/// Create a submatrix. A submatrix is a view into the parent matrix.
/// Lifetime of a submatrix cannot exceed the lifetime of the parent.
/// @param M :: The parent matrix.
/// @param row :: The first row in the submatrix.
/// @param col :: The first column in the submatrix.
/// @param nRows :: The number of rows in the submatrix.
/// @param nCols :: The number of columns in the submatrix.
GSLMatrix::GSLMatrix(const GSLMatrix &M, size_t row, size_t col, size_t nRows,
size_t nCols) {
if (row + nRows > M.size1() || col + nCols > M.size2()) {
throw std::runtime_error("Submatrix exceeds matrix size.");
}
auto view = gsl_matrix_const_submatrix(M.gsl(), row, col, nRows, nCols);
m_matrix = gsl_matrix_alloc(nRows, nCols);
gsl_matrix_memcpy(m_matrix, &view.matrix);
}
/// Calculate the eigensystem of a symmetric matrix
/// @param eigenValues :: Output variable that receives the eigenvalues of this
/// matrix.
/// @param eigenVectors :: Output variable that receives the eigenvectors of
/// this matrix.
void GSLMatrix::eigenSystem(GSLVector &eigenValues, GSLMatrix &eigenVectors) {
size_t n = size1();
if (n != size2()) {
throw std::runtime_error("Matrix eigenSystem: the matrix must be square.");
}
eigenValues.resize(n);
eigenVectors.resize(n, n);
auto workspace = gsl_eigen_symmv_alloc(n);
gsl_eigen_symmv(gsl(), eigenValues.gsl(), eigenVectors.gsl(), workspace);
gsl_eigen_symmv_free(workspace);
}
/**
* Calculates covariance matrix for fitting function's active parameters.
*/
void CostFuncFitting::calActiveCovarianceMatrix(GSLMatrix &covar,
double epsrel) {
// construct the jacobian
GSLJacobian J(m_function, m_values->size());
size_t na = this->nParams(); // number of active parameters
assert(J.getJ()->size2 == na);
covar.resize(na, na);
// calculate the derivatives
m_function->functionDeriv(*m_domain, J);
// let the GSL to compute the covariance matrix
gsl_multifit_covar(J.getJ(), epsrel, covar.gsl());
}
/**
* Calculates covariance matrix for fitting function's active parameters.
* @param covar :: Output cavariance matrix.
* @param epsrel :: Tolerance.
*/
void CostFuncLeastSquares::calActiveCovarianceMatrix(GSLMatrix& covar, double epsrel)
{
UNUSED_ARG(epsrel);
if (m_hessian.isEmpty())
{
valDerivHessian();
}
covar = m_hessian;
covar.invert();
}
/**
* Calculate the transformation matrix T by numeric differentiation
* @param tm :: The output transformation matrix.
*/
void CostFuncFitting::calTransformationMatrixNumerically(GSLMatrix &tm) {
const double epsilon = std::numeric_limits<double>::epsilon() * 100;
size_t np = m_function->nParams();
size_t na = nParams();
tm.resize(na, na);
size_t ia = 0;
for (size_t i = 0; i < np; ++i) {
if (m_function->isFixed(i))
continue;
double p0 = m_function->getParameter(i);
for (size_t j = 0; j < na; ++j) {
double ap = getParameter(j);
double step = ap == 0.0 ? epsilon : ap * epsilon;
setParameter(j, ap + step);
tm.set(ia, j, (m_function->getParameter(i) - p0) / step);
setParameter(j, ap);
}
++ia;
}
}
/**
* Calculates covariance matrix for fitting function's active parameters.
* @param covar :: Output cavariance matrix.
* @param epsrel :: Tolerance.
