void compute(const QUESO::FullEnvironment& env) {
// Step 1 of 5: Instantiate the parameter space
QUESO::VectorSpace<QUESO::GslVector,QUESO::GslMatrix>
paramSpace(env, "param_", 2, NULL);
// Step 2 of 5: Instantiate the parameter domain
QUESO::GslVector paramMins(paramSpace.zeroVector());
paramMins.cwSet(-INFINITY);
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
paramMaxs.cwSet( INFINITY);
QUESO::BoxSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomain("param_",paramSpace,paramMins,paramMaxs);
// Step 3 of 5: Instantiate the likelihood function object
QUESO::GslVector meanVector(paramSpace.zeroVector());
meanVector[0] = -1;
meanVector[1] = 2;
QUESO::GslMatrix covMatrix(paramSpace.zeroVector());
covMatrix(0,0) = 4.; covMatrix(0,1) = 0.;
covMatrix(1,0) = 0.; covMatrix(1,1) = 1.;
likelihoodRoutine_DataType likelihoodRoutine_Data;
likelihoodRoutine_Data.meanVector = &meanVector;
likelihoodRoutine_Data.covMatrix = &covMatrix;
QUESO::GenericScalarFunction<QUESO::GslVector,QUESO::GslMatrix>
likelihoodFunctionObj("like_",
paramDomain,
likelihoodRoutine,
(void *) &likelihoodRoutine_Data,
true); // routine computes [ln(function)]
// Step 4 of 5: Instantiate the inverse problem
QUESO::UniformVectorRV<QUESO::GslVector,QUESO::GslMatrix>
priorRv("prior_", paramDomain);
QUESO::GenericVectorRV<QUESO::GslVector,QUESO::GslMatrix>
postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector,QUESO::GslMatrix>
ip("", NULL, priorRv, likelihoodFunctionObj, postRv);
// Step 5 of 5: Solve the inverse problem
QUESO::GslVector paramInitials(paramSpace.zeroVector());
paramInitials[0] = 0.1;
paramInitials[1] = -1.4;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0,0) = 8.; proposalCovMatrix(0,1) = 4.;
proposalCovMatrix(1,0) = 4.; proposalCovMatrix(1,1) = 16.;
ip.solveWithBayesMetropolisHastings(NULL,paramInitials, &proposalCovMatrix);
return;
}
int main(int argc, char ** argv) {
MPI_Init(&argc, &argv);
// Step 0 of 5: Set up environment
QUESO::FullEnvironment env(MPI_COMM_WORLD, argv[1], "", NULL);
// Step 1 of 5: Instantiate the parameter space
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> paramSpace(env,
"param_", 1, NULL);
// Step 2 of 5: Set up the prior
QUESO::GslVector paramMins(paramSpace.zeroVector());
paramMins.cwSet(min_val);
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
paramMaxs.cwSet(max_val);
QUESO::BoxSubset<QUESO::GslVector, QUESO::GslMatrix> paramDomain("param_",
paramSpace, paramMins, paramMaxs);
// Uniform prior here. Could be a different prior.
QUESO::UniformVectorRV<QUESO::GslVector, QUESO::GslMatrix> priorRv("prior_",
paramDomain);
// Step 3 of 5: Set up the likelihood using the class above
Likelihood<QUESO::GslVector, QUESO::GslMatrix> lhood("llhd_", paramDomain);
// Step 4 of 5: Instantiate the inverse problem
QUESO::GenericVectorRV<QUESO::GslVector, QUESO::GslMatrix>
postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector, QUESO::GslMatrix>
ip("", NULL, priorRv, lhood, postRv);
// Step 5 of 5: Solve the inverse problem
QUESO::GslVector paramInitials(paramSpace.zeroVector());
// Initial condition of the chain
paramInitials[0] = 0.0;
paramInitials[1] = 0.0;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
for (unsigned int i = 0; i < 2; i++) {
// Might need to tweak this
proposalCovMatrix(i, i) = 0.1;
}
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
MPI_Finalize();
return 0;
}
int main(int argc, char ** argv) {
MPI_Init(&argc, &argv);
QUESO::FullEnvironment env(MPI_COMM_WORLD, argv[1], "", NULL);
QUESO::VectorSpace<> paramSpace(env, "param_", 1, NULL);
QUESO::GslVector paramMins(paramSpace.zeroVector());
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
double min_val = 0.0;
double max_val = 1.0;
paramMins.cwSet(min_val);
paramMaxs.cwSet(max_val);
QUESO::BoxSubset<> paramDomain("param_", paramSpace, paramMins, paramMaxs);
QUESO::UniformVectorRV<> priorRv("prior_", paramDomain);
Likelihood<> lhood("llhd_", paramDomain);
QUESO::GenericVectorRV<> postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<> ip("", NULL, priorRv, lhood, postRv);
QUESO::GslVector paramInitials(paramSpace.zeroVector());
paramInitials[0] = 0.0;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0, 0) = 0.1;
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
MPI_Finalize();
return 0;
}
int main(int argc, char ** argv) {
MPI_Init(&argc, &argv);
QUESO::FullEnvironment env(MPI_COMM_WORLD, argv[1], "", NULL);
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> paramSpace(env,
"param_", 2, NULL);
double min_val = 0.0;
double max_val = 1.0;
QUESO::GslVector paramMins(paramSpace.zeroVector());
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
// Model parameter between 0 and 1
paramMins[0] = 0.0;
paramMaxs[0] = 1.0;
// Hyperparameter (multiplicative coefficient of observational error
// covariance matrix) between 0.0 and \infty
paramMins[1] = 0.0;
paramMaxs[1] = INFINITY;
QUESO::BoxSubset<QUESO::GslVector, QUESO::GslMatrix> paramDomain("param_",
paramSpace, paramMins, paramMaxs);
QUESO::UniformVectorRV<QUESO::GslVector, QUESO::GslMatrix> priorRv("prior_",
paramDomain);
// Set up observation space
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> obsSpace(env,
"obs_", 2, NULL);
// Fill up observation vector
QUESO::GslVector observations(obsSpace.zeroVector());
observations[0] = 1.0;
observations[1] = 1.0;
// Fill up covariance 'matrix'
QUESO::GslMatrix covariance(obsSpace.zeroVector());
covariance(0, 0) = 1.0;
covariance(0, 1) = 0.0;
covariance(1, 0) = 0.0;
covariance(1, 1) = 1.0;
// Pass in observations to Gaussian likelihood object
Likelihood<QUESO::GslVector, QUESO::GslMatrix> lhood("llhd_", paramDomain,
observations, covariance);
QUESO::GenericVectorRV<QUESO::GslVector, QUESO::GslMatrix>
postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector, QUESO::GslMatrix>
ip("", NULL, priorRv, lhood, postRv);
QUESO::GslVector paramInitials(paramSpace.zeroVector());
paramInitials[0] = 0.0;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
for (unsigned int i = 0; i < 1; i++) {
proposalCovMatrix(i, i) = 0.1;
}
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
MPI_Finalize();
return 0;
}
int main(int argc, char ** argv) {
#ifdef QUESO_HAS_MPI
MPI_Init(&argc, &argv);
#endif
QUESO::EnvOptionsValues envOptions;
envOptions.m_numSubEnvironments = 1;
envOptions.m_subDisplayFileName = "test_outputNoInputFile/display";
envOptions.m_subDisplayAllowAll = 1;
envOptions.m_displayVerbosity = 2;
envOptions.m_syncVerbosity = 0;
envOptions.m_seed = 0;
#ifdef QUESO_HAS_MPI
QUESO::FullEnvironment env(MPI_COMM_WORLD, "", "", &envOptions);
#else
QUESO::FullEnvironment env("", "", &envOptions);
#endif
unsigned int dim = 2;
QUESO::VectorSpace<> paramSpace(env, "param_", dim, NULL);
QUESO::GslVector paramMins(paramSpace.zeroVector());
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
double min_val = -10.0;
double max_val = 10.0;
paramMins.cwSet(min_val);
paramMaxs.cwSet(max_val);
QUESO::BoxSubset<> paramDomain("param_", paramSpace, paramMins, paramMaxs);
QUESO::UniformVectorRV<> priorRv("prior_", paramDomain);
Likelihood<> lhood("llhd_", paramDomain);
QUESO::GenericVectorRV<> postRv("post_", paramSpace);
QUESO::SipOptionsValues sipOptions;
sipOptions.m_computeSolution = 1;
sipOptions.m_dataOutputFileName = "test_outputNoInputFile/sipOutput";
sipOptions.m_dataOutputAllowedSet.clear();
sipOptions.m_dataOutputAllowedSet.insert(0);
