analyseScript/Analyser/FitAnalyser.py

import numpy as np
from uncertainties import ufloat

import lmfit
from lmfit.models import (ConstantModel, ComplexConstantModel, LinearModel, QuadraticModel,
                          PolynomialModel, SineModel, GaussianModel, Gaussian2dModel, LorentzianModel,
                          SplitLorentzianModel, VoigtModel, PseudoVoigtModel, MoffatModel,
                          Pearson7Model, StudentsTModel, BreitWignerModel, LognormalModel,
                          DampedOscillatorModel, ExponentialGaussianModel, SkewedGaussianModel,
                          SkewedVoigtModel, ThermalDistributionModel, DoniachModel, PowerLawModel,
                          ExponentialModel, StepModel, RectangleModel, ExpressionModel, DampedHarmonicOscillatorModel)
from lmfit.models import (guess_from_peak, guess_from_peak2d, fwhm_expr, height_expr, 
                          update_param_vals)
from lmfit.lineshapes import (not_zero, breit_wigner, damped_oscillator, dho, doniach,
                              expgaussian, exponential, gaussian, gaussian2d,
                              linear, lognormal, lorentzian, moffat, parabolic,
                              pearson7, powerlaw, pvoigt, rectangle, sine,
                              skewed_gaussian, skewed_voigt, split_lorentzian, step,
                              students_t, thermal_distribution, tiny, voigt)
from lmfit import Model
import numpy as np
from numpy import (arctan, copysign, cos, exp, isclose, isnan, log, pi, real,
                   sin, sqrt, where)
from scipy.special import erf, erfc
from scipy.special import gamma as gamfcn
from scipy.special import wofz
from scipy.optimize import curve_fit
from scipy.interpolate import CubicSpline
from scipy.ndimage import gaussian_filter, rotate
import scipy.constants as const

import xarray as xr

import copy

import matplotlib.pyplot as plt


log2 = log(2)
s2pi = sqrt(2*pi)
s2 = sqrt(2.0)

        
def gaussianWithOffset(x, amplitude=1.0, center=0.0, sigma=1.0, offset=0.0):
    """Return a 1-dimensional Gaussian function with an offset.

    gaussian(x, amplitude, center, sigma) =
        (amplitude/(s2pi*sigma)) * exp(-(1.0*x-center)**2 / (2*sigma**2))

    """
    return ((amplitude/(max(tiny, s2pi*sigma)))
            * exp(-(1.0*x-center)**2 / max(tiny, (2*sigma**2))) + offset)
        

def lorentzianWithOffset(x, amplitude=1.0, center=0.0, sigma=1.0, offset=0.0):
    return ((amplitude/(1 + ((1.0*x-center)/max(tiny, sigma))**2))
            / max(tiny, (pi*sigma)) + offset)
    

def exponentialWithOffset(x, amplitude=1.0, decay=1.0, offset=0.0):
    decay = not_zero(decay)
    return amplitude * exp(-x/decay) + offset


def expansion(x, amplitude=1.0, offset=0.0):
    return np.sqrt(amplitude*x*x + offset)


def dampingOscillation(x, center=0, amplitude=1.0, frequency=1.0, decay=1.0, offset=0.0):
    return amplitude * np.exp(-decay*x)*np.sin(2*np.pi*frequency*(x-center)) + offset

    
def two_gaussian2d(x, y=0.0, A_amplitude=1.0, A_centerx=0.0, A_centery=0.0, A_sigmax=1.0,
               A_sigmay=1.0, B_amplitude=1.0, B_centerx=0.0, B_centery=0.0, B_sigmax=1.0,
               B_sigmay=1.0):
    """Return a 2-dimensional Gaussian function.

    gaussian2d(x, y, amplitude, centerx, centery, sigmax, sigmay) =
        amplitude/(2*pi*sigmax*sigmay) * exp(-(x-centerx)**2/(2*sigmax**2)
                                             -(y-centery)**2/(2*sigmay**2))

    """
    z = A_amplitude*(gaussian(x, amplitude=1, center=A_centerx, sigma=A_sigmax) *
                   gaussian(y, amplitude=1, center=A_centery, sigma=A_sigmay))
    z += B_amplitude*(gaussian(x, amplitude=1, center=B_centerx, sigma=B_sigmax) *
                   gaussian(y, amplitude=1, center=B_centery, sigma=B_sigmay))
    return z


def polylog_tab(pow, x, order=100):
    """Calculationg the polylog sum_i(x^i/i^pow), up to the order-th element of the sum

    :param pow: power in denominator of sum
    :type pow: int (can be float)
    :param x: argument of Polylogarithm
    :type x: float or 1D numpy array
    :return: value of polylog(x)
    :rtype: same as x, float or 1D numpy array
    """

    sum = 0
    for k in range(1,order):
        sum  += x ** k /k **pow
    return sum

# Creating array for interpolation
x_int = np.linspace(0, 1.00001, 100000)
poly_tab = polylog_tab(2,x_int)

# Creating function interpolating between the Polylog values calculated before
polylog_int = CubicSpline(x_int, poly_tab)


def thermal(x, x0, amp, sigma):
    """Calculating thermal density distribution in 1D (scaled such that if amp=1, return = 1)

    :param x: axis
    :type x: float or 1d array
    :param x0: position of peak along axis
    :type x0: float
    :param amp: amplitude of function
    :type amp: float
    :param sigma: width of function
    :type sigma: float
    :return: calculated function value
    :rtype: float or 1D array
    """
    res = np.exp(-0.5 * (x-x0)**2 / sigma**2)
    return amp/1.643 * polylog_int(res)


def Thomas_Fermi_1d(x, x0, amp, sigma):
    res = (1- ((x-x0)/sigma)**2)
    res = np.where(res > 0, res, 0)
    res = res**(3/2)
    return amp * res


def density_1d(x, x0_bec, x0_th, amp_bec, amp_th, sigma_bec, sigma_th):
    return thermal(x, x0_th, amp_th, sigma_th) + Thomas_Fermi_1d(x, x0_bec, amp_bec, sigma_bec)


def polylog(pow, x):
    order = 15
    sum = 0
    for k in range(1,order):
        sum  += x ** k /k **pow
    return sum


def ThomasFermi_2d(x, y=0.0, centerx=0.0, centery=0.0, amplitude=1.0, sigmax=1.0, sigmay=1.0):

    res = (1- ((x-centerx)/(sigmax))**2 - ((y-centery)/(sigmay))**2)
    res = np.where(res > 0, res, 0)
    res = res**(3/2)
    return amplitude * res


def polylog2_2d(x, y=0.0, centerx=0.0, centery=0.0, amplitude=1.0, sigmax=1.0, sigmay=1.0):
    ## Approximation of the polylog function with 2D gaussian as argument. -> discribes the thermal part of the cloud
    return amplitude/1.643  * polylog_int(np.exp( -((x-centerx)**2/(2 * sigmax**2))-((y-centery)**2/( 2 * sigmay**2)) ))

def rotate_coord(x,y, rot_angle):
    
    rot_angle *= 2*np.pi/360
    x_og = x
    x = x_og * np.cos(rot_angle) + y * np.sin(rot_angle)
    y = -x_og * np.sin(rot_angle) + y * np.cos(rot_angle)
    return x, y
    
def density_profile_BEC_2d(x, y=0.0, amp_bec=1.0, amp_th=1.0, x0_bec=0.0, y0_bec=0.0, x0_th=0.0, y0_th=0.0,
                           sigmax_bec=1.0, sigmay_bec=1.0, sigma_th=1.0, rot_angle=None):
    
    if rot_angle is not None:
        x, y = rotate_coord(x,y, rot_angle)
        x0_bec, y0_bec = rotate_coord(x0_bec, y0_bec, rot_angle)
        x0_th, y0_th = rotate_coord(x0_th, y0_th, rot_angle)

    
    return ThomasFermi_2d(x=x, y=y, centerx=x0_bec, centery=y0_bec,
                          amplitude=amp_bec, sigmax=sigmax_bec, sigmay=sigmay_bec
                          ) + polylog2_2d(x=x, y=y, centerx=x0_th, centery=y0_th,
                                          amplitude=amp_th, sigmax=sigma_th,sigmay=sigma_th)


class GaussianWithOffsetModel(Model):
    
    fwhm_factor = 2*np.sqrt(2*np.log(2))
    height_factor = 1./np.sqrt(2*np.pi)
    
    def __init__(self, independent_vars=['x'], nan_policy='raise', prefix='', name=None, **kwargs):
        