*/
void CostFuncLeastSquares::calActiveCovarianceMatrix(GSLMatrix &covar,
double epsrel) {
UNUSED_ARG(epsrel);
if (m_hessian.isEmpty()) {
valDerivHessian();
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
std::ostringstream osHess;
osHess << "== Hessian (H) ==\n";
osHess << std::left << std::fixed;
for (size_t i = 0; i < m_hessian.size1(); ++i) {
for (size_t j = 0; j < m_hessian.size2(); ++j) {
osHess << std::setw(10);
osHess << m_hessian.get(i, j) << " ";
}
osHess << "\n";
}
g_log.debug() << osHess.str();
}
covar = m_hessian;
covar.invert();
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
std::ostringstream osCovar;
osCovar << "== Covariance matrix (H^-1) ==\n";
osCovar << std::left << std::fixed;
for (size_t i = 0; i < covar.size1(); ++i) {
for (size_t j = 0; j < covar.size2(); ++j) {
osCovar << std::setw(10);
osCovar << covar.get(i, j) << " ";
}
osCovar << "\n";
}
g_log.debug() << osCovar.str();
}
}
/**
* Calculate the fitting errors and assign them to the fitting function.
* @param covar :: A covariance matrix to use for error calculations.
* It can be calculated with calCovarianceMatrix().
* @param chi2 :: The final chi-squared of the fit.
*/
void CostFuncFitting::calFittingErrors(const GSLMatrix &covar, double chi2) {
size_t np = m_function->nParams();
auto covarMatrix = boost::shared_ptr<Kernel::Matrix<double>>(
new Kernel::Matrix<double>(np, np));
size_t ia = 0;
for (size_t i = 0; i < np; ++i) {
if (m_function->isFixed(i)) {
m_function->setError(i, 0);
} else {
size_t ja = 0;
for (size_t j = 0; j < np; ++j) {
if (!m_function->isFixed(j)) {
(*covarMatrix)[i][j] = covar.get(ia, ja);
++ja;
}
}
double err = sqrt(covar.get(ia, ia));
m_function->setError(i, err);
++ia;
}
}
m_function->setCovarianceMatrix(covarMatrix);
m_function->setChiSquared(chi2);
}
/**
* Calculate the fitting errors and assign them to the fitting function.
* @param covar :: A covariance matrix to use for error calculations.
* It can be calculated with calCovarianceMatrix().
*/
void CostFuncFitting::calFittingErrors(const GSLMatrix& covar)
{
size_t np = m_function->nParams();
size_t ia = 0;
for(size_t i = 0; i < np; ++i)
{
if (m_function->isFixed(i))
{
m_function->setError(i,0);
}
else
{
double err = sqrt(covar.get(ia,ia));
m_function->setError(i,err);
++ia;
}
}
}
/** Executes the algorithm
*
* @throw runtime_error Thrown if algorithm cannot execute
*/
void Fit::execConcrete() {
std::string ties = getPropertyValue("Ties");
if (!ties.empty()) {
m_function->addTies(ties);
}
std::string contstraints = getPropertyValue("Constraints");
if (!contstraints.empty()) {
m_function->addConstraints(contstraints);
}
// prepare the function for a fit
m_function->setUpForFit();
API::FunctionDomain_sptr domain;
API::FunctionValues_sptr values;
m_domainCreator->createDomain(domain, values);
// do something with the function which may depend on workspace
m_domainCreator->initFunction(m_function);
// get the minimizer
std::string minimizerName = getPropertyValue("Minimizer");
API::IFuncMinimizer_sptr minimizer =
API::FuncMinimizerFactory::Instance().createMinimizer(minimizerName);
// Try to retrieve optional properties
int intMaxIterations = getProperty("MaxIterations");
