lmfitxps

https://lmfitxps.readthedocs.io/en/latest/
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lmfitxps is a Python package extension for lmfit that provides comprehensive tools for fitting X-ray...
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### Install Dependencies

Source: https://lmfitxps.readthedocs.io/en/latest/about.html

Install all project dependencies using pip by running this command in your terminal.

```bash
pip install -r requirements.txt
```

--------------------------------

### Install lmfitxps development version

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

Clone the GitHub repository to install the development version or contribute to the project.

```sh
git clone https://github.com/Julian-Hochhaus/lmfitxps.git
```

--------------------------------

### Example: ConvGaussianDoniachSinglett with ShirleyBG Model

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

This Python script demonstrates fitting a ConvGaussianDoniachSinglett model with a ShirleyBG background. It is used for spectral fitting.

```python
from lmfitxps.models import ConvGaussianDoniachSinglett, ShirleyBG

# Initialize the model with ShirleyBG background
model = ConvGaussianDoniachSinglett(background=ShirleyBG, prefix='singlett_')

# Define initial parameters for the model
params = model.make_params(center=10, sigma=1, amplitude=10)

# Fit the model to the data
result = model.fit(y, params, x=x)

# Access the fit results
print(result.fit_report())
```

--------------------------------

### Example: FermiEdgeModel fitting

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

This Python script is an example for fitting the FermiEdgeModel. It is used in conjunction with the FermiModel.

```python
from lmfitxps.models import FermiEdgeModel

# Initialize the model
model = FermiEdgeModel(prefix='fermi_')

# Define initial parameters for the model
params = model.make_params(center=10, sigma=1)

# Fit the model to the data
result = model.fit(y, params, x=x)

# Access the fit results
print(result.fit_report())
```

--------------------------------

### Fit XPS Data with ConvGaussianDoniachDublett and TougaardBG

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

This example demonstrates fitting XPS data using a combination of ConvGaussianDoniachDublett and TougaardBG models. It includes data loading, model definition, parameter initialization, fitting, and plotting the results. Ensure data is in CSV format and adjust paths as needed.

```python
import numpy as np
import matplotlib.pyplot as plt
import lmfit
import sys
import os
sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '../src')))
from lmfitxps import models
import matplotlib as mpl

exec_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))
dublett = models.ConvGaussianDoniachDublett(prefix='dublett_', independent_vars=["x"])
bg=models.TougaardBG(independent_vars=["x","y"], prefix='tougaard_')
fit_model=dublett+bg
data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=0)
x = data[:, 0]
y = data[:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

fig, (ax1, ax2) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
fig.patch.set_facecolor('#FCFCFC')

params = lmfit.Parameters()
params.add('tougaard_B', value=148.969)
params.add('tougaard_C', value=144.506, vary=False)
params.add('tougaard_D', value=268.598, vary=False)
params.add('tougaard_C_d', value=0.281, vary=False)
params.add('tougaard_extend', value=30)
params.add('dublett_amplitude', value=np.max(y))
params.add('dublett_sigma', value=0.2126)
params.add('dublett_gamma', value=0.04)
params.add('dublett_gaussian_sigma', value=0.0892)
params.add('dublett_center', value=92.2273)
params.add('dublett_soc', value=3.67127)
params.add('dublett_height_ratio', value=0.7)
params.add('dublett_fct_coster_kronig', value=1.04)

result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
comps = result.eval_components(x=x, y=y)
print(result.fit_report())

cmap = mpl.colormaps['tab20']
ax1.plot(x, result.best_fit, label='Best Fit', color=cmap(0))
ax1.plot(x, y, 'x', markersize=4, label='Data Points', color=cmap(2))

ax1.plot(x, comps['tougaard_'], label='Tougaard background', color='black')
ax1.plot(x, comps['dublett_'] + comps['tougaard_'], color=cmap(4), label="Doniach-Dublett")

ax1.fill_between(x, comps['dublett_'] + comps['tougaard_'], comps['tougaard_'], alpha=0.5,color=cmap(5))
ax1.legend()
ax1.set_xlabel('bin. energy in eV')
ax1.set_ylabel('intensity in arb. units')
# Set ticks only inside
ax1.tick_params(axis='x', which='both',top=True, direction='in')
ax1.tick_params(axis='y', which='both', right=True,direction='in')
ax2.tick_params(axis='x', which='both',top=True, direction='in')
ax2.tick_params(axis='y', which='both', right=True, direction='in')

ax1.set_yticklabels([])
ax1.set_title(f'ConvGaussian DoniachDublett using kin. energy scale')
fig.subplots_adjust(hspace=0)
ax1.set_xlim(np.min(x), np.max(x))
```

