nPDyn¶

nPDyn is a Python based API for analysis of neutron backscattering data.

The API aims at providing a lightweight, user-friendly and modular tool to process and analyze quasi-elastic neutron scattering (QENS) and fixed-window scans (FWS) obtained with backscattering spectroscopy.

nPDyn can be used in combination with other software for neutron data analysis such as Mantid. The API provides an interface to Mantid workspaces for that.

An important feature of nPDyn is the modelling interface, which is designed to be highly versatile and intuitive for multidimensional dataset with global and non-global parameters. The modelling in nPDyn is provided by builtin classes, params.Parameters, model.Model and model.Component. nPDyn provides also some helper functions to use lmfit as modelling backend. See Fit data for details.

Eventually, some plotting methods are available to examine processed data, model fitting and optimized parameters.

Installation:¶

Unix and Windows¶

For installation within your python framework, use:

make install

or

python3 setup.py install

On Windows, the path to the GSL library can be provided using:

python.exe setup.py install --gsl-path="my/path/to/GSL/root/dir/"

Getting started¶

The nPDyn API is organized around a sample.Sample class. This class inherits from the NumPy ndarray class with some extra features added, such as neutron scattering-specific attributes, binning, data correction algorithm, automatic error propagation and data fitting.

In a neutron backscattering experiment, there is not only the measurement of samples but also some calibration measurements like vanadium, empty cell and solvent signal (often $\rm D_2O$). Some methods of the sample.Sample class can be used to perform normalization or absorption correction using the dataset corresponding to vanadium or empty cell, respectively. These calibration dataset can be used also in the fit function to automatically add a background or perform a convolution with the resolution function.

Details regarding importation of data are available in the Import data section of the documentation.

Importantly, nPDyn provides versatile tools for model building and fitting to the data. See the section Fit data for details.

Finally, a plot.plot() method is provided for easy visualisation of the data and the fit results.

Documentation¶

Import data¶

nPDyn provides various ways to handle data.

The data importation routines are found in nPDyn.dataParsers module.

Sample data are stored in the sample.Sample class. Some useful information about the sample.Sample class and about different data importation routines can be found in the following.

Access the data values¶

Each imported data consists in a sample.Sample class. The class is essentially a NumPy ndarray with extra features specific to neutron scattering dataset. In addition, the class contains several methods for processing and fitting.

The specific attributes are the following:

filename, the name of the file used to extract the data.
errors, the errors associated with scattering data.
energies, the energy transfers associated with the data.
time, the experimental time.
wavelength, the wavelength of the incoming neutrons.
name, the name for the sample.
temperature, the temperature(s) used experimentally.
concentration, the concentration of the sample.
pressure, the pressure used experimentally.
buffer, a description of the buffer used experimentally.
q, the values for the momentum transfer q.
beamline, the name of the beamline used.
observable_name, the name of the observable variable.

These attributes might be empty or not depending on the source file.

Note

The errors metadata is special as it is updated for various operations that are performed on the data array such as indexing or for the use of universal functions. For instance, indexing of the data will be performed on errors as well if its shape is the same as for the data. Also, addition, subtraction and other universal functions will lead to automatic error propagation. Some other metadata might change as well, like q, but only for the use of methods specific of the Sample class and not for methods inherited from numpy.

Raw data¶

Raw dataset, as generated on IN16B at the ILL, can be imported directly. The algorithm has several options allowing for detector grouping, unmirroring, integrating and summation of the scans.

See in16b_qens_scans_reduction.IN16B_QENS or in16b_fws_scans_reduction.IN16B_FWS for example.

To import raw data, the following can be used:

from nPDyn.dataParsers import IN16B_QENS, IN16B_FWS

# we can use a path to a folder or a list of strings
# here for FWS data where we only keep elastic scans
# and we choose the observable to be the temperature
sample = IN16B_FWS(
    'myDataFolder/',
    offset=0.0,
    observable='temperature'
)

# ...and here for a range of QENS data with .xml detector grouping file
sample = IN16B_QENS(
    'myDataFolder/scan01:scan10.nxs',
    detGroup='IN16B_detGroup.xml'
)

Different methods and properties of the dataset are accessible through this list, e.g., the momentum transfers using:

>>> sample.q
array([0.19102381, 0.29274028, 0.43543718, 0.56747019, 0.69687497,
0.82305221, 0.94541753, 1.0634042 , 1.17646584, 1.28407863,
1.38574439, 1.48099215, 1.5693807 , 1.65050083, 1.72397668,
1.78946811, 1.84667172, 1.89532256])

Nexus (hdf5) files¶

Nexus files as generated by Mantid can be read by nPDyn using the dataParsers.mantidNexus.processNexus() method.

The file will be assumed to be a Nexus file if the extension is ‘.nxs’, hence the following:

from nPDyn.dataParsers import processNexus

sample = processNexus('mySample01.nxs', FWS=False)

will import all files using the Nexus file parser.

.inx files¶

Similarly to Nexus files, nPDyn can read ‘.inx’ files as generated by the software SLAW available at the MLZ in Garching, Germany. The usage is essentially the same as for Nexus files:

from nPDyn.dataParsers import inxConvert

sample = inxConvert('mySample01.nxs', FWS=False)

Process data¶

nPDyn provides several data processing methods, which includes binning, normalization, scaling, empty cell correction, Paalman-Pings coefficient calculation and detector selection.

These are described below.

Arithmetic operations¶

The sample.Sample is essentially a NumPy array, so arithmetic operations can be used as for any array.

>>> from nPDyn.dataParsers import processNexus
>>> sample1 = processNexus('mySample1.nxs')
>>> sample2 = processNexus('mySample2.nxs')
>>> corrected_sample = sample1 - 0.95 * sample2

Again, the errors are automatically propagated for most of the commonly used operators (addition, subtraction multiplication, division, exponentiation, logarithm, power, square, square root).

Binning¶

The dataset can be binned along any axis. This can be done using the method sample.Sample.bin().

Here is an example code with quasi-elastic neutron scattering (QENS) data:

>>> from nPDyn.dataParsers import processNexus
>>> sample = processNexus('myData.nxs')
>>> sample.shape
(1, 18, 1004)
>>> # 1 observable, 18 detectors/q values and 1004 energy transfers
>>> sample = sample.bin(5, axis=2)  # bins of 5 points on the energy axis
>>> sample.shape
(1, 18, 200)
>>> sample.energies.shape
(200,)

Normalization¶

Normalization of data can be done by dividing by the integration of themselves, of vanadium or of data at low temperature.

The following:

>>> from nPDyn.dataParsers import processNexus
>>> sample = processNexus('myData.nxs')
>>> sample = sample.normalize()

will apply normalization using the integration of the ‘sample’ dataset.

Using

>>> from nPDyn.dataParsers import processNexus
>>> sample = processNexus('myData.nxs')
>>> vanadium = processNexus('vanadium.nxs')
>>> sample = sample.normalize(vanadium)

The signal of the vanadium will be integrated and used for normalization. If a fitted model exists for the vanadium, it will be used instead of the experimental data.

Background corrections¶

The correction of background, often using empty cell signal, can be done either using simple arithmetic operators or using the sample.Sample.absorptionCorrection() method.

For instance,

>>> from nPDyn.dataParsers import processNexus
>>> sample = processNexus('mySample.nxs')
>>> empty_cell = processNexus('empty_cell.nxs')
>>> sample = sample.absorptionCorrection(
...     empty_cell,
...     canScaling=0.95,
...     canType='tube',
...     useModel=False
... )

will computes the Paalman-Ping coefficient for a tubular sample holder, scale the empty cell data provided factor and apply the absorption correction to the dataset.

Selection of data range¶

The user will very likely want to restrain the analysis to a specific range of momentum transfers q or observable values. To this end, some self-explaining methods are provided to select a range based on values instead of indices:

>>> from nPDyn.dataParsers import processNexus
>>> sample = processNexus('mySample.nxs')
>>> sample.shape
(10, 18, 1004)
>>> sample = sample.get_q_range(0.3, 1.7)
>>> sample = sample.get_observable_range(280, 320)
>>> sample.shape
(4, 14, 1004)

Fit data¶

nPDyn relies on a builtin implementation to model and fit data, but provides also some methods to fit your data using lmfit as modelling and fitting backend.

In the following, we will introduce data modelling using two type of data and analysis, the first being the fit of quasi-elastic neutron scattering (QENS) measurement on a protein solution sample and the second the fit of elastic fixed-window scans (EFWS) of a protein powder sample.

The QENS data will be modelled using the following:

(1)¶\[\rm S(q, \hbar \omega) = R(q, \hbar \omega) \otimes \beta_q \left[\alpha \mathcal{L}_{\Gamma} + (1 - \alpha) \mathcal{L}_{\Gamma + \gamma} \right] + \beta_{D_2O} \mathcal{L}_{D_2O}\]

where $\rm q$ is the momentum transfer, $\rm \hbar \omega$ the energy transfer, $\rm R(q, \hbar \omega)$ is the resolution function (here a pseudo-Voigt profile), $\rm \beta_q$ a vector of scalars accounting for detector efficiency (one scalar for each q), $\rm \alpha$ a scalar between 0 and 1, $\rm \mathcal{L}_{\Gamma}$ a Lorentzian of accounting for center-of-mass diffusion with a explicit q-dependent width $\rm \Gamma = D_s q^2$, where $\rm D_s$ is the self-diffusion coefficient, $\rm \mathcal{L}_{\Gamma + \gamma}$ is a Lorentzian accounting for internal dynamics with $\rm \gamma = \frac{D_i q^2}{1 + D_i q^2 \tau}$ (see [1]) and $\rm \beta_{D_2O} \mathcal{L}_{D_2O}$ accounting for the signal from the $\rm D_2O$.