const size_t maxIterations = static_cast<size_t>(intMaxIterations);
// get the cost function which must be a CostFuncFitting
boost::shared_ptr<CostFuncFitting> costFunc =
boost::dynamic_pointer_cast<CostFuncFitting>(
API::CostFunctionFactory::Instance().create(
getPropertyValue("CostFunction")));
costFunc->setFittingFunction(m_function, domain, values);
minimizer->initialize(costFunc, maxIterations);
const int64_t nsteps = maxIterations * m_function->estimateNoProgressCalls();
API::Progress prog(this, 0.0, 1.0, nsteps);
m_function->setProgressReporter(&prog);
// do the fitting until success or iteration limit is reached
size_t iter = 0;
bool success = false;
std::string errorString;
g_log.debug("Starting minimizer iteration\n");
while (iter < maxIterations) {
g_log.debug() << "Starting iteration " << iter << "\n";
m_function->iterationStarting();
if (!minimizer->iterate(iter)) {
errorString = minimizer->getError();
g_log.debug() << "Iteration stopped. Minimizer status string="
<< errorString << "\n";
success = errorString.empty() || errorString == "success";
if (success) {
errorString = "success";
}
break;
}
prog.report();
m_function->iterationFinished();
++iter;
}
g_log.debug() << "Number of minimizer iterations=" << iter << "\n";
minimizer->finalize();
if (iter >= maxIterations) {
if (!errorString.empty()) {
errorString += '\n';
}
errorString += "Failed to converge after " +
boost::lexical_cast<std::string>(maxIterations) +
" iterations.";
}
// return the status flag
setPropertyValue("OutputStatus", errorString);
// degrees of freedom
size_t dof = domain->size() - costFunc->nParams();
if (dof == 0)
dof = 1;
double rawcostfuncval = minimizer->costFunctionVal();
double finalCostFuncVal = rawcostfuncval / double(dof);
setProperty("OutputChi2overDoF", finalCostFuncVal);
// fit ended, creating output
// get the workspace
API::Workspace_const_sptr ws = getProperty("InputWorkspace");
bool doCreateOutput = getProperty("CreateOutput");
std::string baseName = getPropertyValue("Output");
if (!baseName.empty()) {
doCreateOutput = true;
}
bool doCalcErrors = getProperty("CalcErrors");
if (doCreateOutput) {
doCalcErrors = true;
}
if (costFunc->nParams() == 0) {
doCalcErrors = false;
}
GSLMatrix covar;
if (doCalcErrors) {
// Calculate the covariance matrix and the errors.
costFunc->calCovarianceMatrix(covar);
costFunc->calFittingErrors(covar, rawcostfuncval);
}
if (doCreateOutput) {
copyMinimizerOutput(*minimizer);
if (baseName.empty()) {
baseName = ws->name();
if (baseName.empty()) {
baseName = "Output";
}
}
baseName += "_";
declareProperty(
new API::WorkspaceProperty<API::ITableWorkspace>(
"OutputNormalisedCovarianceMatrix", "", Kernel::Direction::Output),
"The name of the TableWorkspace in which to store the final covariance "
"matrix");
setPropertyValue("OutputNormalisedCovarianceMatrix",
baseName + "NormalisedCovarianceMatrix");
Mantid::API::ITableWorkspace_sptr covariance =
Mantid::API::WorkspaceFactory::Instance().createTable("TableWorkspace");
covariance->addColumn("str", "Name");
// set plot type to Label = 6
covariance->getColumn(covariance->columnCount() - 1)->setPlotType(6);
// std::vector<std::string> paramThatAreFitted; // used for populating 1st
