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https://github.com/radi0sus/fit-mb
Python 3 script for (hassle-free) fitting of Mößbauer (MB) spectra
https://github.com/radi0sus/fit-mb
fit fitting least-squares-optimization levenberg-marquardt lmfit lorentz lorentzian mossbauer mossbauer-spectroscopy non-linear-optimization python python3 spectrum
Last synced: 17 days ago
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Python 3 script for (hassle-free) fitting of Mößbauer (MB) spectra
- Host: GitHub
- URL: https://github.com/radi0sus/fit-mb
- Owner: radi0sus
- License: bsd-3-clause
- Created: 2023-11-27T06:14:11.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-11-13T06:26:51.000Z (about 1 month ago)
- Last Synced: 2024-11-13T07:27:32.737Z (about 1 month ago)
- Topics: fit, fitting, least-squares-optimization, levenberg-marquardt, lmfit, lorentz, lorentzian, mossbauer, mossbauer-spectroscopy, non-linear-optimization, python, python3, spectrum
- Language: Python
- Homepage:
- Size: 24.2 MB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Fit-MB
A Python 3 script for (hassle-free) fitting of Mößbauer (MB) spectra.
It is easy to use but has some limitations. The script is limited to doublets
(with no intensity differences) and singlets, cannot handle magnetic properties and is
restricted to Lorentzian lines shapes.
## External modules
`lmfit`
`numpy`
`scipy`
`matplotlib`
`tabulate`
## Quick start
1. Edit or create a parameter file (e.g. `mb-param.text`) with a text editor:
```
#...
#
MB-data = example_data.dat
#
# ⇦ just a comment
#...
#----------------------------------------
# label | δ | ΔEQ | fwhm | ratio
#----------------------------------------
L1Fe -0.12 2.92
L2Fe -0.09 2.21
# adjust ⇧ ⇧
```
`example_data.dat` is the file that contains data from measurement.
First column should contain velocity, second intensity. Recognized delimiters
are `,` or space(s).
The script can also process WissEl data (`.ws5`) directly. Three additional parameters
from a calibration (folding point: `FP`, channel in which the velocity is zero: `v0`,
and maximum velocity: `vmax`) must be included in the parameter file. It is also necessary
to change the number of channels directly in the script under `N_chan`, if the number
of channels is different from 512. You can obtain these parameters with `mcal` or
[cal-mb](https://github.com/radi0sus/cal-mb), for example.
```
#...
# Note that FP, v0 and vmax must be specified.
MB-data = example_data.ws5
FP = 256.621
v0 = 125.282
vmax = -4.2622
#
# ⇦ just a comment
#...
#----------------------------------------
# label | δ | ΔEQ | fwhm | ratio
#----------------------------------------
L1Fe -0.12 2.92
L2Fe -0.09 2.21
# adjust ⇧ ⇧
```
The number of labels (e.g. `L1Fe`) is equivalent to the number of MB active species.
Furthermore rough estimates of $δ$ (isomer shift) and $ΔE_Q$ (quadrupol splitting)
are required.
> If the number of species is insufficient add or remove (or comment `#`) them
> in the parameter file (e.g. `mb-param.text`) and restart the script as described
> under **2**.
3. Start the script with:
```console
python3 mb-fit.py mb-param.txt
```
After the `matplotlib` window has opened, select a species in the upper legend. Simply
click on the **label** or the **radio button**. Adjust parameters for each species
with the **sliders** at the bottom of the window. It should roughly agree with what
you expect. You can also **fix** some of the parameters, but in general this is not
necessary. Then press the **Fit button**.
> You can also try to fit the data without adjusting any parameters. Simply click
> **Fit**. In this example no alteration of the start parameters was necessary.
3. The result of the fit is displayed in the lower area, parameters and statistics are
also displayed in the terminal (console, cmd, std.out). Check if the results are okay.
Otherwise adjust the **sliders** and click the **Fit button** again.
Terminal output:
```
# Fit report for example_data
## File statistics:
MB data : example_data.dat
data points : 256
variables : 9
χ² : 8.3411e-05
red. χ² : 3.3770e-07
R² : 0.9952
## Fit results:
data in 1σ : 30
data in 3σ : 101
y0 : 0.9995±0.0001
| species | δ /mm·s⁻¹ | ΔEQ /mm·s⁻¹ | fwhm /mm·s⁻¹ | r (area)/% | r (int)/% |
|-----------|--------------|---------------|----------------|--------------|-------------|
| L1Fe | 0.669±0.016 | 1.637±0.026 | 0.877±0.049 | 20.26±0.93 | 19.85 |
| L2Fe | -0.170±0.002 | 2.240±0.003 | 0.519±0.006 | 79.74±0.93 | 80.15 |
```
5. Finally save the results by clicking on the **Save** button. The optimized parameters
will be saved in `mb-param-fit.txt`, a fit report in `example_data-report.txt`
(similar to the last console output), raw data and the fitted curves in
`example_data-fit.dat` (a file which you can open in Gnuplot, Excel or Origin
for example) and the content of the lower plot area in `example_data-fit.png`.