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(gaussianWithOffset, **kwargs)
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('sigma', min=0)
        self.set_param_hint('fwhm', expr=fwhm_expr(self))
        self.set_param_hint('height', expr=height_expr(self))
    
    def guess(self, data, x, negative=False, **kwargs):
        offset = np.min(data)
        data = data - offset
        pars = guess_from_peak(self, data, x, negative)
        pars.add('offset', value=offset)
        return update_param_vals(pars, self.prefix, **kwargs)


class LorentzianWithOffsetModel(Model):

    fwhm_factor = 2.0
    height_factor = 1./np.pi

    def __init__(self, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(lorentzianWithOffset, **kwargs)
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('sigma', min=0)
        self.set_param_hint('fwhm', expr=fwhm_expr(self))
        self.set_param_hint('height', expr=height_expr(self))

    def guess(self, data, x, negative=False, **kwargs):
        """Estimate initial model parameter values from data."""
        offset = np.min(data)
        data = data - offset
        pars = guess_from_peak(self, data, x, negative, ampscale=1.25)
        pars.add('offset', value=offset)
        return update_param_vals(pars, self.prefix, **kwargs)    


class ExponentialWithOffsetModel(Model):

    def __init__(self, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(exponentialWithOffset, **kwargs)

    def guess(self, data, x, **kwargs):
        """Estimate initial model parameter values from data."""
        offset = np.min(data)
        data = data - offset
        try:
            sval, oval = np.polyfit(x, np.log(abs(data)+1.e-15), 1)
        except TypeError:
            sval, oval = 1., np.log(abs(max(data)+1.e-9))
        pars = self.make_params(amplitude=np.exp(oval), decay=-1.0/sval)
        pars.add('offset', value=offset)
        return update_param_vals(pars, self.prefix, **kwargs)
    

class ExpansionModel(Model):

    def __init__(self, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(expansion, **kwargs)

    def guess(self, data, x, **kwargs):
        """Estimate initial model parameter values from data."""
        
        popt1, pcov1 = curve_fit(expansion, x, data)
        pars = self.make_params(amplitude=popt1[0], offset=popt1[1])
        
        return update_param_vals(pars, self.prefix, **kwargs)
        

class DampingOscillationModel(Model):
    
    def __init__(self, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(dampingOscillation, **kwargs)

    def guess(self, data, x, **kwargs):
        """Estimate initial model parameter values from data."""
        try:
            popt1, pcov1 = curve_fit(dampingOscillation, x, data, np.array(0, 5, 5e2, 1e3, 16))
            pars = self.make_params(center=popt1[0], amplitude=popt1[1], frequency=popt1[2], decay=popt1[3], offset=popt1[4])
        except:
            pars = self.make_params(center=0, amplitude=5.0, frequency=5e2, decay=1.0e3, offset=16.0)
        
        return update_param_vals(pars, self.prefix, **kwargs)


class TwoGaussian2dModel(Model):
    
    fwhm_factor = 2*np.sqrt(2*np.log(2))
    height_factor = 1./2*np.pi

    def __init__(self, independent_vars=['x', 'y'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        
        self.helperModel = Gaussian2dModel()
        
        super().__init__(two_gaussian2d, **kwargs)
        
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('delta', value=-1, max=0)
        self.set_param_hint('A_sigmax', expr=f'{self.prefix}delta + {self.prefix}B_sigmax')

    def guess(self, data, x, y, negative=False, **kwargs):
        pars_guess = guess_from_peak2d(self.helperModel, data, x, y, negative)
        pars = self.make_params(A_amplitude=pars_guess['amplitude'].value, A_centerx=pars_guess['centerx'].value, A_centery=pars_guess['centery'].value,
                             A_sigmax=pars_guess['sigmax'].value, A_sigmay=pars_guess['sigmay'].value, 
                             B_amplitude=pars_guess['amplitude'].value, B_centerx=pars_guess['centerx'].value, B_centery=pars_guess['centery'].value,
                             B_sigmax=pars_guess['sigmax'].value, B_sigmay=pars_guess['sigmay'].value)
        
        pars[f'{self.prefix}A_sigmax'].set(expr=f'delta + {self.prefix}B_sigmax')
        pars.add(f'{self.prefix}delta', value=-1, max=0, min=-np.inf, vary=True)
        pars[f'{self.prefix}A_sigmay'].set(min=0.0)
        pars[f'{self.prefix}B_sigmax'].set(min=0.0)
        pars[f'{self.prefix}B_sigmay'].set(min=0.0)
        
        return pars


class Polylog22dModel(Model):

    fwhm_factor = 2*np.sqrt(2*np.log(2))
    height_factor = 1./2*np.pi

    def __init__(self, independent_vars=['x', 'y'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(polylog2_2d, **kwargs)
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('Rx', min=0)
        self.set_param_hint('Ry', min=0)

    def guess(self, data, x, y, negative=False, **kwargs):
        """Estimate initial model parameter values from data."""
        pars = guess_from_peak2d(self, data, x, y, negative)
        return update_param_vals(pars, self.prefix, **kwargs)


class ThomasFermi2dModel(Model):

    fwhm_factor = 1
    height_factor = 0.5

    def __init__(self, independent_vars=['x', 'y'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
        super().__init__(ThomasFermi_2d, **kwargs)
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('Rx', min=0)
        self.set_param_hint('Ry', min=0)

    def guess(self, data, x, y, negative=False, **kwargs):
        """Estimate initial model parameter values from data."""
        pars = guess_from_peak2d(self, data, x, y, negative)
        
        # amplitude = pars['amplitude'].value
        # simgax = pars['sigmax'].value
        # sigmay = pars['sigmay'].value
        
        # pars['amplitude'].set(value=amplitude/s2pi/simgax/sigmay)
        
        simgax = pars['sigmax'].value
        sigmay = pars['sigmay'].value
        pars['simgax'].set(value=simgax / 2.355)
        pars['sigmay'].set(value=sigmay / 2.355)
        
        return update_param_vals(pars, self.prefix, **kwargs)
    

class DensityProfileBEC2dModel(lmfit.Model):
    """ Fitting class to do 2D bimodal fit on OD of absorption images
    """
    def __init__(self,
                independent_vars=['x', 'y'],
                prefix='',
                nan_policy='raise',
                atom_n_conv=144,
                pre_check=False,
                post_check=False,
                is_debug=False,
                **kwargs
        ):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})

        self.atom_n_conv = atom_n_conv
        self.pre_check = pre_check
        self.post_check = post_check
        self.is_debug=is_debug
        super().__init__(density_profile_BEC_2d, **kwargs)
        self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        # self.set_param_hint('BEC_sigmax', min=0)
        self.set_param_hint('amp_bec', min=0)
        self.set_param_hint('amp_th', min=0)
        self.set_param_hint('x0_bec', min=0)
        self.set_param_hint('y0_bec', min=0)
        self.set_param_hint('x0_th', min=0)
        self.set_param_hint('y0_th', min=0)
        self.set_param_hint('sigmax_bec', min=0)
        self.set_param_hint('sigmay_bec', min=0)
        self.set_param_hint('sigma_th', min=0)

        self.set_param_hint('rot_angle', min=-90, max=90)
        
        self.set_param_hint('atom_number_bec', expr=f'{self.prefix}amp_bec / 5 * 2 * 3.14159265359 * {self.prefix}sigmax_bec * {self.prefix}sigmay_bec')
        self.set_param_hint('atom_number_th', expr=f'{self.prefix}amp_th * 2 * 3.14159265359 * 1.20206 / 1.643 * {self.prefix}sigma_th * {self.prefix}sigma_th')
        self.set_param_hint('condensate_fraction', expr=f'{self.prefix}atom_number_bec / ({self.prefix}atom_number_bec + {self.prefix}atom_number_th)')

    def guess(self, data, x, y, rot_angle=0, vary_rot=False, pre_check=False, post_check=False, **kwargs):
        """Estimate and create initial model parameters for 2d  bimodal fit, by doing a 1d bimodal fit along an integrated slice of the image 
    
