def onedgaussfit(xax, data, err=None, params=[0,1,0,1],fixed=[False,False,False,False], limitedmin=[False,False,False,True], limitedmax=[False,False,False,False], minpars=[0,0,0,0], maxpars=[0,0,0,0], quiet=True, shh=True, veryverbose=False, vheight=True, negamp=False, usemoments=False): """ Inputs: xax - x axis data - y axis err - error corresponding to data params - Fit parameters: Height of background, Amplitude, Shift, Width fixed - Is parameter fixed? limitedmin/minpars - set lower limits on each parameter (default: width>0) limitedmax/maxpars - set upper limits on each parameter quiet - should MPFIT output each iteration? shh - output final parameters? usemoments - replace default parameters with moments Returns: Fit parameters Model Fit errors chi2 """ def mpfitfun(x,y,err): if err == None: def f(p,fjac=None): return [0,(y-onedgaussian(x,*p))] else: def f(p,fjac=None): return [0,(y-onedgaussian(x,*p))/err] return f if xax == None: xax = numpy.arange(len(data)) if vheight is False: height = params[0] fixed[0] = True if usemoments: params = onedmoments(xax,data,vheight=vheight,negamp=negamp, veryverbose=veryverbose) if vheight is False: params = [height]+params if veryverbose: print "OneD moments: h: %g a: %g c: %g w: %g" % tuple(params) parinfo = [ {'n':0,'value':params[0],'limits':[minpars[0],maxpars[0]],'limited':[limitedmin[0],limitedmax[0]],'fixed':fixed[0],'parname':"HEIGHT",'error':0} , {'n':1,'value':params[1],'limits':[minpars[1],maxpars[1]],'limited':[limitedmin[1],limitedmax[1]],'fixed':fixed[1],'parname':"AMPLITUDE",'error':0}, {'n':2,'value':params[2],'limits':[minpars[2],maxpars[2]],'limited':[limitedmin[2],limitedmax[2]],'fixed':fixed[2],'parname':"SHIFT",'error':0}, {'n':3,'value':params[3],'limits':[minpars[3],maxpars[3]],'limited':[limitedmin[3],limitedmax[3]],'fixed':fixed[3],'parname':"WIDTH",'error':0}] mp = mpfit(mpfitfun(xax,data,err),parinfo=parinfo,quiet=quiet) mpp = mp.params mpperr = mp.perror chi2 = mp.fnorm if mp.status == 0: raise Exception(mp.errmsg) if (not shh) or veryverbose: print "Fit status: ",mp.status for i,p in enumerate(mpp): parinfo[i]['value'] = p print parinfo[i]['parname'],p," +/- ",mpperr[i] print "Chi2: ",mp.fnorm," Reduced Chi2: ",mp.fnorm/len(data)," DOF:",len(data)-len(mpp) return mpp,onedgaussian(xax,*mpp),mpperr,chi2
def multigaussfit(xax, data, ngauss=1, err=None, params=[1,0,1], fixed=[False,False,False], limitedmin=[False,False,True], limitedmax=[False,False,False], minpars=[0,0,0], maxpars=[0,0,0], quiet=True, shh=True, veryverbose=False): """ An improvement on onedgaussfit. Lets you fit multiple gaussians. Inputs: xax - x axis data - y axis ngauss - How many gaussians to fit? Default 1 (this could supersede onedgaussfit) err - error corresponding to data These parameters need to have length = 3*ngauss. If ngauss > 1 and length = 3, they will be replicated ngauss times, otherwise they will be reset to defaults: params - Fit parameters: [amplitude, offset, width] * ngauss If len(params) % 3 == 0, ngauss will be set to len(params) / 3 fixed - Is parameter fixed? limitedmin/minpars - set lower limits on each parameter (default: width>0) limitedmax/maxpars - set upper limits on each parameter quiet - should MPFIT output each iteration? shh - output final parameters? Returns: Fit parameters Model Fit errors chi2 """ if len(params) != ngauss and (len(params) / 3) > ngauss: ngauss = len(params) / 3 if isinstance(params,numpy.ndarray): params=params.tolist() # make