MinimumError MnPosDef::operator()(const MinimumError& e, const MnMachinePrecision& prec) const {
MnAlgebraicSymMatrix err(e.invHessian());
if(err.size() == 1 && err(0,0) < prec.eps()) {
err(0,0) = 1.;
return MinimumError(err, MinimumError::MnMadePosDef());
}
if(err.size() == 1 && err(0,0) > prec.eps()) {
return e;
}
// std::cout<<"MnPosDef init matrix= "<<err<<std::endl;
double epspdf = std::max(1.e-6, prec.eps2());
double dgmin = err(0,0);
for(unsigned int i = 0; i < err.nrow(); i++) {
if(err(i,i) < prec.eps2()) //std::cout<<"negative or zero diagonal element "<<i<<" in covariance matrix"<<std::endl;
if(err(i,i) < dgmin) dgmin = err(i,i);
}
double dg = 0.;
if(dgmin < prec.eps2()) {
//dg = 1. + epspdf - dgmin;
dg = 0.5 + epspdf - dgmin;
// dg = 0.5*(1. + epspdf - dgmin);
//std::cout<<"added "<<dg<<" to diagonal of error matrix"<<std::endl;
//std::cout << "Error matrix " << err << std::endl;
}
MnAlgebraicVector s(err.nrow());
MnAlgebraicSymMatrix p(err.nrow());
for(unsigned int i = 0; i < err.nrow(); i++) {
err(i,i) += dg;
if(err(i,i) < 0.) err(i,i) = 1.;
s(i) = 1./sqrt(err(i,i));
for(unsigned int j = 0; j <= i; j++) {
p(i,j) = err(i,j)*s(i)*s(j);
}
}
//std::cout<<"MnPosDef p: "<<p<<std::endl;
MnAlgebraicVector eval = eigenvalues(p);
double pmin = eval(0);
double pmax = eval(eval.size() - 1);
//std::cout<<"pmin= "<<pmin<<" pmax= "<<pmax<<std::endl;
pmax = std::max(fabs(pmax), 1.);
if(pmin > epspdf*pmax) return MinimumError(err, e.dcovar());
double padd = 0.001*pmax - pmin;
//std::cout<<"eigenvalues: "<<std::endl;
for(unsigned int i = 0; i < err.nrow(); i++) {
err(i,i) *= (1. + padd);
//std::cout<<eval(i)<<std::endl;
}
// std::cout<<"MnPosDef final matrix: "<<err<<std::endl;
// std::cout<<"matrix forced pos-def by adding "<<padd<<" to diagonal"<<std::endl;
// std::cout<<"eigenvalues: "<<eval<<std::endl;
return MinimumError(err, MinimumError::MnMadePosDef());
}
MinimumState MnHesse::operator()(const MnFcn& mfcn, const MinimumState& st, const MnUserTransformation& trafo, unsigned int maxcalls) const {
const MnMachinePrecision& prec = trafo.precision();
// make sure starting at the right place
double amin = mfcn(st.vec());
double aimsag = sqrt(prec.eps2())*(fabs(amin)+mfcn.up());
// diagonal elements first
unsigned int n = st.parameters().vec().size();
if(maxcalls == 0) maxcalls = 200 + 100*n + 5*n*n;
MnAlgebraicSymMatrix vhmat(n);
MnAlgebraicVector g2 = st.gradient().g2();
MnAlgebraicVector gst = st.gradient().gstep();
MnAlgebraicVector grd = st.gradient().grad();
MnAlgebraicVector dirin = st.gradient().gstep();
MnAlgebraicVector yy(n);
if(st.gradient().isAnalytical()) {
InitialGradientCalculator igc(mfcn, trafo, theStrategy);
FunctionGradient tmp = igc(st.parameters());
gst = tmp.gstep();
dirin = tmp.gstep();
g2 = tmp.g2();
}
MnAlgebraicVector x = st.parameters().vec();
for(unsigned int i = 0; i < n; i++) {
double xtf = x(i);
double dmin = 8.*prec.eps2()*(fabs(xtf) + prec.eps2());
double d = fabs(gst(i));
if(d < dmin) d = dmin;
for(unsigned int icyc = 0; icyc < ncycles(); icyc++) {
double sag = 0.;
double fs1 = 0.;
double fs2 = 0.;
for(unsigned int multpy = 0; multpy < 5; multpy++) {
x(i) = xtf + d;
fs1 = mfcn(x);
x(i) = xtf - d;
fs2 = mfcn(x);
x(i) = xtf;
sag = 0.5*(fs1+fs2-2.*amin);
if(sag > prec.eps2()) goto L30; // break;