Terminal output:
```
mb-param-fit.txt saved.
example_data-report.txt saved.
example_data-fit.dat saved.
example_data-fit.png saved.
```
In the case of WissEl data, the folded spectrum is also saved (same output as above, plus):
```
example_data-fold.dat saved.
```
7. Exit.
## Command-line options
- filename, required: filename, e.g. `mb-param.txt`. A file, that contains the name (and
location) of the file that contains MB data and start parameters for the fit.
## Parameter file
Below is a sample parameter file with all necessary information. Important are the
name (and location) of the file that contains MB data (`MB-data = example_data.dat`)
and start parameters for the fit. The term `MB-data = ` must not be changed. In case
of raw data from a multi-channel analyzer (WissEl .ws5 files for example), the terms
`FP = `, `v0 = ` and `vmax = ` must not be changed. You can obtain these parameters
from a calibration with `mcal` or [cal-mb](https://github.com/radi0sus/cal-mb),
for example.
Only label, $δ$ and $ΔE_Q$ are essential and the labeling must be unique. Every time
something has changed in the parameter file, the script must be restarted.
> Simply add or remove `#` before a label, to include or exclude a MB active species.
> It is strongly recommended to have the parameter file and the data file in the
> same directory.
```
#==============================================================================
# Example of a MB parameter file for fit-mb.py
#==============================================================================
# This is a comment.
# Lines starting with '#' are ignored by the script.
#
# The MB (raw) data file should contain 'velocity' (1st column) and
# 'intensity' (2nd column). Further columns and lines starting with '#'
# are ignored. Recognized delimiters are ',' or ' ' (whitespace(s)).
# WissEl files '.ws5' are also accepted.
# For WissEl '.ws5' files, 'FP' (folding point), 'v0' (channel in which
# the velocity is zero) and 'vmax' (maximum velocity) must also be specified.
#
# The terms 'MB-data = ', FP = ', 'v0 = ', and 'vmax = ' must not
# be changed since they are recognized by the script.
#
MB-data = example_data.dat
FP = 256.621
v0 = 125.282
vmax = -4.2622
#
# The start parameters for the fit must be entered in the following order:
#
# label_1 δ_1 ΔEQ_1 fwhm_1 ratio_1
# label_2 δ_2 ΔEQ_2 fwhm_2 ratio_2
# label_3 δ_3 ΔEQ_3 fwhm_3 ratio_3
# ...
#
# label = unique atom / compound name
# δ = isomeric shift in mm/s
# ΔEQ = quadrupole splitting in mm/s; should be positive
# fwhm = full width at half maximum; line width for broadening
# ratio = ratio of the MB active compound / nucleus
#
# At least one species with label, δ, ΔEQ must be defined.
# The labeling must be unique (e.g. 'Fe1', 'Fe2', ...). Identical labels
# (e.g. 'Fe1', 'Fe1', ...) lead to errors. Labels should be without
# spaces (e.g. 'LFe1' or 'LFe_1' instead of 'LFe 1').
#
# 'fwhm' and 'ratio' are optional. If there is no value for 'fwhm',
# but there is a value for 'ratio', 'ratio' is considered to be 'fwhm',
# because the third parameter in the line is assumed to be 'fwhm'.
#
# If 'fwhm' is not specified it is set to 0.1. If 'fwhm' is not specified
# then 'ratio' cannot be specified (see above remark).
#
# If 'ratio' is not specified it is set to 0.1.
# Defining a ratio different from 1 or 100% can be useful if there is
# a main component and an impurity which is also MB active
# or a mixture of two or more compounds with MB active nuclei.
# However, setting a 'ratio' as start parameter is just for orientation,
# since the fit starts with a fixed value.
#
#----------------------------------------
# label | δ | ΔEQ | fwhm | ratio
#----------------------------------------
#L1Fe 0.24 1.51 0.33 0.40
#L2Fe 0.25 3.12 0.39 0.35
#L3Fe -0.03 1.24 0.44 0.12
#L4Fe -0.06 0.61 0.37 0.13
L1Fe 0.264 2.321 0.434 0.492
L2Fe 0.279 1.551 0.427 0.508
```
## MB data file
Below is a sample data file. Lines starting with `#` are ignored. Only the first two
columns are considered. The first column must contain the velocity, the second column
must contain the intensity data. Recognized delimiters are `,` and spaces.
