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Name | Default | Description |
---|---|---|
Height | 0.1 | Intensity at the origin |
Tau | 100.0 | Relaxation time |
Beta | 1.0 | Stretching exponent |
Centre | 0.0 | Centre of the peak |
Provides the Fourier Transform of the Symmetrized Stretched Exponential Function
with \(h\) Planck’s constant. If the energy units of energy are micro-eV, then tau is expressed in pico-seconds. If E-units are micro-eV then tau is expressed in nano-seconds.
Properties:
Note
To run these usage examples please first download the usage data, and add these to your path. In Mantid this is done using Manage User Directories.
Example - Fit to a QENS signal:
The QENS signal is modeled by the convolution of a resolution function with elastic and StretchedExpFT components. Noise is modeled by a linear background:
\(S(Q,E) = R(Q,E) \otimes (\alpha \delta(E) + StretchedExpFT(Q,E)) + (a+bE)\)
Obtaining an initial guess close to the optimal fit is critical. For this model, it is recommended to follow these steps: - In the Fit Function window of a plot in MantidWorkbench, construct the model. - Tie parameter \(Height\) of StretchedExpFT to zero, then carry out the Fit. This will result in optimized elastic line and background. - Untie parameter \(Height\) of StretchedExpFT and tie parameter \(Beta\) to 1.0, then carry out the fit. This will result in optimized model using an exponential. - Release the tie on Beta and redo the fit.
# Load resolution function and scattered signal
resolution = LoadNexus(Filename="resolution_14955.nxs")
qens_data = LoadNexus(Filename="qens_data_14955.nxs")
# This function_string is obtained by constructing the model
# with the Fit Function window of a plot in MantidWorkbench, then
# Setup--> Manage Setup --> Copy to Clipboard
function_string = "(composite=Convolution,FixResolution=true,NumDeriv=true;"
function_string += "name=TabulatedFunction,Workspace=resolution,WorkspaceIndex=0,Scaling=1,Shift=0,XScaling=1;"
function_string += "(name=DeltaFunction,Height=1,Centre=0;"
function_string += "name=StretchedExpFT,Height=1.0,Tau=100,Beta=0.98,Centre=0));"
function_string += "name=LinearBackground,A0=0,A1=0"
# Carry out the fit. Produces workspaces fit_results_Parameters,
# fit_results_Workspace, and fit_results_NormalisedCovarianceMatrix.
Fit(Function=function_string,
InputWorkspace="qens_data",
WorkspaceIndex=0,
StartX=-0.15, EndX=0.15,
CreateOutput=1,
Output="fit_results")
# Collect and print parameters for StrechtedExpFT
parameters_of_interest = ("Tau", "Beta")
values_found = {}
ws = mtd["fit_results_Parameters"] # Workspace containing optimized parameters
for row_index in range(ws.rowCount()):
full_parameter_name = ws.row(row_index)["Name"]
for parameter in parameters_of_interest:
if parameter in full_parameter_name:
values_found[parameter] = ws.row(row_index)["Value"]
break
if values_found["Beta"] > 0.63 and values_found["Beta"] < 0.71:
print("Beta found within [0.63, 0.71]")
if values_found["Tau"] > 54.0 and values_found["Tau"] < 60.0:
print("Tau found within [54.0, 60.0]")
Output:
Beta found within [0.63, 0.71]
Tau found within [54.0, 60.0]
Categories: FitFunctions | QuasiElastic
Python: StretchedExpFT.py (last modified: 2020-03-27)