// "name" column
for (size_t i = 0; i < m_function->nParams(); i++) {
if (m_function->isActive(i)) {
covariance->addColumn("double", m_function->parameterName(i));
// paramThatAreFitted.push_back(m_function->parameterName(i));
}
}
size_t np = m_function->nParams();
size_t ia = 0;
for (size_t i = 0; i < np; i++) {
if (m_function->isFixed(i))
continue;
Mantid::API::TableRow row = covariance->appendRow();
row << m_function->parameterName(i);
size_t ja = 0;
for (size_t j = 0; j < np; j++) {
if (m_function->isFixed(j))
continue;
if (j == i)
row << 100.0;
else {
if (!covar.gsl()) {
throw std::runtime_error(
"There was an error while allocating the (GSL) covariance "
"matrix "
"which is needed to produce fitting error results.");
}
row << 100.0 * covar.get(ia, ja) /
sqrt(covar.get(ia, ia) * covar.get(ja, ja));
}
++ja;
}
++ia;
}
setProperty("OutputNormalisedCovarianceMatrix", covariance);
// create output parameter table workspace to store final fit parameters
// including error estimates if derivative of fitting function defined
declareProperty(new API::WorkspaceProperty<API::ITableWorkspace>(
"OutputParameters", "", Kernel::Direction::Output),
"The name of the TableWorkspace in which to store the "
"final fit parameters");
setPropertyValue("OutputParameters", baseName + "Parameters");
Mantid::API::ITableWorkspace_sptr result =
Mantid::API::WorkspaceFactory::Instance().createTable("TableWorkspace");
result->addColumn("str", "Name");
// set plot type to Label = 6
result->getColumn(result->columnCount() - 1)->setPlotType(6);
result->addColumn("double", "Value");
result->addColumn("double", "Error");
// yErr = 5
result->getColumn(result->columnCount() - 1)->setPlotType(5);
for (size_t i = 0; i < m_function->nParams(); i++) {
Mantid::API::TableRow row = result->appendRow();
row << m_function->parameterName(i) << m_function->getParameter(i)
<< m_function->getError(i);
}
// Add chi-squared value at the end of parameter table
Mantid::API::TableRow row = result->appendRow();
#if 1
std::string costfuncname = getPropertyValue("CostFunction");
if (costfuncname == "Rwp")
row << "Cost function value" << rawcostfuncval;
else
row << "Cost function value" << finalCostFuncVal;
setProperty("OutputParameters", result);
#else
row << "Cost function value" << finalCostFuncVal;
Mantid::API::TableRow row2 = result->appendRow();
std::string name(getPropertyValue("CostFunction"));
name += " value";
row2 << name << rawcostfuncval;
#endif
setProperty("OutputParameters", result);
bool outputParametersOnly = getProperty("OutputParametersOnly");
if (!outputParametersOnly) {
const bool unrollComposites = getProperty("OutputCompositeMembers");
bool convolveMembers = existsProperty("ConvolveMembers");
if (convolveMembers) {
convolveMembers = getProperty("ConvolveMembers");
}
m_domainCreator->separateCompositeMembersInOutput(unrollComposites,
convolveMembers);
m_domainCreator->createOutputWorkspace(baseName, m_function, domain,
values);
}
}
progress(1.0);
}
/// Copy constructor
/// @param M :: The other matrix.
GSLMatrix::GSLMatrix(const GSLMatrix &M)
: m_data(M.m_data),
m_view(gsl_matrix_view_array(m_data.data(), M.size1(), M.size2())) {}
/// Execute algorithm.
