiag_permut = *m_Dmat_BlockDiag * (m_PD->transpose());
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": finished computing 'm_Dmat_BlockDiag_permut'"
<< std::endl;
}
} // if (allOutputsAreScalar)
//********************************************************************************
// Instantiate Smat spaces
//********************************************************************************
for (unsigned int i = 0; i < m_Imat_v_i_spaces.size(); ++i) {
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": before instantiating a m_Imat_v_i space"
<< ", m_paper_Gs[" << i << "] = " << m_paper_Gs[i]
<< std::endl;
}
m_Imat_v_i_spaces[i] = new VectorSpace<D_V,D_M>(m_env, "Imat_v_i_spaces_", m_paper_Gs[i], NULL); // to be deleted on destructor
D_V unitVec(m_Imat_v_i_spaces[i]->zeroVector());
unitVec.cwSet(1.);
m_Imat_v_is[i] = new D_M(unitVec); // to be deleted on destructor
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": before instantiating the m_Rmat_v_i spaces"
<< ", m_paper_n = " << m_paper_n
<< std::endl;
}
for (unsigned int i = 0; i < m_Rmat_v_i_spaces.size(); ++i) {
m_Rmat_v_i_spaces[i] = new VectorSpace<D_V,D_M>(m_env, "Smat_v_i_spaces_", m_paper_n, NULL); // to be deleted on destructor
m_Rmat_v_is[i] = new D_M(m_Rmat_v_i_spaces[i]->zeroVector()); // to be deleted on destructor
}
unsigned int sumDims = 0;
for (unsigned int i = 0; i < m_Smat_v_i_spaces.size(); ++i) {
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": before instantiating a m_Smat_v_i space"
<< ", m_paper_Gs[" << i << "] = " << m_paper_Gs[i]
<< std::endl;
}
m_Smat_v_i_spaces[i] = new VectorSpace<D_V,D_M>(m_env, "Smat_v_i_spaces_", m_paper_n*m_paper_Gs[i], NULL); // to be deleted on destructor
sumDims += m_paper_n*m_paper_Gs[i];
m_Smat_v_is[i] = new D_M(m_Smat_v_i_spaces[i]->zeroVector()); // to be deleted on destructor
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": finished instantiating the m_Smat_v_i spaces"
<< ", m_paper_n = " << m_paper_n
<< ", m_paper_p_delta = " << m_paper_p_delta
<< ", sumDims = " << sumDims
<< std::endl;
}
UQ_FATAL_TEST_MACRO(sumDims != m_v_size,
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'sumDims' and 'm_v_size' should be equal");
//********************************************************************************
// Instantiate 'v_hat_v_asterisk' matrices
//********************************************************************************
unsigned int sumNumRows = 0;
unsigned int sumNumCols = 0;
for (unsigned int i = 0; i < m_Smat_v_hat_v_asterisk_is.size(); ++i) {
m_Rmat_v_hat_v_asterisk_is[i] = new D_M(m_env, m_paper_n_space.map(), (unsigned int) 1); // to be deleted on destructor; Yes, only 1 column
m_Smat_v_hat_v_asterisk_is[i] = new D_M(m_env, m_paper_n_space.map(), (unsigned int) 1); // to be deleted on destructor; Yes, only 1 column
sumNumRows += m_paper_n_space.dimLocal();
sumNumCols += 1;
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": finished instantiating the m_Smat_v_hat_v_asterisk_i matrices"
<< std::endl;
}
UQ_FATAL_TEST_MACRO(sumNumRows != m_v_size,
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'sumNumRows' and 'm_v_size' should be equal");
UQ_FATAL_TEST_MACRO(sumNumCols != m_paper_p_delta,
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'sumNumCols' and 'm_paper_p_delta' should be equal");
//********************************************************************************
// Display information
//********************************************************************************
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
*m_env.subDisplayFile() << "KEY In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< "\n KEY m_paper_p_x = " << m_paper_p_x
<< "\n KEY m_paper_n = " << m_paper_n
<< "\n KEY m_paper_n_ys_transformed.size() = " << m_paper_n_ys_transformed.size()
<< "\n KEY m_paper_n_ys_transformed =";
for (unsigned int i = 0; i < m_paper_n_ys_transformed.size(); ++i) {
*m_env.subDisplayFile() << " " << m_paper_n_ys_transformed[i];
}
*m_env.subDisplayFile() << "\n KEY m_paper_n_y = " << m_paper_n_y
<< "\n KEY m_paper_p_delta = " << m_paper_p_delta
<< "\n KEY m_paper_F = " << m_paper_F
<< "\n KEY m_paper_Gs.size() = " << m_paper_Gs.size()
<< "\n KEY m_paper_Gs =";
for (unsigned int i = 0; i < m_paper_Gs.size(); ++i) {
*m_env.subDisplayFile() << " " << m_paper_Gs[i];
}
*m_env.subDisplayFile() << "\n KEY m_5lambdaYDim = " << m_5lambdaYDim
<< ", m_5lambdaYGammaAVec = " << m_5lambdaYGammaAVec
<< ", m_5lambdaYGammaBVec = " << m_5lambdaYGammaBVec
<< "\n KEY m_6lambdaVDim = " << m_6lambdaVDim
<< ", m_6lambdaVGammaAVec = " << m_6lambdaVGammaAVec
<< ", m_6lambdaVGammaBVec = " << m_6lambdaVGammaBVec
<< "\n KEY m_7rhoVDim = " << m_7rhoVDim
<< ", m_7rhoVBetaAVec = " << m_7rhoVBetaAVec
<< ", m_7rhoVBetaBVec = " << m_7rhoVBetaBVec
<< "\n KEY m_8thetaDim = " << m_8thetaDim
<< "\n KEY full 'y' vector size = " << m_paper_n_y // = experimentStorage->yVec_transformed().sizeLocal()
<< std::endl;
}
//********************************************************************************
// Make checks
//********************************************************************************
UQ_FATAL_TEST_MACRO(experimentStorage.yVec_transformed().sizeLocal() != m_paper_n_y,
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"incompatible calculations for 'y' vector size");
UQ_FATAL_TEST_MACRO(m_paper_n != m_paper_n_ys_transformed.size(),
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'m_paper_n' and 'm_paper_n_ys_transformed.size()' should be equal");
UQ_FATAL_TEST_MACRO(m_paper_F != m_paper_Gs.size(),
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'m_paper_F' and 'm_paper_Gs.size()' should be equal");
unsigned int sumGs = 0;
for (unsigned int i = 0; i < m_paper_F; ++i) {
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": m_paper_Gs[" << i << "] = " << m_paper_Gs[i]
<< std::endl;
}
sumGs += m_paper_Gs[i];
}
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 3)) {
*m_env.subDisplayFile() << "In GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< ": sumGs = " << sumGs
<< std::endl;
}
UQ_FATAL_TEST_MACRO(m_paper_p_delta != sumGs,
m_env.worldRank(),
"GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()",
"'m_paper_p_delta' and 'sumGs' should be equal");
if ((m_env.subDisplayFile()) && (m_env.displayVerbosity() >= 2)) {
*m_env.subDisplayFile() << "Leaving GcmExperimentInfo<S_V,S_M,D_V,D_M,P_V,P_M>::constructor()"
<< std::endl;
}
}
std::vector<T> eccentricity_Vec() {
return (VecSub( (VecScalDivi(XProd(this->getVel(), XProd(this->getPos(), this->getVel()) ),this->getMu() )) , unitVec(this->getPos()) ) );
}