sure all various things are the right length; if they're not, fix them using the defaults for parlist in (params,fixed,limitedmin,limitedmax,minpars,maxpars): if len(parlist) != 3*ngauss: # if you leave the defaults, or enter something that can be multiplied by 3 to get to the # right number of gaussians, it will just replicate if len(parlist) == 3: parlist *= ngauss elif parlist==params: parlist[:] = [1,0,1] * ngauss elif parlist==fixed or parlist==limitedmax: parlist[:] = [False,False,False] * ngauss elif parlist==limitedmin: parlist[:] = [False,False,True] * ngauss elif parlist==minpars or parlist==maxpars: parlist[:] = [0,0,0] * ngauss def mpfitfun(x,y,err): if err == None: def f(p,fjac=None): return [0,(y-n_gaussian(pars=p)(x))] else: def f(p,fjac=None): return [0,(y-n_gaussian(pars=p)(x))/err] return f if xax == None: xax = numpy.arange(len(data)) parnames = {0:"AMPLITUDE",1:"SHIFT",2:"WIDTH"} parinfo = [ {'n':ii, 'value':params[ii], 'limits':[minpars[ii],maxpars[ii]], 'limited':[limitedmin[ii],limitedmax[ii]], 'fixed':fixed[ii], 'parname':parnames[ii%3]+str(ii%3), 'error':ii} for ii in xrange(len(params)) ] if veryverbose: print "GUESSES: " print "\n".join(["%s: %s" % (p['parname'],p['value']) for p in parinfo]) mp = mpfit(mpfitfun(xax,data,err),parinfo=parinfo,quiet=quiet) mpp = mp.params mpperr = mp.perror chi2 = mp.fnorm if mp.status == 0: raise Exception(mp.errmsg) if not shh: print "Final fit values: " for i,p in enumerate(mpp): parinfo[i]['value'] = p print parinfo[i]['parname'],p," +/- ",mpperr[i] print "Chi2: ",mp.fnorm," Reduced Chi2: ",mp.fnorm/len(data)," DOF:",len(data)-len(mpp) return mpp,n_gaussian(pars=mpp)(xax),mpperr,chi2
def gaussfit(data,err=None,params=[],autoderiv=1,return_all=0,circle=0, fixed=numpy.repeat(False,7),limitedmin=[False,False,False,False,True,True,True], limitedmax=[False,False,False,False,False,False,True], usemoment=numpy.array([],dtype='bool'), minpars=numpy.repeat(0,7),maxpars=[0,0,0,0,0,0,360], rotate=1,vheight=1,quiet=True,returnmp=False, returnfitimage=False,**kwargs): """ Gaussian fitter with the ability to fit a variety of different forms of 2-dimensional gaussian. Input Parameters: data - 2-dimensional data array err=None - error array with same size as data array params=[] - initial input parameters for Gaussian function. (height, amplitude, x, y, width_x, width_y, rota) if not input, these will be determined from the moments of the system, assuming no rotation autoderiv=1 - use the autoderiv provided in the lmder.f function (the alternative is to us an analytic derivative with lmdif.f: this method is less robust) return_all=0 - Default is to return only the Gaussian parameters. 1 - fit params, fit error returnfitimage - returns (best fit params,best fit image) returnmp - returns the full mpfit struct circle=0 - default is an elliptical gaussian (different x, y widths), but can reduce the input by one parameter if it's a circular gaussian rotate=1 - default allows rotation of the gaussian ellipse. Can remove last parameter by setting rotate=0. numpy.expects angle in DEGREES vheight=1 - default allows a variable height-above-zero, i.e. an additive constant for the Gaussian function. Can remove first parameter by setting this to 0 usemoment - can choose which parameters to use a moment estimation for. Other parameters will be taken from params. Needs to be a boolean array. Output: Default output is a set of Gaussian parameters