void Schrodinger1D::exec()
{
double startX = get("StartX");
double endX = get("EndX");
if (endX <= startX)
{
throw std::invalid_argument("StartX must be <= EndX");
}
IFunction_sptr VPot = getClass("VPot");
chebfun vpot( 0, startX, endX );
vpot.bestFit( *VPot );
size_t nBasis = vpot.n() + 1;
std::cerr << "n=" << nBasis << std::endl;
//if (n < 3)
{
nBasis = 200;
vpot.resize( nBasis );
}
const double beta = get("Beta");
auto kinet = new ChebCompositeOperator;
kinet->addRight( new ChebTimes(-beta) );
kinet->addRight( new ChebDiff2 );
auto hamiltonian = new ChebPlus;
hamiltonian->add('+', kinet );
hamiltonian->add('+', new ChebTimes(VPot) );
GSLMatrix L;
hamiltonian->createMatrix( vpot.getBase(), L );
GSLVector d;
GSLMatrix v;
L.diag( d, v );
std::vector<double> norms = vpot.baseNorm();
assert(norms.size() == L.size1());
assert(norms.size() == L.size2());
for(size_t i = 0; i < norms.size(); ++i)
{
double factor = 1.0 / norms[i];
for(size_t j = i; j < norms.size(); ++j)
{
v.multiplyBy(i,j,factor);
}
}
// eigenvectors orthogonality check
// GSLMatrix v1 = v;
// GSLMatrix tst;
// tst = Tr(v1) * v;
// std::cerr << tst << std::endl;
std::vector<size_t> indx(L.size1());
getSortedIndex( d, indx );
auto eigenvalues = API::TableWorkspace_ptr(dynamic_cast<API::TableWorkspace*>(
API::WorkspaceFactory::instance().create("TableWorkspace"))
);
eigenvalues->setRowCount(nBasis);
setProperty("Eigenvalues", eigenvalues);
eigenvalues->addColumn("double","N");
auto nColumn = static_cast<API::TableColumn<double>*>(eigenvalues->getColumn("N").get());
nColumn->asNumeric()->setPlotRole(API::NumericColumn::X);
auto& nc = nColumn->data();
eigenvalues->addDoubleColumn("Energy");
auto eColumn = static_cast<API::TableColumn<double>*>(eigenvalues->getColumn("Energy").get());
eColumn->asNumeric()->setPlotRole(API::NumericColumn::Y);
auto& ec = eigenvalues->getDoubleData("Energy");
boost::scoped_ptr<ChebfunVector> eigenvectors(new ChebfunVector);
chebfun fun0(nBasis,startX,endX);
ChebFunction_sptr theSum(new ChebFunction(fun0));
// collect indices of spurious eigenvalues to move them to the back
std::vector<size_t> spurious;
// index for good eigenvalues
size_t n = 0;
for(size_t j = 0; j < nBasis; ++j)
{
size_t i = indx[j];
chebfun fun(fun0);
fun.setP(v,i);
// check eigenvalues for spurious ones
chebfun dfun(fun);
dfun.square();
double norm = dfun.integr();
// I am not sure that it's a solid condition
if ( norm < 0.999999 )
{
// bad eigenvalue
spurious.push_back(j);
}
else
{
nc[n] = double(n);
ec[n] = d[i];
eigenvectors->add(ChebFunction_sptr(new ChebFunction(fun)));
// test sum of functions squares
*theSum += dfun;
// chebfun dfun(fun);
// hamiltonian->apply(fun,dfun);
// dfun *= fun;
// std::cerr << "ener["<<n<<"]=" << ec[n] << ' ' << norm << ' ' << dfun.integr() << std::endl;
++n;
}
}
GSLVector eigv;
ChebfunVector *eigf = NULL;
improve(hamiltonian, eigenvectors.get(), eigv, &eigf);
eigenvalues->setRowCount( eigv.size() );
for(size_t i = 0; i < eigv.size(); ++i)
{
nc[i] = double(i);
ec[i] = eigv[i];
}
eigf->add(theSum);
setProperty("Eigenvectors",ChebfunVector_sptr(eigf));
//makeQuadrature(eigf);
}
//----------------------------------------------------------------------------------------------
/// Examine the chi squared as a function of fitting parameters and estimate
/// errors for each parameter.
void CalculateChiSquared::estimateErrors() {
// Number of fiting parameters
auto nParams = m_function->nParams();
// Create an output table for displaying slices of the chi squared and
// the probabilitydensity function
auto pdfTable = API::WorkspaceFactory::Instance().createTable();
std::string baseName = getProperty("Output");
if (baseName.empty()) {
baseName = "CalculateChiSquared";
}
declareProperty(new API::WorkspaceProperty<API::ITableWorkspace>(
"PDFs", "", Kernel::Direction::Output),
"The name of the TableWorkspace in which to store the "
"pdfs of fit parameters");
setPropertyValue("PDFs", baseName + "_pdf");
setProperty("PDFs", pdfTable);
// Create an output table for displaying the parameter errors.