        :param data: Flattened 2d array, in form [a_00, a_10, a_20, ..., a_01, a_02, .. ,a_XY] with a_xy, x_dim=X, y_dim=Y
        :type data: 1d numpy array
        :param x: flattened X output of np.meshgrid(x_axis,y_axis) in form: [x1, x2, .., xX, x1, x2, .., xX, .. Y times ..]
        :type x: 1d numpy array
        :param y: flattened Y output of np.meshgrid(x_axis,y_axis) in form: [y1, y1, .., y1 (X times), y2, y2, .., y2 (X times), .. Y times ..]
        :type y: 1d numpy array
        :param pre_check: if True the amplitude of the 1d fit is used to guess if the image is purely BEC or thermal and 
                            the corresponding amplitude of the 2d fit is set to zero and not varied to speed up the fitting, defaults to False
        :type pre_check: bool, optional
        :param post_check: if True, after doing a 2d bimodal fit the number of atoms surrounding the fitted BEC is counted and if the value is
                            below a certain threshhold the fit is done again with the thermal amplitude set to zero, defaults to False
        :type post_check: bool, optional
        :return: initial parameters for 2d fit
        :rtype: params object (lmfit)
        """
        self.pre_check = pre_check 
        self.post_check = post_check
        
        # reshaping the image to 2D in the form [[a_00, a_01, .., a_0Y], [a_10,.., a_1Y], .., [a_X0, .., a_XY]], with a_xy
        x_width = len(np.unique(x))
        y_width = len(np.unique(y))
        x_1d = np.linspace(x[0], x[-1], x_width)
        y_1d = np.linspace(y[0], y[-1], y_width)

        data = np.reshape(data, (y_width, x_width))
        data = data.T

        if rot_angle != 0:
            data = rotate(data, rot_angle, reshape=False)

        shape = np.shape(data)
        if self.is_debug:
            print(f'shape: {shape}')
        max_width = np.max(shape)

        # binarizing image to guess BEC width and calculate center
        thresh = self.calc_thresh(data,thresh_val=0.5)
        # calculating center of cloud by statistical distribution of binarized image
        center_pix = self.calc_cen_pix(thresh)
        center = self.center_pix_conv(center_pix, x_1d, y_1d)
        # guessing BEC width, or better of width of center blob if no BEC is present
        BEC_width_guess = self.guess_BEC_width(thresh, center_pix)

        # plot binarized image and center position for debugging
        if self.is_debug:
            X, Y = np.meshgrid(x_1d,y_1d)
            plt.pcolormesh(X,Y, thresh.T, cmap='jet')
            plt.plot(center[0], center[1], marker='x', markersize=25, color='green')
            plt.gca().set_aspect('equal')
            plt.title(f'Binarized image for guessing BEC width + center position (BEC_width: x={BEC_width_guess[0]:.0f}, y={BEC_width_guess[1]:.0f} pix)')
            plt.xlabel('x_axis')
            plt.ylabel('y_axis')
            plt.show()

        # The 1d fit is done along the short axis of the BEC (decided via the BEC_width guess)
        if BEC_width_guess[0] < BEC_width_guess[1]:
            if self.is_debug:
                print(f'x smaller y, 1d fit along x')
            s_width_ind = 0
            x_fit = x_1d
            # slice of the image along the short BEC axis with width of BEC width is taken
            X_guess = np.sum(data[:, round(center_pix[1] - BEC_width_guess[1]/2) : round(center_pix[1] + BEC_width_guess[1]/2)], 1) / len(data[0,round(center_pix[1] - BEC_width_guess[1]/2) : round(center_pix[1] + BEC_width_guess[1]/2)])
        else:
            if self.is_debug:
                print(f'y smaller x, 1d fit along y')
            s_width_ind = 1
            x_fit = y_1d
            X_guess = np.sum(data[round(center_pix[0] - BEC_width_guess[0]/2) : round(center_pix[0] + BEC_width_guess[0]/2), :], 0) / len(data[0,round(center_pix[0] - BEC_width_guess[0]/2) : round(center_pix[0] + BEC_width_guess[0]/2)])


        # Creating 1d fit init params + Performing fit 
        

        max_val = np.max(X_guess)

        fitmodel_1d = lmfit.Model(density_1d, independent_vars=['x'])
        params_1d = lmfit.Parameters()
        params_1d.add_many(
            ('x0_bec', center[s_width_ind], True, center[s_width_ind]-10, center[s_width_ind]+10),
            ('x0_th',center[s_width_ind], True, center[s_width_ind]-10, center[s_width_ind]+10),
            ('amp_bec', 0.5 * max_val, True, 0, 1.3 * max_val),
            ('amp_th', 0.5 * max_val, True, 0, 1.3 * max_val),
            ('deltax', 3*BEC_width_guess[s_width_ind], True, 0, max_width),
            # ('sigma_bec',BEC_width_guess[i,j,0]/1.22, True, 0, 50)
            ('sigma_bec',BEC_width_guess[s_width_ind]/1.22, True, 0, BEC_width_guess[s_width_ind]*2)
        )
        params_1d.add('sigma_th', 3*BEC_width_guess[0], min=0, expr=f'0.632*sigma_bec + 0.518*deltax')


        res_1d = fitmodel_1d.fit(X_guess, x=x_fit, params=params_1d)
        bval_1d = res_1d.best_values

        if self.is_debug:
            print('')
            print('1d fit initialization')
            print(f'center = {center}')
            print(f'BEC widths: {BEC_width_guess}')
            print('')
            print('1d init fit values')
            params_1d.pretty_print()
            print('1d fitted values')
            self.print_bval(res_1d)

            plt.plot(x_fit, X_guess, label='1d int. data')
            plt.plot(x_fit, density_1d(x_fit,**bval_1d), label='bimodal fit')
            plt.plot(x_fit, thermal(x_fit,x0=bval_1d['x0_th'], amp=bval_1d['amp_th'], sigma=bval_1d['sigma_th']), label='thermal part')
            plt.legend()
            if s_width_ind==0:
                plt.title('1d fit of data along x-axis')
                plt.xlabel('x_')
            else:
                plt.title('1d fit of data along y-axis')
                plt.xlabel('y_axis')
            plt.show()

        # scaling amplitudes of 1d fit with the maximum value of blurred 2d data 
        amp_conv_1d_2d = np.max(gaussian_filter(data, sigma=1)) / (bval_1d['amp_bec'] + bval_1d['amp_th'])
        max_val = np.max(data)

        params = self.make_params()