QUESO::StatisticalInverseProblem<> ip("", &sipOptions, priorRv, lhood,
postRv);
QUESO::GslVector paramInitials(paramSpace.zeroVector());
paramInitials[0] = 0.0;
paramInitials[1] = 0.0;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0, 0) = 1.0;
proposalCovMatrix(0, 1) = 0.0;
proposalCovMatrix(1, 0) = 0.0;
proposalCovMatrix(1, 1) = 1.0;
QUESO::MhOptionsValues mhOptions;
mhOptions.m_dataOutputFileName = "test_outputNoInputFile/sipOutput";
mhOptions.m_dataOutputAllowAll = 1;
mhOptions.m_rawChainGenerateExtra = 0;
mhOptions.m_rawChainDisplayPeriod = 50000;
mhOptions.m_rawChainMeasureRunTimes = 1;
mhOptions.m_rawChainDataOutputFileName = "test_outputNoInputFile/ip_raw_chain";
mhOptions.m_rawChainDataOutputAllowAll = 1;
mhOptions.m_displayCandidates = 0;
mhOptions.m_tkUseLocalHessian = 0;
mhOptions.m_tkUseNewtonComponent = 1;
mhOptions.m_filteredChainGenerate = 0;
mhOptions.m_rawChainSize = 1000;
mhOptions.m_putOutOfBoundsInChain = false;
mhOptions.m_drMaxNumExtraStages = 1;
mhOptions.m_drScalesForExtraStages.resize(1);
mhOptions.m_drScalesForExtraStages[0] = 5.0;
mhOptions.m_amInitialNonAdaptInterval = 100;
mhOptions.m_amAdaptInterval = 100;
mhOptions.m_amEta = (double) 2.4 * 2.4 / dim; // From Gelman 95
mhOptions.m_amEpsilon = 1.e-8;
mhOptions.m_doLogitTransform = false;
mhOptions.m_algorithm = "random_walk";
mhOptions.m_tk = "random_walk";
ip.solveWithBayesMetropolisHastings(&mhOptions, paramInitials,
&proposalCovMatrix);
#ifdef QUESO_HAS_MPI
MPI_Finalize();
#endif
return 0;
}
void computeGravityAndTraveledDistance(const QUESO::FullEnvironment& env) {
struct timeval timevalNow;
gettimeofday(&timevalNow, NULL);
if (env.fullRank() == 0) {
std::cout << "\nBeginning run of 'Gravity + Projectile motion' example at "
<< ctime(&timevalNow.tv_sec)
<< "\n my fullRank = " << env.fullRank()
<< "\n my subEnvironmentId = " << env.subId()
<< "\n my subRank = " << env.subRank()
<< "\n my interRank = " << env.inter0Rank()
<< std::endl << std::endl;
}
// Just examples of possible calls
if ((env.subDisplayFile() ) &&
(env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Beginning run of 'Gravity + Projectile motion' example at "
<< ctime(&timevalNow.tv_sec)
<< std::endl;
}
env.fullComm().Barrier();
env.subComm().Barrier(); // Just an example of a possible call
//================================================================
// Statistical inverse problem (SIP): find posterior PDF for 'g'
//================================================================
gettimeofday(&timevalNow, NULL);
if (env.fullRank() == 0) {
std::cout << "Beginning 'SIP -> Gravity estimation' at "
<< ctime(&timevalNow.tv_sec)
<< std::endl;
}
//------------------------------------------------------
// SIP Step 1 of 6: Instantiate the parameter space
//------------------------------------------------------
QUESO::VectorSpace<QUESO::GslVector,QUESO::GslMatrix> paramSpace(env, "param_", 1, NULL);
//------------------------------------------------------
// SIP Step 2 of 6: Instantiate the parameter domain
//------------------------------------------------------
QUESO::GslVector paramMinValues(paramSpace.zeroVector());
QUESO::GslVector paramMaxValues(paramSpace.zeroVector());
paramMinValues[0] = 8.;
paramMaxValues[0] = 11.;
QUESO::BoxSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomain("param_",
paramSpace,
paramMinValues,
paramMaxValues);
//------------------------------------------------------
// SIP Step 3 of 6: Instantiate the likelihood function
// object to be used by QUESO.
//------------------------------------------------------
likelihoodRoutine_Data likelihoodRoutine_Data(env);
QUESO::GenericScalarFunction<QUESO::GslVector,QUESO::GslMatrix>
likelihoodFunctionObj("like_",
paramDomain,
likelihoodRoutine,
(void *) &likelihoodRoutine_Data,
true); // the routine computes [ln(function)]
//------------------------------------------------------
// SIP Step 4 of 6: Define the prior RV
//------------------------------------------------------
#ifdef PRIOR_IS_GAUSSIAN
QUESO::GslVector meanVector( paramSpace.zeroVector() );
meanVector[0] = 9;
QUESO::GslMatrix covMatrix = QUESO::GslMatrix(paramSpace.zeroVector());
covMatrix(0,0) = 1.;
// Create a Gaussian prior RV
QUESO::GaussianVectorRV<QUESO::GslVector,QUESO::GslMatrix> priorRv("prior_",paramDomain,meanVector,covMatrix);
#else
// Create an uniform prior RV
QUESO::UniformVectorRV<QUESO::GslVector,QUESO::GslMatrix> priorRv("prior_",paramDomain);
#endif
//------------------------------------------------------
// SIP Step 5 of 6: Instantiate the inverse problem
//------------------------------------------------------
QUESO::GenericVectorRV<QUESO::GslVector,QUESO::GslMatrix>
postRv("post_", // Extra prefix before the default "rv_" prefix
paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector,QUESO::GslMatrix>
ip("", // No extra prefix before the default "ip_" prefix
NULL,
priorRv,
likelihoodFunctionObj,
postRv);
//------------------------------------------------------
// SIP Step 6 of 6: Solve the inverse problem, that is,
// set the 'pdf' and the 'realizer' of the posterior RV
//------------------------------------------------------
std::cout << "Solving the SIP with Metropolis Hastings"
<< std::endl << std::endl;
QUESO::GslVector paramInitials(paramSpace.zeroVector());
priorRv.realizer().realization(paramInitials);
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0,0) = std::pow( fabs(paramInitials[0])/20. , 2. );
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
//================================================================
// Statistical forward problem (SFP): find the max distance
// traveled by an object in projectile motion; input pdf for 'g'
// is the solution of the SIP above.
//================================================================
gettimeofday(&timevalNow, NULL);
std::cout << "Beginning 'SFP -> Projectile motion' at "
<< ctime(&timevalNow.tv_sec)
<< std::endl;
//------------------------------------------------------
// SFP Step 1 of 6: Instantiate the parameter *and* qoi spaces.
// SFP input RV = FIP posterior RV, so SFP parameter space
// has been already defined.
//------------------------------------------------------
QUESO::VectorSpace<QUESO::GslVector,QUESO::GslMatrix> qoiSpace(env, "qoi_", 1, NULL);
//------------------------------------------------------
// SFP Step 2 of 6: Instantiate the parameter domain
//------------------------------------------------------
// Not necessary because input RV of the SFP = output RV of SIP.
// Thus, the parameter domain has been already defined.
//------------------------------------------------------
// SFP Step 3 of 6: Instantiate the qoi function object
// to be used by QUESO.
//------------------------------------------------------
qoiRoutine_Data qoiRoutine_Data;
qoiRoutine_Data.m_angle = M_PI/4.0; //45 degrees (radians)
qoiRoutine_Data.m_initialVelocity= 5.; //initial speed (m/s)
qoiRoutine_Data.m_initialHeight = 0.; //initial height (m)
QUESO::GenericVectorFunction<QUESO::GslVector,QUESO::GslMatrix,QUESO::GslVector,QUESO::GslMatrix>
qoiFunctionObj("qoi_",
paramDomain,
qoiSpace,
qoiRoutine,
(void *) &qoiRoutine_Data);
//------------------------------------------------------
// SFP Step 4 of 6: Define the input RV
//------------------------------------------------------
// Not necessary because input RV of SFP = output RV of SIP
// (postRv).