--------------------------------

### Install required packages for lmfitxps

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

If required packages are not automatically installed, use this command to install them. Ensure you have pip installed.

```bash
lmfit>=1.1.0
matplotlib>=3.6
numpy>=1.19
scipy>=1.6

```

--------------------------------

### Example: ConvGaussianDoniachDublett with TougaardBG Model

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

This Python script shows how to fit a ConvGaussianDoniachDublett model using the TougaardBG background. This is useful for analyzing doublet peaks in XPS data.

```python
from lmfitxps.models import ConvGaussianDoniachDublett, TougaardBG

# Initialize the model with TougaardBG background
model = ConvGaussianDoniachDublett(background=TougaardBG, prefix='dublett_')

# Define initial parameters for the model
params = model.make_params(center=10, sigma=1, amplitude=10)

# Fit the model to the data
result = model.fit(y, params, x=x)

# Access the fit results
print(result.fit_report())
```

--------------------------------

### Install lmfitxps using pip

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

Use this command to install the stable version of the lmfitxps package. Ensure you have pip installed.

```bash
$ pip install lmfitxps

```

--------------------------------

### Install lmfitxps using pip

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

Use this command to install the stable version of lmfitxps. Ensure required packages are present.

```bash
pip install lmfitxps
```

--------------------------------

### Clone lmfitxps repository for development

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

Clone the GitHub repository to install the development version or contribute to lmfitxps. Ensure you have git installed.

```bash
$ git clone https://github.com/Julian-Hochhaus/lmfitxps.git

```

--------------------------------

### Fit Background Spectra with lmfit

Source: https://lmfitxps.readthedocs.io/en/latest/backgrounds.html

This code snippet demonstrates fitting a complex background model to XPS data using lmfit. It includes parameter initialization, model definition, fitting, and component evaluation. Ensure lmfit, numpy, and matplotlib are installed.

```python
data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=1)

x = 180-data[:, 0]
y = data[:, 1]
output_dir = os.path.join(exec_dir, 'docs/src/', 'plots')
os.makedirs(output_dir, exist_ok=True)




params = lmfit.Parameters()
params.add('tougaard_B', value= 197.643926)
params.add('tougaard_C', value=144.506, vary=False)
params.add('tougaard_C_d', value=0.281, vary=False)
params.add('tougaard_D', value=268.598, vary=False)
params.add('tougaard_extend', value=0)
params.add('d1_amplitude', value=71980)
params.add('d1_sigma', value=0.21)
params.add('d1_gamma', value=0.01)
params.add('d1_gaussian_sigma', value=0.0892)
params.add('d1_center', value=180-92.2273)
params.add('d1_soc', value=3.67127)
params.add('d1_height_ratio', value=0.7)
params.add('d1_fct_coster_kronig', value=1.04, vary=False)
params.add('d2_amplitude', value=43966)
params.add('d2_sigma', value=0.2, expr='d1_sigma')
params.add('d2_gamma', value=0.0, expr='d1_gamma')
params.add('d2_gaussian_sigma', value=0.14, expr='d1_gaussian_sigma')
params.add('diff', value=-0.31165)
params.add('d2_center', value=180-92.4, expr='d1_center+diff')
params.add('d2_soc', value=-3.67, expr="d1_soc")
params.add('d2_height_ratio', value=0.7, expr='d1_height_ratio')
params.add('d2_fct_coster_kronig', value=1, expr='d1_fct_coster_kronig')
params.add('const_c', value=2677.97771)
fit_model = tougaard_model + d1+d2  + const

result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
```

