Пример #1
0
def LinearFit():

    from ConstrainedFit import clsq

    xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ]
    data= [ 1.1, 1.9, 2.9, 4.1, 5.1, 6.1, 6.9, 7.9, 9.1 ]
    errors= [ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 ]
    covm= clsq.covmFromErrors( errors )

    upar= [ 0.1, 1.1 ]
    upnames= { 0: "a", 1: "b" }

    def linearConstrFun( mpar, upar, xv ):
        constraints= []
        for mparval, xval in zip( mpar, xv ):
            constraints.append( upar[0]+upar[1]*xval - mparval )
        return constraints

    solver= clsq.clsqSolver( data, covm, upar, linearConstrFun, 
                             uparnames=upnames, args=(xabs,) )
    print "Constraints before solution"
    print solver.getConstraints()
    solver.solve()
    ca= clsq.clsqAnalysis( solver )
    ca.printResults()

    return
Пример #2
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def LinearFit():

    from ConstrainedFit import clsq

    xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ]
    data= [ 1.1, 1.9, 2.9, 4.1, 5.1, 6.1, 6.9, 7.9, 9.1 ]
    errors= [ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 ]
    covm= clsq.covmFromErrors( errors )

    upar= [ 0.1, 1.1 ]
    upnames= { 0: "a", 1: "b" }

    def linearConstrFun( mpar, upar, xv ):
        constraints= []
        for mparval, xval in zip( mpar, xv ):
            constraints.append( upar[0]+upar[1]*xval - mparval )
        return constraints

    solver= clsq.clsqSolver( data, covm, upar, linearConstrFun,
                             uparnames=upnames, args=(xabs,) )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    solver.solve()
    ca= clsq.clsqAnalysis( solver )
    ca.printResults()

    return
Пример #3
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 def printResults( self, ffmt=".4f", cov=False, corr=False ):
     if isinstance( self.__solver, minuitSolver ):
         self.__solver.printResults( ffmt=ffmt, cov=cov, corr=corr )
     elif isinstance( self.__solver, clsq.clsqSolver ):
         ca= clsq.clsqAnalysis( self.__solver )
         ca.printResults( ffmt=ffmt, cov=cov, corr=corr )
     print
     return
Пример #4
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 def printResults(self, ffmt=".4f", cov=False, corr=False):
     if isinstance(self.__solver, minuitSolver):
         self.__solver.printResults(ffmt=ffmt, cov=cov, corr=corr)
     elif isinstance(self.__solver, clsq.clsqSolver):
         ca = clsq.clsqAnalysis(self.__solver)
         ca.printResults(ffmt=ffmt, cov=cov, corr=corr)
     print
     return
Пример #5
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def _doMinos( solver, ipar=0, ptype="u" ):
    from ConstrainedFit import clsq
    par= clsq.createClsqPar( ipar, ptype, solver )
    result= par.getParVal()
    name= par.getParName()
    ca= clsq.clsqAnalysis( solver )
    errhi, errlo= ca.minos( par )
    fmtstr= "{0:>10s}: {1:10.4f} + {2:6.4f} - {3:6.4f}"
    print( fmtstr.format( name, result, errhi, abs(errlo) ) )
Пример #6
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def _doMinos( solver, ipar=0, ptype="u" ):
    from ConstrainedFit import clsq
    par= clsq.createClsqPar( ipar, ptype, solver )
    result= par.getParVal()
    name= par.getParName()
    ca= clsq.clsqAnalysis( solver )
    errhi, errlo= ca.minos( par )
    fmtstr= "{0:>10s}: {1:10.4f} + {2:6.4f} - {3:6.4f}"
    print fmtstr.format( name, result, errhi, abs(errlo) )
Пример #7
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def Triangle( opt="" ):

    from ConstrainedFit import clsq
    from math import sqrt, tan

    data= [ 10.0, 7.0, 9.0, 1.0 ]
    errors= [ 0.05, 0.2, 0.2, 0.02 ]
    covm= clsq.covmFromErrors( errors )
    mpnames= { 0: "a", 1: "b", 2: "c", 3: "gamma" }