//------------------------------------------------------
// SFP Step 5 of 6: Instantiate the forward problem
//------------------------------------------------------
QUESO::GenericVectorRV<QUESO::GslVector,QUESO::GslMatrix> qoiRv("qoi_", qoiSpace);
QUESO::StatisticalForwardProblem<QUESO::GslVector,QUESO::GslMatrix,QUESO::GslVector,QUESO::GslMatrix>
fp("",
NULL,
postRv,
qoiFunctionObj,
qoiRv);
//------------------------------------------------------
// SFP Step 6 of 6: Solve the forward problem
//------------------------------------------------------
std::cout << "Solving the SFP with Monte Carlo"
<< std::endl << std::endl;
fp.solveWithMonteCarlo(NULL);
//------------------------------------------------------
gettimeofday(&timevalNow, NULL);
if ((env.subDisplayFile() ) &&
(env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Ending run of 'Gravity + Projectile motion' example at "
<< ctime(&timevalNow.tv_sec)
<< std::endl;
}
if (env.fullRank() == 0) {
std::cout << "Ending run of 'Gravity + Projectile motion' example at "
<< ctime(&timevalNow.tv_sec)
<< std::endl;
}
return;
}
void solveSip(const uqFullEnvironmentClass& env)
{
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Entering solveSip()..."
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 1 of 5: Instantiate the parameter space
////////////////////////////////////////////////////////
unsigned int p = 2;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> paramSpace(env, "param_", p, NULL);
uqGslVectorClass aVec(paramSpace.zeroVector());
aVec[0] = 2.;
aVec[1] = 5.;
uqGslVectorClass xGiven(paramSpace.zeroVector());
xGiven[0] = -1.;
xGiven[1] = 7.;
////////////////////////////////////////////////////////
// Step 2 of 5: Instantiate the parameter domain
////////////////////////////////////////////////////////
//uqGslVectorClass paramMins (paramSpace.zeroVector());
//uqGslVectorClass paramMaxs (paramSpace.zeroVector());
//paramMins [0] = -1.e+16;
//paramMaxs [0] = 1.e+16;
//paramMins [1] = -1.e+16;
//paramMaxs [1] = 1.e+16;
//uqBoxSubsetClass<uqGslVectorClass,uqGslMatrixClass> paramDomain("param_",paramSpace,paramMins,paramMaxs);
uqVectorSetClass<uqGslVectorClass,uqGslMatrixClass>* paramDomain = ¶mSpace;
////////////////////////////////////////////////////////
// Step 3 of 5: Instantiate the likelihood function object
////////////////////////////////////////////////////////
unsigned int n = 5;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> dataSpace(env, "data_", n, NULL);
uqGslVectorClass yMeanVec(dataSpace.zeroVector());
double tmp = scalarProduct(aVec,xGiven);
for (unsigned int i = 0; i < n; ++i) {
yMeanVec[i] = tmp;
}
double sigmaEps = 2.1;
uqGslMatrixClass yCovMat(dataSpace.zeroVector());
tmp = sigmaEps*sigmaEps;
for (unsigned int i = 0; i < n; ++i) {
yCovMat(i,i) = tmp;
}
uqGslVectorClass ySamples(dataSpace.zeroVector());
uqGaussianVectorRVClass<uqGslVectorClass,uqGslMatrixClass> yRv("y_", dataSpace, yMeanVec, yCovMat);
yRv.realizer().realization(ySamples);
double ySampleMean = 0.;
for (unsigned int i = 0; i < n; ++i) {
ySampleMean += ySamples[i];
}
ySampleMean /= ((double) n);
struct likelihoodDataStruct likelihoodData;
likelihoodData.aVec = &aVec;
likelihoodData.sigmaEps = sigmaEps;
likelihoodData.ySamples = &ySamples;
uqGenericScalarFunctionClass<uqGslVectorClass,uqGslMatrixClass>
likelihoodFunctionObj("like_",
*paramDomain,
likelihoodRoutine,
(void *) &likelihoodData,
true); // routine computes [ln(function)]
////////////////////////////////////////////////////////
// Step 4 of 5: Instantiate the inverse problem
////////////////////////////////////////////////////////
uqGslVectorClass xPriorMeanVec(paramSpace.zeroVector());
xPriorMeanVec[0] = 0.;
xPriorMeanVec[1] = 0.;
uqGslMatrixClass sigma0Mat(paramSpace.zeroVector());
sigma0Mat(0,0) = 1.e-3;
sigma0Mat(0,1) = 0.;
sigma0Mat(1,0) = 0.;
sigma0Mat(1,1) = 1.e-3;
uqGslMatrixClass sigma0MatInverse(paramSpace.zeroVector());
sigma0MatInverse = sigma0Mat.inverse();
uqGaussianVectorRVClass<uqGslVectorClass,uqGslMatrixClass> priorRv("prior_", *paramDomain, xPriorMeanVec, sigma0MatInverse);
uqGenericVectorRVClass <uqGslVectorClass,uqGslMatrixClass> postRv ("post_", paramSpace);
uqStatisticalInverseProblemClass<uqGslVectorClass,uqGslMatrixClass> sip("sip_", NULL, priorRv, likelihoodFunctionObj, postRv);
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "In solveSip():"
<< "\n p = " << p
<< "\n xGiven = " << xGiven
<< "\n sigma0Mat = " << sigma0Mat
<< "\n sigma0MatInverse = " << sigma0MatInverse
<< "\n aVec = " << aVec
<< "\n n = " << n
<< "\n sigmaEps = " << sigmaEps
<< "\n yMeanVec = " << yMeanVec
<< "\n yCovMat = " << yCovMat
<< "\n ySamples = " << ySamples
<< "\n ySampleMean = " << ySampleMean
<< std::endl;
}
uqGslMatrixClass sigmaMatInverse(paramSpace.zeroVector());
sigmaMatInverse = matrixProduct(aVec,aVec);
sigmaMatInverse *= (((double) n)/sigmaEps/sigmaEps);
sigmaMatInverse += sigma0Mat;
uqGslMatrixClass sigmaMat(paramSpace.zeroVector());
sigmaMat = sigmaMatInverse.inverse();
uqGslVectorClass muVec(paramSpace.zeroVector());
muVec = sigmaMat * aVec;
muVec *= (((double) n) * ySampleMean)/sigmaEps/sigmaEps;
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "In solveSip():"
<< "\n muVec = " << muVec
<< "\n sigmaMat = " << sigmaMat
<< "\n sigmaMatInverse = " << sigmaMatInverse
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 5 of 5: Solve the inverse problem
////////////////////////////////////////////////////////
uqGslVectorClass initialValues(paramSpace.zeroVector());
initialValues[0] = 25.;
initialValues[1] = 25.;
uqGslMatrixClass proposalCovMat(paramSpace.zeroVector());
proposalCovMat(0,0) = 10.;
proposalCovMat(0,1) = 0.;
proposalCovMat(1,0) = 0.;
proposalCovMat(1,1) = 10.;
sip.solveWithBayesMetropolisHastings(NULL,initialValues,&proposalCovMat);
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Leaving solveSip()"
<< std::endl;
}
return;
}
int main(int argc, char ** argv) {
#ifdef QUESO_HAS_MPI
MPI_Init(&argc, &argv);
QUESO::FullEnvironment env(MPI_COMM_WORLD, argv[1], "", NULL);
#else
QUESO::FullEnvironment env(argv[1], "", NULL);
#endif
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> paramSpace(env,
"param_", 1, NULL);
double min_val = 0.0;
double max_val = 1.0;
QUESO::GslVector paramMins(paramSpace.zeroVector());
paramMins.cwSet(min_val);
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
paramMaxs.cwSet(max_val);
QUESO::BoxSubset<QUESO::GslVector, QUESO::GslMatrix> paramDomain("param_",
paramSpace, paramMins, paramMaxs);
QUESO::UniformVectorRV<QUESO::GslVector, QUESO::GslMatrix> priorRv("prior_",
paramDomain);
// Set up observation space
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> obsSpace(env,
"obs_", 2, NULL);
// Fill up observation vector
QUESO::GslVector observations(obsSpace.zeroVector());
observations[0] = 1.0;
observations[1] = 1.0;
// Pass in observations to Gaussian likelihood object
Likelihood<QUESO::GslVector, QUESO::GslMatrix> lhood("llhd_", paramDomain,
observations, 1.0);
QUESO::GenericVectorRV<QUESO::GslVector, QUESO::GslMatrix>
postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector, QUESO::GslMatrix>
ip("", NULL, priorRv, lhood, postRv);
QUESO::GslVector paramInitials(paramSpace.zeroVector());
paramInitials[0] = 0.0;
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
for (unsigned int i = 0; i < 1; i++) {
proposalCovMatrix(i, i) = 0.1;
}
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
#ifdef QUESO_HAS_MPI
MPI_Finalize();
#endif
return 0;
}
int main(int argc, char ** argv) {
// Step 0: Set up some variables
unsigned int numExperiments = 10; // Number of experiments
unsigned int numUncertainVars = 5; // Number of things to calibrate
unsigned int numSimulations = 50; // Number of simulations
unsigned int numConfigVars = 1; // Dimension of configuration space
unsigned int numEta = 1; // Number of responses the model is returning
unsigned int experimentSize = 1; // Size of each experiment
#ifdef QUESO_HAS_MPI
MPI_Init(&argc, &argv);
// Step 1: Set up QUESO environment
QUESO::FullEnvironment env(MPI_COMM_WORLD, argv[1], "", NULL);
#else
QUESO::FullEnvironment env(argv[1], "", NULL);
#endif
// Step 2: Set up prior for calibration parameters
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> paramSpace(env,
"param_", numUncertainVars, NULL);
// Parameter (theta) bounds:
// descriptors 'k_tmasl' 'k_xkle' 'k_xkwew' 'k_xkwlx' 'k_cd'
// upper_bounds 1.05 1.1 1.1 1.1 1.1
// lower_bounds 0.95 0.9 0.9 0.9 0.9
//
// These bounds are dealt with when reading in the data
QUESO::GslVector paramMins(paramSpace.zeroVector());
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
paramMins.cwSet(0.0);
paramMaxs.cwSet(1.0);
QUESO::BoxSubset<QUESO::GslVector, QUESO::GslMatrix> paramDomain("param_",
paramSpace, paramMins, paramMaxs);
QUESO::UniformVectorRV<QUESO::GslVector, QUESO::GslMatrix> priorRv("prior_",
paramDomain);
// Step 3: Instantiate the 'scenario' and 'output' spaces for simulation
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> configSpace(env,
"scenario_", numConfigVars, NULL);
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> nEtaSpace(env,
"output_", numEta, NULL);
// Step 4: Instantiate the 'output' space for the experiments
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> experimentSpace(env,
"experimentspace_", experimentSize, NULL);
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix> totalExperimentSpace(env,
"experimentspace_", experimentSize * numExperiments, NULL);
// Step 5: Instantiate the Gaussian process emulator object
//
// Regarding simulation scenario input values, the user should standardise
// them so that they exist inside a hypercube.
//
// Regarding simulation output data, the user should transform it so that the
// mean is zero and the variance is one.
//
// Regarding experimental scenario input values, the user should standardize
// them so that they exist inside a hypercube.
//
// Regarding experimental data, the user should transformed it so that it has
// zero mean and variance one.
// GPMSA stores all the information about our simulation
// data and experimental data. It also stores default information about the
// hyperparameter distributions.
QUESO::GPMSAFactory<QUESO::GslVector, QUESO::GslMatrix>
gpmsaFactory(env,
NULL,
priorRv,
configSpace,
paramSpace,
nEtaSpace,
experimentSpace,
numSimulations,
numExperiments);
// std::vector containing all the points in scenario space where we have
// simulations
std::vector<QUESO::GslVector *> simulationScenarios(numSimulations,
(QUESO::GslVector *) NULL);
// std::vector containing all the points in parameter space where we have
// simulations
std::vector<QUESO::GslVector *> paramVecs(numSimulations,
(QUESO::GslVector *) NULL);
// std::vector containing all the simulation output data
std::vector<QUESO::GslVector *> outputVecs(numSimulations,
(QUESO::GslVector *) NULL);
// std::vector containing all the points in scenario space where we have
// experiments
std::vector<QUESO::GslVector *> experimentScenarios(numExperiments,
(QUESO::GslVector *) NULL);
// std::vector containing all the experimental output data
std::vector<QUESO::GslVector *> experimentVecs(numExperiments,
(QUESO::GslVector *) NULL);
// The experimental output data observation error covariance matrix
QUESO::GslMatrix experimentMat(totalExperimentSpace.zeroVector());
// Instantiate each of the simulation points/outputs
for (unsigned int i = 0; i < numSimulations; i++) {
simulationScenarios[i] = new QUESO::GslVector(configSpace.zeroVector()); // 'x_{i+1}^*' in paper
paramVecs [i] = new QUESO::GslVector(paramSpace.zeroVector()); // 't_{i+1}^*' in paper
outputVecs [i] = new QUESO::GslVector(nEtaSpace.zeroVector()); // 'eta_{i+1}' in paper
}
for (unsigned int i = 0; i < numExperiments; i++) {
experimentScenarios[i] = new QUESO::GslVector(configSpace.zeroVector()); // 'x_{i+1}' in paper
experimentVecs[i] = new QUESO::GslVector(experimentSpace.zeroVector());
}
// Read in data and store the standard deviation of the simulation data. We
// will need the standard deviation when we pass the experiment error
// covariance matrix to QUESO.
double stdsim = readData(simulationScenarios,
paramVecs,
outputVecs,
experimentScenarios,
experimentVecs);
for (unsigned int i = 0; i < numExperiments; i++) {
// Passing in error of experiments (standardised).
experimentMat(i, i) = (0.025 / stdsim) * (0.025 / stdsim);
}
// Add simulation and experimental data
gpmsaFactory.addSimulations(simulationScenarios, paramVecs, outputVecs);
gpmsaFactory.addExperiments(experimentScenarios, experimentVecs, &experimentMat);
QUESO::GenericVectorRV<QUESO::GslVector, QUESO::GslMatrix> postRv(
"post_",
gpmsaFactory.prior().imageSet().vectorSpace());
QUESO::StatisticalInverseProblem<QUESO::GslVector, QUESO::GslMatrix> ip("",
NULL, gpmsaFactory, postRv);
QUESO::GslVector paramInitials(
gpmsaFactory.prior().imageSet().vectorSpace().zeroVector());
// Initial condition of the chain
// Have to set each of these by hand, *and* the sampler is sensitive to these
// values
paramInitials[0] = 0.5; // param 1
paramInitials[1] = 0.5; // param 2
paramInitials[2] = 0.5; // param 3
paramInitials[3] = 0.5; // param 4
paramInitials[4] = 0.5; // param 5
paramInitials[5] = 0.4; // not used. emulator mean
paramInitials[6] = 0.4; // emulator precision
paramInitials[7] = 0.97; // emulator corr str
paramInitials[8] = 0.97; // emulator corr str
paramInitials[9] = 0.97; // emulator corr str
paramInitials[10] = 0.97; // emulator corr str
paramInitials[11] = 0.20; // emulator corr str
paramInitials[12] = 0.80; // emulator corr str
paramInitials[13] = 10.0; // discrepancy precision
paramInitials[14] = 0.97; // discrepancy corr str
paramInitials[15] = 8000.0; // emulator data precision
QUESO::GslMatrix proposalCovMatrix(
gpmsaFactory.prior().imageSet().vectorSpace().zeroVector());
// Setting the proposal covariance matrix by hand. This requires great
// forethough, and can generally be referred to as a massive hack. These
// values were taken from the gpmsa matlab code and fiddled with.