if(trafo.parameter(i).hasLimits()) {
if(d > 0.5) goto L26;
d *= 10.;
if(d > 0.5) d = 0.51;
continue;
}
d *= 10.;
}
L26:
std::cout<<"MnHesse: 2nd derivative zero for parameter "<<i<<std::endl;
std::cout<<"MnHesse fails and will return diagonal matrix "<<std::endl;
for(unsigned int j = 0; j < n; j++) {
double tmp = g2(j) < prec.eps2() ? 1. : 1./g2(j);
vhmat(j,j) = tmp < prec.eps2() ? 1. : tmp;
}
return MinimumState(st.parameters(), MinimumError(vhmat, MinimumError::MnHesseFailed()), st.gradient(), st.edm(), mfcn.numOfCalls());
L30:
double g2bfor = g2(i);
g2(i) = 2.*sag/(d*d);
grd(i) = (fs1-fs2)/(2.*d);
gst(i) = d;
dirin(i) = d;
yy(i) = fs1;
double dlast = d;
d = sqrt(2.*aimsag/fabs(g2(i)));
if(trafo.parameter(i).hasLimits()) d = std::min(0.5, d);
if(d < dmin) d = dmin;
// see if converged
if(fabs((d-dlast)/d) < tolerstp()) break;
if(fabs((g2(i)-g2bfor)/g2(i)) < tolerg2()) break;
d = std::min(d, 10.*dlast);
d = std::max(d, 0.1*dlast);
}
vhmat(i,i) = g2(i);
if(mfcn.numOfCalls() > maxcalls) {
//std::cout<<"maxcalls " << maxcalls << " " << mfcn.numOfCalls() << " " << st.nfcn() << std::endl;
std::cout<<"MnHesse: maximum number of allowed function calls exhausted."<<std::endl;
std::cout<<"MnHesse fails and will return diagonal matrix "<<std::endl;
for(unsigned int j = 0; j < n; j++) {
double tmp = g2(j) < prec.eps2() ? 1. : 1./g2(j);
vhmat(j,j) = tmp < prec.eps2() ? 1. : tmp;
}
return MinimumState(st.parameters(), MinimumError(vhmat, MinimumError::MnHesseFailed()), st.gradient(), st.edm(), mfcn.numOfCalls());
}
}
if(theStrategy.strategy() > 0) {
// refine first derivative
HessianGradientCalculator hgc(mfcn, trafo, theStrategy);
FunctionGradient gr = hgc(st.parameters(), FunctionGradient(grd, g2, gst));
grd = gr.grad();
}
//off-diagonal elements
for(unsigned int i = 0; i < n; i++) {
x(i) += dirin(i);
for(unsigned int j = i+1; j < n; j++) {
x(j) += dirin(j);
double fs1 = mfcn(x);
double elem = (fs1 + amin - yy(i) - yy(j))/(dirin(i)*dirin(j));
vhmat(i,j) = elem;
x(j) -= dirin(j);
}
x(i) -= dirin(i);
}
//verify if matrix pos-def (still 2nd derivative)
MinimumError tmp = MnPosDef()(MinimumError(vhmat,1.), prec);
vhmat = tmp.invHessian();
int ifail = invert(vhmat);
if(ifail != 0) {
std::cout<<"MnHesse: matrix inversion fails!"<<std::endl;
std::cout<<"MnHesse fails and will return diagonal matrix."<<std::endl;
MnAlgebraicSymMatrix tmpsym(vhmat.nrow());
for(unsigned int j = 0; j < n; j++) {
double tmp = g2(j) < prec.eps2() ? 1. : 1./g2(j);
tmpsym(j,j) = tmp < prec.eps2() ? 1. : tmp;
}
return MinimumState(st.parameters(), MinimumError(tmpsym, MinimumError::MnHesseFailed()), st.gradient(), st.edm(), mfcn.numOfCalls());
}
FunctionGradient gr(grd, g2, gst);
// needed this ? (if posdef and inversion ok continue. it is like this in the Fortran version
// if(tmp.isMadePosDef()) {
// std::cout<<"MnHesse: matrix is invalid!"<<std::endl;
// std::cout<<"MnHesse: matrix is not pos. def.!"<<std::endl;
// std::cout<<"MnHesse: matrix was forced pos. def."<<std::endl;
// return MinimumState(st.parameters(), MinimumError(vhmat, MinimumError::MnMadePosDef()), gr, st.edm(), mfcn.numOfCalls());
// }
//calculate edm
MinimumError err(vhmat, 0.);
VariableMetricEDMEstimator estim;
double edm = estim.estimate(gr, err);
return MinimumState(st.parameters(), err, gr, edm, mfcn.numOfCalls());
}