        # if precheck enabled and amp_th is 7x higher than amp_bec (value might be changed), amplitude of BEC in 2d fit is set to zero
        if bval_1d['amp_th']/bval_1d['amp_bec'] > 7 and self.pre_check:
            print(f'Image seems to be purely thermal (guessed from 1d fit amplitude)')

            params[f'{self.prefix}amp_bec'].set(value=0, vary=False)
            params[f'{self.prefix}amp_th'].set(value=amp_conv_1d_2d * bval_1d['amp_th'], max=1.3 * max_val, vary=True)
            params[f'{self.prefix}x0_bec'].set(value=1, vary=False)
            params[f'{self.prefix}y0_bec'].set(value=1, vary=False)
            params[f'{self.prefix}x0_th'].set(value=center[0], min=center[0] -10, max=center[0] + 10, vary=True)
            params[f'{self.prefix}y0_th'].set(value=center[1], min=center[1] -10, max=center[1] + 10, vary=True)
            params[f'{self.prefix}sigmax_bec'].set(value=1, vary=False)
            params[f'{self.prefix}sigmay_bec'].set(value=1, vary=False)
            params[f'{self.prefix}sigma_th'].set(value=bval_1d['sigma_th'], max=max_width, vary=True)

        # if precheck enabled and amp_bec is 10x higher than amp_th (value might be changed), amplitude of thermal part in 2d fit is set to zero
        elif bval_1d['amp_bec']/bval_1d['amp_th'] > 10 and self.pre_check:
            print('Image seems to be pure BEC (guessed from 1d fit amplitude)')

            params[f'{self.prefix}amp_bec'].set(value=amp_conv_1d_2d * bval_1d['amp_bec'], max=1.3 * max_val, vary=True)
            params[f'{self.prefix}amp_th'].set(value=0, vary=False)
            params[f'{self.prefix}x0_bec'].set(value=center[0], min=center[0] -10, max=center[0] + 10, vary=True)
            params[f'{self.prefix}y0_bec'].set(value=center[1], min=center[1] -10, max=center[1] + 10, vary=True)
            params[f'{self.prefix}x0_th'].set(value=1, vary=False)
            params[f'{self.prefix}y0_th'].set(value=1, vary=False)
            params[f'{self.prefix}sigma_th'].set(value=1, vary=False)

            if s_width_ind == 0:
                params[f'{self.prefix}sigmax_bec'].set(value=bval_1d['sigma_bec'], max= 2*BEC_width_guess[0], vary=True)
                params[f'{self.prefix}sigmay_bec'].set(value=BEC_width_guess[1]/1.22, max= 2*BEC_width_guess[1], vary=True)
            elif s_width_ind == 1:
                params[f'{self.prefix}sigmax_bec'].set(value=BEC_width_guess[0]/1.22, max= 2*BEC_width_guess[0], vary=True)
                params[f'{self.prefix}sigmay_bec'].set(value=bval_1d['sigma_bec'], max= 2*BEC_width_guess[1], vary=True)
            else:
                print('Error in small width BEC recogintion, s_width_ind should be 0 or 1')

        # params for normal 2d bimodal fit are initialized
        else:
            params[f'{self.prefix}amp_bec'].set(value=amp_conv_1d_2d * bval_1d['amp_bec'], max=1.3 * max_val, vary=True)
            params[f'{self.prefix}amp_th'].set(value=amp_conv_1d_2d * bval_1d['amp_th'], max=1.3 * max_val, vary=True)
            params[f'{self.prefix}x0_bec'].set(value=center[0], min=center[0] -10, max=center[0] + 10, vary=True)
            params[f'{self.prefix}y0_bec'].set(value=center[1], min=center[1] -10, max=center[1] + 10, vary=True)
            params[f'{self.prefix}x0_th'].set(value=center[0], min=center[0] -10, max=center[0] + 10, vary=True)
            params[f'{self.prefix}y0_th'].set(value=center[1], min=center[1] -10, max=center[1] + 10, vary=True)
            params[f'{self.prefix}sigma_th'].set(value=bval_1d['sigma_th'], max=max_width, vary=True)

            if s_width_ind == 0:
                params[f'{self.prefix}sigmax_bec'].set(value=bval_1d['sigma_bec'], max= 2*BEC_width_guess[0], vary=True)
                params[f'{self.prefix}sigmay_bec'].set(value=BEC_width_guess[1]/1.22, max= 2*BEC_width_guess[1], vary=True)
            elif s_width_ind == 1:
                params[f'{self.prefix}sigmax_bec'].set(value=BEC_width_guess[0]/1.22, max= 2*BEC_width_guess[0], vary=True)
                params[f'{self.prefix}sigmay_bec'].set(value=bval_1d['sigma_bec'], max= 2*BEC_width_guess[1], vary=True)
            else:
                print('Error in small width BEC recogintion, s_width_ind should be 0 or 1')

        params[f'{self.prefix}rot_angle'].set(value=-rot_angle, min=-rot_angle-30, max=-rot_angle+30, vary=vary_rot)

        if self.is_debug:
            print('')
            print('Init Params')
            params.pretty_print()
            print('')
        return lmfit.models.update_param_vals(params, self.prefix, **kwargs)


    def fit(self, data, **kwargs):
        """fitting function overwrites parent class fitting function of lmfit, in order to check (if post_check is enabled) 
            if thermal fit completely lies in BEC fit by counting sourrounding number of atoms and comparing it to threshold value

        :param data: Flattened 2d array, in form [a_00, a_10, a_20, ..., a_01, a_02, .. ,a_XY] with a_xy, x_dim=X, y_dim=Y
        :type data: 1d numpy array
        :return: result of 2d fit
        :rtype: result object (lmfit)
        """

        res = super().fit(data, **kwargs)

        if self.is_debug:
            print('bval first fit')
            self.print_bval(res)

        bval = res.best_values
        # Do described post_check if enabled

        if res.params['amp_bec'].vary and res.params['amp_th'].vary and bval['amp_bec']>0.5*bval['amp_th'] and self.post_check:
            
            # creating image by cutting out region around BEC and counting number of atoms
            sigma_cut = max(bval['sigmay_bec'], bval['sigmax_bec'])
            tf_fit = ThomasFermi_2d(kwargs['x'],kwargs['y'],centerx=bval['x0_bec'], centery=bval['y0_bec'], amplitude=bval['amp_bec'], sigmax=bval['sigmax_bec'], sigmay=bval['sigmay_bec'])
            tf_fit_2 = ThomasFermi_2d(kwargs['x'],kwargs['y'],centerx=bval['x0_bec'], centery=bval['y0_bec'], amplitude=bval['amp_bec'], sigmax=1.5 * sigma_cut, sigmay=1.5*sigma_cut)
            mask = np.where(tf_fit > 0, np.nan, data)
            mask = np.where(tf_fit_2 > 0, mask, np.nan)

            N_c = np.nansum(mask)
            # conversion N_count to Pixels
            N_a = self.atom_n_conv * N_c

            #TODO change fixed threshhold to variable
            # If number of atoms around BEC is small the image is guessed to be purely BEC and another 2d fit is performed with setting the thermal amplitude to zero
            if N_a < 6615:
                print('No thermal part detected, performing fit without thermal function')
                params = res.params
                params[f'{self.prefix}amp_th'].set(value=0, vary=False)
                params[f'{self.prefix}x0_th'].set(value=1, vary=False)
                params[f'{self.prefix}y0_th'].set(value=1, vary=False)
                params[f'{self.prefix}sigma_th'].set(value=1, vary=False)

                res = super().fit(data, x=kwargs['x'], y=kwargs['y'], params=params)

                return res

        return res

    def calc_thresh(self, data, thresh_val=0.3, sigma=0.4):
        """Returns thresholded binary image after blurring to guess BEC size

        :param data: 2d image 
        :type data: 2d numpy array
        :param thresh_val: relative threshhold value for binarization with respect to maximum of blurred image
        :param sigma: sigma of gaussian blur filter (see scipy.ndimage.gaussian_filter)
        :return: binary 2d image 
        :rtype: 2d numpy array
        """
        shape = np.shape(data)
        thresh = np.zeros(shape)

        blurred = gaussian_filter(data, sigma=sigma)

        thresh = np.where(blurred < np.max(blurred)*thresh_val, 0, 1)

        return thresh

    def calc_cen_pix(self, thresh1):
        """Calculating the center (in pixel) of a blob (atom cloud) in a binarized image by first calculating the probability distribution along both axes and afterwards the expectation value