--------------------------------

### Fit Fermi-Edge Model with lmfitxps

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

Example of fitting a Fermi-Edge model combined with a constant background to experimental data. Includes data loading, parameter initialization, fitting, and plotting of results and residuals.

```python
import numpy as np
import matplotlib.pyplot as plt
import lmfit
import sys
import os
sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '../src')))
from lmfitxps import models
import matplotlib as mpl

exec_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))
fermi = models.FermiEdgeModel(prefix='fermi_', independent_vars=["x"])
const = lmfit.models.ConstantModel(prefix='const_')
fit_model=fermi+const
data = np.genfromtxt(exec_dir + '/examples/FermiEdge.csv', delimiter=',', skip_header=1)
x = data[:, 0]
y = data[:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

fig, (ax1, ax2) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
fig.patch.set_facecolor('#FCFCFC')
params = lmfit.Parameters()
params.add('fermi_amplitude', value=232)
params.add('fermi_sigma', value=0.2126)
params.add('fermi_kt', value=0.0026, vary=False)
params.add('fermi_center', value=236)
params.add('const_c', value=np.min(y))


result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
comps = result.eval_components(x=x, y=y)
print(result.fit_report())

cmap = mpl.colormaps['tab20']
ax1.plot(x, result.best_fit, label='Best Fit', color=cmap(0))
ax1.plot(x, y, 'x', markersize=4, label='Data Points', color=cmap(2))

ax1.plot(x, comps['const_'], label='const. background', color='black')
ax1.plot(x, comps['fermi_'] + comps['const_'], color=cmap(4), label="fermi-edge")

ax1.fill_between(x, comps['fermi_'] + comps['const_'], comps['const_'], alpha=0.5,color=cmap(5))
ax1.legend()
ax1.set_xlabel('kin. energy in eV')
ax1.set_ylabel('intensity in arb. units')
# Set ticks only inside
ax1.tick_params(axis='x', which='both',top=True, direction='in')
ax1.tick_params(axis='y', which='both', right=True,direction='in')
ax2.tick_params(axis='x', which='both',top=True, direction='in')
ax2.tick_params(axis='y', which='both', right=True, direction='in')

ax1.set_yticklabels([])
ax1.set_title(f'FermiEdgeModel using kin. energy scale')
fig.subplots_adjust(hspace=0)
ax1.set_xlim(np.min(x), np.max(x))
# Residual plot
residual = result.residual
ax2.plot(x, residual)
ax2.set_xlabel('kin. energy in eV')
ax2.set_ylabel('Residual')

plot_filename = os.path.join(output_dir, f'plot_fermi_kin.png')
fig.savefig(plot_filename, dpi=300)
plt.close(fig)
```

--------------------------------

### Fit Fermi-Edge Model with Reversed Energy Scale

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

Example of fitting a Fermi-Edge model with a reversed energy scale. Demonstrates parameter constraints (min/max) and plotting of fit results and residuals.

```python
fermi = models.FermiEdgeModel(prefix='fermi_', independent_vars=["x"])
const = lmfit.models.ConstantModel(prefix='const_')
fit_model=fermi+const
data = np.genfromtxt(exec_dir + '/examples/FermiEdge.csv', delimiter=',', skip_header=1)
x = 240-data[:, 0]
y = data[:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

fig2, (ax21, ax22) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
fig2.patch.set_facecolor('#FCFCFC')
params = lmfit.Parameters()
params.add('fermi_amplitude', value=232, min=220, max=240)
params.add('fermi_sigma', value=0.15, min=0.12,max=0.17)
params.add('fermi_kt', value=0.0026, vary=False)
params.add('fermi_center', value=3.5, min=3, max=4)
params.add('const_c', value=np.min(y), min=np.min(y), max=np.mean(y))


result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
comps = result.eval_components(x=x, y=y)
print(result.fit_report())

cmap = mpl.colormaps['tab20']
ax21.plot(x, result.best_fit, label='Best Fit', color=cmap(0))
ax21.plot(x, y, 'x', markersize=4, label='Data Points', color=cmap(2))

ax21.plot(x, comps['const_'], label='const. background', color='black')
ax21.plot(x, comps['fermi_'] + comps['const_'], color=cmap(4), label="fermi-edge")

ax21.fill_between(x, comps['fermi_'] + comps['const_'], comps['const_'], alpha=0.5,color=cmap(5))
ax21.legend()
ax21.set_xlabel('bin. energy in eV')
ax21.set_ylabel('intensity in arb. units')
```

--------------------------------

### Setting up XPS Fitting Models

Source: https://lmfitxps.readthedocs.io/en/latest/backgrounds.html

This code initializes TougaardBG and ConvGaussianDoniachDublett models for XPS analysis. It sets up parameters for background and peak fitting, including fixed and variable parameters.

```python
exec_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))
tougaard_model = models.TougaardBG(prefix='tougaard_', independent_vars=['y', 'x'])
d1 = models.ConvGaussianDoniachDublett(prefix='d1_')
d2 = models.ConvGaussianDoniachDublett(prefix='d2_')
const = lmfit.models.ConstantModel(prefix='const_')

data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=1)
x = data[:, 0]
y = data[:, 1]
guess_extend(x,y,156.969,144.506,0.281,268.598)
output_dir = os.path.join(exec_dir, 'docs/src/', 'plots')
os.makedirs(output_dir, exist_ok=True)

combined_fig, (combined_ax1, combined_ax2) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
combined_fig.patch.set_facecolor('#FCFCFC')
residual_fig, residual_ax = plt.subplots(figsize=(6, 4))
residual_fig.patch.set_facecolor('#FCFCFC')
combined2_fig, combined2_ax = plt.subplots(figsize=(6, 4))
combined2_fig.patch.set_facecolor('#FCFCFC')
tg_bgs=[]
tg_res=[]
for j in [0]+[i for i in range(27,35,1)]:
    params = lmfit.Parameters()
    params.add('tougaard_B', value=148.969)
    params.add('tougaard_C', value=144.506, vary=False)
    params.add('tougaard_C_d', value=0.281, vary=False)
    params.add('tougaard_D', value=268.598, vary=False)
    params.add('tougaard_extend', value=j)
    params.add('d1_amplitude', value=71980, vary=False)
    params.add('d1_sigma', value=0.2126, vary=False)
    params.add('d1_gamma', value=0.01, vary=False)
    params.add('d1_gaussian_sigma', value=0.0892, vary=False)
    params.add('d1_center', value=92.2273, vary=False)
    params.add('d1_soc', value=3.67127, vary=False)
    params.add('d1_height_ratio', value=0.7, vary=False)
    params.add('d1_fct_coster_kronig', value=1.04, vary=False)
    params.add('d2_amplitude', value=43966, vary=False)
    params.add('d2_sigma', value=0.2, expr='d1_sigma')
    params.add('d2_gamma', value=0.0, expr='d1_gamma')
    params.add('d2_gaussian_sigma', value=0.14, expr='d1_gaussian_sigma')
    params.add('diff', value=0.31)
```