    upar= [ 30.0 ]
    upnames= { 0: "A" }

    def triangleConstrFun( mpar, upar ):
        a= mpar[0]
        b= mpar[1]
        c= mpar[2]
        gamma= mpar[3]
        aa= upar[0]
        p= (a+b+c)/2.0
        s= sqrt( p*(p-a)*(p-b)*(p-c) )
        return [ tan(gamma/2.0)-s/(p*(p-c)), aa-s ]

    solver= clsq.clsqSolver( data, covm, upar, triangleConstrFun,
                             uparnames=upnames, mparnames=mpnames )

    print( "Constraints before solution" )
    print( solver.getConstraints() )
    lBlobel= False
    lCorr= False
    lResidual= True
    if "b" in opt:
        lBlobel= True
    if "corr" in opt:
        lCorr= True
    if "r" in opt:
        lResidual= False
    solver.solve( lBlobel=lBlobel, lResidual=lResidual )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    if "m" in opt:
        _doMinosAll( solver )

    if "cont" in opt:
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="m" )

    print( "Profile A" )
    par= clsq.createClsqPar( 0, "u", solver )
    results= ca.profile( par )
    print( results )

    return solver
Пример #8
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def PoissonLikelihood( opt="" ):
    
    from ConstrainedFit import clhood
    from ConstrainedFit import clsq
    from scipy.special import gammaln
    from scipy.stats import poisson, norm
    from math import log

    # Data, two counts, errors not needed(!):
    data= [ 9.0, 16.0 ]
    # errors= [ 3.0, 4.0 ]
    mpnames= { 0: "count 1", 1: "count 2" }

    # Fit variable is parameter of poisson distribution:
    upar= [ 12.0 ]
    upnames= { 0: "mu" }

    # Likelihood is sum of log(poisson) for each data point:
    def lfun( mpar ):
        result= 0.0
        for datum, parval in zip( data, mpar ):
            parval= parval.item()
            result-= log( poisson.pmf( datum, parval ) )
            # Calculated log(poisson):
            # result-= datum*log( parval ) - gammaln( datum+1.0 ) - parval
        return result

    # Constraints force poisson distribution with same parameter
    # for every data point:
    def constrFun( mpar, upar ):
        return [ mpar[0] - upar[0], 
                 mpar[1] - upar[0] ]

    solver= clhood.clhoodSolver( data, upar, lfun, constrFun, 
                                 uparnames=upnames, mparnames=mpnames )
    print "Constraints before solution"
    print solver.getConstraints()
    lBlobel=False
    lPrint= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "p" in opt:
        lPrint= True
    if "c" in opt:
        lCorr= True
    solver.solve( lBlobel=lBlobel, lpr=lPrint )

    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    return
Пример #9
0
def Triangle( opt="" ):

    from ConstrainedFit import clsq
    from math import sqrt, tan

    data= [ 10.0, 7.0, 9.0, 1.0 ]
    errors= [ 0.05, 0.2, 0.2, 0.02 ]
    covm= clsq.covmFromErrors( errors )
    mpnames= { 0: "a", 1: "b", 2: "c", 3: "gamma" }

    upar= [ 30.0 ]
    upnames= { 0: "A" }

    def triangleConstrFun( mpar, upar ):
        a= mpar[0]
        b= mpar[1]
        c= mpar[2]
        gamma= mpar[3]
        aa= upar[0]
        p= (a+b+c)/2.0
        s= sqrt( p*(p-a)*(p-b)*(p-c) )
        return [ tan(gamma/2.0)-s/(p*(p-c)), aa-s ]

    solver= clsq.clsqSolver( data, covm, upar, triangleConstrFun,
                             uparnames=upnames, mparnames=mpnames )
    print "Constraints before solution"
    print solver.getConstraints()
    lBlobel= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "corr" in opt:
        lCorr= True
    solver.solve( lBlobel=lBlobel )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    if "m" in opt:
        _doMinosAll( solver )

    if "cont" in opt:
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="m" )