        :param thresh1: Binary 2D image in the form [[a_00, a_01, .., a_0Y], [a_10,.., a_1Y], .., [a_X0, .., a_XY]], with a_xy, x_dim=X, y_dim=Y
        :type thresh1: 2D numpy array
        :return: center coordinates of blob in form [x_center, y_center]
        :rtype: 1d numpy array (shape=(1,2))
        """
        cen = np.zeros(2)
        (X,Y) = np.shape(thresh1)

        thresh1 = thresh1 /np.sum(thresh1)

        # marginal distributions
        dx = np.sum(thresh1, 1)
        dy = np.sum(thresh1, 0)

        # expected values
        cen[0] = np.sum(dx * np.arange(X))
        cen[1] = np.sum(dy * np.arange(Y))
        return cen
    
    def center_pix_conv(self, center_pix, x, y):
        """Converts center in pixel to center in values of x and y 

        :param center_pix: pixel values of center
        :type center_pix: numpy array (shape=(1,2))
        :param x: x-axis
        :type x: 1d numpy array
        :param y: y-axis
        :type y: 1d numpy array
        :return: center coordinates in form [x_center, y_center] with respect to the axes
        :rtype: numpy array (shap=(1,2))
        """
        center = np.empty(2)
        center[0] = x[round(center_pix[0])]
        center[1] = y[round(center_pix[1])]
        return center

    def guess_BEC_width(self, thresh, center):
        """ returns width of blob in binarized image along both axis through the center 

        :param thresh: Binary 2D image in the form [[a_00, a_01, .., a_0Y], [a_10,.., a_1Y], .., [a_X0, .., a_XY]], with a_xy, x_dim=X, y_dim=Y
        :type thresh: 2d numpy array
        :param center: center of blob in image in form [x_center, y_center] in pixel
        :type center: 1d numpy array (shape=(1,2))
        :return: width of blob in image as [x_width, y_width]
        :rtype: 1d numpy array (shape=(1,2))
        """
        shape = np.shape(thresh)

        if len(shape) == 2:
            BEC_width_guess = np.array([np.sum(thresh[:, round(center[1])]), np.sum(thresh[round(center[0]), :]) ])
            for i in range(2):
                if BEC_width_guess[i] <= 0:
                    BEC_width_guess[i] = 1

        else:
            print("Shape of data is wrong, output is empty")

        return BEC_width_guess

    def cond_frac(self, results, X, Y):
        """Returns condensate fraction of 2d fitting result

        :param results: result of 2d bimodal fit
        :type results: result object (lmfit)
        :param X: X output of np.meshgrid(x_axis,y_axis) in form: [[x1, x2, .., xX], [x1, x2, .., xX] .. Y times ..]
        :type X: 2d numpy array
        :param Y: Y output of np.meshgrid(x_axis,y_axis) in form: [[y1, y1, .., y1 (X times)], [y2, y2, .., y2 (X times)], .. Y times ..]
        :type Y: 2d numpy array
        :return: condensate fraction 
        :rtype: float between 0 and 1
        """
        bval = results.best_values
        tf_fit = ThomasFermi_2d(X,Y,centerx=bval['x0_bec'], centery=bval['y0_bec'], amplitude=bval['amp_bec'], sigmax=bval['sigmax_bec'], sigmay=bval['sigmay_bec'])
        N_bec = np.sum(tf_fit)
        fit = density_profile_BEC_2d(X,Y, **bval)
        N_ges = np.sum(fit)
        return N_bec/N_ges

    def return_atom_number(self, result, X, Y, is_print=True):
        """Calculating (and printing if enabled) fitted atom number in BEC + thermal state, and condensate fraction

        :param result: result of 2d bimodal fit
        :type result: result object (lmfit)
        :param X: X output of np.meshgrid(x_axis,y_axis) in form: [[x1, x2, .., xX], [x1, x2, .., xX] .. Y times ..]
        :type X: 2d numpy array
        :param Y: Y output of np.meshgrid(x_axis,y_axis) in form: [[y1, y1, .., y1 (X times)], [y2, y2, .., y2 (X times)], .. Y times ..]
        :type Y: 2d numpy array
        :param is_print: if true results are printed, defaults to True
        :type is_print: bool, optional
        :return: dictionary with total atom number N, BEC N_bec, thermal N_th and condensate fraction cond_f
        :rtype: dictionary
        """
        bval = result.best_values
        tf_fit = ThomasFermi_2d(X,Y,centerx=bval['x0_bec'], centery=bval['y0_bec'], amplitude=bval['amp_bec'], sigmax=bval['sigmax_bec'], sigmay=bval['sigmay_bec'])
        N_bec = self.atom_n_conv * np.sum(tf_fit)

        th_fit = polylog2_2d(X, Y, centerx=bval['x0_th'], centery=bval['y0_th'], amplitude=bval['amp_th'], sigmax=bval['sigma_th'], sigmay=bval['sigma_th'])
        N_th = self.atom_n_conv * np.sum(th_fit)

        N = N_bec + N_th
        frac = N_bec/N
        # fit = density_profile_BEC_2d(X,Y, **bval)
        # N_ges = self.atom_n_conv * np.sum(fit)

        if is_print:
            print()
            print('Atom numbers:')
            print(f'   N_bec: {N_bec :.0f}')
            print(f'   N_th: {N_th :.0f}')
            print(f'   N_ges: {N:.0f}')
            print(f'   Cond. frac: {frac *1e2:.2f} %')
            print('')

        atom_n = {'N' : N, 'N_bec' : N_bec, 'N_th' : N_th, 'cond_f' : frac}
        return atom_n


    def return_temperature(self, result, tof, omg=None, is_print=True, eff_pix=2.472e-6):
        """Returns temperature of thermal cloud

        :param result: result of 2d bimodal fit
        :type result: result object (lmfit)
        :param tof: time of flight
        :type tof: float
        :param omg: geometric average of trapping frequencies, defaults to None
        :type omg: float, if NONE initial cloud size is neglected optional
        :param is_print: if True temperature is printed, defaults to True
        :type is_print: bool, optional
        :param eff_pix: effective pixel size of imaging setup, defaults to 2.472e-6
        :type eff_pix: float, optional
        :return: temperature of atom cloud
        :rtype: float
        """
        R_th = result.best_values['sigma_th'] * eff_pix * np.sqrt(2)
        # print(R_th)
        if omg is None:
            T = R_th**2 * 164*const.u/const.k * (tof**2)**(-1)
        else:
            T = R_th**2 * 164*const.u/const.k * (1/omg**2 + tof**2)**(-1)

        if is_print:
            print(f'Temperature: {T*1e9:.2f} nK')
        return T

    def print_bval(self, res_s):
        """nicely print best fitted values + init values + bounds