with the same shape as the input parameters Can also output the covariance matrix, 'infodict' that contains a lot more detail about the fit (see scipy.optimize.leastsq), and a message from leastsq telling what the exit status of the fitting routine was Warning: Does NOT necessarily output a rotation angle between 0 and 360 degrees. """ usemoment=numpy.array(usemoment,dtype='bool') params=numpy.array(params,dtype='float') if usemoment.any() and len(params)==len(usemoment): moment = numpy.array(moments(data,circle,rotate,vheight,**kwargs),dtype='float') params[usemoment] = moment[usemoment] elif params == [] or len(params)==0: params = (moments(data,circle,rotate,vheight,**kwargs)) if vheight==0: vheight=1 params = numpy.concatenate([[0],params]) fixed[0] = 1 # mpfit will fail if it is given a start parameter outside the allowed range: for i in xrange(len(params)): if params[i] > maxpars[i] and limitedmax[i]: params[i] = maxpars[i] if params[i] < minpars[i] and limitedmin[i]: params[i] = minpars[i] if err == None: errorfunction = lambda p: numpy.ravel((twodgaussian(p,circle,rotate,vheight)\ (*numpy.indices(data.shape)) - data)) else: errorfunction = lambda p: numpy.ravel((twodgaussian(p,circle,rotate,vheight)\ (*numpy.indices(data.shape)) - data)/err) def mpfitfun(data,err): if err == None: def f(p,fjac=None): return [0,numpy.ravel(data-twodgaussian(p,circle,rotate,vheight)\ (*numpy.indices(data.shape)))] else: def f(p,fjac=None): return [0,numpy.ravel((data-twodgaussian(p,circle,rotate,vheight)\ (*numpy.indices(data.shape)))/err)] return f parinfo = [ {'n':1,'value':params[1],'limits':[minpars[1],maxpars[1]],'limited':[limitedmin[1],limitedmax[1]],'fixed':fixed[1],'parname':"AMPLITUDE",'error':0}, {'n':2,'value':params[2],'limits':[minpars[2],maxpars[2]],'limited':[limitedmin[2],limitedmax[2]],'fixed':fixed[2],'parname':"XSHIFT",'error':0}, {'n':3,'value':params[3],'limits':[minpars[3],maxpars[3]],'limited':[limitedmin[3],limitedmax[3]],'fixed':fixed[3],'parname':"YSHIFT",'error':0}, {'n':4,'value':params[4],'limits':[minpars[4],maxpars[4]],'limited':[limitedmin[4],limitedmax[4]],'fixed':fixed[4],'parname':"XWIDTH",'error':0} ] if vheight == 1: parinfo.insert(0,{'n':0,'value':params[0],'limits':[minpars[0],maxpars[0]],'limited':[limitedmin[0],limitedmax[0]],'fixed':fixed[0],'parname':"HEIGHT",'error':0}) if circle == 0: parinfo.append({'n':5,'value':params[5],'limits':[minpars[5],maxpars[5]],'limited':[limitedmin[5],limitedmax[5]],'fixed':fixed[5],'parname':"YWIDTH",'error':0}) if rotate == 1: parinfo.append({'n':6,'value':params[6],'limits':[minpars[6],maxpars[6]],'limited':[limitedmin[6],limitedmax[6]],'fixed':fixed[6],'parname':"ROTATION",'error':0}) if autoderiv == 0: # the analytic derivative, while not terribly difficult, is less # efficient and useful. I only bothered putting it here because I was # instructed to do so for a class project - please ask if you would # like this feature implemented raise ValueError("I'm sorry, I haven't implemented this feature yet.") else: # p, cov, infodict, errmsg, success = optimize.leastsq(errorfunction,\ # params, full_output=1) mp = mpfit(mpfitfun(data,err),parinfo=parinfo,quiet=quiet) if returnmp: returns = (mp) elif return_all == 0: returns = mp.params elif return_all == 1: returns = mp.params,mp.perror if returnfitimage: fitimage = twodgaussian(mp.params,circle,rotate,vheight)(*numpy.indices(data.shape)) returns = (returns,fitimage) return returns