The EFWS data will be modelled using a simple Gaussian to extract the mean-squared displacement (MSD) as a function of temperature:

(2)¶\[\rm S(q, 0) = e^{-\frac{q^2 MSD}{6}}\]

We use the sample data in the the test suite of nPDyn (from package root directory, use cd nPDyn/tests/sample_data/ and we initiate our dataset using, for QENS:

>>> from nPDyn.dataParsers import processNexus
>>> import numpy as np
>>> qens = processNexus('lys_part_01_QENS_before_280K.nxs')
>>> vana = processNexus('vana_QENS_280K.nxs')
>>> ec = processNexus('empty_cell_QENS_280K.nxs')
>>> buffer = processNexus('D2O_QENS_280K.nxs')
>>> # Perform some data processing
>>> qens, vana, ec, buffer = (
... val.bin(5) for val in (qens, vana, ec, buffer)
... )
>>> qens, vana, buffer = (
... val - 0.95 * ec for val in (qens, vana, buffer)
... )
>>> qens, vana, ec, buffer = (
... val.get_q_range(0.4, 1.8) for val in (qens, vana, ec, buffer)
... )
>>> # Extract momentum transfers for modelling and make it 2D
>>> q = qens.q[:, None]

and for EFWS:

>>> from nPDyn.dataParsers import inxConvert
>>> efws = inxConvert.convert('D_syn_fibers_elastic_10to300K.inx', True)
>>> efws = efws.bin(5, 0)
>>> efws /= efws[:5].mean(0)
>>> efws = efws.get_q_range(0.2, 0.8)

Using builtin model backend¶

The builtin modelling interface has been designed to be easy to use and adapted to the multi-dimensional dataset obtained with neutron backscattering spectroscopy and a mix of global and non-global parameters.

The basic workflow is as follows:

Create a Parameter instance with parameters that can be scalar, 1D, 2D or any shaped arrays.
Create a Model instance that is initiated with the prviously created parameters.
Add several Component or other Model to this model. Each component is associated with a Python function, the arguments of which can be dynamically defined at the creation of the component using an expression as a string as shown below.
Fit your data!

For the QENS data, we first model the resolution function using a pseudo-voigt profile. To this end, we use the builtins.modelPVoigt() builtin model from nPDyn. The same is done for $\rm D_2O$ background using the builtins.modelD2OBackground() builtin model.

Simply use:

>>> from nPDyn.models.builtins import modelPVoigt
>>> from nPDyn.models.builtins import modelCalibratedD2O
>>> vana.fit(modelPVoigt(q, 'resolution'))
>>> buffer.fit(modelCalibratedD2O(q, temp=280))

With a little anticipation on this documentation, you can use the following to look at the fit result:

>>> from nPDyn.plot import plot
>>> plot(vana, buffer)

Create parameters¶

For the QENS sample, there are 6 parameters, namely $\rm \beta_q$, $\rm \alpha$, $\rm D_s$, $\rm D_i$, $\rm \tau$, and $\rm \beta_{D_2O}$.

We can thus create the Parameters instance:

>>> from nPDyn.models import Parameters
>>> pQENS = Parameters(
...     beta={'value': np.zeros_like(q) + 1, 'bounds': (0., np.inf)},
...     alpha={'value': 0.5, 'bounds': (0., 1)},
...     Ds={'value': 5, 'bounds': (0., 100)},
...     Di={'value': 20, 'bounds': (0., 100)},
...     tau={'value': 1, 'bounds': (0., np.inf)},
... )

For the EFWS sample, we only have the MSD and we use a slightly different way to instantiate the Parameters instance for demonstration purpose:

>>> from nPDyn.models import Model
>>> pEFWS = Parameters(msd=0.5)
>>> pEFWS.set('msd', bounds=(0., np.inf), fixed=False)

Instantiate a Model¶

Instantiating a Model is very straightforward, just use:

>>> modelQENS = Model(pQENS, 'QENS')  # for QENS data
>>> modelEFWS = Model(pEFWS, 'EFWS')  # for EFWS data

Add components¶

The modelQENS model should contain three components, or three lineshapes, as we can see in equation (1), namely a Lorentzian for center-of-mass diffusion, a Lorentzian for internal dynamics and the model we used for $\rm D_2O$ background. We can add them using:

>>> from nPDyn.models import Component
>>> from nPDyn.models.presets import lorentzian
>>> modelQENS.addComponent(Component(
...     'center-of-mass',
...     lorentzian,
...     scale='beta * alpha',  # will find the parameters values in pQENS
...     width='Ds * q**2',  # we will give q on the call to the fit method
...     center=0))  # we force the center to be at 0
...                 # (as it is given by the convolution with resolution)
>>> # we can add, subtract, multiply or divide a model using a Component or
>>> # another Model
>>> internal = Component(
...     'internal',
...     lorentzian,
...     scale='beta * (1 - alpha)',
...     width='Di * q**2 / (1 + Di * q**2 * tau)',
...     center=0)  # we force the center to be at 0
...                # (as it is given by the convolution with resolution)
>>> modelQENS += internal
>>> # for the D2O signal, we use a lambda function to include the scaling
>>> # note this can be done automatically with the 'bkgd' and
>>> # 'volume_fraction_bkgd' arguments of the fit function.
>>> modelQENS.addComponent(Component(
...     '$D_2O$',  # we can use LaTeX for the component and model names
...     lambda x, scale: scale * buffer.fit_best(x=x)[0],
...     scale=0.95,
...     skip_convolve=True))  # we do not want to convolve this
>>>                           # component with resolution

The modelEFWS model uses the momentum transfer q as independent variable, which will be passed later upon fitting and it contains only one component. Here, we use:

>>> from nPDyn.models.presets import gaussian
>>> modelEFWS.addComponent(Component(
...     'EISF',
...     lambda x, scale, msd: scale * np.exp(-x**2 * msd / 6)))

Fit data¶

The class sample.Sample provides a method to fit the data.

Here, we use it and write for QENS:

>>> qens.fit(
...     modelQENS,
...     res=vana,
...     fit_method='basinhopping',
...     fit_kws={'niter': 10, 'disp': True}
... )

and for EFWS, where we set the independent variable to a column vector containing the momentum transfer q values:

>>> efws.fit(
...     modelEFWS,
...     x=efws.q[:, None]
... )

The fitted parameters can be saved in JSON format using (for the first observable):

>>> qens.params[0].writeParams(<'file_name'>)

Subsequently, the parameters can be imported using:

>>> qens.params[0].loadParams(<'file_name'>)

Using lmfit backend¶

In addition to the builtin model interface of nPDyn, the API also provides some helper functions to use the lmfit package. This package is more advanced and exhaustive than the builtin model interface but it is less adapted to multi-dimensional dataset with global and non-global parameters.

This is where the presets and builtin models in nPDyn come into play, to make it easier to use within the analysis workflow of neutron backscattering data.

The interface with lmfit relies on the lmfit_presets.build_2D_model() function.

We present here the analysis of QENS data using equation (1).

Build model¶

The function lmfit_presets.build_2D_model() uses a formatted string to build a 2D model where the words flanked by curly braces {} are considered as parameters.

The resolution function and the $\rm D_2O$ background signal can make use of the provided presets lmfit_presets.pseudo_voigt() and lmfit_presets.calibratedD2O(), we thus use:

>>> from nPDyn.lmfit.lmfit_presets import pseudo_voigt, calibratedD2O
>>> vana.fit(pseudo_voigt(q, prefix='res_'))
>>> buffer.fit(calibratedD2O(q, 0.95, 280, prefix='D2O_'))
>>> q = qens.q

To build the model for the protein sample, we use the function lmfit_presets.build_2D_model() to get the part inside square brackets in (1) and we will convolve with the resolution and add the D2O manually:

>>> from nPDyn.lmfit.lmfit_presets import build_2D_model
>>> # let us start with the formatted text for the center-of-mass term.
>>> comText = ("{beta} * {alpha} * {Ds} * {q}**2 / (np.pi * "
...            "(x**2 + ({Ds} * {q}**2)**2))")
>>> # same for the internal dynamics term
>>> jumpDiffText = ("{beta} * (1 - {alpha}) * "
...                 "{Di} * {q}**2 / (1 + {Di} * {q}**2 * {tau}) / "
...                 "(np.pi * (x**2 + ({Di} * {q}**2 / "
...                 "(1 + {Di} * {q}**2 * {tau}))**2))")
>>> # now we build the components
>>> comModel = build_2D_model(
...     q,
...     'com',
...     comText,
...     paramGlobals=['alpha', 'Ds'],
...     bounds={
...         'beta': (0., np.inf),
...         'alpha': (0, 1),
...         'Ds': (0.01, np.inf)},  # non-zero min to avoid infinites
...     defVals={'alpha': 0.5,
...              'Ds': 5,
...              'beta': 1},
...     prefix='com_')
>>> jumpDiffModel = build_2D_model(
...     q,
...     'jumpDiff',
...     jumpDiffText,
...     paramGlobals=['alpha', 'Di', 'tau'],
...     bounds={
...         'beta': (0., np.inf),
...             'alpha': (0, 1),
...             'Di': (0.01, np.inf),  # non-zero min to avoid infinites
...             'tau': (0., np.inf)},
...         defVals={'beta': 1,
...                  'alpha': 0.5,
...                  'Di': 30,
...                  'tau': 10},
...         prefix='jd_')
>>> # and we assemble them
>>> model = comModel + jumpDiffModel
>>> # some parameters are the same for the two components,
>>> # so we set them equals using 'expr' hint
>>> model.set_param_hint('com_alpha', expr='jd_alpha')
>>> for i in range(q.size):
...     model.set_param_hint('com_beta_%i' % i, expr='jd_beta_%i' % i)

And finally, we add the $\rm D_2O$ signal with a scaling factor:

>>> # now we add the component for the D2O signal
>>> from nPDyn.lmfit.lmfit_presets import hline
>>> scale = hline(q, prefix='bD2O_')
>>> d2OModel = scale * qens.D2OData.model
>>> d2OModel.param_hints.update(qens.D2OData.getFixedOptParams(0))
>>> fitModel = model + d2OModel

Fit data¶

Data fitting can be done using the same functions as when using the builtin models. The fit_method and some other keywords are different and should correspond to the keywords expected in lmfit (see lmfit documentation for details).