    print "Profile A"
    par= clsq.createClsqPar( 0, "u", solver )
    results= ca.profile( par )
    print results

    return solver
Пример #10
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def _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2= "m" ):
    from ConstrainedFit import clsq
    from ROOT import TGraph2D, TMarker, gPad
    from array import array
    global tg2d, hist, te1, te2, te3, tm
    par1= clsq.createClsqPar( ipar1, type1, solver )
    par2= clsq.createClsqPar( ipar2, type2, solver )
    parval1, parerr1, name1= _getUMParErrName( par1 )
    parval2, parerr2, name2= _getUMParErrName( par2 )
    print( "\nChi^2 profile plot " + name1 + " - " + name2 + ":" )
    corr= solver.getCorrMatrix()
    icorr1= ipar1
    icorr2= ipar2
    if type1 == "u" or type2 == "u":
        nmpar= len(solver.getMpars())
        if type1 == "u":
            icorr1= nmpar + ipar1
        if type2 == "u":
            icorr2= nmpar + ipar2
    rho= corr[icorr1,icorr2]
    te1= _makeEllipse( parval1, parval2, parerr1, parerr2, rho )
    te2= _makeEllipse( parval1, parval2, 2.0*parerr1, 2.0*parerr2, rho )
    te3= _makeEllipse( parval1, parval2, 3.0*parerr1, 3.0*parerr2, rho )
    ca= clsq.clsqAnalysis( solver )
    points= ca.profile2d( par1, par2 )
    npoints= len(points)
    tg2d= TGraph2D( npoints )
    for i in range( npoints ):
        point= points[i]
        tg2d.SetPoint( i, point[0], point[1], point[2] )
    hist= tg2d.GetHistogram()
    contourlevels= array( "d", [ 1.0, 4.0, 9.0 ] )
    hist.SetContour( 3, contourlevels )
    hist.GetXaxis().SetTitle( name1 )
    hist.GetYaxis().SetTitle( name2 )
    hist.SetTitle( "Triangle fit "+name2+" vs "+name1 )
    hist.Draw( "cont1" )
    tm= TMarker( parval1, parval2, 20 )
    tm.Draw( "s" )
    te1.Draw( "s" )
    te2.Draw( "s" )
    te3.Draw( "s" )
    gPad.Print( "triangle_errorellipse.png" )
    return
Пример #11
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def _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2= "m" ):
    from ConstrainedFit import clsq
    from ROOT import TGraph2D, TMarker
    from array import array
    global tg2d, hist, te1, te2, te3, tm
    par1= clsq.createClsqPar( ipar1, type1, solver )
    par2= clsq.createClsqPar( ipar2, type2, solver )
    parval1, parerr1, name1= _getUMParErrName( par1 )
    parval2, parerr2, name2= _getUMParErrName( par2 )
    print "\nChi^2 profile plot " + name1 + " - " + name2 + ":"
    corr= solver.getCorrMatrix()
    icorr1= ipar1
    icorr2= ipar2
    if type1 == "u" or type2 == "u":
        nmpar= len(solver.getMpars())
        if type1 == "u":
            icorr1= nmpar + ipar1
        if type2 == "u":
            icorr2= nmpar + ipar2
    rho= corr[icorr1,icorr2]
    te1= _makeEllipse( parval1, parval2, parerr1, parerr2, rho )
    te2= _makeEllipse( parval1, parval2, 2.0*parerr1, 2.0*parerr2, rho )
    te3= _makeEllipse( parval1, parval2, 3.0*parerr1, 3.0*parerr2, rho )
    ca= clsq.clsqAnalysis( solver )
    points= ca.profile2d( par1, par2 )
    npoints= len(points)
    tg2d= TGraph2D( npoints )
    for i in range( npoints ):
        point= points[i]
        tg2d.SetPoint( i, point[0], point[1], point[2] )
    hist= tg2d.GetHistogram()
    contourlevels= array( "d", [ 1.0, 4.0, 9.0 ] )
    hist.SetContour( 3, contourlevels )     
    xa= hist.GetXaxis()
    ya= hist.GetYaxis()
    xa.SetTitle( name1 )
    ya.SetTitle( name2 )
    hist.Draw( "cont1" )
    tm= TMarker( parval1, parval2, 20 )
    tm.Draw( "s" )
    te1.Draw( "s" )
    te2.Draw( "s" )
    te3.Draw( "s" )
    return
Пример #12
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def PoissonLikelihood( opt="" ):

    from ConstrainedFit import clhood
    from ConstrainedFit import clsq
    from scipy.special import gammaln
    from scipy.stats import poisson
    from math import log