double scale = 600.0;
proposalCovMatrix(0, 0) = 3.1646 / 10.0; // param 1
proposalCovMatrix(1, 1) = 3.1341 / 10.0; // param 2
proposalCovMatrix(2, 2) = 3.1508 / 10.0; // param 3
proposalCovMatrix(3, 3) = 0.3757 / 10.0; // param 4
proposalCovMatrix(4, 4) = 0.6719 / 10.0; // param 5
proposalCovMatrix(5, 5) = 0.1 / scale; // not used. emulator mean
proposalCovMatrix(6, 6) = 0.4953 / scale; // emulator precision
proposalCovMatrix(7, 7) = 0.6058 / scale; // emulator corr str
proposalCovMatrix(8, 8) = 7.6032e-04 / scale; // emulator corr str
proposalCovMatrix(9, 9) = 8.3815e-04 / scale; // emulator corr str
proposalCovMatrix(10, 10) = 7.5412e-04 / scale; // emulator corr str
proposalCovMatrix(11, 11) = 0.2682 / scale; // emulator corr str
proposalCovMatrix(12, 12) = 0.0572 / scale; // emulator corr str
proposalCovMatrix(13, 13) = 1.3417 / scale; // discrepancy precision
proposalCovMatrix(14, 14) = 0.3461 / scale; // discrepancy corr str
proposalCovMatrix(15, 15) = 495.3 / scale; // emulator data precision
// Square to get variances
for (unsigned int i = 0; i < 16; i++) {
proposalCovMatrix(i, i) = proposalCovMatrix(i, i) * proposalCovMatrix(i, i);
}
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
#ifdef QUESO_HAS_MPI
MPI_Finalize();
#endif
return 0;
}
void compute(const QUESO::FullEnvironment& env, unsigned int numModes) {
////////////////////////////////////////////////////////
// Step 1 of 5: Instantiate the parameter space
////////////////////////////////////////////////////////
#ifdef APPLS_MODAL_USES_CONCATENATION
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix>
paramSpaceA(env, "paramA_", 2, NULL);
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix>
paramSpaceB(env, "paramB_", 1, NULL);
#endif
QUESO::VectorSpace<QUESO::GslVector, QUESO::GslMatrix>
paramSpace(env, "param_", 3, NULL);
////////////////////////////////////////////////////////
// Step 2 of 5: Instantiate the parameter domain
////////////////////////////////////////////////////////
#ifdef APPLS_MODAL_USES_CONCATENATION
QUESO::GslVector paramMinsA(paramSpaceA.zeroVector());
paramMinsA[0] = 0.;
paramMinsA[1] = 0.;
QUESO::GslVector paramMaxsA(paramSpaceA.zeroVector());
paramMaxsA[0] = 3.;
paramMaxsA[1] = 3.;
QUESO::BoxSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomainA("paramA_",paramSpaceA,paramMinsA,paramMaxsA);
QUESO::GslVector paramMinsB(paramSpaceB.zeroVector());
paramMinsB[0] = 0.;
QUESO::GslVector paramMaxsB(paramSpaceB.zeroVector());
paramMaxsB[0] = INFINITY;
QUESO::BoxSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomainB("paramB_",paramSpaceB,paramMinsB,paramMaxsB);
QUESO::ConcatenationSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomain("",paramSpace,paramDomainA,paramDomainB);
#else
QUESO::GslVector paramMins(paramSpace.zeroVector());
paramMins[0] = 0.;
paramMins[1] = 0.;
paramMins[2] = 0.;
QUESO::GslVector paramMaxs(paramSpace.zeroVector());
paramMaxs[0] = 3.;
paramMaxs[1] = 3.;
paramMaxs[2] = .3;
QUESO::BoxSubset<QUESO::GslVector,QUESO::GslMatrix>
paramDomain("param_",paramSpace,paramMins,paramMaxs);
#endif
////////////////////////////////////////////////////////
// Step 3 of 5: Instantiate the likelihood function object
////////////////////////////////////////////////////////
likelihoodRoutine_DataType likelihoodRoutine_Data;
likelihoodRoutine_Data.numModes = numModes;
QUESO::GenericScalarFunction<QUESO::GslVector,QUESO::GslMatrix>
likelihoodFunctionObj("like_",
paramDomain,
likelihoodRoutine,
(void *) &likelihoodRoutine_Data,
true); // routine computes [-2.*ln(function)]
////////////////////////////////////////////////////////
// Step 4 of 5: Instantiate the inverse problem
////////////////////////////////////////////////////////
#ifdef APPLS_MODAL_USES_CONCATENATION
QUESO::UniformVectorRV<QUESO::GslVector,QUESO::GslMatrix>
priorRvA("priorA_", paramDomainA);
QUESO::GslVector alpha(paramSpaceB.zeroVector());
alpha[0] = 3.;
QUESO::GslVector beta(paramSpaceB.zeroVector());
if (numModes == 1) {
beta[0] = 0.09709133373799;
}
else {
beta[0] = 0.08335837191688;
}
QUESO::InverseGammaVectorRV<QUESO::GslVector,QUESO::GslMatrix>
priorRvB("priorB_", paramDomainB,alpha,beta);
QUESO::ConcatenatedVectorRV<QUESO::GslVector,QUESO::GslMatrix>
priorRv("prior_", priorRvA, priorRvB, paramDomain);
#else
QUESO::UniformVectorRV<QUESO::GslVector,QUESO::GslMatrix>
priorRv("prior_", paramDomain);
#endif
QUESO::GenericVectorRV<QUESO::GslVector,QUESO::GslMatrix>
postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<QUESO::GslVector,QUESO::GslMatrix>
ip("", NULL, priorRv, likelihoodFunctionObj, postRv);
////////////////////////////////////////////////////////
// Step 5 of 5: Solve the inverse problem
////////////////////////////////////////////////////////
ip.solveWithBayesMLSampling();
////////////////////////////////////////////////////////
// Print some statistics
////////////////////////////////////////////////////////
unsigned int numPosTotal = postRv.realizer().subPeriod();
if (env.subDisplayFile()) {
*env.subDisplayFile() << "numPosTotal = " << numPosTotal
<< std::endl;
}
QUESO::GslVector auxVec(paramSpace.zeroVector());
unsigned int numPosTheta1SmallerThan1dot5 = 0;
for (unsigned int i = 0; i < numPosTotal; ++i) {
postRv.realizer().realization(auxVec);
if (auxVec[0] < 1.5) numPosTheta1SmallerThan1dot5++;
}
if (env.subDisplayFile()) {
*env.subDisplayFile() << "numPosTheta1SmallerThan1dot5 = " << numPosTheta1SmallerThan1dot5
<< ", ratio = " << ((double) numPosTheta1SmallerThan1dot5)/((double) numPosTotal)
<< std::endl;
}
return;
}
void GaussianMean1DRegressionCompute(const QUESO::BaseEnvironment& env,
double priorMean, double priorVar, const likelihoodData& dat)
{
// parameter space: 1-D on (-infinity, infinity)
QUESO::VectorSpace<P_V, P_M> paramSpace(
env, // queso environment
"param_", // name prefix
1, // dimensions
NULL); // names
P_V paramMin(paramSpace.zeroVector());
P_V paramMax(paramSpace.zeroVector());
paramMin[0] = -INFINITY;
paramMax[0] = INFINITY;
QUESO::BoxSubset<P_V, P_M> paramDomain(
"paramBox_", // name prefix
paramSpace, // vector space
paramMin, // min values
paramMax); // max values
// gaussian prior with user supplied mean and variance
P_V priorMeanVec(paramSpace.zeroVector());
P_V priorVarVec(paramSpace.zeroVector());
priorMeanVec[0] = priorMean;
priorVarVec[0] = priorVar;
QUESO::GaussianVectorRV<P_V, P_M> priorRv("prior_", paramDomain, priorMeanVec,
priorVarVec);
// likelihood is important
QUESO::GenericScalarFunction<P_V, P_M> likelihoodFunctionObj(
"like_", // name prefix
paramDomain, // image set
LikelihoodFunc<P_V, P_M>, // routine
(void *) &dat, // routine data ptr
true); // routineIsForLn
QUESO::GenericVectorRV<P_V, P_M> postRv(
"post_", // name prefix
paramSpace); // image set
// Initialize and solve the Inverse Problem with Bayes multi-level sampling
QUESO::StatisticalInverseProblem<P_V, P_M> invProb(
"", // name prefix
NULL, // alt options
priorRv, // prior RV
likelihoodFunctionObj, // likelihood fcn
postRv); // posterior RV
invProb.solveWithBayesMLSampling();
// compute mean and second moment of samples on each proc via Knuth online mean/variance algorithm