--------------------------------

### ConvGaussianDoniachDublett Initialization and Parameter Hints

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Details the initialization of the ConvGaussianDoniachDublett model and the parameter hints set for its components, including amplitude, sigma, gamma, and broadening factors.

```APIDOC
## ConvGaussianDoniachDublett

### Description
Initializes the ConvGaussianDoniachDublett model, inheriting from `lmfit.model.Model`. It sets default parameter hints for various components of the Doniach-Sunjic lineshape and a Gaussian broadening.

### Method
```python
def __init__(self, *args, **kwargs):
    super().__init__(dublett, *args, **kwargs)
    self._set_paramhints_prefix()
```

### Parameters

- **amplitude** (:obj:`float`) - Amplitude of the larger peak (P1) of the dublett.
- **sigma** (:obj:`float`) - Doniach-broadening of the larger peak (P1) of the dublett.
- **gamma** (:obj:`float`) - Asymmetry of the larger peak (P1) of the dublett.
- **center** (:obj:`float`) - Center of peak P1.
- **soc** (:obj:`float`) - Distance (energy) between the two peaks.
- **height_ratio** (:obj:`float`) - Ratio of the amplitude of the smaller peak with respect to the larger one.
- **fct_coster_kronig** (:obj:`float`) - Factor that scales P2's broadening with respect to P1 (Coster-Kronig effect).
- **gaussian_sigma** (:obj:`float`) - Broadening of the gaussian kernel.

### Parameter Hints

- **amplitude**: value=100, min=0
- **sigma**: value=0.2, min=0
- **gamma**: value=0.02
- **gaussian_sigma**: value=0.2, min=0
- **center**: value=285
- **soc**: value=2.0
- **height_ratio**: value=0.75, min=0
- **fct_coster_kronig**: value=1, min=0
- **gaussian_fwhm**: expr='2*{pre:s}gaussian_sigma*1.1774'
- **lorentzian_fwhm_p1**: expr='{pre:s}sigma*(2+{pre:s}gamma*2.5135+({pre:s}gamma*3.6398)**4)'
- **lorentzian_fwhm_p2**: expr='{pre:s}sigma*(2+{pre:s}gamma*2.5135+({pre:s}gamma*3.6398)**4)*{pre:s}fct_coster_kronig'
```

--------------------------------

### Set TougaardBG Parameter Hints

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Sets initial values and constraints for the TougaardBG model parameters: 'B', 'C', 'C_d', 'D', and 'extend'.

```python
def _set_paramhints_prefix(self):
    """
    Sets parameter hints for the model.

    The method sets initial values and constraints for the parameters 'B', 'C', 'C_d', 'D', and 'extend'.

    """
    self.set_param_hint('B', value=2886)
    self.set_param_hint('C', value=1643)
    self.set_param_hint('C_d', value=1)
    self.set_param_hint('D', value=1)
    self.set_param_hint('extend', value=0, vary=False)
```

--------------------------------

### General workflow for predefined models in lmfitxps

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/introduction.rst.txt

This Python script demonstrates the typical workflow for using predefined models in lmfitxps. It includes importing data, initializing a model, defining parameters, fitting the model to the data, and printing the fit report.

```python
import numpy as np
from lmfitxps.models import ChoosenModel

# Import your data, ensuring that energy (x) and intensity (y) values are stored in arrays
x = np.array([...])  # Replace with your energy data
y = np.array([...])  # Replace with your intensity data

# Initialize the model
model = ChoosenModel(prefix='choosen_model_')  # Model parameters will have the specified prefix

# Define initial parameters for the model
params = model.make_params(param1=10, param2=40)

# Fit the model to the data
result = model.fit(y, params, x=x)

# Access the fit results
print(result.fit_report())
```

