package org.freehep.math.minuit;
import org.apache.commons.math3.util.FastMath;
/**
* With MnHesse the user can instructs MINUIT to calculate, by finite differences, the
* Hessian or error matrix. That is, it calculates the full matrix of second derivatives
* of the function with respect to the currently variable parameters, and inverts it.
* @version $Id: MnHesse.java 8584 2006-08-10 23:06:37Z duns $
*/
public class MnHesse
{
/** default constructor with default strategy */
public MnHesse()
{
theStrategy = new MnStrategy(1);
}
/** constructor with user-defined strategy level */
public MnHesse(int stra)
{
theStrategy = new MnStrategy(stra);
}
/** conctructor with specific strategy */
public MnHesse(MnStrategy stra)
{
theStrategy = stra;
}
///
/// low-level API
///
public MnUserParameterState calculate(FCNBase fcn,double[] par,double[] err)
{
return calculate(fcn,par,err,0);
}
/** FCN + parameters + errors */
public MnUserParameterState calculate(FCNBase fcn,double[] par,double[] err,int maxcalls)
{
return calculate(fcn, new MnUserParameterState(par, err), maxcalls);
}
public MnUserParameterState calculate(FCNBase fcn ,double[] par,MnUserCovariance cov)
{
return calculate(fcn,par,cov,0);
}
/** FCN + parameters + MnUserCovariance */
public MnUserParameterState calculate(FCNBase fcn ,double[] par,MnUserCovariance cov,int maxcalls)
{
return calculate(fcn, new MnUserParameterState(par, cov), maxcalls);
}
///
/// high-level API
///
public MnUserParameterState calculate(FCNBase fcn,MnUserParameters par)
{
return calculate(fcn,par,0);
}
/** FCN + MnUserParameters */
public MnUserParameterState calculate(FCNBase fcn,MnUserParameters par,int maxcalls)
{
return calculate(fcn, new MnUserParameterState(par), maxcalls);
}
public MnUserParameterState calculate(FCNBase fcn,MnUserParameters par,MnUserCovariance cov)
{
return calculate(fcn, par, 0);
}
/** FCN + MnUserParameters + MnUserCovariance */
public MnUserParameterState calculate(FCNBase fcn,MnUserParameters par,MnUserCovariance cov,int maxcalls)
{
return calculate(fcn, new MnUserParameterState(par, cov), maxcalls);
}
/** FCN + MnUserParameterState */
public MnUserParameterState calculate(FCNBase fcn,MnUserParameterState state,int maxcalls)
{
double errDef = 1; // FixMe!
int n = state.variableParameters();
MnUserFcn mfcn = new MnUserFcn(fcn, errDef, state.trafo());
MnAlgebraicVector x = new MnAlgebraicVector(n);
for(int i = 0; i < n; i++) x.set(i,state.intParameters().get(i));
double amin = mfcn.valueOf(x);
Numerical2PGradientCalculator gc = new Numerical2PGradientCalculator(mfcn, state.trafo(), theStrategy);
MinimumParameters par = new MinimumParameters(x, amin);
FunctionGradient gra = gc.gradient(par);
MinimumState tmp = calculate(mfcn, new MinimumState(par, new MinimumError(new MnAlgebraicSymMatrix(n), 1.), gra, state.edm(), state.nfcn()), state.trafo(), maxcalls);
return new MnUserParameterState(tmp, errDef, state.trafo());
}
///
/// internal interface
///
MinimumState calculate(MnFcn mfcn,MinimumState st,MnUserTransformation trafo,int maxcalls)
{
MnMachinePrecision prec = trafo.precision();
// make sure starting at the right place
double amin = mfcn.valueOf(st.vec());
double aimsag = FastMath.sqrt(prec.eps2())*(FastMath.abs(amin)+mfcn.errorDef());
// diagonal elements first
int n = st.parameters().vec().size();
if(maxcalls == 0) maxcalls = 200 + 100*n + 5*n*n;
MnAlgebraicSymMatrix vhmat = new MnAlgebraicSymMatrix(n);
MnAlgebraicVector g2 = st.gradient().g2().clone();
MnAlgebraicVector gst = st.gradient().gstep().clone();
MnAlgebraicVector grd = st.gradient().grad().clone();
MnAlgebraicVector dirin = st.gradient().gstep().clone();
MnAlgebraicVector yy = new MnAlgebraicVector(n);
if(st.gradient().isAnalytical())
{
InitialGradientCalculator igc = new InitialGradientCalculator(mfcn, trafo, theStrategy);
FunctionGradient tmp = igc.gradient(st.parameters());