auto errorsTable = API::WorkspaceFactory::Instance().createTable();
auto nameColumn = errorsTable->addColumn("str", "Parameter");
auto valueColumn = errorsTable->addColumn("double", "Value");
auto minValueColumn = errorsTable->addColumn("double", "Value at Min");
auto leftErrColumn = errorsTable->addColumn("double", "Left Error");
auto rightErrColumn = errorsTable->addColumn("double", "Right Error");
auto quadraticErrColumn = errorsTable->addColumn("double", "Quadratic Error");
auto chiMinColumn = errorsTable->addColumn("double", "Chi2 Min");
errorsTable->setRowCount(nParams);
declareProperty(new API::WorkspaceProperty<API::ITableWorkspace>(
"Errors", "", Kernel::Direction::Output),
"The name of the TableWorkspace in which to store the "
"values and errors of fit parameters");
setPropertyValue("Errors", baseName + "_errors");
setProperty("Errors", errorsTable);
// Calculate initial values
double chiSquared = 0.0;
double chiSquaredWeighted = 0.0;
double dof = 0;
API::FunctionDomain_sptr domain;
API::FunctionValues_sptr values;
m_domainCreator->createDomain(domain, values);
calcChiSquared(*m_function, nParams, *domain, *values, chiSquared,
chiSquaredWeighted, dof);
// Value of chi squared for current parameters in m_function
double chi0 = chiSquared;
// Fit data variance
double sigma2 = chiSquared / dof;
bool useWeighted = getProperty("Weighted");
if (useWeighted) {
chi0 = chiSquaredWeighted;
sigma2 = 0.0;
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "chi0=" << chi0 << std::endl;
g_log.debug() << "sigma2=" << sigma2 << std::endl;
g_log.debug() << "dof=" << dof << std::endl;
}
// Parameter bounds that define a volume in the parameter
// space within which the chi squared is being examined.
GSLVector lBounds(nParams);
GSLVector rBounds(nParams);
// Number of points in lines for plotting
size_t n = 100;
pdfTable->setRowCount(n);
const double fac = 1e-4;
// Loop over each parameter
for (size_t ip = 0; ip < nParams; ++ip) {
// Add columns for the parameter to the pdf table.
auto parName = m_function->parameterName(ip);
nameColumn->read(ip, parName);
// Parameter values
auto col1 = pdfTable->addColumn("double", parName);
col1->setPlotType(1);
// Chi squared values
auto col2 = pdfTable->addColumn("double", parName + "_chi2");
col2->setPlotType(2);
// PDF values
auto col3 = pdfTable->addColumn("double", parName + "_pdf");
col3->setPlotType(2);
double par0 = m_function->getParameter(ip);
double shift = fabs(par0 * fac);
if (shift == 0.0) {
shift = fac;
}
// Make a slice along this parameter
GSLVector dir(nParams);
dir.zero();
dir[ip] = 1.0;
ChiSlice slice(*m_function, dir, *domain, *values, chi0, sigma2);
// Find the bounds withn which the PDF is significantly above zero.
// The bounds are defined relative to par0:
// par0 + lBound is the lowest value of the parameter (lBound <= 0)
// par0 + rBound is the highest value of the parameter (rBound >= 0)
double lBound = slice.findBound(-shift);
double rBound = slice.findBound(shift);
lBounds[ip] = lBound;
rBounds[ip] = rBound;
// Approximate the slice with a polynomial.
// P is a vector of values of the polynomial at special points.
// A is a vector of Chebyshev expansion coefficients.