--------------------------------

### General Workflow for Predefined Models in lmfitxps

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

This schematic demonstrates the typical workflow for using predefined models in lmfitxps. It involves importing data, initializing a chosen model, defining initial parameters, and fitting the model to the data.

```python
import numpy as np
from lmfitxps.models import ChoosenModel

# Import your data, ensuring that energy (x) and intensity (y) values are stored in arrays
x = np.array([...])  # Replace with your energy data
y = np.array([...])  # Replace with your intensity data

# Initialize the model
model = ChoosenModel(prefix='choosen_model_')  # Model parameters will have the specified prefix

# Define initial parameters for the model
params = model.make_params(param1=10, param2=40)

# Fit the model to the data
result = model.fit(y, params, x=x)

```

--------------------------------

### ConvGaussianDoniachSinglett

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

A model representing a convolution of a Gaussian and a Doniach-Sunjic profile, suitable for fitting XPS signals with asymmetry. It combines experimental setup influences (Gaussian) with sample physics (Doniach-Sunjic).

```APIDOC
## ConvGaussianDoniachSinglett

### Description
A model based on a convolution of a Gaussian and a Doniach-Sunjic profile. The model is designed for fitting XPS signals with asymmetry. The Gaussian thereby represents the gaussian-like influences of the experimental setup and the Doniach-Sunjic represents the sample's physics.

The implementation is based on the `Gaussian <https://github.com/lmfit/lmfit-py/blob/7710da6d7e878ffee0dc90a85286f1ec619fc20f/lmfit/lineshapes.py#L46>`_ and `Doniach <https://github.com/lmfit/lmfit-py/blob/7710da6d7e878ffee0dc90a85286f1ec619fc20f/lmfit/lineshapes.py#L296>`_ lineshapes of the LMFIT package. The convolution is calculated using the FFT-Convolution implemented in `scipy.signal.fftconvolve <https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.fftconvolve.html>`_.

The Convolution is, in analogy to the Voigt profile given by:

.. math::
    
    (DS * G)(E, A, \mu, \gamma, \alpha, \sigma) = A \cdot \int_{-\infty}^{\infty} DS(E', \mu,\gamma,\alpha) G(E - E', \sigma)\, dE'

The Doniach-Sunjic profile (:math:`DS`) is convolved with the Gaussian kernel (:math:`G`).

Thereby:
    - :math:`A` is the amplitude of the peak profile,
    - :math:`\mu` is the center of the peak,
    - :math:`\gamma` represents the broadening of the Doniach-Sunjic lineshape,
    - :math:`\alpha` is the asymmetry of the Doniach-Sunjic lineshape,
    - :math:`\sigma` is the broadening parameter of the Gaussian kernel.

### Parameters
#### Model Parameters
- **amplitude** (float) - Amplitude :math:`A` of the peak profile
- **sigma** (float) - Broadening of the Doniach-Sunjic.
- **gamma** (float) - Asymmetry of the Doniach-Sunjic.
- **center** (float) - Center of the peak profile.
- **gaussian_sigma** (float) - Broadening of the gaussian kernel.

#### Inherited Parameters (from lmfit.model.Model)
- **x** (array) - 1D-array containing the x-values (energies) of the spectrum.
- **y** (array) - 1D-array containing the y-values (intensities) of the spectrum.

### Usage
```python
from lmfitxps.models import ConvGaussianDoniachSinglett

# Instantiate the model
model = ConvGaussianDoniachSinglett()

# Fit the model to data (example)
# params = model.make_params()
# result = model.fit(data, params, x=x_values)
# print(result.fit_report())
```

### Notes
The `ConvGaussianDoniachSinglett` class inherits from `lmfit.model.Model` and only extends it. Therefore, the `lmfit.model.Model` class parameters are inherited as well.
```

--------------------------------

### Set Parameter Hints for ConvGaussianDoniachDublett

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Sets default parameter hints including values, minimums, and expressions for peak amplitudes, broadening, and ratios.

```python
def _set_paramhints_prefix(self):
    self.set_param_hint('amplitude', value=100, min=0)
    self.set_param_hint('sigma', value=0.2, min=0)
    self.set_param_hint('gamma', value=0.02)
    self.set_param_hint('gaussian_sigma', value=0.2, min=0)
    self.set_param_hint('center', value=285)
    self.set_param_hint('soc', value=2.0)
    self.set_param_hint('height_ratio', value=0.75, min=0)
    self.set_param_hint('fct_coster_kronig', value=1, min=0)
    g_fwhm_expr = '2*{pre:s}gaussian_sigma*1.1774'
    self.set_param_hint('gaussian_fwhm', expr=g_fwhm_expr.format(pre=self.prefix))
    l_p1_fwhm_expr = '{pre:s}sigma*(2+{pre:s}gamma*2.5135+({pre:s}gamma*3.6398)**4)'
    l_p2_fwhm_expr = '{pre:s}sigma*(2+{pre:s}gamma*2.5135+({pre:s}gamma*3.6398)**4)*{pre:s}fct_coster_kronig'
    self.set_param_hint('lorentzian_fwhm_p1', expr=l_p1_fwhm_expr.format(pre=self.prefix))
    self.set_param_hint('lorentzian_fwhm_p2', expr=l_p2_fwhm_expr.format(pre=self.prefix))
```