gst = tmp.gstep().clone();
dirin = tmp.gstep().clone();
g2 = tmp.g2().clone();
}
try
{
MnAlgebraicVector x = st.parameters().vec().clone();
for(int i = 0; i < n; i++)
{
double xtf = x.get(i);
double dmin = 8.*prec.eps2()*(FastMath.abs(xtf) + prec.eps2());
double d = FastMath.abs(gst.get(i));
if(d < dmin) d = dmin;
for(int icyc = 0; icyc < ncycles(); icyc++)
{
double sag = 0.;
double fs1 = 0.;
double fs2 = 0.;
int multpy = 0;
for(; multpy < 5; multpy++)
{
x.set(i,xtf + d);
fs1 = mfcn.valueOf(x);
x.set(i,xtf - d);
fs2 = mfcn.valueOf(x);
x.set(i,xtf);
sag = 0.5*(fs1+fs2-2.*amin);
if(sag > prec.eps2()) break;
if(trafo.parameter(i).hasLimits())
{
if(d > 0.5)
{
throw new MnHesseFailed("MnHesse: 2nd derivative zero for parameter");
}
d *= 10.;
if(d > 0.5) d = 0.51;
continue;
}
d *= 10.;
}
if (multpy >= 5) throw new MnHesseFailed("MnHesse: 2nd derivative zero for parameter");
double g2bfor = g2.get(i);
g2.set(i, 2.*sag/(d*d));
grd.set(i, (fs1-fs2)/(2.*d));
gst.set(i, d);
dirin.set(i, d);
yy.set(i, fs1);
double dlast = d;
d = FastMath.sqrt(2.*aimsag/FastMath.abs(g2.get(i)));
if(trafo.parameter(i).hasLimits()) d = FastMath.min(0.5, d);
if(d < dmin) d = dmin;
// see if converged
if(FastMath.abs((d-dlast)/d) < tolerstp()) break;
if(FastMath.abs((g2.get(i)-g2bfor)/g2.get(i)) < tolerg2()) break;
d = FastMath.min(d, 10.*dlast);
d = FastMath.max(d, 0.1*dlast);
}
vhmat.set(i,i,g2.get(i));
if(mfcn.numOfCalls() - st.nfcn() > maxcalls) throw new MnHesseFailed("MnHesse: maximum number of allowed function calls exhausted.");
}
if(theStrategy.strategy() > 0)
{
// refine first derivative
HessianGradientCalculator hgc = new HessianGradientCalculator(mfcn, trafo, theStrategy);
FunctionGradient gr = hgc.gradient(st.parameters(), new FunctionGradient(grd, g2, gst));
grd = gr.grad();
}
//off-diagonal elements
for(int i = 0; i < n; i++)
{
x.set(i, x.get(i) + dirin.get(i));
for(int j = i+1; j < n; j++)
{
x.set(j, x.get(j) + dirin.get(j));
double fs1 = mfcn.valueOf(x);
double elem = (fs1 + amin - yy.get(i) - yy.get(j))/(dirin.get(i)*dirin.get(j));
vhmat.set(i,j, elem);
x.set(j, x.get(j) - dirin.get(j));
}
x.set(i , x.get(i) - dirin.get(i));
}
//verify if matrix pos-def (still 2nd derivative)
MinimumError tmp = MnPosDef.test(new MinimumError(vhmat,1.), prec);
vhmat = tmp.invHessian();
try
{
vhmat.invert();
}
catch (MatrixInversionException xx)
{
throw new MnHesseFailed("MnHesse: matrix inversion fails!");
}
FunctionGradient gr = new FunctionGradient(grd, g2, gst);
if(tmp.isMadePosDef())
{
System.err.println("MnHesse: matrix is invalid!");
System.err.println("MnHesse: matrix is not pos. def.!");
System.err.println("MnHesse: matrix was forced pos. def.");
return new MinimumState(st.parameters(), new MinimumError(vhmat, new MinimumError.MnMadePosDef()), gr, st.edm(), mfcn.numOfCalls());
}
//calculate edm
MinimumError err = new MinimumError(vhmat, 0.);
double edm = new VariableMetricEDMEstimator().estimate(gr, err);
return new MinimumState(st.parameters(), err, gr, edm, mfcn.numOfCalls());
}
catch (MnHesseFailed x)
{
System.err.println(x.getMessage());
System.err.println("MnHesse fails and will return diagonal matrix ");
for(int j = 0; j < n; j++)
{
double tmp = g2.get(j) < prec.eps2() ? 1. : 1./g2.get(j);
vhmat.set(j,j,tmp < prec.eps2() ? 1. : tmp);
}
return new MinimumState(st.parameters(), new MinimumError(vhmat, new MinimumError.MnHesseFailed()), st.gradient(), st.edm(), st.nfcn()+mfcn.numOfCalls());
}
}
/// forward interface of MnStrategy
int ncycles()
{
return theStrategy.hessianNCycles();
}
double tolerstp()
{
return theStrategy.hessianStepTolerance();
}
double tolerg2()
{
return theStrategy.hessianG2Tolerance();
}
private MnStrategy theStrategy;
private class MnHesseFailed extends Exception
{
MnHesseFailed(String message)
{
super(message);
}
}
}
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