Here, we can simply use:

>>> qens.fit(fitModel, res=vana)

to fit the data using lmfit default parameters.

References¶

[1]	https://doi.org/10.1103/PhysRev.119.863

Plot data¶

nPDyn provides a plot window for quasi-elastic neutron scattering (QENS) and elastic/inelastic fixed-window scans (E/IFWS) data.

It can be used as follows:

>>> from nPDyn.plot import plot
>>> plot(sample)

Using the result of the fitting procedure presented in the Fit data section, the data, the fitted model model and the parameters can be examined using the window as shown below:

The experimental data are plotted alone with their errors for the selected observable and momentum transfer q value.

Here, the fitted model and its components are added by clicking on the associated checkboxes.

An 3D view of all spectra is available by clicking on the ‘3D plot’ button.

The optimized parameters can be plotted by clicking on the ‘Analysis’ button. The global parameters (which are unique for all q-values) are represented by a single horizontal line.

The data are plotted along the momentum-transfer q-values. The fitted model, which is used to extract the mean-squared displacement is added.

The whole dataset can be plotted using the ‘3D plot’ button.

_images/fwsPlot_analysis_with_errors.png

The optimized parameters can be plotted along different axis (observable, energy, q-values). Here, the uncertainty on the parameters is represented by the blue shaded area around the curve.

API reference¶

Sample¶

Handle data associated with a sample.

class sample.Sample(arr, errors=None, **kwargs)¶

Handle the measured data along with metadata.

This class is a subclass of the numpy.ndarray class with additional methods and attributes that are specific to neutron backscattering experiments.

It can handle various operations such as addition and subtraction of sample data or numpy array, scaling by a scalar or an array, indexing, broadcasting, reshaping, binning, sliding average or data cleaning.

Parameters:

input_arr (np.ndarray, list, tuple or scalar) – Input array corresponding to sample scattering data.
kwargs (dict (optional)) –
Additional keyword arguments either for np.asarray() or for sample metadata. The metadata are:
- filename, the name of the file used to extract the data.
- errors, the errors associated with scattering data.
- energies, the energy transfers associated with the data.
- time, the experimental time.
- wavelength, the wavelength of the incoming neutrons.
- name, the name for the sample.
- temperature, the temperature(s) used experimentally.
- concentration, the concentration of the sample.
- pressure, the pressure used experimentally.
- buffer, a description of the buffer used experimentally.
- q, the values for the momentum transfer q.
- beamline, the name of the beamline used.
- observable_name, the name of the observable variable.

Note

The errors metadata is special as it is updated for various operations that are performed on the data array such as indexing or for the use of universal functions. For instance, indexing of the data will be performed on errors as well if its shape is the same as for the data. Also, addition, subtraction and other universal functions will lead to automatic error propagation. Some other metadata might change as well, like q, but only for the use of methods specific of the Sample class and not for methods inherited from numpy.

Examples

A sample can be created using the following:

>>> s1 = Sample(
...     np.arange(5),
...     dtype='float32',
...     errors=np.array([0.1, 0.2, 0.12, 0.14, 0.15])
... )

>>> buffer = Sample(
...     [0., 0.2, 0.4, 0.3, 0.1],
...     dtype='float32',
...     errors=np.array([0.1, 0.2, 0.05, 0.1, 0.2])
... )

where my_data, my_errors and q_values are numpy arrays. A buffer subtraction can be performed using:

>>> s1 = s1 - buffer
Sample([0. , 0.80000001, 1.60000002, 2.70000005, 3.9000001], dtype=float32)

where buffer1 is another instance of Sample. The error propagation is automatically performed and the other attributes are taken from the first operand (here s1). Other operations such as scaling can be performed using:

>>> s1 = 0.8 * s1
Sample([0. , 0.80000001, 1.60000002, 2.4000001, 3.20000005], dtype=float32)

You can transform another Sample instance into a column vector and look how broadcasting and error propagation work:

>>> s2 = Sample(
...     np.arange(5, 10),
...     dtype='float32',
...     errors=np.array([0.1, 0.3, 0.05, 0.1, 0.2])
... )
>>> s2 = s2[:, np.newaxis]
>>> res = s1 * s2
>>> res.errors
array([[0.5       , 1.00498756, 0.63245553, 0.76157731, 0.85      ],
       [0.6       , 1.23693169, 0.93722996, 1.23109707, 1.5       ],
       [0.7       , 1.40089257, 0.84593144, 0.99141313, 1.06887792],
       [0.8       , 1.60312195, 0.98061205, 1.15948264, 1.26491106],
       [0.9       , 1.81107703, 1.1516944 , 1.3955644 , 1.56923548]])

T¶: Override the corresponding NumPy function to process axes too.

absorptionCorrection(ec, canType='tube', canScaling=0.9, neutron_wavelength=6.27, absco_kwargs=None, useModel=True)¶

Computes absorption Paalman-Pings coefficients

Can be used for sample in a flat or tubular can and apply corrections to data, for each q-value in data.qVals attribute.

Parameters:

ec (Sample) – The data corresponding to the empty can.
canType ({'tube', 'slab'}) – Type of can used, either ‘tube’ or ‘slab’. (default, ‘tube’)
canScaling (float) – Scaling factor for empty can contribution term, set it to 0 to use only correction of sample self-attenuation.
neutron_wavelength (float) – Incident neutrons wavelength.
absco_kwargs (dict) – Geometry arguments for absco library. from Joachim Wuttke [1].

References

[1]	http://apps.jcns.fz-juelich.de/doku/sc/absco

bin(bin_size, axis=-1)¶

Bin data with the given bin size along specified axis.

Parameters:	bin_size (int) – The size of the bin (in number of data points). axis (int, optional) – The axis over which the binning is to be performed. (default, -1 for energies)
Returns:	out_arr – A binned instance of `Sample` with the same metadata except for errors and the corresponding axis values, which are binned as well.
Return type:	`Sample`

discardData(indices, axis=0)¶

Discard data at given indices along the given axis.

Parameters:	indices (int, list) – The indices of the data to be discarded. axis (int) – The index of the axis along which the data are discarded.

fit(model=None, cleanData='replace', res=None, ec=None, bkgd=None, volume_fraction_bkgd=0.95, **kwargs)¶

Fit the dataset using the model attribute.

Parameters:

model (Model instance) – The model to be used for fitting. If None, will look for a model instance in ‘model’ attribute of the class instance. If not None, will override the model attribute of the class instance.
cleanData ({'replace', 'omit'} or anything else for no, optional) – If set to ‘replace’ the locations of null or inf values in data are set to np.inf in weights prior to fitting. If set to ‘omit’ the locations of null or inf values in data are removed from data, weights and x prior to fitting. Else, nothing is done.
res (bool, optional) – If True, will use the attribute resData, fix the parameters, and convolve it with the data using: model = ConvolvedModel(self, resModel)
ec (bool, optional) – If True, will use the attribute ECData, fix the parameters, model by calling: ECModel = self.ECData.fixedModel and generate a new model by calling: model = self.model + ECModel
bkgd (bool, optional) – If True, will use the attribute D2OData to obtain the fixed model by calling: D2OModel = self.D2OData.fixedModel and generate a new model by calling: model = self.model + D2OModel
volume_fraction_bkgd (float [0, 1]) – Volume fraction for the D2O in the sample. (default 0.95)
kwargs (dict, optional) – Additional keyword arguments to pass to Model.fit method. It can override any parameters obtained from the dataset, which are passed to the fit function (‘data’, ‘errors’, ‘x’,…).

fit_best(**kwargs)¶

Return the fitted model.

Parameters:	kwargs (dict) – Additional keyword arguments to pass to ModelResult.eval.

fit_components(**kwargs)¶

Return the fitted components.

Parameters:	kwargs (dict) – Additional keyword arguments to pass to ModelResult.eval_components.

fit_result¶: Return the full result of the fit, if available.

getFixedOptParams(obsIdx)¶

Return the fixed optimal parameters

The parameters are return for the given observable value at index obsIdx or the first entry if there is only one observable.

get_energy_range(min, max)¶

Helper function to select a specific energy range.

The function assumes that time values correspond to the first dimension of the data set.

Parameters:	min (int) – The minimum value for time. max (int) – The maximum value for time.
Returns:	out – A new instance of the class with the selected energy range.
Return type:	`Sample`

get_observable_range(min, max)¶

Helper function to select a specific observable range.

The function assumes that time values correspond to the first dimension of the data set.

Parameters:	min (int) – The minimum value for the observable. max (int) – The maximum value for the observable.
Returns:	out – A new instance of the class with the selected observable range.
Return type:	`Sample`

get_q_range(min, max)¶

Helper function to select a specific momentum transfer range.

The function assumes that q values correspond to the last dimension of the data set.