    # Data, two counts, errors not needed(!):
    data= [ 9.0, 16.0 ]
    # errors= [ 3.0, 4.0 ]
    mpnames= { 0: "count 1", 1: "count 2" }

    # Fit variable is parameter of poisson distribution:
    upar= [ 12.0 ]
    upnames= { 0: "mu" }

    # Likelihood is sum of log(poisson) for each data point:
    def lfun( mpar ):
        result= 0.0
        for datum, parval in zip( data, mpar ):
            parval= parval.item()
            result-= poisson.logpmf( datum, parval )
            # Calculated log(poisson):
            # result-= datum*log( parval ) - gammaln( datum+1.0 ) - parval
        return result

    # Constraints force poisson distribution with same parameter
    # for every data point:
    def constrFun( mpar, upar ):
        return [ mpar[0] - upar[0],
                 mpar[1] - upar[0] ]

    solver= clhood.clhoodSolver( data, upar, lfun, constrFun,
                                 uparnames=upnames, mparnames=mpnames )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    lBlobel=False
    lPrint= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "p" in opt:
        lPrint= True
    if "c" in opt:
        lCorr= True
    solver.solve( lBlobel=lBlobel, lpr=lPrint )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    # Minuit fit of the two count likelihood, corresponds
    # to max L solution
    from AverageTools import minuitSolver
    def fcn( n, grad, fval, par, ipar ):
        mu= par[0]
        lsum= 0.0
        for datum in data:
            lsum-= poisson.logpmf( datum, mu )
            # Calculated log(poisson):
            # lsum-= datum*log( mu ) - gammaln( datum+1.0 ) - mu
        fval.value= lsum
        return
    par= [ 12.0 ]
    parerr= [ 1.0 ]
    parname= [ "mu" ]
    ndof= 1
    solver= minuitSolver.minuitSolver( fcn, par, parerr, parname, ndof )
    solver.minuitCommand( "SET ERRDEF 0.5" )
    solver.solve()
    solver.printResults()

    return
Пример #13
0
def StraightLine( opt="" ):

    from ConstrainedFit import clsq
    from numpy import matrix, zeros

    # Data, errors and correlations:
    xdata= [ 1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0 ]
    ydata= [ 3.0, 2.5, 3.0, 5.0, 7.0, 5.5, 7.5 ]
    xerrs= [ 0.5, 0.3, 0.3, 0.5, 0.5, 0.3, 0.3 ]
    yerrs= [ 0.7, 1.0, 0.5, 0.7, 0.7, 1.0, 0.7 ]
    xyrho= [ -0.25, 0.5, 0.5, -0.25, 0.25, 0.95, -0.25 ]
    #xyrho= [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
    covm= matrix( zeros( (14,14) ) )
    data= []
    npoints= len(xdata)
    for i in range( npoints ):
        subcovm= matrix( [ [ xerrs[i]**2, xyrho[i]*xerrs[i]*yerrs[i] ],
                           [ xyrho[i]*xerrs[i]*yerrs[i], yerrs[i]**2 ] ] )
        covm[2*i:2*i+2,2*i:2*i+2]= subcovm
        data.append( xdata[i] )
        data.append( ydata[i] )
    print( covm )
    print( data )

    # Fit parameters for straight line:
    upar= [ 1.0, 0.5 ]
    upnames= { 0: "a", 1: "b" }
    # or parabola, see possible mpar[.]**2 term in constraints
    #upar= [ 0.0, 1.0, 1.0 ]
    #upnames= { 0: "a", 1: "b", 2: "c" }