int N = invProb.postRv().realizer().subPeriod();
double subMean = 0.0;
double subM2 = 0.0;
double delta;
P_V sample(paramSpace.zeroVector());
for (int n = 1; n <= N; n++) {
invProb.postRv().realizer().realization(sample);
delta = sample[0] - subMean;
subMean += delta / n;
subM2 += delta * (sample[0] - subMean);
}
// gather all Ns, means, and M2s to proc 0
std::vector<int> unifiedNs(env.inter0Comm().NumProc());
std::vector<double> unifiedMeans(env.inter0Comm().NumProc());
std::vector<double> unifiedM2s(env.inter0Comm().NumProc());
MPI_Gather(&N, 1, MPI_INT, &(unifiedNs[0]), 1, MPI_INT, 0,
env.inter0Comm().Comm());
MPI_Gather(&subMean, 1, MPI_DOUBLE, &(unifiedMeans[0]), 1, MPI_DOUBLE, 0,
env.inter0Comm().Comm());
MPI_Gather(&subM2, 1, MPI_DOUBLE, &(unifiedM2s[0]), 1, MPI_DOUBLE, 0,
env.inter0Comm().Comm());
// get the total number of likelihood calls at proc 0
unsigned long totalLikelihoodCalls = 0;
MPI_Reduce(&likelihoodCalls, &totalLikelihoodCalls, 1, MPI_UNSIGNED_LONG,
MPI_SUM, 0, env.inter0Comm().Comm());
// compute global posterior mean and std via Chan algorithm, output results on proc 0
if (env.inter0Rank() == 0) {
int postN = unifiedNs[0];
double postMean = unifiedMeans[0];
double postVar = unifiedM2s[0];
for (unsigned int i = 1; i < unifiedNs.size(); i++) {
delta = unifiedMeans[i] - postMean;
postMean = (postN * postMean + unifiedNs[i] * unifiedMeans[i]) /
(postN + unifiedNs[i]);
postVar += unifiedM2s[i] + delta * delta *
(((double)postN * unifiedNs[i]) / (postN + unifiedNs[i]));
postN += unifiedNs[i];
}
postVar /= postN;
//compute exact answer - available in this case since the exact posterior is a gaussian
N = dat.dataSet.size();
double dataSum = 0.0;
for (int i = 0; i < N; i++)
dataSum += dat.dataSet[i];
double datMean = dataSum / N;
double postMeanExact = (N * priorVar / (N * priorVar + dat.samplingVar)) *
datMean + (dat.samplingVar / (N * priorVar + dat.samplingVar)) * priorMean;
double postVarExact = 1.0 / (N / dat.samplingVar + 1.0 / priorVar);
std::cout << "Number of posterior samples: " << postN << std::endl;
std::cout << "Estimated posterior mean: " << postMean << " +/- "
<< std::sqrt(postVar) << std::endl;
std::cout << "Likelihood function calls: " << totalLikelihoodCalls
<< std::endl;
std::cout << "\nExact posterior: Gaussian with mean " << postMeanExact
<< ", standard deviation " << std::sqrt(postVarExact) << std::endl;
}
}
void solveSip(const uqFullEnvironmentClass& env, bool useML)
{
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Entering solveSip()..."
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 1 of 5: Instantiate the parameter space
////////////////////////////////////////////////////////
unsigned int p = 1;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> paramSpace(env, "param_", p, NULL);
uqGslVectorClass bVec(paramSpace.zeroVector());
bVec[0] = 0.045213;
////////////////////////////////////////////////////////
// Step 2 of 5: Instantiate the parameter domain
////////////////////////////////////////////////////////
//uqGslVectorClass paramMins (paramSpace.zeroVector());
//uqGslVectorClass paramMaxs (paramSpace.zeroVector());
//paramMins [0] = -1.e+16;
//paramMaxs [0] = 1.e+16;
//paramMins [1] = -1.e+16;
//paramMaxs [1] = 1.e+16;
//uqBoxSubsetClass<uqGslVectorClass,uqGslMatrixClass> paramDomain("param_",paramSpace,paramMins,paramMaxs);
uqVectorSetClass<uqGslVectorClass,uqGslMatrixClass>* paramDomain = ¶mSpace;
////////////////////////////////////////////////////////
// Step 3 of 5: Instantiate the likelihood function object
////////////////////////////////////////////////////////
unsigned int nAll = 100000;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> dataSpaceAll(env, "data_", nAll, NULL);
double sigmaTotal = bVec[0]/2.;
std::set<unsigned int> tmpSet;
tmpSet.insert(env.subId());
uqGslVectorClass ySamplesAll(dataSpaceAll.zeroVector());
ySamplesAll.subReadContents("input/dataPoints",
"m",
tmpSet);
unsigned int numCases = 5;
std::vector<unsigned int> ns(numCases,0);
ns[0] = 1;
ns[1] = 10;
ns[2] = 100;
ns[3] = 500;
ns[4] = 1000;
for (unsigned int caseId = 0; caseId < numCases; ++caseId) {
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> dataSpace(env, "data_", ns[caseId], NULL);
uqGslVectorClass ySamples(dataSpace.zeroVector());
for (unsigned int i = 0; i < ns[caseId]; ++i) {
ySamples[i] = ySamplesAll[i];
}
struct likelihoodDataStruct likelihoodData;
likelihoodData.bVec = &bVec;
likelihoodData.sigmaTotal = sigmaTotal;
likelihoodData.ySamples = &ySamples;
uqGenericScalarFunctionClass<uqGslVectorClass,uqGslMatrixClass>
likelihoodFunctionObj("like_",
*paramDomain,
likelihoodRoutine,
(void *) &likelihoodData,
true); // routine computes [ln(function)]
////////////////////////////////////////////////////////
// Step 4 of 5: Instantiate the inverse problem
////////////////////////////////////////////////////////
uqUniformVectorRVClass<uqGslVectorClass,uqGslMatrixClass> priorRv("prior_", *paramDomain);
uqGenericVectorRVClass<uqGslVectorClass,uqGslMatrixClass> postRv ("post_", paramSpace);
char prefixStr[16+1];
sprintf(prefixStr,"sip%d_",caseId+1);
uqStatisticalInverseProblemClass<uqGslVectorClass,uqGslMatrixClass> sip(prefixStr, NULL, priorRv, likelihoodFunctionObj, postRv);
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "In solveSip():"
<< "\n caseId = " << caseId
<< "\n prefixStr = " << prefixStr
<< "\n p = " << p
<< "\n bVec = " << bVec
<< "\n ns[caseId] = " << ns[caseId]
<< "\n sigmaTotal = " << sigmaTotal
<< "\n ySamples = " << ySamples
<< "\n useML = " << useML
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 5 of 5: Solve the inverse problem
////////////////////////////////////////////////////////
uqGslVectorClass initialValues(paramSpace.zeroVector());
initialValues[0] = 0.;
uqGslMatrixClass proposalCovMat(paramSpace.zeroVector());
proposalCovMat(0,0) = 1.;
if (useML) {
sip.solveWithBayesMLSampling();
}
else {
sip.solveWithBayesMetropolisHastings(NULL,initialValues,&proposalCovMat);
}
} // for caseId
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Leaving solveSip()"
<< std::endl;
}
return;
}
void compute(const QUESO::FullEnvironment& env) {
struct timeval timevalNow;
gettimeofday(&timevalNow, NULL);
std::cout << std::endl << "Beginning run of 'Hysteretic' example at "
<< ctime(&timevalNow.tv_sec);
//------------------------------------------------------
// Step 1 of 5: Instantiate the parameter space
//------------------------------------------------------
QUESO::VectorSpace<> paramSpaceA(env, "paramA_", 1, NULL);
QUESO::VectorSpace<> paramSpaceB(env, "paramB_", 14, NULL);
QUESO::VectorSpace<> paramSpace (env, "param_", 15, NULL);
//------------------------------------------------------
// Step 2 of 5: Instantiate the parameter domain
//------------------------------------------------------
QUESO::GslVector paramMinsA(paramSpaceA.zeroVector());
paramMinsA.cwSet(0);
QUESO::GslVector paramMaxsA(paramSpaceA.zeroVector());
paramMaxsA.cwSet(5);
QUESO::BoxSubset<> paramDomainA("paramA_",paramSpaceA,paramMinsA,paramMaxsA);
QUESO::GslVector paramMinsB(paramSpaceB.zeroVector());
paramMinsB.cwSet(-INFINITY);