```
# filename
# sample: sample name
# 80 K : temperature
# 0 T : field
# 125.69, -4.693
# ---------------------------
-4.5893, 587126.4, 1
-4.5525, 588314.7, 2
-4.5157, 586286.4, 3
-4.4789, 586907.1, 4
-4.4421, 587216.4, 5
-4.4052, 586408.4, 6
....
```
## WissEl ws5 file
Below is a sample WissEl ws5 file. Lines starting with `<` are ignored. It is necessary
to change the number of channels directly in the script under `N_chan`, if the number of
channels is different from 512.
> In principle any raw data (not only WissEl) can be processed, as long as `FP`,
> `v0`, `vmax` are included in the parameter file.
```
http://www.wissel-gmbh.de
132130
132207
131879
132294
132142
....
```
## Pre-fit plot
The pre-fit plot is in the upper part of the `matplotlib` window. The active species
is selected in the **legend** of plot. The plot is updated if any of the parameters is
changed using the **sliders** at the bottom of the window.
The purpose of the pre-fit plot in combination with the **sliders** is to set the fitting
parameters so that they roughly reflect the shape of the measured data.
If `errbar_ws5 = True` is set in the script, error bars are displayed for folded raw
data (e.g. WissEl .ws5).
> The most important parameters to be changed are **$δ$** and **$ΔE_Q$**. **Fwhm** is
> recognized by the fitting procedure, but is less important. The **ratio** is only for
> orientation and is ignored as a start parameter for the fit.
## Adjustment sliders and check (fix) buttons
There are four separate **sliders** for **$δ$** (isomer shift), **$ΔE_Q$** (quadropule
splitting), **fwhm** (full width at half maximum), and **ratio** (ratio of the species /
component). For the fit, the start value for **ratio** is always set to 0.1 regardless
of the slider value. Changing the **ratio** is therefore only for orientation.
Three parameters can be fixed at a certain value with the check buttons **fix $δ$**,
**fix $ΔE_Q$**, and **fix fwhm**. Fixed values are not changed during fit.
Select the species/component in the **legend** of the diagram at the top and change the
parameters for each component individually.
> The most important parameters to be changed are **$δ$** and **$ΔE_Q$**. **Fwhm** is
> recognized by the fitting procedure, but is less important. The **ratio** is only for
> orientation and is ignored as a start parameter for the fit.
> If **$ΔE_Q$** is zero or close to zero and the fit fails, **$ΔE_Q$** should be
> **fixed** around **0**. In a subsequent fit, this **fix** can often be removed.
## Curve fitting
After clicking on the **Fit button**, (raw) data, the fitted curves for each component,
the resulting curve and the residuals are displayed in the lower area of the plot window.
The **ratio** of the components (in %), **$δ$** and **$ΔE_Q$** (in mm/s) and **$R^2$**
are given in the legend.
Optionally, the **3σ** uncertainty band can be displayed (set `plot_3s_band = True` in the
script).
If the result is not suitable, the parameters should be adjusted with the **sliders**
and the **Fit** should be restarted.
> If a fit fails or is poor, try changing the number of species
> (components), **$δ$**, **$ΔE_Q$** and **fwhm** in that order.
The terminal provides a more detailed fit report.
```
# Fit report for example_data
## File statistics:
MB data : example_data.dat ⇦ name of the file that contains the (raw) data
data points : 256 ⇦ number of data points
variables : 9 ⇦ number of variables
mean σ data : 9.2035e-04 ⇦ in case of .ws5 data (`weights` for χ² and red. χ²)
χ² : 8.3411e-05 ⇦ Chi square(d); close to the numer of data in case of .ws5
red. χ² : 3.3770e-07 ⇦ reduced Chi square(d); close to 1 in case of .ws5
R² : 0.9952 ⇦ R square(d)
## Fit results:
data in 1σ : 30 ⇦ data points in 1σ (optional)
data in 3σ : 101 ⇦ data points in 3σ (optional)
y0 : 0.9995±0.0001 ⇦ y0±error (offset)
| species | δ /mm·s⁻¹ | ΔEQ /mm·s⁻¹ | fwhm /mm·s⁻¹ | r (area)/% | r (int)/% |
|-----------|--------------|---------------|----------------|--------------|-------------|
| L1Fe | 0.669±0.016 | 1.637±0.026 | 0.877±0.049 | 20.26±0.93 | 19.85 |
| L2Fe | -0.170±0.002 | 2.240±0.003 | 0.519±0.006 | 79.74±0.93 | 80.15 |
⇧ ⇧ ⇧ ⇧ ⇧ ⇧
label δ±error ΔEQ±error fwhm±error ratio from ratio from
area integral
```
> A good fit result has a **$R²$** close to **1** (> 0.98) and a **χ²** below 1e⁻³
> or less. But this strongly depends on the quality of the measured data.