    # Constraint function forces y_i = a + b*x_i for every
    # pair of measurements x_i, y_i:
    def straightlineConstraints( mpar, upar ):
        constraints= []
        for i in range( npoints ):
            constraints.append( upar[0] + upar[1]*mpar[2*i]
                                # + upar[2]*mpar[2*i]**2
                                - mpar[2*i+1] )
        return constraints

    # Setup the solver and solve:
    solver= clsq.clsqSolver( data, covm, upar, straightlineConstraints,
                             uparnames=upnames )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    lBlobel= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "corr" in opt:
        lCorr= True
    solver.solve( lBlobel=lBlobel )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    if "m" in opt:
        _doMinosAll( solver, "u" )

    global tg, lell, tf, tt, canvc, canvp
    from ROOT import TGraph, TF1, TText, TCanvas

    if "cont" in opt:
        canvc= TCanvas( "canv", "Chi^2 Contours", 600, 600 )
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )

    # Plot:
    from array import array
    xarr= array( "f", xdata )
    yarr= array( "f", ydata )
    tg= TGraph( npoints, xarr, yarr )
    tg.SetMarkerStyle( 20 )
    tg.SetMinimum( 0.0 )
    tg.SetMaximum( 9.0 )
    tg.SetTitle( "straight line 2D fit" )
    xa= tg.GetXaxis()
    ya= tg.GetYaxis()
    xa.SetTitle( "X" )
    ya.SetTitle( "Y" )
    canvp= TCanvas( "canp", "Straight line 2D fit", 600, 400 )
    tg.Draw( "ap" )
    lell= []
    for i in range( npoints ):
        te= _makeEllipse( xdata[i], ydata[i], xerrs[i], yerrs[i], xyrho[i] )
        lell.append( te )
        te.Draw( "s" )
    solution= solver.getUpars()
    tf= TF1( "tf", "[0]+[1]*x", 0.0, 15.0 )
    for i in range( len(upar) ):
        tf.SetParameter( i, solution[i] )
        tf.SetParName( 0, upnames[i] )
    tf.Draw( "same" )
    tt= TText( 1, 8, "y= a + b*x" )
    tt.Draw( "same" )

    return
Пример #14
0
def Branchingratios( opt="m" ):

    from ConstrainedFit import clsq

    data= [ 0.265, 0.28, 0.37, 0.166, 0.42, 0.5, 0.20, 0.16, 
            0.72, 0.6, 0.37, 0.64, 0.45, 0.028, 10.0, 7.5 ]
    errors= [ 0.014, 0.05, 0.06, 0.013, 0.15, 0.2, 0.08, 0.08,
              0.15, 0.4, 0.16, 0.40, 0.45, 0.009, 5.0, 2.5 ]
    # Error scale factor a la Blobel lecture:
    if "e" in opt:
        print "Apply scaling *2.8 of error[13]"
        errors[13]= errors[13]*2.8
    covm= clsq.covmFromErrors( errors )

    upar= [ 0.33, 0.36, 0.16, 0.09, 0.055 ]
    upnames= { 0: "B1", 1: "B2", 2: "B3", 3: "B4", 4: "B5" }

    def brConstrFun( mpar, upar ):
        constraints= []
        x= []
        for i in range( 5 ):
            x.append( upar[i] )
        for i in range( 5, 21 ):
            x.append( mpar[i-5] )

        constraints.append( x[0]+x[1]+x[2]+x[3]+x[4]-1.0 )
        constraints.append( x[3]-x[5]*x[0] )
        constraints.append( x[3]-x[6]*x[0] )
        constraints.append( x[3]-x[7]*x[0] )
        
        constraints.append( x[3]-(x[1]+x[2])*x[8] )
        constraints.append( x[3]-(x[1]+x[2])*x[9] )
        constraints.append( x[3]-(x[1]+x[2])*x[10] )
        constraints.append( x[3]-(x[1]+x[2])*x[11] )
        constraints.append( x[3]-(x[1]+x[2])*x[12] )
        