Parameters:	min (int) – The minimum value for the momentum transfer q range. max (int) – The maximum value for the momentum transfer q range.
Returns:	out – A new instance of the class with the selected q range.
Return type:	`Sample`

model¶: Return the model instance.

model_best¶: Return the model with the fitted parameters.

normalize(ref=None)¶

Normalize the data using sample intensities or reference sample.

The integration to get the normalization factor is performed along the energy axis.

Parameters:	ref (`Sample`) – A reference sample that is used for as resolution function.

params¶: Return the best values and errors from the fit result.

plot(fig_ax=None, cb_ax=None, axis=-1, xlabel=None, ylabel='$\\rm S(q, \\hbar \\omega)$', label=None, yscale='log', plot_errors=True, plot_legend=True, max_lines=15, colormap='jet')¶

Helper function for quick plotting.

Parameters:

fig_ax (matplotlib Axis, optional) – An instance of Axis from matplotlib to be used for plotting. (default, None)
cb_ax (matplotlib Axis, optional) – An instance of Axis from matplotlib to be used for the colorbar if needed. (default, None, for 1D arrays)
axis (int) – The axis corresponding abscissa. (default, -1)
xlabel (str) – The label for the x-axis. (default None, will be guessed for axes attribute)
ylabel (str) – The label for the y-axis. (default ‘$rm S(q, hbar omega)$’)
label (str) – The label for curve. (default, the name attribute of the sample)
yscale (str) – The scale of the y-axis. (default, ‘log’)
plot_errors (bool) – If True, plot the error bars for each data point.
plot_legend (bool) – If True, add the legend to the plot.
max_lines (int) – For 2D data, maximum number of lines to be plotted.
colormap (str) – The colormap to be used for 2D data.

plot_3D(fig_ax=None, axis='observable', index=0, xlabel=None, ylabel=None, zlabel='$\\rm S(q, \\hbar \\omega)$', zscale='log', colormap='winter')¶

Helper function for quick plotting.

Parameters:

fig_ax (matplotlib axis) – An instance of Axis from matplotlib to be used for plotting. (default, None)
axis ({'observable', 'q', 'energies', 'time', 'temperature'}) – The axis along which the data are plotted. Valid for 3D arrays, has no effect for 2D arrays. (default, ‘observable’)
index (int) – The index on the axis given for plotting. Valid for 3D arrays. For 2D, the whole dataset is plotted.
xlabel (str) – The label for the x-axis. (default None, will be guessed for axes attribute)
ylabel (str) – The label for the y-axis. (default None, will be guessed for axes attribute)
zlabel (str) – The label for the z-axis. (default ‘$rm S(q, hbar omega)$’)
zscale (str) – The scale of the z-axis. (default, ‘linear’)
new_fig (bool) – If true, create a new figure instead of plotting on the existing one.
colormap (str) – The colormap to be used. (default, ‘winter’)

sliding_average(win_size, axis=0)¶

Performs a sliding average of data and errors along given axis.

Parameters:	win_size (int) – axis (int, optional) – The axis over which the average is to be performed. (default, 0)
Returns:	out_arr – An averaged instance of `Sample` with the same metadata except for errors and the corresponding axis values, which are processed as well.
Return type:	`Sample`

squeeze(axis=None)¶: Override the corresponding NumPy function to process axes too.

swapaxes(axis1, axis2)¶: Override the corresponding NumPy function to process axes too.

take(indices, axis=None)¶: Override the corresponding NumPy function to process axes too.

transpose(*axes)¶: Override the corresponding NumPy function to process axes too.

sample.ensure_fit(func)¶: Ensures the class has a fitted model.

sample.implements(np_function)¶: Register an __array_function__ implementation for DiagonalArray objects.

dataParsers¶

mantidNexus¶

mantidNexus.processNexus(dataFile, FWS=False)¶

This script is meant to be used with IN16B data pre-processed (reduction, (EC correction) and vanadium centering) with Mantid.

It can handle both QENS and fixed-window scans.

Then the result is stored as a namedtuple containing several members (all being numpy arrays).

intensities - 3D array of counts values for each frame

(axis 0), q-value (axis 1) and energy channels (axis 2)

errors - 3D array of errors values for each frame

(axis 0), q-value (axis 0) and energy channels (axis 2)

energies - 1D array of energy offsets used

temps - 2D array of temperatures, the first dimension

is of size 1 for QENS, and of the same size as the number of energy offsets for FWS. The second dimensions represents the frames

times - same structure as for temps but representing

the time

name - name that is stored in the ‘subtitle’ entry

qVals - 1D array of q-values used

qIdx - same as selQ but storing the indices

observable - data for the observable used for data series

(‘time’ or ‘temperature’)

observable_name - name of the observable used for data series

norm - boolean, whether data were normalized or not

mantidWorkspace¶

inxConvert¶

inxConvert.convert(datafile, FWS=None)¶

This method takes a single dataFile as argument and returns the corresponding dataSet.

Then the result is stored as a namedtuple containing several members (all being numpy arrays).

intensities - 3D array of counts values for each frame

(axis 0), q-value (axis 1) and energy channels (axis 2)

errors - 3D array of errors values for each frame

(axis 0), q-value (axis 0) and energy channels (axis 2)

energies - 1D array of energy offsets used

temps - 2D array of temperatures, the first dimension

is of size 1 for QENS, and of the same size as the number of energy offsets for FWS. The second dimensions represents the frames

times - same structure as for temps but representing

the time

name - name that is stored in the ‘subtitle’ entry

qVals - 1D array of q-values used

selQ - same as qVals, used later to define a q-range

for analysis

qIdx - same as selQ but storing the indices

observable - data for the observable used for data series

(‘time’ or ‘temperature’)

observable_name - name of the observable used for data series

norm - boolean, whether data were normalized or not

IN16B_nexus¶

Parser for .nxs files from IN16B

class in16b_nexus.IN16B_nexus(scanList, observable='time')¶

This class can handle raw data from IN16B at the ILL in the hdf5 format.

Parameters:

scanList – a string or a list of files to be read and parsed to extract the data. It can be a path to a folder as well.
sumScans – whether the scans should be summed or not
alignPeaks – if True, will try to align peaks of the monitor with the ones from the PSD data.
peakFindWindow – the size (in number of channels) of the window to find and align the peaks of the monitor to the peaks of the data.
detGroup – detector grouping, i.e. the channels that are summed over along the position-sensitive detector tubes. It can be an integer, then the same number is used for all detectors, where the integer defines a region (middle of the detector +/- detGroup). It can be a list of integers, then each integers of the list should corresponds to a detector. Or it can be a string, defining a path to an xml file as used in Mantid. If set to no, no detector gouping is performed and the data represents the signal for each pixel on the detectors. In this case, the observable become the momentum transfer q in the vertical direction.
normalize – whether the data should be normalized to the monitor
observable – the observable that might be changing over scans. It can be time, temperature
offset – If not None, only the data with energy offset that equals the given value will be imported.

process()¶: Extract data from the provided files and reduce them using the given parameters.

IN16B_QENS¶

This module is used for importation of raw data from IN16B instrument.

class in16b_qens_scans_reduction.IN16B_QENS(scanList, sumScans=True, unmirroring=True, vanadiumRef=None, refPeaks=None, detGroup=None, normalize=True, strip=25, observable='time', slidingSum=None)¶

This class can handle raw QENS data from IN16B at the ILL in the hdf5 format.

Parameters:

scanList – a string or a list of files to be read and parsed to extract the data. It can be a path to a folder as well.
sumScans – whether the scans should be summed or not.
unmirroring – whether the data should be unmirrored or not.
vanadiumRef – if :arg unmirroring: is True, then the peaks positions are identified using the data provided with this argument. If it is None, then the peaks positions are identified using the data in scanList.
refPeaks – if :arg unmirroring: is True, and :arg vanadiumRef: is False, then the given peak positions are used. If it is None, then the peaks positions are identified using the data in scanList.
detGroup – detector grouping, i.e. the channels that are summed over along the position-sensitive detector tubes. It can be an integer, then the same number is used for all detectors, where the integer defines a region (middle of the detector +/- detGroup). It can be a list of integers, then each integers of the list should corresponds to a detector. Or it can be a string, defining a path to an xml file as used in Mantid. If set to no, no detector gouping is performed and the data represents the signal for each pixel on the detectors. In this case, the observable become the momentum transfer q in the vertical direction.
normalize – whether the data should be normalized to the monitor
strip – an integer defining the number of points that are ignored at each extremity of the spectrum.
observable – the observable that might be changing over scans. It can be time or temperature

getReference()¶: Process files to obtain reference values for elastic signal.

process()¶: Extract data from the provided files and reduce them using the given parameters.

IN16B_FWS¶

Classes¶

class in16b_fws_scans_reduction.IN16B_FWS(scanList, sumScans=False, alignPeaks=True, detGroup=None, normalize=True, observable='time', offset=None)¶

This class can handle raw E/IFWS data from IN16B at the ILL in the hdf5 format.

Parameters:

scanList – a string or a list of files to be read and parsed to extract the data. It can be a path to a folder as well.
sumScans – whether the scans should be summed or not
alignPeaks – if True, will try to align peaks of the monitor with the ones from the PSD data.
detGroup – detector grouping, i.e. the channels that are summed over along the position-sensitive detector tubes. It can be an integer, then the same number is used for all detectors, where the integer defines a region (middle of the detector +/- detGroup). It can be a list of integers, then each integers of the list should corresponds to a detector. Or it can be a string, defining a path to an xml file as used in Mantid. If set to no, no detector gouping is performed and the data represents the signal for each pixel on the detectors. In this case, the observable become the momentum transfer q in the vertical direction.
normalize – whether the data should be normalized to the monitor
observable – the observable that might be changing over scans. It can be time, temperature
offset – If not None, only the data with energy offset that equals the given value will be imported.

process()¶: Extract data from the provided files and reduce them using the given parameters.