// The polynomial is defined on interval [lBound, rBound]
// The value of the polynomial at 0 == chi squared at par0
std::vector<double> P, A;
bool ok = true;
auto base = slice.makeApprox(lBound, rBound, P, A, ok);
if (!ok) {
g_log.warning() << "Approximation failed for parameter " << ip << std::endl;
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "Parameter " << ip << std::endl;
g_log.debug() << "Slice approximated by polynomial of order "
<< base->size() - 1;
g_log.debug() << " between " << lBound << " and " << rBound << std::endl;
}
// Write n slice points into the output table.
double dp = (rBound - lBound) / static_cast<double>(n);
for (size_t i = 0; i < n; ++i) {
double par = lBound + dp * static_cast<double>(i);
double chi = base->eval(par, P);
col1->fromDouble(i, par0 + par);
col2->fromDouble(i, chi);
}
// Check if par0 is a minimum point of the chi squared
std::vector<double> AD;
// Calculate the derivative polynomial.
// AD are the Chebyshev expansion of the derivative.
base->derivative(A, AD);
// Find the roots of the derivative polynomial
std::vector<double> minima = base->roots(AD);
if (minima.empty()) {
minima.push_back(par0);
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "Minima: ";
}
// If only 1 extremum is found assume (without checking) that it's a
// minimum.
// If there are more than 1, find the one with the smallest chi^2.
double chiMin = std::numeric_limits<double>::max();
double parMin = par0;
for (size_t i = 0; i < minima.size(); ++i) {
double value = base->eval(minima[i], P);
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << minima[i] << " (" << value << ") ";
}
if (value < chiMin) {
chiMin = value;
parMin = minima[i];
}
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << std::endl;
g_log.debug() << "Smallest minimum at " << parMin << " is " << chiMin
<< std::endl;
}
// Points of intersections with line chi^2 = 1/2 give an estimate of
// the standard deviation of this parameter if it's uncorrelated with the
// others.
A[0] -= 0.5; // Now A are the coefficients of the original polynomial
// shifted down by 1/2.
std::vector<double> roots = base->roots(A);
std::sort(roots.begin(), roots.end());
if (roots.empty()) {
// Something went wrong; use the whole interval.
roots.resize(2);
roots[0] = lBound;
roots[1] = rBound;
} else if (roots.size() == 1) {
// Only one root found; use a bound for the other root.
if (roots.front() < 0) {
roots.push_back(rBound);
} else {
roots.insert(roots.begin(), lBound);
}
} else if (roots.size() > 2) {
// More than 2 roots; use the smallest and the biggest
auto smallest = roots.front();
auto biggest = roots.back();
roots.resize(2);
roots[0] = smallest;
roots[1] = biggest;
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "Roots: ";
for (size_t i = 0; i < roots.size(); ++i) {
g_log.debug() << roots[i] << ' ';
}
g_log.debug() << std::endl;
}
// Output parameter info to the table.
valueColumn->fromDouble(ip, par0);
minValueColumn->fromDouble(ip, par0 + parMin);
leftErrColumn->fromDouble(ip, roots[0] - parMin);
rightErrColumn->fromDouble(ip, roots[1] - parMin);
chiMinColumn->fromDouble(ip, chiMin);
// Output the PDF
for (size_t i = 0; i < n; ++i) {
double chi = col2->toDouble(i);
col3->fromDouble(i, exp(-chi + chiMin));
}
// make sure function parameters don't change.
m_function->setParameter(ip, par0);
}
// Improve estimates for standard deviations.
// If parameters are correlated the found deviations
// most likely underestimate the true values.
unfixParameters();
GSLJacobian J(m_function, values->size());
m_function->functionDeriv(*domain, J);
refixParameters();
// Calculate the hessian at the current point.
GSLMatrix H;
if (useWeighted) {
H.resize(nParams, nParams);
for (size_t i = 0; i < nParams; ++i) {
for (size_t j = i; j < nParams; ++j) {
double h = 0.0;
for (size_t k = 0; k < values->size(); ++k) {
double w = values->getFitWeight(k);
h += J.get(k, i) * J.get(k, j) * w * w;
}
H.set(i, j, h);
if (i != j) {
H.set(j, i, h);
}
}
}
} else {
H = Tr(J.matrix()) * J.matrix();
}
// Square roots of the diagonals of the covariance matrix give
// the standard deviations in the quadratic approximation of the chi^2.