QUESO::GslVector paramMaxsB(paramSpaceB.zeroVector());
paramMaxsB.cwSet( INFINITY);
QUESO::BoxSubset<> paramDomainB("paramB_",paramSpaceB,paramMinsB,paramMaxsB);
QUESO::ConcatenationSubset<> paramDomain("",paramSpace,paramDomainA,paramDomainB);
//------------------------------------------------------
// Step 3 of 5: Instantiate the likelihood function object
//------------------------------------------------------
std::cout << "\tInstantiating the Likelihood; calling internally the hysteretic model"
<< std::endl;
Likelihood<> likelihood("like_", paramDomain);
likelihood.floor.resize(4,NULL);
unsigned int numTimeSteps = 401;
for (unsigned int i = 0; i < 4; ++i) {
likelihood.floor[i] = new std::vector<double>(numTimeSteps,0.);
}
likelihood.accel.resize(numTimeSteps,0.);
FILE *inp;
inp = fopen("an.txt","r");
unsigned int numObservations = 0;
double tmpA;
while (fscanf(inp,"%lf",&tmpA) != EOF) {
likelihood.accel[numObservations] = tmpA;
numObservations++;
}
numObservations=1;
FILE *inp1_1;
inp1_1=fopen("measured_data1_1.txt","r");
while (fscanf(inp1_1,"%lf",&tmpA) != EOF) {
(*likelihood.floor[0])[numObservations]=tmpA;
numObservations++;
}
numObservations=0;
FILE *inp1_2;
inp1_2=fopen("measured_data1_2.txt","r");
while (fscanf(inp1_2,"%lf",&tmpA) != EOF) {
(*likelihood.floor[1])[numObservations]=tmpA;
numObservations++;
}
numObservations=0;
FILE *inp1_3;
inp1_3=fopen("measured_data1_3.txt","r");
while (fscanf(inp1_3,"%lf",&tmpA) != EOF) {
(*likelihood.floor[2])[numObservations]=tmpA;
numObservations++;
}
numObservations=0;
FILE *inp1_4;
inp1_4=fopen("measured_data1_4.txt","r");
while (fscanf(inp1_4,"%lf",&tmpA) != EOF) {
(*likelihood.floor[3])[numObservations]=tmpA;
numObservations++;
}
//------------------------------------------------------
// Step 4 of 5: Instantiate the inverse problem
//------------------------------------------------------
std::cout << "\tInstantiating the SIP" << std::endl;
QUESO::UniformVectorRV<> priorRvA("priorA_", paramDomainA);
QUESO::GslVector meanVec(paramSpaceB.zeroVector());
QUESO::GslVector diagVec(paramSpaceB.zeroVector());
diagVec.cwSet(0.6*0.6);
QUESO::GslMatrix covMatrix(diagVec);
QUESO::GaussianVectorRV<> priorRvB("priorB_", paramDomainB,meanVec,covMatrix);
QUESO::ConcatenatedVectorRV<> priorRv("prior_", priorRvA, priorRvB, paramDomain);
QUESO::GenericVectorRV<> postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<> ip("", NULL, priorRv, likelihood, postRv);
//------------------------------------------------------
// Step 5 of 5: Solve the inverse problem
//------------------------------------------------------
std::cout << "\tSolving the SIP with Multilevel method" << std::endl;
ip.solveWithBayesMLSampling();
gettimeofday(&timevalNow, NULL);
std::cout << "Ending run of 'Hysteretic' example at "
<< ctime(&timevalNow.tv_sec) << std::endl;
return;
}
void solveSip(const uqFullEnvironmentClass& env, bool useML)
{
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Entering solveSip()..."
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 1 of 5: Instantiate the parameter space
////////////////////////////////////////////////////////
unsigned int p = 1;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> paramSpace(env, "param_", p, NULL);
uqGslVectorClass aVec(paramSpace.zeroVector());
aVec[0] = 126831.7;
uqGslVectorClass bVec(paramSpace.zeroVector());
bVec[0] = 112136.1;
////////////////////////////////////////////////////////
// Step 2 of 5: Instantiate the parameter domain
////////////////////////////////////////////////////////
//uqGslVectorClass paramMins (paramSpace.zeroVector());
//uqGslVectorClass paramMaxs (paramSpace.zeroVector());
//paramMins [0] = -1.e+16;
//paramMaxs [0] = 1.e+16;
//paramMins [1] = -1.e+16;
//paramMaxs [1] = 1.e+16;
//uqBoxSubsetClass<uqGslVectorClass,uqGslMatrixClass> paramDomain("param_",paramSpace,paramMins,paramMaxs);
uqVectorSetClass<uqGslVectorClass,uqGslMatrixClass>* paramDomain = ¶mSpace;
////////////////////////////////////////////////////////
// Step 3 of 5: Instantiate the likelihood function object
////////////////////////////////////////////////////////
unsigned int n = 400;
uqVectorSpaceClass<uqGslVectorClass,uqGslMatrixClass> dataSpace(env, "data_", n, NULL);
double sigmaTotal = 4229.55;
std::set<unsigned int> tmpSet;
tmpSet.insert(env.subId());
uqGslVectorClass ySamples(dataSpace.zeroVector());
ySamples.subReadContents("input/dataPoints",
"m",
tmpSet);
struct likelihoodDataStruct likelihoodData;
likelihoodData.aVec = &aVec;
likelihoodData.bVec = &bVec;
likelihoodData.sigmaTotal = sigmaTotal;
likelihoodData.ySamples = &ySamples;
uqGenericScalarFunctionClass<uqGslVectorClass,uqGslMatrixClass>
likelihoodFunctionObj("like_",
*paramDomain,
likelihoodRoutine,
(void *) &likelihoodData,
true); // routine computes [ln(function)]
////////////////////////////////////////////////////////
// Step 4 of 5: Instantiate the inverse problem
////////////////////////////////////////////////////////
uqUniformVectorRVClass<uqGslVectorClass,uqGslMatrixClass> priorRv("prior_", *paramDomain);
uqGenericVectorRVClass<uqGslVectorClass,uqGslMatrixClass> postRv ("post_", paramSpace);
uqStatisticalInverseProblemClass<uqGslVectorClass,uqGslMatrixClass> sip("sip_", NULL, priorRv, likelihoodFunctionObj, postRv);
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "In solveSip():"
<< "\n p = " << p
<< "\n aVec = " << aVec
<< "\n bVec = " << bVec
<< "\n n = " << n
<< "\n sigmaTotal = " << sigmaTotal
<< "\n ySamples = " << ySamples
<< "\n useML = " << useML
<< std::endl;
}
////////////////////////////////////////////////////////
// Step 5 of 5: Solve the inverse problem
////////////////////////////////////////////////////////
uqGslVectorClass initialValues(paramSpace.zeroVector());
initialValues[0] = 0.;
uqGslMatrixClass proposalCovMat(paramSpace.zeroVector());
proposalCovMat(0,0) = 1.;
if (useML) {
sip.solveWithBayesMLSampling();
}
else {
sip.solveWithBayesMetropolisHastings(NULL,initialValues,&proposalCovMat);
}
if ((env.subDisplayFile()) && (env.displayVerbosity() >= 2)) {
*env.subDisplayFile() << "Leaving solveSip()"
<< std::endl;
}
return;
}
void infer_slope(const QUESO::FullEnvironment & env) {
// Statistical Inverse Problem: Compute posterior pdf for slope 'm' and y-intercept c
// Step 1: Instantiate the parameter space
QUESO::VectorSpace<> paramSpace(env, "param_", 2, NULL); // 2 since we have a 2D problem
// Step 2: Parameter domain
QUESO::GslVector paramMinValues(paramSpace.zeroVector());
QUESO::GslVector paramMaxValues(paramSpace.zeroVector());
paramMinValues[0] = 2.;
paramMaxValues[0] = 5.;
paramMinValues[1] = 3.;
paramMaxValues[1] = 7.;
QUESO::BoxSubset<> paramDomain("param_", paramSpace, paramMinValues, paramMaxValues);
// Step 3: Instantiate likelihood
Likelihood<> lhood("like_", paramDomain);
// Step 4: Define the prior RV
QUESO::UniformVectorRV<> priorRv("prior_", paramDomain);
// Step 5: Instantiate the inverse problem
QUESO::GenericVectorRV<> postRv("post_", paramSpace);
QUESO::StatisticalInverseProblem<> ip("", NULL, priorRv, lhood, postRv);
// Step 6: Solve the inverse problem
// Randomly sample for the initial state?