--------------------------------

### Set Parameter Hints for a Model

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Sets default values, minimum, and maximum constraints for model parameters like 'center', 'kt', 'amplitude', and 'sigma'. Useful for initializing model fitting.

```python
        kb = scipy.constants.physical_constants['Boltzmann constant in eV/K'][0]
        self.set_param_hint('center', value=np.mean(x), min=min(x), max=max(x))
        self.set_param_hint('kt', value=kb * 300, min=0, max=kb * 1500)
        self.set_param_hint('amplitude', value=(max(data) - min(data)) / 10, min=0, max=(max(data) - min(data)))
        self.set_param_hint('sigma', value=(max(x) - min(x)) / len(x), min=0, max=2)
        params = self.make_params()
        return lmfit.models.update_param_vals(params, self.prefix, **kwargs)
```

--------------------------------

### ConvGaussianDoniachSinglett Class

Source: https://lmfitxps.readthedocs.io/en/latest/peaks.html

The ConvGaussianDoniachSinglett class is a model designed for fitting XPS signals with asymmetry. It convolves a Gaussian profile (representing experimental setup influences) with a Doniach-Sunjic profile (representing sample physics). The convolution is computed using FFT-Convolution.

```APIDOC
## `ConvGaussianDoniachSinglett`

### Description
A model based on a convolution of a Gaussian and a Doniach-Sunjic profile. The model is designed for fitting XPS signals with asymmetry. The Gaussian thereby represents the gaussian-like influences of the experimental setup and the Doniach-Sunjic represents the sample’s physics.

### Mathematical Basis
The convolution is, in analogy to the Voigt profile given by:
(DS∗G)(E,A,μ,γ,α,σ)=A⋅∫−∞∞DS(E′,μ,γ,α)G(E−E′,σ)dE′
Where DS is the Doniach-Sunjic profile and G is the Gaussian kernel.

### Parameters

#### Model-specific Parameters
- **x** (array) - 1D-array containing the x-values (energies) of the spectrum.
- **y** (array) - 1D-array containing the y-values (intensities) of the spectrum.
- **amplitude** (float) - Amplitude A of the peak profile.
- **sigma** (float) - Broadening of the Doniach-Sunjic.
- **gamma** (float) - Asymmetry of the Doniach-Sunjic.
- **center** (float) - Center of the peak profile.
- **gaussian_sigma** (float) - Broadening of the gaussian kernel.

#### Inherited Parameters from `lmfit.model.Model`
- **independent_vars** (list of str, optional) - Arguments to the model function that are independent variables (default is ['x']).
- **prefix** (str, optional) - String to prepend to parameter names, needed to add two Models that have parameter names in common.
- **nan_policy** ({'raise', 'propagate', 'omit'}, optional) - How to handle NaN and missing values in data. Options are:
  - 'raise': raise a ValueError (default)
  - 'propagate': do nothing
  - 'omit': drop missing data
- **kwargs** (optional) - Keyword arguments to pass to `Model`.
```