IN16B_BATS¶

This module is used for importation of raw data from IN16B instrument.

class in16b_bats_scans_reduction.IN16B_BATS(scanList, sumScans=True, detGroup=None, normalize=True, strip=0, observable='time', tElastic=None, monitorCutoff=0.8, pulseChopper='C34', slidingSum=None)¶

This class can handle raw data from IN16B-BATS at the ILL in the hdf5 format.

Parameters:

scanList (string or list) – A string or a list of files to be read and parsed to extract the data. It can be a path to a folder as well.
sumScans (bool) – Whether the scans should be summed or not.
detGroup (string, int) – Detector grouping, i.e. the channels that are summed over along the position-sensitive detector tubes. It can be an integer, then the same number is used for all detectors, where the integer defines a region (middle of the detector +/- detGroup). It can be a list of integers, then each integers of the list should corresponds to a detector. Or it can be a string, defining a path to an xml file as used in Mantid. If set to no, no detector gouping is performed and the data represents the signal for each pixel on the detectors. In this case, the observable become the momentum transfer q in the vertical direction.
normalize – Whether the data should be normalized to the monitor
strip – An integer defining the number of points that are ignored at each extremity of the spectrum.
observable – The observable that might be changing over scans. It can be time or temperature.
tElastic (int, float) – Time for the elastic peak. Optional, if None, will be guessed from peak fitting.
monitorCutoff – Cutoff with respect to monitor maximum to discard data.
pulseChopper ({'C12', 'C34'}) – Chopper pair that is used to define the pulse.

getReference()¶: Process files to obtain reference values for elastic signal.

process(center=None, peaks=None, monPeaks=None)¶

Extract data from the provided files and reduce them using the given parameters.

Parameters:	center (int) – Position of the elastic signal along channels. peaks (2D array) – Reference position of the peaks in dataset. Column vector with integer position for each q value. monPeaks (int) – Reference position of monitor peak signal.

Process functions¶

Process functions for raw data from position sensitive detectors.

process_functions.alignGroups(data, position=None)¶

Align the peaks along the z-axis of the detectors.

Parameters:

data (sample.Sample) – Instance of sample.Sample. First axis is assumed to be q-values.
position (int (optional)) – Position of the center along the ‘channels’ axis. (default, None, is determined automatically)

Returns:

data (sample.Sample) – Instance of sample.Sample for which the data maxima were aligned along the z direction.
center (int) – The center determined by the algorithm, which can then be used to convert the time-of-flight to energies as it defines the elastic peak.

process_functions.alignTo(data, refPos, peaks=None)¶

Align data peaks to zero energy transfer.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. refPos (int) – Reference index on energy/channels axis. peaks (np.ndarray (optional)) – Array of peak positions for each momentum transfer q value. (default, None - will be determined automatically)

process_functions.alignToZero(data, peaks=None)¶

Align data peaks to the zero of energy transfers.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. peaks (np.ndarray (optional)) – Array of peak positions for each momentum transfer q value. (default, None - will be determined automatically)

process_functions.avgAlongObservable(data)¶

Average a single dataset along with monitor over the observable.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. peaks (np.ndarray (optional)) – Array of peak positions for each momentum transfer q value. (default, None - will be determined automatically)

process_functions.convertChannelsToEnergy(data, type, refDist=33.388, tElastic=None)¶

Convert the ‘channels’ axis to ‘energies’

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. type ({'qens', 'fws', 'bats'}) – Type of dataset that is being processed. refDist (float (optional)) – Reference distance from the pulse chopper used in BATS mode to the sample. tElastic (int (optional)) – Reference value of time-of-flight for the elastic signal.

process_functions.detGrouping(data, detGroup=None)¶

The function performs a sum along detector tubes using the provided range to be kept.

It makes use of the :arg detGroup: argument.

Parameters:

data (sample.Sample) – Instance of sample.Sample
detGroup (int, list, file path) –
If the argument is a scalar, it sums over all values that are in the range [center of the tube - detGroup : center of the tube + detGroup].

If the argument is a list of integers, then each element of the list is assumed to correspond to a range for each corresponding detector in ascending order.

If the argument is a mantid-related xml file (a python string), the xml_detector_grouping module is then used to parse the xml file and the provided values are used to define the range.

process_functions.findPeaks(data, peakFindingMask=None)¶

Find the peak for each momentum transfer in data.

The function always return a single peak for each momentum transfer value. Hence, it should be called twice for mirrored data, once for each wing, before unmirroring.

The data are expected to have the momentum transfer q-values in the first dimension, the channels in the second dimension and, for 3D arrays, the momentum transfer in vertical position qz in the third dimension.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample` peakFindingMask (np.ndarray (optional)) – A mask to exclude some points from peak search. (default None, use a small window centered on the ‘channel’ axis)

process_functions.findPeaksFWS(data)¶

Find peaks in FWS data.

For arrays with more than one dimension, the function assumes that the first axis is the momentum tansfer q values (‘q’) and the second the recorded channels (‘channels’).

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`

process_functions.mergeDataset(dataList, observable='time')¶

Produce a single dataset from multiple FWS data.

In the case of different sampling for the energy transfers used in FWS data, the function interpolates the smallest arrays to produce a unique numpy array of FWS data.

Parameters:	data (list of `sample.Sample`) – list of instances of `sample.Sample`. observable ({'time', 'temperature', 'pressure'} (optional)) – The name of the observable used for series of data. (default, ‘time’)

process_functions.normalizeToMonitor(data, peaks=None, monPeaks=None, fws=False)¶

Normalize the data by divinding by the monitor.

If peaks an monPeaks are not None, the data are aligned to monitor peaks for each momenum transfer prior to normalization. For FWS data, only the values at peak positions are used.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample` peaks (np.ndarray) – The position of the peak(s) for each momentum transfer. Requires ‘monPeaks’ as well. monPeaks (np.ndarray) – The position of the peak(s) in monitor. Requires ‘peaks’ as well. fws (bool) – Whether data are FWS or not.

process_functions.sumAlongObservable(data)¶

Sum a single dataset along with monitor over the observable.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. peaks (np.ndarray (optional)) – Array of peak positions for each momentum transfer q value. (default, None - will be determined automatically)

process_functions.unmirror(data, refPeaks=None)¶

Unmirror data using the elastic peak as a reference.

Parameters:	data (`sample.Sample`) – Instance of `sample.Sample`. refPeaks (np.ndarray (optional)) – Reference peak positions for the elastic signal. Should have one entry for each momentum transfer q-values in the first dimension and two entries in the second dimension for the peak in the left and right wing, respectively. (default None, will be determined automatically)

models¶

Model¶

This module provides a template class to build models that can be used to fit the data.

class model.Component(name, func, skip_convolve=False, **funcArgs)¶

Component class to be used with the Model class.

Parameters:

name (str) – Name for the component.
func (callable) – The function to be used for this component.
skip_convolve (bool) – If True, no convolution is performed for this model. It can be useful for background or normalization terms.
funcArgs (dict of str, int, float or arrays) –
Values to be passed to the function arguments. This is a dicitonary of argument names mapped to values. The values can be of different types:
- int, float or array, the values are directly passed to the function.
- str, the values are evaluated first. If any word in the string is present in the Model.params dictionary keys, the corresponding parameter value is substituted.

Examples

For a Model class that has the following key in its params attribute: (‘amplitude’, ‘sigma’), the component for a Lorentzian, the width of which depends on a defined vector q, can be created using:

>>> def lorentzian(x, scale, width):
...     return scale / np.pi * width / (x**2 + width**2)
>>> myComp = Component(
...     'lor', lorentzian, scale='scale', width='width * q**2')

If the Lorentzian width is constant, use:

>>> myComp = Component('lor', lorentzian, scale='scale', width=5)

Some math functions can be used as well (below the exponential):

>>> myComp = Component('lor', lorentzian, scale='np.exp(-q**2 * msd)')

eval(x, params, **kwargs)¶

Evaluate the components using the given parameters.

Parameters:	params (`Parameters` instance) – Parameters to be passed to the component kwargs (dict) – Additional parameters to be passed to the function. Can override params.

processFuncArgs(params, **kwargs)¶: Return the evaluated argument for the function using given parameters and keyword arguments.

class model.FindParamNames(key, params)¶

Helper class to parse strings to evaluation for function arguments in Component.

Parameters:	params (`Parameters`) – An instance of Parameters from which the parameter names are to be found and substituted by the corresponding values.

visit_Name(node)¶: Name visitor.

class model.Model(params, name='Model', convolutions=None, on_undef_conv='numeric')¶

Model class to be used within nPDyn.

The model is structured in components that can be added together, each component consisting of a name, a callable function and a dictionary of parameters. The parameters of two different components can have the same name such that they can be shared by several components just like for the switching diffusive state model.

Also, the components are separated in two classes, namely eisfComponents and qisfComponents, in order to provide the possibility to separately extract the elastic and quasi-elastic parts for analysis and plotting.

Parameters:

params (Parameters instance) – Parameters to be used with the model
name (str, optional) – A name for the model.
convolutions (dict of dict) – Dictionary that defines the mapping ‘(function1, function2)’ to ‘convolutionFunction(function1, function2)’. Analytic convolutions or user defined operators can be defined this way.
on_undef_conv ({'raise', 'numeric'}) – Defines the behavior of the class on missing convolution function in the ‘convolutions’ attribute. The option ‘raise’ leads to a KeyError and the option ‘numeric’ to a numerical convolution.

addComponent(comp, op='+')¶

Add a component to the model.