        :param res_s: result of 2d bimodal fit
        :type res_s: result object (lmfit)
        """
        keys = res_s.best_values.keys()
        bval = res_s.best_values
        init = res_s.init_params

        for item in keys:
            print(f'{item}: {bval[item]:.3f}, (init = {init[item].value:.3f}), bounds = [{init[item].min:.2f} : {init[item].max :.2f}] ')
        print('')
    

class NewFitModel(Model):
    
    def __init__(self, func, independent_vars=['x'], prefix='', nan_policy='raise',
                 **kwargs):
        kwargs.update({'prefix': prefix, 'nan_policy': nan_policy,
                       'independent_vars': independent_vars})
       
        super().__init__(func, **kwargs)
        
    def guess(self, *args, **kwargs):
        return self.make_params()
    

lmfit_models = {'Constant': ConstantModel,
                'Complex Constant': ComplexConstantModel,
                'Linear': LinearModel,
                'Quadratic': QuadraticModel,
                'Polynomial': PolynomialModel,
                'Gaussian': GaussianModel,
                'Gaussian-2D': Gaussian2dModel,
                'Lorentzian': LorentzianModel,
                'Split-Lorentzian': SplitLorentzianModel,
                'Voigt': VoigtModel,
                'PseudoVoigt': PseudoVoigtModel,
                'Moffat': MoffatModel,
                'Pearson7': Pearson7Model,
                'StudentsT': StudentsTModel,
                'Breit-Wigner': BreitWignerModel,
                'Log-Normal': LognormalModel,
                'Damped Oscillator': DampedOscillatorModel,
                'Damped Harmonic Oscillator': DampedHarmonicOscillatorModel,
                'Exponential Gaussian': ExponentialGaussianModel,
                'Skewed Gaussian': SkewedGaussianModel,
                'Skewed Voigt': SkewedVoigtModel,
                'Thermal Distribution': ThermalDistributionModel,
                'Doniach': DoniachModel,
                'Power Law': PowerLawModel,
                'Exponential': ExponentialModel,
                'Step': StepModel,
                'Rectangle': RectangleModel,
                'Expression': ExpressionModel,
                'Gaussian With Offset':GaussianWithOffsetModel,
                'Lorentzian With Offset':LorentzianWithOffsetModel,
                'Expansion':ExpansionModel,
                'Damping Oscillation Model':DampingOscillationModel,
                'Two Gaussian-2D':TwoGaussian2dModel,
                'Thomas Fermi-2D': ThomasFermi2dModel,
                'Density Profile of BEC-2D': DensityProfileBEC2dModel,
                'Polylog2-2D': polylog2_2d, 
                }


class FitAnalyser():
    """This is a class integrated all the functions to do a fit.
    """

    def __init__(self, fitModel, fitDim=1, **kwargs) -> None:
        """Initialize function

        :param fitModel: The fitting model of fit function 
        :type fitModel: lmfit Model
        :param fitDim: The dimension of the fit, defaults to 1
        :type fitDim: int, optional
        """

        if isinstance(fitModel, str):
            self.fitModel = lmfit_models[fitModel](**kwargs)
        else:
            self.fitModel = fitModel
        
        self.fitDim = fitDim

    def print_params_set_template(self, params=None):
        """Print a template to manually set the initial parameters of the fit

        :param params: An object of Parameters class to print, defaults to None
        :type params: lmfit Paraemters, optional
        """
        
        if params is None:
            params = self.fitModel.make_params()
        
        for key in params:
            res = "params.add("
            res += "name=\"" + key + "\", "
            if not params[key].expr is None:
                res += "expr=\"" + params[key].expr +"\")"
            else:
                res += "value=" + f'{params[key].value:3g}' + ", "
                if str(params[key].max)=="inf":
                    res += "max=np.inf, "
                else:
                    res += "max=" + f'{params[key].max:3g}' + ", "
                if str(params[key].min)=="-inf":
                    res += "min=-np.inf, "
                else:
                    res += "min=" + f'{params[key].min:3g}' + ", "
                res += "vary=" + str(params[key].vary) + ")"
            print(res)
    
    def _guess_1D(self, data, x, **kwargs):
        """Call the guess function of the 1D fit model to guess the initial value.

        :param data: The data to fit
        :type data: 1D numpy array
        :param x: The data of x axis
        :type x: 1D numpy array
        :return: The guessed initial parameters for the fit
        :rtype: lmfit Parameters
        """
        return self.fitModel.guess(data=data, x=x, **kwargs)
    
    def _guess_2D(self, data, x, y, **kwargs):
        """Call the guess function of the 2D fit model to guess the initial value.
        
        :param data: The flattened data to fit
        :type data: 1D numpy array
        :param x: The flattened data of x axis
        :type x: 1D numpy array
        :param y: The flattened data of y axis
        :type y: 1D numpy array
        :return: The guessed initial parameters for the fit
        :rtype: lmfit Parameters
        """
        data = data.flatten(order='F')
        return self.fitModel.guess(data=data, x=x, y=y, **kwargs)
    
    def guess(self, dataArray, x=None, y=None, guess_kwargs={}, input_core_dims=None, dask='parallelized', vectorize=True, keep_attrs=True, daskKwargs=None, **kwargs):
        """Call the guess function of the fit model to guess the initial value.

        :param dataArray: The data for the fit
        :type dataArray: xarray DataArray
        :param x: The name of x axis in data or the data of x axis, defaults to None
        :type x: str or numpy array, optional
        :param y: The name of y axis in data or the data of y axis, defaults to None
        :type y: str or numpy array, optional
        :param guess_kwargs: the keyworded arguments to send to the guess function, defaults to {}
        :type guess_kwargs: dict, optional
        :param input_core_dims: over write of the same argument in xarray.apply_ufunc, defaults to None
        :type input_core_dims: list or array like, optional
        :param dask: over write of the same argument in xarray.apply_ufunc,, defaults to 'parallelized'
        :type dask: str, optional
        :param vectorize: over write of the same argument in xarray.apply_ufunc, defaults to True
        :type vectorize: bool, optional
        :param keep_attrs: over write of the same argument in xarray.apply_ufunc, defaults to True
        :type keep_attrs: bool, optional
        :param daskKwargs: over write of the same argument in xarray.apply_ufunc, defaults to None
        :type daskKwargs: dict, optional
        :return: The guessed initial parameters for the fit
        :rtype: xarray DataArray
        """
        
        kwargs.update(
            {
                "dask": dask,
                "vectorize": vectorize,
                "input_core_dims": input_core_dims,
                'keep_attrs': keep_attrs,

            }
        )

        if not daskKwargs is None:
            kwargs.update({"dask_gufunc_kwargs": daskKwargs})

        if input_core_dims is None:
            kwargs.update(
                {
                    "input_core_dims": [['x']],
                }
            )

        if x is None:
            if 'x' in dataArray.dims:
                x = dataArray['x'].to_numpy()
        else:
            if isinstance(x, str):
                if input_core_dims is None:
                    kwargs.update(
                        {
                            "input_core_dims": [[x]],
                        }
                    )
                x = dataArray[x].to_numpy()

        if self.fitDim == 1:
            
            guess_kwargs.update(
                {
                    'x':x, 
                }
            )
            
            return xr.apply_ufunc(self._guess_1D, dataArray, kwargs=guess_kwargs,
                                    output_dtypes=[type(self.fitModel.make_params())],
                                    **kwargs
                                    )
        
        if self.fitDim == 2:
            
            if y is None:
                if 'y' in dataArray.dims:
                    y = dataArray['y'].to_numpy()
                if input_core_dims is None:
                    kwargs.update(
                        {
                            "input_core_dims": [['x', 'y']],
                        }
                    )
            else:
                if isinstance(y, str):
                    kwargs["input_core_dims"][0] = np.append(kwargs["input_core_dims"][0], y)
                    y = dataArray[y].to_numpy()
                elif input_core_dims is None:
                    kwargs.update(
                        {
                            "input_core_dims": [['x', 'y']],
                        }
                    )
            
            _x, _y = np.meshgrid(x, y)
            _x = _x.flatten()
            _y = _y.flatten()

            # dataArray = dataArray.stack(_z=(kwargs["input_core_dims"][0][0], kwargs["input_core_dims"][0][1]))
            
            # kwargs["input_core_dims"][0] = ['_z']

            guess_kwargs.update(
                {
                    'x':_x, 
                    'y':_y,
                }
            )
            
            return xr.apply_ufunc(self._guess_2D, dataArray, kwargs=guess_kwargs,
                                    output_dtypes=[type(self.fitModel.make_params())],
                                    **kwargs
                                    )
    
    def _fit_1D(self, data, params, x):
        """Call the fit function of the 1D fit model to do the fit.