        constraints.append( x[1]-(x[1]+x[2])*x[13] )
        constraints.append( x[1]-(x[1]+x[2])*x[14] )
        
        constraints.append( x[0]-(x[1]+x[2])*x[15] )
        constraints.append( x[0]-(x[1]+x[2])*x[16] )
        
        constraints.append( 3.0*x[4]-x[0]*x[17] )
        
        constraints.append( x[3]-x[18] )
        
        constraints.append( (x[1]+x[2])-x[4]*x[19] )
        constraints.append( (x[1]+x[2])-x[4]*x[20] )

        return constraints

    solver= clsq.clsqSolver( data, covm, upar, brConstrFun, epsilon=0.00001,
                             uparnames=upnames )
    print "Constraints before solution"
    print solver.getConstraints()
    lBlobel= False
    if "b" in opt:
        lBlobel= True
    solver.solve( lBlobel=lBlobel )
    lcov= False
    lcorr= False
    if "corr" in opt:
        lcov= True
        lcorr= True

    ca= clsq.clsqAnalysis( solver )
    ca.printResults( cov=lcov, corr=lcorr )

    if "m" in opt:
        _doMinosAll( solver, "u" )
    if "cont" in opt:
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )

    return
Пример #15
0
def StraightLine( opt="" ):

    from ConstrainedFit import clsq
    from numpy import matrix, zeros

    # Data, errors and correlations:
    xdata= [ 1.0, 3.0, 5.0, 7.0, 9.0, 11.0, 13.0 ]
    ydata= [ 3.0, 2.5, 3.0, 5.0, 7.0, 5.5, 7.5 ]
    xerrs= [ 0.5, 0.3, 0.3, 0.5, 0.5, 0.3, 0.3 ]
    yerrs= [ 0.7, 1.0, 0.5, 0.7, 0.7, 1.0, 0.7 ]
    xyrho= [ -0.25, 0.5, 0.5, -0.25, 0.25, 0.95, -0.25 ]
    #xyrho= [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
    covm= matrix( zeros( (14,14) ) )
    data= []
    npoints= len(xdata)
    for i in range( npoints ):
        subcovm= matrix( [ [ xerrs[i]**2, xyrho[i]*xerrs[i]*yerrs[i] ], 
                           [ xyrho[i]*xerrs[i]*yerrs[i], yerrs[i]**2 ] ] )
        covm[2*i:2*i+2,2*i:2*i+2]= subcovm
        data.append( xdata[i] )
        data.append( ydata[i] )
    print covm
    print data

    # Fit parameters for straight line:
    upar= [ 1.0, 0.5 ]
    upnames= { 0: "a", 1: "b" }
    #upar= [ 0.0, 1.0, 1.0 ]
    #upnames= { 0: "a", 1: "b", 2: "c" }

    # Constraint function forces y_i = a + b*x_i for every
    # pair of measurements x_i, y_i:
    def straightlineConstraints( mpar, upar ):
        constraints= []
        for i in range( npoints ):
            constraints.append( upar[0] + upar[1]*mpar[2*i] 
                                # + upar[2]*mpar[2*i]**2
                                - mpar[2*i+1] )
        return constraints

    # Setup the solver and solve:
    solver= clsq.clsqSolver( data, covm, upar, straightlineConstraints,
                             uparnames=upnames )
    print "Constraints before solution"
    print solver.getConstraints()
    lBlobel= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "corr" in opt:
        lCorr= True
    solver.solve( lBlobel=lBlobel )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    if "m" in opt:
        _doMinosAll( solver, "u" )

    global tg, lell, tf, tt, canvc, canvp
    from ROOT import TGraph, TF1, TText, TCanvas

    if "cont" in opt:
        canvc= TCanvas( "canv", "Chi^2 Contours", 600, 600 )
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )


    # Plot:
    from array import array
    xarr= array( "f", xdata )
    yarr= array( "f", ydata )
    tg= TGraph( npoints, xarr, yarr )
    tg.SetMarkerStyle( 20 )
    tg.SetMinimum( 0.0 )
    tg.SetMaximum( 9.0 )
    tg.SetTitle( "straight line 2D fit" )
    xa= tg.GetXaxis()
    ya= tg.GetYaxis()
    xa.SetTitle( "X" )
    ya.SetTitle( "Y" )
    canvp= TCanvas( "canp", "Straight line 2D fit", 600, 400 )
    tg.Draw( "ap" )
    lell= []
    for i in range( npoints ):
        te= _makeEllipse( xdata[i], ydata[i], xerrs[i], yerrs[i], xyrho[i] )
        lell.append( te )
        te.Draw( "s" )
    solution= solver.getUpars()
    tf= TF1( "tf", "[0]+[1]*x", 0.0, 15.0 )
    for i in range( len(upar) ):
        tf.SetParameter( i, solution[i] )
        tf.SetParName( 0, upnames[i] )
    tf.Draw( "same" )
    tt= TText( 1, 8, "y= a + b*x" )
    tt.Draw( "same" )

    return
Пример #16
0
def GaussLikelihood( opt="" ):

    from ConstrainedFit import clhood, clsq
    from scipy.stats import norm
    from math import log

    # Data and errors:
    xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
    data= [ 1.1, 1.9, 2.9, 4.1, 5.1 ]
    errors= [ 0.1, 0.1, 0.1, 0.1, 0.1 ]

    # Linear function (straight line) parameters:
    upar= [ 0.0, 1.0 ]
    upnames= { 0: "a", 1: "b" }

    # Likelihood is sum of log(Gauss) for each data point:
    def lfun( mpar ):
        result= 0.0
        for datum, parval, error in zip( data, mpar, errors ):
            parval= parval.item()
            result-= log( norm.pdf( datum, parval, error ) )
            # result+= 0.5*((datum-parval)/error)**2
        return result

    # Constraints force linear function for each data point:
    def constrFun( mpar, upar ):
        constraints= []
        for xval, parval in zip( xabs, mpar ):
            constraints.append( upar[0] + upar[1]*xval - parval )
        return constraints

    # Configure options:
    lBlobel=False
    lPrint= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "p" in opt:
        lPrint= True
    if "c" in opt:
        lCorr= True

    # Solution using constrained log(likelihood) minimisation:
    print "\nMax likelihood constrained fit"
    solver= clhood.clhoodSolver( data, upar, lfun, constrFun, uparnames=upnames )
    print "Constraints before solution"
    print solver.getConstraints()
    solver.solve( lBlobel=lBlobel, lpr=lPrint )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    # Solution using constrained least squares:
    print "\nLeast squares constrained fit"
    covm= clsq.covmFromErrors( errors )
    solver= clsq.clsqSolver( data, covm, upar, constrFun, uparnames=upnames )
    print "Constraints before solution"
    print solver.getConstraints()
    solver.solve( lBlobel=lBlobel, lpr=lPrint )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    return
Пример #17
0
def GaussLikelihood( opt="" ):

    from ConstrainedFit import clhood, clsq
    from scipy.stats import norm
    from math import log

    # Data and errors:
    xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
    data= [ 1.1, 1.9, 2.9, 4.1, 5.1 ]
    errors= [ 0.1, 0.1, 0.1, 0.1, 0.1 ]

    # Linear function (straight line) parameters:
    upar= [ 0.0, 1.0 ]
    upnames= { 0: "a", 1: "b" }

    # Likelihood is sum of log(Gauss) for each data point:
    def lfun( mpar ):
        result= 0.0
        for datum, parval, error in zip( data, mpar, errors ):
            parval= parval.item()
            result-= log( norm.pdf( datum, parval, error ) )
            # result+= 0.5*((datum-parval)/error)**2
        return result

    # Constraints force linear function for each data point:
    def constrFun( mpar, upar ):
        constraints= []
        for xval, parval in zip( xabs, mpar ):
            constraints.append( upar[0] + upar[1]*xval - parval )
        return constraints