Parameters:	comp (`Component`) – An instance of Component to be added to the model. op ({"+", "-", "", "/"}, optional*) – Operator to be used to combine the new component with the others. If this is the first component, the operator is ignored. (default “+”)

bic¶: Return the bayesian information criterion (BIC).

components¶: Return the model components.

copy()¶: Return a copy of the model.

eval(x, params=None, convolve=None, **kwargs)¶

Perform the assembly of the components and call: the provided functions with their parameters to compute the model.

Parameters:

x (np.ndarray) – Values for the x-axis variable
params (list, np.array, optional) – Parameters to be passed to the components. Will override existing parameters in self.params.
convolve (Model) – Another model to be convolved with this one.
kwargs – Additional keyword arguments to be passed to the components. Can override params too.

Returns:

If returnComponents is False – The computed model in an array, the dimensions of which depend on x and params attributes and the function called.
else – A dictionary with key being the component names and the values are the evaluated components.

eval_components(x, params=None, convolve=None, **kwargs)¶

Alias for eval with ‘returnComponents’ set to True.

Perform the computation of the components with the given x-axis values, parameters and convolutions.

Returns:	A dictionary with key being the component names and the values are the evaluated components.

fit(x, data=None, weights=None, fit_method='curve_fit', fit_kws=None, params=None, **kwargs)¶

Fit the experimental data using the provided arguments.

Parameters:	x (np.ndarray) – Values for the indenpendent variable. data (np.ndarray) – Experimental data to be fitted. weights (np.ndarray, optional) – Weights associated with the experimental data (the experimental errors). fit_method (str, optional) – The method to be used for fitting. Currently available methods are (from Scipy): - “curve_fit” - “basinhopping” - “differential_evolution” - “shgo” - “minimize” fit_kws (dict, optional) – Additional keywords to be passed to the fit method. params (`Parameters` class instance, optional) – Parameters to be used (default None, will use the parameters associated with the model). kwargs (dict, optional) – Additional keywords arguments to give for the evaluation of the model. Can override parameters too.
Returns:
Return type:	A copy of the fitted model instance.

fitResult¶: Return the full result of the fit.

on_undef_conv¶: Return the class behavior on undefined convolution.

optParams¶: Return the result of the fit.

userkws¶: Return the keywords used for the fit.

Params¶

The module contains a Parameter class to be used with the Model class.

class params.Parameters(params=None, **kwargs)¶

A parameter class that handles names, values and bounds.

Parameters:	params (dict of dict) – A dictionary of parameter names, each being associated with a namedtuple containing the ‘value’, the ‘bounds’, the ‘fixed’, and the ‘error’ attributes. kwargs (keywords) – Additional keywords argument to set parameter names, values (and possibly bounds and fixed attributes). Can override params too.

listToParams(pList, errList=None)¶: Use the given list to convert a list of parameters to a dictionary similar to the current one.

loadParams(fileName)¶: Load parameters from a file in JSON format.

paramList¶: Accessor for parameter list.

set(name, **kwargs)¶

Set a parameter entry with given attributes in ‘kwargs’.

Parameters:	name (str) – Parameter name to be updated. kwargs (dict of float, tuple or namedtuple) – Parameters to be updates with the associated attributes. The call should be of the form: >>> params.set('amplitude', value=1.2, fixed=True) >>> params.set('width', value=2.3, bounds=(0., np.inf))

update(**kwargs)¶: Update the parameters.

writeParams(fileName)¶: Write parameters to given file in JSON format.

params.pTuple(value=1, bounds=(-inf, inf), fixed=False, error=0.0)¶: Helper function to create a namedtuple with default values.

Presets¶

This module provides several preset functions that can be used to create model components and fit your data.

presets.calibratedD2O(x, q, volFraction, temp, amplitude=1.0)¶

Lineshape for D2O where the Lorentzian width was obtained from a measurement on IN6 at the ILL.

Parameters:	q (np.array or list) – Array of momentum transfer q values volFraction (float in [0, 1]) – Volume fraction of the D2O in the sample. temp (float) – Sample temperature used for the experiment. amplitude (float) – Amplitude of the D2O signal. The parameter to be fitted.

presets.conv_delta(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between a Lorentzian and a Gaussian

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_gaussian_gaussian(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between two Gaussians

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_linear(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution with a linear model.

The linear model is assumed to be used for a background and is thus not convolved. The function returns simply the linear model. If comp2 is also a linear model, the two models are simply added.

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_lorentzian_gaussian(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between a Lorentzian and a Gaussian

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_lorentzian_lorentzian(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between two Lorentzians

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_lorentzian_rotations(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between a Lorentzian and rotationLorentzians

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.conv_rotations_gaussian(x, comp1, comp2, params1, params2, **kwargs)¶

Convolution between a Lorentzian and a Gaussian

Parameters:

x (np.ndarray) – x-axis values
comp1 (Component) – First component to be used for the convolution.
comp2 (Component) – Second component to be used for the convolution.
params1 (Parameters) – Parameters for comp1.
params2 (Parameters) – Parameters for comp2.
kwargs (dict) – Additional keyword arguments to pass to the method processFuncArgs() for comp1 and comp2.

presets.delta(x, scale=1, center=0)¶

A Dirac delta centered on center

Parameters:	x (np.ndarray) – x-axis values, can be an array of any shape scale (int, float, np.ndarray) – scale factor for the normalized function center (int, float, np.ndarray) – position of the Dirac Delta in energy

presets.gaussian(x, scale=1, width=1, center=0)¶

A normalized Gaussian function

Parameters:	x (np.ndarray) – x-axis values, can be an array of any shape scale (int, float, np.ndarray) – scale factor for the normalized function width (int, np.ndarray) – width of the lineshape center (int, float, np.ndarray) – center from the zero-centered lineshape

presets.generalizedLorentzian(x, scale=1, alpha=1, tau=1, center=0)¶

A generalized Lorentzian function.

This is the Fourier transform of the Mittag-Leffler function. See [1].

References

[1]	https://doi.org/10.1063/1.5121703

presets.kww(x, scale=1, beta=2, tau=1, center=0)¶

The Fourier transform of the stretched exponential function.

Parameters:	x (np.ndarray) – Values for the x-axis, can be an array of any shape scale (int, float, np.ndarray) – Scale factor for the normalized function beta (int, float) – Value for power of the exponential tau (int, float, np.ndarray) – Characteristic relaxation time. center (int, float, np.ndarray) – Center from the zero-centered lineshape

presets.linear(x, a=0.0, b=1.0)¶: A linear model of the form $a x + b$

presets.lorentzian(x, scale=1, width=1, center=0)¶

A normalized Lorentzian function.

Parameters:	x (np.ndarray) – x-axis values, can be an array of any shape scale (int, float, np.ndarray) – scale factor for the normalized function width (int, np.ndarray) – width of the lineshape center (int, float, np.ndarray) – center from the zero-centered lineshape

presets.rotations(x, q, scale=1, width=1, center=0)¶

A sum of normalized Lorentzian functions for rotations.

Parameters:	x (np.ndarray) – x-axis values, can be an array of any shape q (np.ndarray) – Values for the momentum transfers q scale (int, float, np.ndarray) – scale factor for the normalized function width (int, np.ndarray) – width of the lineshape center (int, float, np.ndarray) – center from the zero-centered lineshape

presets.voigt(x, scale=1, sigma=1, gamma=1, center=0)¶

A normalized Voigt profile.

Parameters:

x (np.ndarray) – Values for the x-axis, can be an array of any shape
scale (int, float, np.ndarray) – Scale factor for the normalized function
sigma (int, float, np.ndarray) – Line width of the Gaussian component.
gamma (int, float, np.ndarray) – Line width of the Lorentzian component.
center (int, float, np.ndarray) – Center from the zero-centered lineshape

Builtins¶

This module provides several built-in models for incoherent neutron scattering data fitting.

These functions generate a Model class instance.

nPDyn.models.builtins.modelCalibratedD2O(q, name='$D_2O$', volFraction=1, temp=300, **kwargs)¶

A model for D2O background containing a single Lorentzian.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelD2OBackground(q, name='$D_2O$', **kwargs)¶

A model for D2O background containing a single Lorentzian.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelGaussBkgd(q, name='GaussBkgd', **kwargs)¶

A model containing a Gaussian with a background term.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelGeneralizedLorentzian(q, name='GeneralizedLorentzian', qWise=True, **kwargs)¶

A model containing a delta and a generalized lorentzian.

This model has been described elsewhere [1].

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

References

[1]	https://doi.org/10.1063/1.5121703

nPDyn.models.builtins.modelLorentzianSum(q, name='LorentzianSum', nLor=2, qWise=True, **kwargs)¶

A model containing a delta and a sum of Lorentzians.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model nLor (2) – Number of Lorentzian to be used. qWise (bool) – If True, no q dependence is imposed on the parameters and the each spectrum is fitted independently. kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelPVoigt(q, name='PVoigt', **kwargs)¶

A model containing a pseudo-Voigt profile.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelPVoigtBkgd(q, name='PVoigtBkgd', **kwargs)¶

A model containing a pseudo-Voigt profile with a background term.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

nPDyn.models.builtins.modelProteinJumpDiff(q, name='proteinJumpDiff', qWise=False, **kwargs)¶

A model for protein in liquid state.