--------------------------------

### Fit ConvGaussianDoniachSinglett with ShirleyBG Model

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

This snippet demonstrates fitting a combined model of ConvGaussianDoniachSinglett and ShirleyBG to XPS data. It includes data loading, parameter initialization, model fitting, and plotting of the best fit, data points, Shirley background, and the combined peak. Residuals are also plotted. Ensure the 'clean_Au_4f.csv' file is available and the 'src' directory is in the Python path.

```python
import numpy as np
import matplotlib.pyplot as plt
import lmfit
import sys
import os
sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '../src')))
from lmfitxps import models
import matplotlib as mpl

exec_dir = os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))
singlett = models.ConvGaussianDoniachSinglett(prefix='singlett_', independent_vars=["x"])
bg=models.ShirleyBG(independent_vars=["y"], prefix='shirley_')
fit_model=singlett+bg
data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=0)
x = data[150:, 0]
y = data[150:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

fig, (ax1, ax2) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
fig.patch.set_facecolor('#FCFCFC')

params = lmfit.Parameters()
params.add('shirley_k', value=0.002)
params.add('shirley_const', value=100)
params.add('singlett_amplitude', value=np.max(y))
params.add('singlett_sigma', value=0.2126)
params.add('singlett_gamma', value=0.0, vary=False)
params.add('singlett_gaussian_sigma', value=0.0892)
params.add('singlett_center', value=92)


result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
comps = result.eval_components(x=x, y=y)
print(result.fit_report())

cmap = mpl.colormaps['tab20']
ax1.plot(x, result.best_fit, label='Best Fit', color=cmap(0))
ax1.plot(x, y, 'x', markersize=4, label='Data Points', color=cmap(2))

ax1.plot(x, comps['shirley_'], label='Shirley background', color='black')
ax1.plot(x, comps['singlett_'] + comps['shirley_'], color=cmap(4), label="Doniach-Peak")

ax1.fill_between(x, comps['singlett_'] + comps['shirley_'], comps['shirley_'], alpha=0.5,color=cmap(5))
ax1.legend()
ax1.set_xlabel('bin. energy (eV)')
ax1.set_ylabel('intensity in arb. units')
# Set ticks only inside
ax1.tick_params(axis='x', which='both',top=True, direction='in')
ax1.tick_params(axis='y', which='both', right=True,direction='in')
ax2.tick_params(axis='x', which='both',top=True, direction='in')
ax2.tick_params(axis='y', which='both', right=True, direction='in')

ax1.set_yticklabels([])
ax1.set_title(f'ConvGaussianDoniachSinglett using kin. energy scale')
fig.subplots_adjust(hspace=0)
ax1.set_xlim(np.min(x), np.max(x))
# Residual plot
residual = result.residual
ax2.plot(x, residual)
ax2.set_xlabel('kin. energy in eV')
ax2.set_ylabel('Residual')

plot_filename = os.path.join(output_dir, f'plot_singlett_kin.png')
fig.savefig(plot_filename, dpi=300)
plt.close(fig)
```

```python
singlett = models.ConvGaussianDoniachSinglett(prefix='singlett_', independent_vars=["x"])
bg=models.ShirleyBG(independent_vars=["y"], prefix='shirley_')
fit_model=singlett+bg
data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=0)
x = 180-data[150:, 0]
y = data[150:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

fig2, (ax21, ax22) = plt.subplots(nrows=2,gridspec_kw={'height_ratios': [1, 1]}, sharex=True)
fig2.patch.set_facecolor('#FCFCFC')

params = lmfit.Parameters()
params.add('shirley_k', value=0.002)
params.add('shirley_const', value=3000)
params.add('singlett_amplitude', value=np.max(y))
params.add('singlett_sigma', value=0.15)
params.add('singlett_gamma', value=0.0, vary=False)
params.add('singlett_gaussian_sigma', value=0.15)
params.add('singlett_center', value=87)


result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
comps = result.eval_components(x=x, y=y)
print(result.fit_report())
cmap = mpl.colormaps['tab20']
ax21.plot(x, result.best_fit, label='Best Fit', color=cmap(0))
ax21.plot(x, y, 'x', markersize=4, label='Data Points', color=cmap(2))

ax21.plot(x, comps['shirley_'], label='Shirley background', color='black')
ax21.plot(x, comps['singlett_'] + comps['shirley_'], color=cmap(4), label="Doniach-Peak")

ax21.fill_between(x, comps['singlett_'] + comps['shirley_'], comps['shirley_'], alpha=0.5,color=cmap(5))
ax21.legend()
ax21.set_xlabel('bin. energy (eV)')
ax21.set_ylabel('intensity in arb. units')

```

--------------------------------

### Define and Fit a ConvGaussianDoniachDublettModel with TougaardBG

Source: https://lmfitxps.readthedocs.io/en/latest/introduction.html

This snippet demonstrates defining a composite model, initializing parameters, loading data, performing a fit, and printing the fit report. Ensure necessary libraries like lmfit, numpy, and matplotlib are imported.

```python
dublett = models.ConvGaussianDoniachDublett(prefix='dublett_', independent_vars=["x"])
bg=models.TougaardBG(independent_vars=["x","y"], prefix='tougaard_')
fit_model=dublett+bg
data = np.genfromtxt(exec_dir + '/examples/clean_Au_4f.csv', delimiter=',', skip_header=0)
x = 180-data[:, 0]
y = data[:, 1]
output_dir = os.path.join(exec_dir, 'examples/', 'plots')
os.makedirs(output_dir, exist_ok=True)

params = lmfit.Parameters()
params.add('tougaard_B', value=148.969)
params.add('tougaard_C', value=144.506, vary=False)
params.add('tougaard_D', value=268.598, vary=False)
params.add('tougaard_C_d', value=0.281, vary=False)
params.add('tougaard_extend', value=30)
params.add('dublett_amplitude', value=np.max(y))
params.add('dublett_sigma', value=0.2126)
params.add('dublett_gamma', value=0.04, min=0)
params.add('dublett_gaussian_sigma', value=0.0892)
params.add('dublett_center', value=87.663)
params.add('dublett_soc', value=3.67127)
params.add('dublett_height_ratio', value=0.7)
params.add('dublett_fct_coster_kronig', value=1.04)


result = fit_model.fit(y, params, y=y, x=x, weights=1 /(np.sqrt(y)))
```