> In case of unfolded data, uncertainties (standard deviations)
> are calculated from the difference of the intensities from the left-hand side and
> the right-hand side of the unfolded spectrum. **χ²** and **red. χ²** a are then weigthed by
> the mean standard deviation (or square root of the mean variance of all data pairs).
> **χ²** should be close to the number of data and **red. χ²** should be close to 1 for
> a good fit result.
**χ²** from `lmfit`:
$$\chi^2 = \sum_{i}^N [\rm Residuals_i]^2$$
(weighted in case of .ws5 files)
**red. χ²** from `lmfit`
$$\chi^2_\nu = \chi^2 / (N-N_{\rm varys})$$
$N$ is the number of data points and $N_{varys}$ is number of variable parameters.
(weighted in case of .ws5 files)
**$R²$**: coefficient of determination
Data points in **1σ** or **3σ** are optional (set `print_in_sigma = True` in the script).
**r (area)** in % is the ratio of a component calculated by the area of the individual
component divided by the sum of all components.
**r (int)** in % is the ratio of a component calculated by the integral (area under
the curve) of an individual component divided by the total area / integral of all
components. Integrals or areas under curves are calculated with the trapezoidal rule.
**r (int)** is often closer to the values calculated by the `mfit2` program.
The errors are calculated by the `lmfit` module.
## Saving results
After clicking the **Save button** the following files are saved:
```
parameterfile-fit.txt ⇦ new parameter file with fitted parameters
data_filename-report.txt ⇦ fit report; similar to the last terminal output
data_filename-fit.dat ⇦ a file that contains all data from fit and raw data
data_filename-fit.png ⇦ exactly the plot (as PNG) in the lower window
data_filename-fold.dat ⇦ folded spectrum (only if a WissEl ws5 file has been processed)
```
In case of the **parameter file** `-fit` is added to the filename of the new parameter-file.
The filename (without extension) of the file that contains the measured data is the prefix
for the **report**, **data** and **plot** files. `-fit` is added to the prefix in case of
the latter two files. The **folded** spectrum is saved, if if a WissEl ws5 file has been processed
(`-fold` is added to the filename).
The file `data_filename-fit.dat` contains the following data:
```
#velocity data residuals fit L1Fe L2Fe
-4.58930 0.99832 1.00224 0.99917 0.99924 0.99942
-4.55250 0.99906 1.00149 0.99916 0.99923 0.99942
-4.51570 0.99900 1.00154 0.99916 0.99923 0.99942
-4.47890 0.99909 1.00145 0.99915 0.99922 0.99942
-4.44210 0.99952 1.00101 0.99914 0.99922 0.99942
...
⇧ ⇧ ⇧ ⇧ ⇧ ⇧
velocity raw data residuals best-fit single fit curves
(+ extra) curve for each component
```
To the `residuals` some extra in `y` is added to display them above data and fit curves.
## Exit
To exit the script, klick on the **Exit button** or close the `matplotlib` window.
## Known Issues
- If $ΔE_Q$ is 0 or close to 0, the fitting procedure has sometimes problems finding the correct solution.
In this case **fix $ΔE_Q$** at a value close to zero, **Fit**, remove **fix $ΔE_Q$** and **Fit** again.
- If $ΔE_Q$ is 0 or close to 0, the error is very large. This results from the calculation of errors in
`lmfit`. There is no solution for this behaviour.
- The script has not been tested with raw data from 1024 channel multi-channel analyzers.
## Remarks
- The script is benchmarked against the `mfit2` program from Dr. Eckhard Bill. Within the given restrictions,
the results for $δ$ and $ΔE_Q$ match down to the second decimal place.
- Raw spectra (WissEl .ws5 for example) are expected to start at channel 1 and be folded to the right.
- χ² and red. χ² are rather meaningless in case of files that contain only velocity and intensity. However, if
the fit is good both values get smaller.
- In case of unfolded data, the error can be estimated from the differences in the intensities of the left-hand
side and right-hand side sub-spectra. The weighting for χ² and red. χ² is 1 / (mean standard deviation).
The mean standard deviation is the square root of the mean variance of two times the intensities of the left-hand
side and right-hand side data pairs which are supposed to be equal. χ² is close to the number of data points and
red. χ² is close to 1 in case of a good fit. All values are normalized.
Please note that parameters like $δ$ or $ΔE_Q$ are mainly derived from channel or velocity data (x-values),
while only errors from transmission or intensity data (y-values) are taken into account for the weigths of χ² and red. χ².
- R² is calculated by 1 - variance(residual * mean standard deviation) / variance(intensities), because
R² is calculated wrongly by `lmfit` in case of weights.
## Example