The model contains a Lorentzian of Fickian-type diffusion accounting for center-of-mass motions, a Lorentzian of width that obeys the jump diffusion model [2] accounting for internal dynamics.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model qWise (bool) – If True, no q dependence is imposed on the parameters and the each spectrum is fitted independently. kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

References

[2]	https://doi.org/10.1103/PhysRev.119.863

nPDyn.models.builtins.modelTwoStatesSwitchDiff(q, name='TwoStatesSwitch', **kwargs)¶

A model for protein in liquid state.

This model implements the two states switching diffusion model for nPDyn [3].

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

References

[3]	https://doi.org/10.1103/PhysRev.119.863

nPDyn.models.builtins.modelWater(q, name='waterDynamics', **kwargs)¶

A model containing a delta, a Lorentzian for translational motions, a Lorentzian for rotational motions, and a background term.

Parameters:	q (np.ndarray) – Array of values for momentum transfer q. name (str) – Name for the model kwargs (dict) – Additional arguments to pass to Parameters. Can override default parameter attributes.

lmfit¶

ConvolvedModel¶

Can be used to perform analytic convolutions between models.

class convolvedModel.ConvolvedModel(left, right, on_undefined_conv='numeric', convMap=None, **kws)¶

Combine two models (left and right) with the provided analytic convolution function(s).

Parameters:

left (Model or CompositeModel) – Left-hand model.
right (Model or CompositeModel) – Right-hand model.
on_undefined_conv ({'numeric', 'raise'}, optional) –
Determine the behavior when a pair of model has no analytic convolution associated with it:
- ’numeric’ results in a numerical convolution
- ’raise’ raises a KeyError
(default ‘numeric’)
convMap (mapping, optional) – Dictionary of dictionaries to map the convolution function to a pair of model. A default convMap is already present in the class but can be overridden by this argument.
**kws (optional) – Additional keywords are passed to Model when creating this new model.

Notes

The two models must use the same independent variables. Only the parameters from left and right are used and exposed. The parameters of the convolution function are not exposed outside the class. They are only used internally and determined inside the convolution function by the combination of the parameters and keywords provided for left and right.

The eval_components() returns the convoluted components from left by default. This behavior can be changed by using returnComponents=”right” in the keyword arguments passed to the method.

Examples

First create two models to be convolved (here two Lorentzians):

>>> l1 = lmfit.Model.LorentzianModel()
>>> l2 = lmfit.Model.LorentzianModel()

Define the convolution function using:

>>> def myConv(left, right, params, **kwargs):
...     lp = left.make_funcargs(params, **kwargs)
...     rp = right.make_funcargs(params, **kwargs)
...     amplitude = lp['amplitude'] * rp['amplitude']
...     sigma = lp['sigma'] + rp['sigma']
...     center = lp['center'] + rp['center']
...     out = sigma / (np.pi * ((lp['x'] - center)**2 + sigma**2))
...     return out

Eventually perform the convolution:

>>> convModel = ConvolvedModel(l1, l2)

Assign the convolution function myConv to the pair of ‘lorentzian’ using:

>>> convModel.convMap = {'lorentzian': {'lorentzian': myConv}}

components¶: Return components for composite model.

eval(params=None, **kwargs)¶: Evaluate model function for convolved model.

eval_components(**kwargs)¶: Return OrderedDict of name, results for each component.

on_undefined_conv¶: Return the parameter ‘on_undefined_conv’

param_names¶: Return parameter names for composite model.

Presets¶

This module provides several function builders that can be used to fit your data.

These functions generate a Model class instance from the lmfit package [1].

References

[1]	https://lmfit.github.io/lmfit-py/

lmfit_presets.build_2D_model(q, funcName, funcBody, defVals=None, bounds=None, vary=None, expr=None, paramGlobals=None, prefix='', var='x')¶

Builds a 2D lmfit.Model.

Parameters:

q (np.array or list) – momentum transfer q values of scattering.
funcName (str) – name of the function to be built.
funcBody (str) – formatted string for the function to be used (in 1D). For a gaussian the string “{a} * np.exp(-(x - {cen})**2 / {width}*{q}**2)” will lead to a model with parameters of root names ‘a’, ‘cen’ and ‘width’. If these parameters are not in argument paramGlobals, the parameter names will be ‘a_1’, ‘a_2’, ‘a_3’, …, ‘a_n’, where n is the length of the array q.
defVals (dict, optional) – dictionary of default values for the parameters of the form {‘a’: 1., ‘cen’: 0.05, ‘width’: 2}. If None, set to 1.0 for all parameters.
bounds (dict, optional) – dictionary of bounds for the parameters of the form {‘a’: (0., np.inf}, ‘cen’: (-10, 10)}. If None, set to (-np.inf, np.inf) for all parameters.
vary (dict, optional) – dictionary of parameter hint ‘vary’ for the parameters of the form {‘a’: False, ‘cen’: True}. If None, set to True for all parameters.
expr (dict, optional) – dictionary of parameter hint ‘expr’ for the parameters of the form {‘a’: ‘width / sqrt(2)’}. If None, set to None for all parameters.
paramGlobals (list, optional) – defines which parameters should be considered as ‘global’, that is, a parameter that is fixed for all momentum transfer q values. If set to [‘width’], then the resulting model will have parameters of the form (‘a_1’, …, ‘a_n’, ‘cen_1’, …, ‘cen_n’, ‘width’), where n is the length of the parameter q.
prefix (str, optional) – prefix to be given to the model name
var (str, optional) – name of the primary independent variable (default ‘x’)

lmfit_presets.calibratedD2O(q, temp=300, **kwargs)¶

Lineshape for D2O where the Lorentzian width was obtained from a measurement on IN6 at the ILL.

Parameters:	q (np.array or list) – Array of momentum transfer q values temp (float) – Sample temperature used for the experiment. kwargs (dict, optional) – Additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude

lmfit_presets.delta(q, **kwargs)¶

Normalized Dirac delta.

where the shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center

lmfit_presets.gaussian(q, qwise=True, **kwargs)¶

Normalized Gaussian lineshape.

\[\rm G(x, q; a, c, \sigma) = \frac{a}{\sqrt(\pi \sigma} e^{-(x - c)^2 / \sigma}\]

where the shape of the output array depends on the shape of the independent variable q and $\sigma$ can have an explicit dependence on q as $\sigma q**2$.

Parameters:	q (np.array or list) – array of momentum transfer q values qwise (bool, optional) – whether the width (sigma) has explicit dependence on q (default False) kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
sigma

lmfit_presets.getDelta(x, amplitude, center)¶: Helper function for the Dirac delta model.

lmfit_presets.hline(q, **kwargs)¶: A horizontal line.

lmfit_presets.jump_diff(q, qwise=False, **kwargs)¶

Normalized Lorentzian with jump-diffusion model.

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values qwise (bool, optional) – whether the width (sigma) has explicit dependence on q (default False) kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
sigma
tau

References

For more information see: http://doi.org/10.1103/PhysRev.119.863

lmfit_presets.kww(q, **kwargs)¶

Fourier transform of the Kohlrausch-William-Watts (KWW) function.

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
tau
beta

References

For more information, see: https://en.wikipedia.org/wiki/Stretched_exponential_function

lmfit_presets.linear(q, **kwargs)¶

Linear model that can be used for background.

The model reads: $a*x + b$

Notes

Two parameters:

a
b

lmfit_presets.lorentzian(q, qwise=False, **kwargs)¶

Normalized Lorentzian lineshape.

\[\rm \mathcal{L}(x, q; a, c, \sigma) = \frac{a}{\pi} \frac{\sigma}{(x - c)^2 + \sigma^2}\]

where the shape of the output array depends on the shape of the independent variable q and $\sigma$ can have an explicit dependence on q as $\sigma q**2$.

Parameters:	q (np.array or list) – array of momentum transfer q values qwise (bool, optional) – whether the width (sigma) has explicit dependence on q (default False) kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
sigma

lmfit_presets.protein_liquid(q, qWise=False, **kwargs)¶

Model for protein in solution and jump diffusion for internal dynamics.

Parameters:	q (np.array or list) – Array of momentum transfer q-values to be used. qWise (bool) – Whether the Lorentzian width are independent for each momentum transfer q or not (explicit q-dependence of the form ‘width * q2’). kwargs** (dict) – Additional keyword arguments to pass to `build_2D_model()`

Notes

The parameter root names are:

beta
amplitude
center
sigma_g
sigma_i
tau

lmfit_presets.pseudo_voigt(q, **kwargs)¶

Pseudo-Voigt profile.

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
fraction
center
sigma

lmfit_presets.rotations(q, qwise=False, **kwargs)¶

Normalized Lorentzian accounting for rotational motions in liquids.

\[S_r(q, \omega) = A_r J_0^2(qd) \delta(\omega) + \sum_{l=1} (2l + 1) J_l^2(qd) \frac{1}{\pi} \frac{l(l+1) \sigma}{(\omega - center)^2 + (l(l+1) \sigma)^2}\]

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values qwise (bool, optional) – whether the width (sigma) has explicit dependence on q (default False) kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
sigma
bondDist

References

For more information see: http://doi.org/10.1139/p66-108

lmfit_presets.two_diff_state(q, qwise=False, **kwargs)¶

Two state switching diffusion model.

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
gamma1
gamma2
tau1
tau2

References

For more information, see: http://doi.org/10.1063/1.4950889 or http://doi.org/10.1039/C4CP04944F

lmfit_presets.voigt(q, **kwargs)¶

Voigt profile.

The shape of the output array depends on the shape of the independent variable q.

Parameters:	q (np.array or list) – array of momentum transfer q values kwargs (dict, optional) – additional keywords to pass to `build_2D_model()`.