        :param data: The data to fit
        :type data: 1D numpy array
        :param params: The initial paramters of the fit
        :type params: lmfit Parameters
        :param x: The data of x axis
        :type x: 1D numpy array
        :return: The result of the fit
        :rtype: lmfit FitResult
        """
        return self.fitModel.fit(data=data, x=x, params=params, nan_policy='omit')

    def _fit_2D(self, data, params, x, y):
        """Call the fit function of the 2D fit model to do the fit.

        :param data: The flattened data to fit
        :type data: 1D numpy array
        :param params: The flattened initial paramters of the fit
        :type params: lmfit Parameters
        :param x: The flattened data of x axis
        :type x: 1D numpy array
        :param y: The flattened data of y axis
        :type y: 1D numpy array
        :return: The result of the fit
        :rtype: lmfit FitResult
        """
        data = data.flatten(order='F')
        return self.fitModel.fit(data=data, x=x, y=y, params=params, nan_policy='omit')

    def fit(self, dataArray, paramsArray, x=None, y=None, input_core_dims=None, dask='parallelized', vectorize=True, keep_attrs=True, daskKwargs=None, **kwargs):
        """Call the fit function of the fit model to do the fit.

        :param dataArray: The data for the fit
        :type dataArray: xarray DataArray
        :param paramsArray: The flattened initial paramters of the fit
        :type paramsArray: xarray DataArray or lmfit Parameters
        :param x: The name of x axis in data or the data of x axis, defaults to None
        :type x: str or numpy array, optional
        :param y: The name of y axis in data or the data of y axis, defaults to None
        :type y: str or numpy array, optional
        :param input_core_dims: over write of the same argument in xarray.apply_ufunc, defaults to None, defaults to None
        :type input_core_dims: list or array like, optional
        :param dask: over write of the same argument in xarray.apply_ufunc, defaults to None, defaults to 'parallelized'
        :type dask: str, optional
        :param vectorize: over write of the same argument in xarray.apply_ufunc, defaults to None, defaults to True
        :type vectorize: bool, optional
        :param keep_attrs: over write of the same argument in xarray.apply_ufunc, defaults to None, defaults to True
        :type keep_attrs: bool, optional
        :param daskKwargs: over write of the same argument in xarray.apply_ufunc, defaults to None, defaults to None
        :type daskKwargs: dict, optional
        :return: The fit result
        :rtype: xarray DataArray
        """
        kwargs.update(
            {
                "dask": dask,
                "vectorize": vectorize,
                "input_core_dims": input_core_dims,
                'keep_attrs': keep_attrs,
            }
        )

        if not daskKwargs is None:
            kwargs.update({"dask_gufunc_kwargs": daskKwargs})
        
        if isinstance(paramsArray, type(self.fitModel.make_params())):

            if input_core_dims is None:
                kwargs.update(
                    {
                        "input_core_dims": [['x']],
                    }
                )

            if x is None:
                if 'x' in dataArray.dims:
                    x = dataArray['x'].to_numpy()
            else:
                if isinstance(x, str):
                    if input_core_dims is None:
                        kwargs.update(
                            {
                                "input_core_dims": [[x]],
                            }
                        )
                    x = dataArray[x].to_numpy()

            if self.fitDim == 1:
                
                res = xr.apply_ufunc(self._fit_1D, dataArray, kwargs={'params':paramsArray,'x':x},
                                        output_dtypes=[type(lmfit.model.ModelResult(self.fitModel, self.fitModel.make_params()))], 
                                        **kwargs)
                
                if keep_attrs:
                    res.attrs = copy.copy(dataArray.attrs)
                
                return res
            
            if self.fitDim == 2:
                
                if y is None:
                    if 'y' in dataArray.dims:
                        y = dataArray['y'].to_numpy()
                    if input_core_dims is None:
                        kwargs.update(
                            {
                                "input_core_dims": [['x', 'y']],
                            }
                        )
                else:
                    if isinstance(y, str):
                        kwargs["input_core_dims"][0] = np.append(kwargs["input_core_dims"][0], y)
                        y = dataArray[y].to_numpy()
                    elif input_core_dims is None:
                        kwargs.update(
                            {
                                "input_core_dims": [['x', 'y']],
                            }
                        )
                
                _x, _y = np.meshgrid(x, y)
                _x = _x.flatten()
                _y = _y.flatten()

                # dataArray = dataArray.stack(_z=(kwargs["input_core_dims"][0][0], kwargs["input_core_dims"][0][1]))

                # kwargs["input_core_dims"][0] = ['_z']

                res = xr.apply_ufunc(self._fit_2D, dataArray, kwargs={'params':paramsArray,'x':_x, 'y':_y},
                                        output_dtypes=[type(lmfit.model.ModelResult(self.fitModel, self.fitModel.make_params()))], 
                                        **kwargs)
                
                if keep_attrs:
                    res.attrs = copy.copy(dataArray.attrs)
                    
                return res

        else:

            if input_core_dims is None:
                kwargs.update(
                    {
                        "input_core_dims": [['x'], []],
                    }
                )

            if x is None:
                if 'x' in dataArray.dims:
                    x = dataArray['x'].to_numpy()
            else:
                if isinstance(x, str):
                    if input_core_dims is None:
                        kwargs.update(
                            {
                                "input_core_dims": [[x], []],
                            }
                        )
                    x = dataArray[x].to_numpy()

            if self.fitDim == 1:
                return xr.apply_ufunc(self._fit_1D, dataArray, paramsArray, kwargs={'x':x},
                                        output_dtypes=[type(lmfit.model.ModelResult(self.fitModel, self.fitModel.make_params()))], 
                                        **kwargs)

            if self.fitDim == 2:

                if input_core_dims is None:
                    kwargs.update(
                        {
                            "input_core_dims": [['x', 'y'], []],
                        }
                    )
                
                if y is None:
                    if 'y' in dataArray.dims:
                        y = dataArray['y'].to_numpy()
                else:
                    if isinstance(y, str):
                        y = dataArray[y].to_numpy()
                        kwargs["input_core_dims"][0] = np.append(kwargs["input_core_dims"][0], y)
                
                _x, _y = np.meshgrid(x, y)
                _x = _x.flatten()
                _y = _y.flatten()

                # dataArray = dataArray.stack(_z=(kwargs["input_core_dims"][0][0], kwargs["input_core_dims"][0][1]))

                # kwargs["input_core_dims"][0] = ['_z']

                return xr.apply_ufunc(self._fit_2D, dataArray, paramsArray, kwargs={'x':_x, 'y':_y},
                                        output_dtypes=[type(lmfit.model.ModelResult(self.fitModel, self.fitModel.make_params()))], 
                                        **kwargs)

    def _eval_1D(self, fitResult, x):
        """Call the eval function of the 1D fit model to calculate the curve.

        :param fitResult: The result of fit
        :type fitResult: lmfit FitResult
        :param x: The data of x axis
        :type x: 1D numpy array
        :return: The curve based on the fit result
        :rtype: 1D numpy array        
        """
        return self.fitModel.eval(x=x, **fitResult.best_values)
    
    def _eval_2D(self, fitResult, x, y, shape):
        """Call the eval function of the 2D fit model to calculate the curve.

        :param fitResult: The result of fit
        :type fitResult: lmfit FitResult
        :param x: The data of x axis
        :type x: 1D numpy array
        :param y: The flattened data of y axis
        :type y: 1D numpy array
        :param shape: The desired shape for output
        :type shape: list, tuple or array like
        :return: The curve based on the fit result
        :rtype: 2D numpy array 
        """
        res = self.fitModel.eval(x=x, y=y, **fitResult.best_values)
        return res.reshape(shape, order='F')

    def eval(self, fitResultArray, x=None, y=None, output_core_dims=None, prefix="", dask='parallelized', vectorize=True, daskKwargs=None, **kwargs):
        """Call the eval function of the fit model to calculate the curve.