    # Configure options:
    lBlobel=False
    lPrint= False
    lCorr= False
    if "b" in opt:
        lBlobel= True
    if "p" in opt:
        lPrint= True
    if "c" in opt:
        lCorr= True

    # Solution using constrained log(likelihood) minimisation:
    print( "\nMax likelihood constrained fit" )
    solver= clhood.clhoodSolver( data, upar, lfun, constrFun, uparnames=upnames )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    solver.solve( lBlobel=lBlobel, lpr=lPrint )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    # Solution using constrained least squares:
    print( "\nLeast squares constrained fit" )
    covm= clsq.covmFromErrors( errors )
    solver= clsq.clsqSolver( data, covm, upar, constrFun, uparnames=upnames )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    solver.solve( lBlobel=lBlobel, lpr=lPrint )
    ca= clsq.clsqAnalysis( solver )
    ca.printResults( corr=lCorr )

    return
Пример #18
0
def Branchingratios( opt="m" ):

    from ConstrainedFit import clsq

    data= [ 0.265, 0.28, 0.37, 0.166, 0.42, 0.5, 0.20, 0.16,
            0.72, 0.6, 0.37, 0.64, 0.45, 0.028, 10.0, 7.5 ]
    errors= [ 0.014, 0.05, 0.06, 0.013, 0.15, 0.2, 0.08, 0.08,
              0.15, 0.4, 0.16, 0.40, 0.45, 0.009, 5.0, 2.5 ]
    # Error scale factor a la Blobel lecture:
    if "e" in opt:
        print( "Apply scaling *2.8 of error[13]" )
        errors[13]= errors[13]*2.8
    covm= clsq.covmFromErrors( errors )

    # PDG values as start values, last number is 5.5%, not 0.55 as in br.txt
    upar= [ 0.33, 0.36, 0.16, 0.09, 0.055 ]
    upnames= { 0: "B1", 1: "B2", 2: "B3", 3: "B4", 4: "B5" }

    def brConstrFun( mpar, upar ):
        constraints= []
        x= []
        for i in range( 5 ):
            x.append( upar[i] )
        for i in range( 5, 21 ):
            x.append( mpar[i-5] )

        constraints.append( x[0]+x[1]+x[2]+x[3]+x[4]-1.0 )
        constraints.append( x[3]-x[5]*x[0] )
        constraints.append( x[3]-x[6]*x[0] )
        constraints.append( x[3]-x[7]*x[0] )

        constraints.append( x[3]-(x[1]+x[2])*x[8] )
        constraints.append( x[3]-(x[1]+x[2])*x[9] )
        constraints.append( x[3]-(x[1]+x[2])*x[10] )
        constraints.append( x[3]-(x[1]+x[2])*x[11] )
        constraints.append( x[3]-(x[1]+x[2])*x[12] )

        constraints.append( x[1]-(x[1]+x[2])*x[13] )
        constraints.append( x[1]-(x[1]+x[2])*x[14] )

        constraints.append( x[0]-(x[1]+x[2])*x[15] )
        constraints.append( x[0]-(x[1]+x[2])*x[16] )

        constraints.append( 3.0*x[4]-x[0]*x[17] )

        constraints.append( x[3]-x[18] )

        constraints.append( (x[1]+x[2])-x[4]*x[19] )
        constraints.append( (x[1]+x[2])-x[4]*x[20] )

        return constraints

    solver= clsq.clsqSolver( data, covm, upar, brConstrFun, epsilon=0.00001,
                             uparnames=upnames )
    print( "Constraints before solution" )
    print( solver.getConstraints() )
    lBlobel= False
    if "b" in opt:
        lBlobel= True
    lResidual= False
    if "r" in opt:
        lResidual= True
    solver.solve( lBlobel=lBlobel, lResidual=lResidual )
    lcov= False
    lcorr= False
    if "corr" in opt:
        lcov= True
        lcorr= True

    ca= clsq.clsqAnalysis( solver )
    ca.printResults( cov=lcov, corr=lcorr )

    if "m" in opt:
        _doMinosAll( solver, "u" )
    if "cont" in opt:
        _doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )

    return