Notes

The parameter root names are:

amplitude
center
sigma
gamma

Convolutions¶

Basic analytical convolutions between preset functions.

convolutions.conv_delta(left, right, params, **kwargs)¶: Convolution with a Dirac delta.

convolutions.conv_gaussian_gaussian(left, right, params, **kwargs)¶: Convolution between two Gaussians.

\[a_1 G_{\sigma_1, center_1} \otimes a_2 G_{\sigma_2, center_2} = a_1 a_2 . G_{\sigma_1 + \sigma2, center_1 + center_2}\]

convolutions.conv_gaussian_jumpdiff(left, right, params, **kwargs)¶

Convolution of a Gaussian and a jump-diffusion Lorentzian.

Results in a Voigt profile as defined in lineshapes.

convolutions.conv_gaussian_lorentzian(left, right, params, **kwargs)¶

Convolution of a Gaussian and a Lorentzian.

Results in a Voigt profile as defined in lineshapes.

convolutions.conv_gaussian_pvoigt(left, right, params, **kwargs)¶

Convolution between a Gaussian and a pseudo-Voigt profile.

\[ \begin{align}\begin{aligned}\begin{aligned} & a_L G_{\sigma_G, center_G} \otimes a_V . \mathcal{pV}_{\sigma, center, fraction} =\\& \quad a_G a_V \left[fraction \mathcal{V}_{\sigma_G, \sigma, center + center_G} + (1 - fraction) G_{\sigma_g + \sigma_G, center + center_G} \right] \end{aligned}\end{aligned}\end{align} \]

where $\mathcal{pV}$ is the pseudo-Voigt, $\mathcal{V}$ is a Voigt profile, and $\sigma_g = \frac{\sigma}{\sqrt{(2 log(2))}}$.

convolutions.conv_gaussian_rotations(left, right, params, **kwargs)¶: Convolution of a Gaussian and a liquid rotations model.

convolutions.conv_jumpdiff_pvoigt(left, right, params, **kwargs)¶: Convolution between the jump diffusion model and a pseudo-Voigt profile.

convolutions.conv_linear(left, right, params, **kwargs)¶

Convolution with a linear model.

Simply returns the linear model itself as it is assumed to serve as a background term by default.

convolutions.conv_lorentzian_lorentzian(left, right, params, **kwargs)¶: Convolution between two Lorentzians.

\[a_1 \mathcal{L}_{\sigma_1, center_1} \otimes a_2 \mathcal{L}_{sigma_2, center_2} = a_1 a_2 . \mathcal{L}_{\sigma_1 + \sigma_2, center_1 + center_2}\]

convolutions.conv_lorentzian_pvoigt(left, right, params, **kwargs)¶

Convolution between a Lorentzian and a pseudo-Voigt profile.

\[ \begin{align}\begin{aligned}\begin{aligned} & a_L \mathcal{L}_{\sigma_L, center_L} \otimes a_V . p\mathcal{V}_{\sigma, center, fraction} =\\&\quad a_L a_V \left[ (1 - fraction) \mathcal{V}_{\sigma_g, \sigma, center + center_L} + fraction \mathcal{L}_{\sigma + \sigma_L, center + center_L} \right] \end{aligned}\end{aligned}\end{align} \]

where $p\mathcal{V}$ is the pseudo-Voigt, $\mathcal{V}$ is a Voigt profile, $\sigma_g = \frac{\sigma}{\sqrt{(2 log(2))}}$ and $\mathcal{L}$ is a Lorentzian.

convolutions.conv_rotations_pvoigt(left, right, params, **kwargs)¶: Convolution between the rotation model and a pseudo-Voigt profile.

convolutions.getGlobals(params)¶: Helper function to get the global parameters.

Builtins¶

This module provides several built-in models for incoherent neutron scattering data fitting.

These functions generate a Model class instance from the lmfit package [1].

References

[1]	https://lmfit.github.io/lmfit-py/

class lmfit_builtins.ModelDeltaLorentzians(q, nLor=2, **kwargs)¶

A Dirac delta with a given number of Lorentzians.

Parameters:	q (np.array or list) – Array of momentum transfer q-values to be used. nLor (int, optional) – Number of Lorentzians to be included in the model. kwargs (dict) – Additional keyword arguments to pass to `build_2D_model()`

class lmfit_builtins.ModelGaussBkgd(q, **kwargs)¶

A Gaussian with a background term.

Can be useful for empty can signal.

Parameters:	q (np.array or list) – Array of momentum transfer q-values to be used. kwargs (dict) – Additional keyword arguments to pass to `build_2D_model()`

class lmfit_builtins.ModelPVoigtBkgd(q, **kwargs)¶

A pseudo-voigt profile with a background term.

Parameters:	q (np.array or list) – Array of momentum transfer q-values to be used. kwargs (dict) – Additional keyword arguments to pass to `build_2D_model()`

lmfit_builtins.guess_from_qens(pars, pGlobals, data, x, q, prefix=None)¶

Estimate starting values from 2D peak data and create Parameters.

Notes

The dataset should be of shape (number of q-values, energies), that is, the function should be called for each value of ‘observable’.

lmfit_builtins.update_param_vals(pars, prefix, **kwargs)¶: Update parameter values with keyword arguments.

plot¶

Plotting window for Sample class instances.

class plot.Plot(dataset)¶

analysisObsPlot()¶: Plot the fitted parameters.

analysisQPlot()¶: Plot the fitted parameters.

compare()¶: Plot the experimental data on one subplot, with or without fit

get_eRange(idx=0)¶

Return the energy values used in the dataset(s).

This assumes the q-values are the same for all datasets.

get_obsRange(idx=0)¶

Return the observables used in the dataset(s).

This assumes the observables are the same for all datasets.

get_qRange(idx=0)¶

Return the q-values used in the dataset(s).

This assumes the q-values are the same for all datasets.

initChecks()¶: This methods is used to perform some checks before finishing class initialization.

obsIdx¶: Return a list of index of the closest observable value to the slider value for each dataset.

plot()¶: Plot the experimental data, with or without fit

plot3D()¶: 3D plot of the whole dataset.

updateLabels()¶: Update the labels on the right of the sliders.

updatePlot()¶: Redraw the current plot based on the selected parameters.

plot.plot(*samples)¶

This methods plot the sample data in a PyQt5 widget allowing the user to show different types of plots.

The resolution function and other parameters are automatically obtained from the current dataset class instance.

Parameters:	samples (`nPDyn.Sample`) – Samples to be plotted.

subPlotsFormat¶

subPlotsFormat.subplotsFormat(caller, sharex=False, sharey=False, projection=None, params=False, FWS=False)¶

This method is used to try to determine the best number of rows and columns for plotting. Depending on the size of the fileIdxList, the plot will have a maximum of subplots per row, typically around 4-5 and the required number of rows. :arg sharex: matplotlib’s parameter for x-axis sharing :arg sharey: matplotlib’s parameter for y-axis sharing :arg projection: projection type for subplots (None, ‘3d’,…)

(optional, default None)

Parameters:	params – if True, use size of paramsNames instead of fileIdxList FWS – if True, use numbers of energy offsets in fixed-window scans instead
Returns:	axis list from figure.subplots method of matplotlib

subPlotsFormat.subplotsFormatWithColorBar(caller, sharex=False, sharey=False, projection=None, params=False)¶

This method is used to try to determine the best number of rows and columns for plotting. Depending on the size of the fileIdxList, the plot will have a maximum of subplots per row, typically around 4-5 and the required number of rows. Axes are added to plot colorbars as well, so that the number of columns will be twice the number required initially by the data. :arg sharex: matplotlib’s parameter for x-axis sharing :arg sharey: matplotlib’s parameter for y-axis sharing :arg projection: projection type for subplots (None, ‘3d’,…)

(optional, default None)

Parameters:	params – if True, use size of paramsNames instead of fileIdxList
Returns:	axis list from figure.subplots method of matplotlib

License¶

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How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest

possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest

to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.

Analysis routines for neutron backscattering data Copyright (C) 2019 Kevin Pounot

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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Also add information on how to contact you by electronic and paper mail.

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nPDyn Copyright (C) 2019 Kevin Pounot This program comes with ABSOLUTELY NO WARRANTY; for details type `show w’. This is free software, and you are welcome to redistribute it under certain conditions; type `show c’ for details.

The hypothetical commands `show w’ and `show c’ should show the appropriate parts of the General Public License. Of course, your program’s commands might be different; for a GUI interface, you would use an “about box”.

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The GNU General Public License does not permit incorporating your program

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Help¶

A google group is available for any question, discussion on features or comment.

In case of bugs or obvious change to be done in the code use GitHub Issues.

nPDyn¶

Installation:¶

Unix and Windows¶

Getting started¶

Documentation¶

Import data¶

Access the data values¶

Raw data¶

Nexus (hdf5) files¶

.inx files¶

Process data¶

Arithmetic operations¶

Binning¶

Normalization¶

Background corrections¶

Selection of data range¶

Fit data¶

Using builtin model backend¶

Create parameters¶

Instantiate a Model¶

Add components¶

Fit data¶

Using lmfit backend¶

Build model¶

Fit data¶

References¶

Plot data¶

API reference¶

Sample¶

dataParsers¶

mantidNexus¶

mantidWorkspace¶

inxConvert¶

IN16B_nexus¶

IN16B_QENS¶

IN16B_FWS¶

Classes¶

IN16B_BATS¶

Process functions¶

models¶

Model¶

Params¶

Presets¶

Builtins¶

lmfit¶

ConvolvedModel¶

Presets¶

Convolutions¶

Builtins¶

plot¶

plot¶

subPlotsFormat¶

License¶

Help¶

Indices and tables¶