        :param fitResultArray: The result of fit
        :type fitResultArray: xarray DataArray
        :param x: The name of x axis in data or the data of x axis, defaults to None
        :type x: str or numpy array, optional
        :param y: The name of y axis in data or the data of y axis, defaults to None
        :type y: str or numpy array, optional
        :param output_core_dims: over write of the same argument in xarray.apply_ufunc, defaults to None
        :type output_core_dims: list, optional
        :param prefix: prefix str of the fit model, defaults to ""
        :type prefix: str, optional
        :param dask: over write of the same argument in xarray.apply_ufunc, defaults to 'parallelized'
        :type dask: str, optional
        :param vectorize: over write of the same argument in xarray.apply_ufunc, defaults to True
        :type vectorize: bool, optional
        :param daskKwargs: over write of the same argument in xarray.apply_ufunc, defaults to None
        :type daskKwargs: dict, optional
        :return: The curve based on the fit result
        :rtype: xarray
        """
        
        kwargs.update(
            {
                "dask": dask,
                "vectorize": vectorize,
                "output_core_dims": output_core_dims,
            }
        )

        if daskKwargs is None:
            daskKwargs = {}

        if self.fitDim == 1:

            if output_core_dims is None:
                kwargs.update(
                    {
                        "output_core_dims": prefix+'x',
                    }
                )
                output_core_dims = [prefix+'x']
            
            daskKwargs.update(
                {
                    'output_sizes': {
                        output_core_dims[0]: np.size(x),
                    },
                    'meta': np.ndarray((0,0), dtype=float)
                }
            )

            kwargs.update(
                {   
                    "dask_gufunc_kwargs": daskKwargs,
                }
            )

            res = xr.apply_ufunc(self._eval_1D, fitResultArray, kwargs={"x":x}, **kwargs)
            return res.assign_coords({prefix+'x':np.array(x)})

        if self.fitDim == 2:
            if output_core_dims is None:
                kwargs.update(
                    {
                        "output_core_dims": [[prefix+'x', prefix+'y']],
                    }
                )
                output_core_dims = [prefix+'x', prefix+'y']

            daskKwargs.update(
                {
                    'output_sizes': {
                        output_core_dims[0]: np.size(x),
                        output_core_dims[1]: np.size(y),
                    },
                    'meta': np.ndarray((0,0), dtype=float)
                },
            )
            
            kwargs.update(
                {   
                    "dask_gufunc_kwargs": daskKwargs,
                }
            )

            _x, _y = np.meshgrid(x, y)
            _x = _x.flatten()
            _y = _y.flatten()

            res = xr.apply_ufunc(self._eval_2D, fitResultArray, kwargs={"x":_x, "y":_y, "shape":(len(x), len(y))}, **kwargs)
            return res.assign_coords({prefix+'x':np.array(x), prefix+'y':np.array(y)})

    def _get_fit_value_single(self, fitResult, key):
        """get value of one single parameter from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param key: The name of the parameter
        :type key: str
        :return: The vaule of the parameter
        :rtype: float
        """
        return fitResult.params[key].value

    def _get_fit_value(self, fitResult, params):
        """get value of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param params: A list of the name of paramerters to read
        :type params: list or array like
        :return: The vaule of the parameter
        :rtype: 1D numpy array
        """
        func = np.vectorize(self._get_fit_value_single)
        res = tuple(
                func(fitResult, key)
                for key in params
            )

        return res

    def get_fit_value(self, fitResult, dask='parallelized', **kwargs):
        """get value of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param dask: over write of the same argument in xarray.apply_ufunc, defaults to 'parallelized'
        :type dask: str, optional
        :return: The vaule of the parameter
        :rtype: xarray DataArray
        """
        firstIndex = {
            key: fitResult[key][0]
            for key in fitResult.dims
            }
        firstFitResult = fitResult.sel(firstIndex).item()

        params = list(firstFitResult.params.keys())

        output_core_dims=[ [] for _ in range(len(params))]

        kwargs.update(
            {
                "dask": dask,
                "output_core_dims": output_core_dims,
            }
        )

        value = xr.apply_ufunc(self._get_fit_value, fitResult, kwargs=dict(params=params), **kwargs)

        value = xr.Dataset(
            data_vars={
                params[i]: value[i]
                for i in range(len(params))
            },
            attrs=fitResult.attrs
        )

        return value

    def _get_fit_std_single(self, fitResult, key):
        """get standard deviation of one single parameter from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param key: The name of the parameter
        :type key: str
        :return: The vaule of the parameter
        :rtype: float
        """
        return fitResult.params[key].stderr

    def _get_fit_std(self, fitResult, params):
        """get standard deviation of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param params: A list of the name of paramerters to read
        :type params: list or array like
        :return: The vaule of the parameter
        :rtype: 1D numpy array
        """
        func = np.vectorize(self._get_fit_std_single)
        res = tuple(
                func(fitResult, key)
                for key in params
            )

        return res

    def get_fit_std(self, fitResult, dask='parallelized', **kwargs):
        """get standard deviation of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param dask: over write of the same argument in xarray.apply_ufunc, defaults to 'parallelized'
        :type dask: str, optional
        :return: The vaule of the parameter
        :rtype: xarray DataArray
        """
        firstIndex = {
            key: fitResult[key][0]
            for key in fitResult.dims
            }
        firstFitResult = fitResult.sel(firstIndex).item()

        params = list(firstFitResult.params.keys())

        output_core_dims=[ [] for _ in range(len(params))]

        kwargs.update(
            {
                "dask": dask,
                "output_core_dims": output_core_dims,
            }
        )

        value = xr.apply_ufunc(self._get_fit_std, fitResult, kwargs=dict(params=params), **kwargs)

        value = xr.Dataset(
            data_vars={
                params[i]: value[i]
                for i in range(len(params))
            },
            attrs=fitResult.attrs
        )

        return value

    def _get_fit_full_result_single(self, fitResult, key):
        """get the full result of one single parameter from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param key: The name of the parameter
        :type key: str
        :return: The vaule of the parameter
        :rtype: float
        """
        
        if not fitResult.params[key].value is None:
            value = fitResult.params[key].value
        else:
            value = np.nan
            
        if not fitResult.params[key].stderr is None:
            std = fitResult.params[key].stderr
        else:
            std = np.nan
            
        return ufloat(value, std)

    def _get_fit_full_result(self, fitResult, params):
        """get the full result of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param params: A list of the name of paramerters to read
        :type params: list or array like
        :return: The vaule of the parameter
        :rtype: 1D numpy array
        """
        func = np.vectorize(self._get_fit_full_result_single)
        res = tuple(
                func(fitResult, key)
                for key in params
            )

        return res

    def get_fit_full_result(self, fitResult, dask='parallelized', **kwargs):
        """get the full result of parameters from fit result

        :param fitResult: The result of the fit 
        :type fitResult: lmfit FitResult
        :param dask: over write of the same argument in xarray.apply_ufunc, defaults to 'parallelized'
        :type dask: str, optional
        :return: The vaule of the parameter
        :rtype: xarray DataArray
        """
        firstIndex = {
            key: fitResult[key][0]
            for key in fitResult.dims
            }
        firstFitResult = fitResult.sel(firstIndex).item()

        params = list(firstFitResult.params.keys())

        output_core_dims=[ [] for _ in range(len(params))]

        kwargs.update(
            {
                "dask": dask,
                "output_core_dims": output_core_dims,
            }
        )

        value = xr.apply_ufunc(self._get_fit_full_result, fitResult, kwargs=dict(params=params), **kwargs)

        value = xr.Dataset(
            data_vars={
                params[i]: value[i]
                for i in range(len(params))
            },
            attrs=fitResult.attrs
        )

        return value