xrf_model Module

class skbeam.core.fitting.xrf_model.ElementModel(*args, **kwargs)

Bases: lmfit.model.Model

Wrap the element_peak_xrf function for fitting within lmfit framework

This is a function to construct xrf element peak, which is based on gauss profile, but more specific requirements need to be considered. For instance, the standard deviation is replaced by global fitting parameters, and energy calibration on x is taken into account.

Parameters

xarray

independent variable, channel number instead of energy

areafloat

area of gaussian function

centerfloat

center position

delta_centerfloat

adjustment to center position

delta_sigmafloat

adjustment to standard deviation

ratiofloat

branching ratio

ratio_adjustfloat

value used to adjust peak height

fwhm_offsetfloat

global fitting parameter for peak width

fwhm_fanoprimefloat

global fitting parameter for peak width

e_offsetfloat

offset of energy calibration

e_linearfloat

linear coefficient in energy calibration

e_quadraticfloat

quadratic coefficient in energy calibration

Returns

array:

gaussian peak profile

class skbeam.core.fitting.xrf_model.ModelSpectrum(params, elemental_lines)

Bases: object

Construct Fluorescence spectrum which includes elastic peak, compton and element peaks.

assemble_models(self)

Put all models together to form a spectrum.

model_fit(self, channel_number, spectrum, weights=None, method='leastsq', **kwargs)

Parameters

channel_numberarray

independent variable

spectrumarray

intensity

weightsarray, optional

weight for fitting

methodstr

default as leastsq

kwargsdict

fitting criteria, such as max number of iteration

Returns

result object from lmfit

setup_compton_model(self)

setup parameters related to Compton model

setup_elastic_model(self)

setup parameters related to Elastic model

setup_element_model(self, elemental_line, default_area=100000.0)

Construct element model. Elemental line that can be add include elemental peak, pileup peak and user peak. User peak is a fake peak, but can be used as a quick replacement for pileup peaks, escape peaks or other unknown peaks due to detector defects or scattering process.

Parameters

elemental_linestr

elemental line, such as ‘Fe_K’ pileup peak, such as ‘Si_Ka1-Si_Ka1’ user peak, such as ‘user_peak1’, ‘user_peak2’

default_areafloat, optional

value for the initial area of a given element default is 1e5, found to be a good value

class skbeam.core.fitting.xrf_model.ParamController(params, elemental_lines)

Bases: object

Update element peak information in parameter dictionary. This is an important step in dynamical fitting.

add_param(self, kind, element, constraint=None)

Create a Parameter controlling peak position, width, branching ratio, or area.

Parameters

kind{‘pos’, ‘width’, ‘ratio’, ‘area’}

elementstr

element name

constraint{‘lo’, ‘hi’, ‘lohi’, ‘fixed’, ‘none’}, optional

default “bound strategy” (fitting constraints)

.. note:: Element that can be add include elemental peak, pileup peak and user peak.

User peak is a fake peak, but can be used as a quick replacement for pileup peaks,

escape peaks or other unknown peaks due to detector defects or scattering process.

set_strategy(self, strategy_name)

Update the default value of bounds.

Parameters

strategy_namestr

fitting strategy that this Model will use

update_element_prop(self, element_list, **kwargs)

Update element properties, such as pos, width, area and ratio.

Parameters

element_listlist

define which element to update

kwargsdict

define what kind of property to change

Returns

dictupdated value

skbeam.core.fitting.xrf_model.calculate_area(e_select, matv, results, param, first_peak_area=False)

Parameters

e_selectlist

elements

matv2D array

matrix constains elemental profile as columns

results3D array

x, y positions, and each element’s weight on third dim

paramdict

parameters of fitting

first_peak_areaBool, optional

get overal peak area or only the first peak area, such as Ar_Ka1

Returns

dict :

dict of each 2D elemental distribution

skbeam.core.fitting.xrf_model.compute_escape_peak(spectrum, ratio, params, escape_e=1.73998)

Calculate the escape peak for given detector.

Parameters

spectrumarray

original, uncorrected spectrum

ratiofloat

ratio of shadow to full spectrum

paramdict

fitting parameters

escape_efloat

Units: keV By default, 1.73998 (Ka1 line of Si)

Returns

array:

x after shift, and adjusted y

skbeam.core.fitting.xrf_model.construct_linear_model(channel_number, params, elemental_lines, default_area=100)

Create spectrum with parameters given from params.

Parameters

channel_numberarray

N.B. This is the raw independent variable, not energy.

paramsdict

fitting parameters

elemental_lineslist

e.g., [‘Na_K’, Mg_K’, ‘Pt_M’] refers to the K lines of Sodium, the K lines of Magnesium, and the M lines of Platinum

default_areafloat

value for the initial area of a given element

Returns

selected_elementslist

selected elements for given energy

matvarray

matrix for linear fitting

element_areadict

area of the given elements

skbeam.core.fitting.xrf_model.define_range(data, low, high, a0, a1)

Cut x range based on offset and linear term of a linear function. a0 and a1 should be defined in param_dict.

Parameters

data1D array

raw spectrum

lowfloat

low bound in KeV

highfloat

high bound in KeV

a0float

offset term of energy calibration

a1float

linear term of energy calibration

Returns

xarray

trimmed channel number

yarray

trimmed spectrum according to x

skbeam.core.fitting.xrf_model.element_peak_xrf(x, area, center, delta_center, delta_sigma, ratio, ratio_adjust, fwhm_offset, fwhm_fanoprime, e_offset, e_linear, e_quadratic, epsilon=2.96)

This is a function to construct xrf element peak, which is based on gauss profile, but more specific requirements need to be considered. For instance, the standard deviation is replaced by global fitting parameters, and energy calibration on x is taken into account.