--------------------------------

### Set Parameter Hints for XPS Models

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Defines default parameter hints for XPS spectral components like amplitude, sigma, and center. Includes expressions for derived parameters such as Gaussian and Lorentzian FWHM.

```python
self._set_paramhints_prefix()

    def _set_paramhints_prefix(self):
        self.set_param_hint('amplitude', value=100, min=0)
        self.set_param_hint('sigma', value=0.2, min=0)
        self.set_param_hint('gamma', value=0.02)
        self.set_param_hint('gaussian_sigma', value=0.2, min=0)
        self.set_param_hint('center', value=100, min=0)
        g_fwhm_expr = '2*{pre:s}gaussian_sigma*1.1774'
        self.set_param_hint('gaussian_fwhm', expr=g_fwhm_expr.format(pre=self.prefix))
        l_fwhm_expr = '{pre:s}sigma*(2+{pre:s}gamma*2.5135+({pre:s}gamma*3.6398)**4)'
        self.set_param_hint('lorentzian_fwhm', expr=l_fwhm_expr.format(pre=self.prefix))
```

--------------------------------

### Set ShirleyBG Parameter Hints

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Sets parameter hints for the ShirleyBG model, providing initial values for 'k' and 'const'.

```python
def _set_paramhints_prefix(self):
    """
    Sets parameter hints for the model.

    The method sets initial values and constraints for the parameters :math:`k` and :math: `const`.

    """
    self.set_param_hint('k', value=0.03)
    self.set_param_hint('const', value=1000)
```

--------------------------------

### Initialize TougaardBG Model

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Initializes the TougaardBG model instance, inheriting parameters from lmfit.model.Model.

```python
def __init__(self, *args, **kwargs):
    """
    Initializes the TougaardBG model instance.

    """
    super().__init__(tougaard, *args, **kwargs)
    self._set_paramhints_prefix()
```

--------------------------------

### Combine TougaardBG with ConstantModel

Source: https://lmfitxps.readthedocs.io/en/latest/backgrounds.html

Use TougaardBG with 'extend' set to 0 and combine it with an additional ConstantModel for accurate background approximation when dealing with substantial peak asymmetry.

```python
import lmfit
import lmfitxps

tougaard_bg=lmfitxps.models.TougaardBG(prefix='tougaard_', independent_vars=['y', 'x'])
const_bg=lmfit.models.ConstantModel(prefix='const_')

bg_model=tougaard_bg+const_bg

params = lmfit.Parameters()
params.add('tougaard_extend', value=0)
```

--------------------------------

### Set Parameter Hints for SlopeBG

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Sets parameter hints for the SlopeBG model, specifically providing an initial value for the 'k' parameter.

```python
def _set_paramhints_prefix(self):
    """
    Sets parameter hints for the model.

    The method sets an initial value for the parameter 'k'.

    """
    self.set_param_hint('k', value=0.01)
```

--------------------------------

### Clone lmfitxps Repository

Source: https://lmfitxps.readthedocs.io/en/latest/about.html

Use this command to clone the lmfitxps repository to your local machine. Replace <your name> with your GitHub username.

```bash
git clone https://github.com/<your name>/lmfitxps.git
```

--------------------------------

### Combine TougaardBG and ConstantModel

Source: https://lmfitxps.readthedocs.io/en/latest/_sources/backgrounds.rst.txt

Use TougaardBG with 'extend' set to 0 and combine it with lmfit's ConstantModel to approximate background, particularly when dealing with asymmetric peaks. Ensure 'independent_vars' are correctly set for both models.

```python
import lmfit
import lmfitxps

tougaard_bg=lmfitxps.models.TougaardBG(prefix='tougaard_', independent_vars=['y', 'x'])
const_bg=lmfit.models.ConstantModel(prefix='const_')

bg_model=tougaard_bg+const_bg

params = lmfit.Parameters()
params.add('tougaard_extend', value=0)

# Set all other parameters
```

--------------------------------

### Initialize ShirleyBG Model

Source: https://lmfitxps.readthedocs.io/en/latest/_modules/lmfitxps/models.html

Initializes the ShirleyBG model instance. It inherits parameters from lmfit.model.Model and sets parameter hints for 'k' and 'const'.

```python
def __init__(self, *args, **kwargs):
    """
    Initializes the ShirleyBG model instance.

    """
    super().__init__(shirley, *args, **kwargs)
    self._set_paramhints_prefix()
```
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