QUESO::GslVector paramInitials(paramSpace.zeroVector());
priorRv.realizer().realization(paramInitials);
// Initialize the Cov matrix:
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0,0) = std::pow(std::abs(paramInitials[0]) / 20.0, 2.0);
proposalCovMatrix(1,1) = std::pow(std::abs(paramInitials[1]) / 20.0, 2.0);
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
// Using the posterior pdfs for m and c, compute 'y' at a given 'x'
// Step 1: Instantiate the qoi space
QUESO::VectorSpace<> qoiSpace(env, "qoi_", 1, NULL);
// Step 2: Instantiate the parameter domain
// Not necessary here because the posterior from SIP is used as the RV for SFP
// Step 3: Instantiate the qoi object to be used by QUESO
Qoi<> qoi("qoi_", paramDomain, qoiSpace);
// Step 4: Define the input RV
// Not required because we use the posterior as RV
// Step 5: Instantiate the forward problem
QUESO::GenericVectorRV<> qoiRv("qoi_", qoiSpace);
QUESO::StatisticalForwardProblem<> fp("", NULL, postRv, qoi, qoiRv);
// Step 6: Solve the forward problem
std::cout << "Solving the SFP with Monte Carlo" << std::endl << std::endl;
fp.solveWithMonteCarlo(NULL);
system("mv outputData/sfp_lineSlope_qoi_seq.txt outputData/sfp_lineSlope_qoi_seq_post.txt");
// SENSITIVITY ANALYSIS
// For m
Qoi_m<> qoi_m("qoi_", paramDomain, qoiSpace);
// Step 4: Define the input RV
// Not required because we use the prior as RV for sensitivity analysis
// Step 5: Instantiate the forward problem
QUESO::StatisticalForwardProblem<> fp_m("", NULL, priorRv, qoi_m, qoiRv);
// Step 6: Solve the forward problem
fp_m.solveWithMonteCarlo(NULL);
system("mv outputData/sfp_lineSlope_qoi_seq.txt outputData/sense_m.txt");
// For c
Qoi_c<> qoi_c("qoi_", paramDomain, qoiSpace);
// Step 4: Define the input RV
// Not required because we use the prior as RV for sensitivity analysis
// Step 5: Instantiate the forward problem
QUESO::StatisticalForwardProblem<> fp_c("", NULL, priorRv, qoi_c, qoiRv);
// Step 6: Solve the forward problem
fp_c.solveWithMonteCarlo(NULL);
system("mv outputData/sfp_lineSlope_qoi_seq.txt outputData/sense_c.txt");
// For both, m and c
Qoi_mc<> qoi_mc("qoi_", paramDomain, qoiSpace);
// Step 4: Define the input RV
// Not required because we use the prior as RV for sensitivity analysis
// Step 5: Instantiate the forward problem
QUESO::StatisticalForwardProblem<> fp_mc("", NULL, priorRv, qoi_mc, qoiRv);
// Step 6: Solve the forward problem
fp_mc.solveWithMonteCarlo(NULL);
system("mv outputData/sfp_lineSlope_qoi_seq.txt outputData/sense_mc.txt");
}
int main(int argc, char* argv[])
{
#ifndef QUESO_HAS_MPI
// Skip this test if we're not in parallel
return 77;
#else
MPI_Init(&argc, &argv);
std::string inputFileName = argv[1];
const char * test_srcdir = std::getenv("srcdir");
if (test_srcdir)
inputFileName = test_srcdir + ('/' + inputFileName);
// Initialize QUESO environment
QUESO::FullEnvironment env(MPI_COMM_WORLD, inputFileName, "", NULL);
//================================================================
// Statistical inverse problem (SIP): find posterior PDF for 'g'
//================================================================
//------------------------------------------------------
// SIP Step 1 of 6: Instantiate the parameter space
//------------------------------------------------------
QUESO::VectorSpace<> paramSpace(env, "param_", 1, NULL);
//------------------------------------------------------
// SIP Step 2 of 6: Instantiate the parameter domain
//------------------------------------------------------
QUESO::GslVector paramMinValues(paramSpace.zeroVector());
QUESO::GslVector paramMaxValues(paramSpace.zeroVector());
paramMinValues[0] = 8.;
paramMaxValues[0] = 11.;
QUESO::BoxSubset<> paramDomain("param_", paramSpace, paramMinValues,
paramMaxValues);
//------------------------------------------------------
// SIP Step 3 of 6: Instantiate the likelihood function
// object to be used by QUESO.
//------------------------------------------------------
Likelihood<> lhood("like_", paramDomain);
//------------------------------------------------------
// SIP Step 4 of 6: Define the prior RV
//------------------------------------------------------
QUESO::UniformVectorRV<> priorRv("prior_", paramDomain);
//------------------------------------------------------
// SIP Step 5 of 6: Instantiate the inverse problem
//------------------------------------------------------
// Extra prefix before the default "rv_" prefix
QUESO::GenericVectorRV<> postRv("post_", paramSpace);
// No extra prefix before the default "ip_" prefix
QUESO::StatisticalInverseProblem<> ip("", NULL, priorRv, lhood, postRv);
//------------------------------------------------------
// SIP Step 6 of 6: Solve the inverse problem, that is,
// set the 'pdf' and the 'realizer' of the posterior RV
//------------------------------------------------------
QUESO::GslVector paramInitials(paramSpace.zeroVector());
priorRv.realizer().realization(paramInitials);
QUESO::GslMatrix proposalCovMatrix(paramSpace.zeroVector());
proposalCovMatrix(0,0) = std::pow(std::abs(paramInitials[0]) / 20.0, 2.0);
ip.solveWithBayesMetropolisHastings(NULL, paramInitials, &proposalCovMatrix);
//================================================================
// Statistical forward problem (SFP): find the max distance
// traveled by an object in projectile motion; input pdf for 'g'
// is the solution of the SIP above.
//================================================================
//------------------------------------------------------
// SFP Step 1 of 6: Instantiate the parameter *and* qoi spaces.
// SFP input RV = FIP posterior RV, so SFP parameter space
// has been already defined.
//------------------------------------------------------
QUESO::VectorSpace<> qoiSpace(env, "qoi_", 1, NULL);
//------------------------------------------------------
// SFP Step 2 of 6: Instantiate the parameter domain
//------------------------------------------------------
// Not necessary because input RV of the SFP = output RV of SIP.
// Thus, the parameter domain has been already defined.
//------------------------------------------------------
// SFP Step 3 of 6: Instantiate the qoi object
// to be used by QUESO.
//------------------------------------------------------
Qoi<> qoi("qoi_", paramDomain, qoiSpace);
//------------------------------------------------------
// SFP Step 4 of 6: Define the input RV
//------------------------------------------------------
// Not necessary because input RV of SFP = output RV of SIP
// (postRv).
//------------------------------------------------------
// SFP Step 5 of 6: Instantiate the forward problem
//------------------------------------------------------
QUESO::GenericVectorRV<> qoiRv("qoi_", qoiSpace);
QUESO::StatisticalForwardProblem<> fp("", NULL, postRv, qoi, qoiRv);
//------------------------------------------------------
// SFP Step 6 of 6: Solve the forward problem
//------------------------------------------------------
fp.solveWithMonteCarlo(NULL);
MPI_Finalize();
return 0;
#endif // QUESO_HAS_MPI
}