GSLMatrix V(H);
if (!useWeighted) {
V *= 1. / sigma2;
}
V.invert();
// In a non-quadratic asymmetric case the following procedure can give a
// better result:
// Find the direction in which the chi^2 changes slowest and the positive and
// negative deviations in that direction. The change in a parameter at those
// points can be a better estimate for the standard deviation.
GSLVector v(nParams);
GSLMatrix Q(nParams, nParams);
// One of the eigenvectors of the hessian is the direction of the slowest
// change.
H.eigenSystem(v, Q);
// Loop over the eigenvectors
for (size_t i = 0; i < nParams; ++i) {
auto dir = Q.copyColumn(i);
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "Direction " << i << std::endl;
g_log.debug() << dir << std::endl;
}
// Make a slice in that direction
ChiSlice slice(*m_function, dir, *domain, *values, chi0, sigma2);
double rBound0 = dir.dot(rBounds);
double lBound0 = dir.dot(lBounds);
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "lBound " << lBound0 << std::endl;
g_log.debug() << "rBound " << rBound0 << std::endl;
}
double lBound = slice.findBound(lBound0);
double rBound = slice.findBound(rBound0);
std::vector<double> P, A;
// Use a polynomial approximation
bool ok = true;
auto base = slice.makeApprox(lBound, rBound, P, A, ok);
if (!ok) {
g_log.warning() << "Approximation failed in direction " << i << std::endl;
}
// Find the deviation points where the chi^2 = 1/2
A[0] -= 0.5;
std::vector<double> roots = base->roots(A);
std::sort(roots.begin(), roots.end());
// Sort out the roots
auto nRoots = roots.size();
if (nRoots == 0) {
roots.resize(2, 0.0);
} else if (nRoots == 1) {
if (roots.front() > 0.0) {
roots.insert(roots.begin(), 0.0);
} else {
roots.push_back(0.0);
}
} else if (nRoots > 2) {
roots[1] = roots.back();
roots.resize(2);
}
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << "Roots " << roots[0] << " (" << slice(roots[0]) << ") " << roots[1] << " (" << slice(roots[1]) << ") " << std::endl;
}
// Loop over the parameters and see if there deviations along
// this direction is greater than any previous value.
for (size_t ip = 0; ip < nParams; ++ip) {
auto lError = roots.front() * dir[ip];
auto rError = roots.back() * dir[ip];
if (lError > rError) {
std::swap(lError, rError);
}
if (lError < leftErrColumn->toDouble(ip)) {
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << " left for " << ip << ' ' << lError << ' ' << leftErrColumn->toDouble(ip) << std::endl;
}
leftErrColumn->fromDouble(ip, lError);
}
if (rError > rightErrColumn->toDouble(ip)) {
if (g_log.is(Kernel::Logger::Priority::PRIO_DEBUG)) {
g_log.debug() << " right for " << ip << ' ' << rError << ' ' << rightErrColumn->toDouble(ip) << std::endl;
}
rightErrColumn->fromDouble(ip, rError);
}
}
// Output the quadratic estimate for comparrison.
quadraticErrColumn->fromDouble(i, sqrt(V.get(i, i)));
}
}
/// Copy constructor
/// @param M :: The other matrix.
GSLMatrix::GSLMatrix(const GSLMatrix &M) {
m_matrix = gsl_matrix_alloc(M.size1(), M.size2());
gsl_matrix_memcpy(m_matrix, M.gsl());
}
/** Returns the number of rows in TNT-based matrix */
size_t GSLUtility::Rows(const GSLMatrix &m) const {
return (m.dim2());
}
/** Returns the number of columns in TNT-based matrix */
size_t GSLUtility::Columns(const GSLMatrix &m) const {
return (m.dim1());
}