Parameters

xarray

independent variable, channel number instead of energy

areafloat

area of gaussian function

centerfloat

center position

delta_centerfloat

adjustment to center position

delta_sigmafloat

adjustment to standard deviation

ratiofloat

branching ratio

ratio_adjustfloat

value used to adjust peak height

fwhm_offsetfloat

global fitting parameter for peak width

fwhm_fanoprimefloat

global fitting parameter for peak width

e_offsetfloat

offset of energy calibration

e_linearfloat

linear coefficient in energy calibration

e_quadraticfloat

quadratic coefficient in energy calibration

Returns

array:

gaussian peak profile

skbeam.core.fitting.xrf_model.extract_strategy(param, name)

Extract given strategy from param dict.

Parameters

paramdict

saving all parameters for data fitting

namestr

strategy name

Returns

dict :

with given strategy as value

skbeam.core.fitting.xrf_model.fit_per_line_nnls(data, matv, param, use_snip)

Fit experiment data for a given row using nnls algorithm.

Parameters

dataarray

selected one row of experiment spectrum

matvarray

matrix for regression analysis

paramdict

fitting parameters

use_snipbool

use snip algorithm to remove background or not

Returns

array :

fitting values for all the elements at a given row. Background is calculated as a summed value. Also residual is included.

skbeam.core.fitting.xrf_model.fit_pixel_multiprocess_nnls(exp_data, matv, param, use_snip=False)

Multiprocess fit of experiment data.

Parameters

exp_dataarray

3D data of experiment spectrum, with x,y positions as the first 2-dim, and energy as the third one.

matvarray

matrix for regression analysis

paramdict

fitting parameters

use_snipbool, optional

use snip algorithm to remove background or not

Returns

array

Fitting values for all the elements

skbeam.core.fitting.xrf_model.get_activated_lines(incident_energy, elemental_lines)

Parameters

incident_energyfloat

beam energy

element_lineslist

e.g., [‘Na_K’, ‘Mg_K’, ‘Pt_M’]

Returns

list

all activated lines for given elements

skbeam.core.fitting.xrf_model.get_line_energy(elemental_line)

Return the energy of the first line in K, L or M series.

Parameters

elemental_linestr

For instance, Eu_L is the format for L lines and Pt_M for M lines. And for K lines, user needs to define lines like ka1, kb1, because for K lines, we consider contributions from either ka1 or kb1, while for L or M lines, we only consider the primary peak.

Returns

float :

energy of emission line

skbeam.core.fitting.xrf_model.get_relative_cs_ratio(elemental_line, energy)

At given energy, multiple elemental lines may be activated. This function is used to calculate the ratio of the first line’s cross section (cs) to the summed cross section from all the lines.

Parameters

elemental_linestr

e.g., ‘Mg_K’, refers to the K lines of Magnesium

energyfloat

incident energy in keV

Returns

float :

calculated ratio

skbeam.core.fitting.xrf_model.linear_spectrum_fitting(x, y, params, elemental_lines=None, weights=None)

Fit a spectrum to a linear model.

This is a convenience function that wraps up construct_linear_model and nnls_fit.

Parameters

xarray

channel array

yarray

spectrum intensity

paramdict

fitting parameters

elemental_lineslist, optional

e.g., [‘Na_K’, Mg_K’, ‘Pt_M’] refers to the K lines of Sodium, the K lines of Magnesium, and the M lines of Platinum. If elemental_lines is set as None, all the possible lines activated at given energy will be used.

weightsarray, optional

for weighted nnls fitting. Setting weights as None means fitting without weights.

Returns

x_energyarray

x axis with unit in energy

result_dictdict

Fitting results

area_dictdict

the area of the first main peak, such as Ka1, of a given element

skbeam.core.fitting.xrf_model.nnls_fit(spectrum, expected_matrix, weights=None)

Non-negative least squares fitting.

Parameters

spectrumarray

spectrum of experiment data

expected_matrixarray

2D matrix of activated element spectrum

weightsarray, optional

for weighted nnls fitting. Setting weights as None means fitting without weights.

Returns

resultsarray

weights of different element

residuefloat

error

Note

nnls is chosen as amplitude of each element should not be negative. ..

skbeam.core.fitting.xrf_model.register_strategy(key, strategy, overwrite=True)

Register new strategy.

Parameters

keystr

strategy name

strategydict

bound for every parameter

skbeam.core.fitting.xrf_model.set_parameter_bound(param, bound_option, extra_config=None)

Update the default value of bounds.

Warning

This function mutates the input values.

Parameters

paramdict

saving all the fitting values and their bounds

bound_optionstr

define bound type

extra_configdict

strategy-specific configuration

skbeam.core.fitting.xrf_model.sum_area(elemental_line, result_val)

Return the total area for given element.

Parameters

elemental_linestr

name of a given element line, such as Na_K

result_valobj

result obj from lmfit to save all the fitting results

Returns

sumvfloat

the total area

skbeam.core.fitting.xrf_model.trim(x, y, low, high)

Mask two arrays applying bounds to the first array.

Parameters

xarray

independent variable

yarray

dependent variable

lowfloat

low bound

highfloat

high bound

Returns

array :

x with new range

array :

y with new range

skbeam.core.fitting.xrf_model.update_parameter_dict(param, fit_results)

Update fitting parameters dictionary according to given fitting results, usually obtained from previous run.

Warning

This function mutates param.

Parameters

paramdict

saving all the fitting values and their bounds

fit_resultsobject

ModelFit object from lmfit