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 is 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 is 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=True, return_all=False, circle=False, 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 is 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 is 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