.. _FitFunctionsInPython:
Fit Functions In Python
=======================
Introduction
------------
Mantid enables Fit function objects to be produced in python. For example
.. code:: python
g = Gaussian()
will make ``g`` into a Gaussian function with default values and
.. code:: python
g = Gaussian(Height=1, Sigma=0.1)
will make ``g`` into a Gaussian function with ``Height`` set to 1, ``Sigma`` set to 0.1 and ``PeakCentre`` set to default value.
One can also make function with attributes such as
.. code:: python
p = Polynomial(n=3, A0=1, A1=2, A2=4, A3=3)
One can get and set function parameters and attributes, by array operations, for example:
.. code:: python
gSigma = g["Sigma"]
g["Height"] = 1.5
One can also get and set function parameters and attributes, by dot operations, for example:
.. code:: python
gSigma = g.Sigma
g.Height = 1.5
Composite Functions
-------------------
Composite functions can be created by means of the plus operation and
individual functions can be accessed by array index operations.
For example:
.. code:: python
spectrum = LinearBackground() + Gaussian(PeakCentre=1) + Gaussian(PeakCentre=2)
peak1 = spectrum[1]
peak1['Sigma'] = 0.123
spectrum[2] = Lorentzian(PeakCentre=2)
which sets ``Sigma`` of the second function (first Gaussian) to 0.123 and changes the third function to a Lorentzian.
Similarly product functions can be constructed using the multiplication operator.
.. code:: python
p = ExpDecay() * Gaussian(Height=1,Sigma=0.2)
One can get and set the parameters of a composite function, by array operations,
but not by dot operations because the parameter name already contains a dot, for example:
.. code:: python
f1Sigma = spectrum["f1.Sigma"]
spectrum["f1.Height"] = 1.5
One can add a function by the ``+-`` operator or remove be the ``del`` function.
.. code:: python
spectrum += Lorentzian(PeakCentre=3)
del spectrum[1]
Also available is the ``len`` function and iteration over the member functions:
.. code:: python
n_peaks = len(spectrum)
for func in spectrum:
print(func)
The plus and times operators are associative and
so may not preserve a composite function within a composite function as such,
but replace it with a list of its member functions.
Instead you may use:
.. code:: python
spectrum = CompositeFunctionWrapper(LinearBackground(), Gaussian(PeakCentre=1), Gaussian(PeakCentre=2))
P = ProductFunctionWrapper(ExpDecay(), Gaussian(Height=1,Sigma=0.2))
Multi-Domain Functions
----------------------
Multi-Domain functions can be constructed like this:
.. code:: python
md_fun = MultiDomainFunction(Gaussian(PeakCentre=1, Sigma=0.1), Gaussian(PeakCentre=1, Sigma=0.2), ..., global=['Height'])
Setting Ties
------------
The parameters of functions can be tied or fixed like this:
.. code:: python
func1.tie(A0=2.0)
func2.tie({'f1.A2': '2*f0.A1', 'f2.A2': '3*f0.A1 + 1'})
func3.fix('A0')
func4.fix('f2.A2')
Both fixes and ties can be removed by ``untie``:
.. code:: python
func.untie('f3.Sigma')
To tie all parameters of the same local name in a composite function, one can use ``TieAll``:
.. code:: python
func.tieAll('Sigma')
All members of the composite function must have this parameter (in this case ``Sigma``).
Similarly with fixing:
.. code:: python
spectrum1.fixAll('FWHM')
Also parameters of a function can be fixed with ``fixAllParameters`` and unfixed with ``untieAllParameters``.
.. code:: python
c.fixAllParameters()
...
c.untieAllParameters()
Setting Constraints
-------------------
One can set and remove constraints as follows:
.. code:: python
g.constrain("Sigma < 2.0, Height > 7.0")
...
g.unconstrain("Sigma")
g.unconstrain("Height")
comp.constrain("f1.Sigma < 2, f0.Height > 7")
...
comp.unconstrain("f1.Sigma")
comp.unconstrain("f0.Height")
One can all constrain a given parameter in all members of a composite function that have this parameter
and also remove such constraints.
.. code:: python
comp.constrainAll("Sigma < 1.8")
...
comp.unconstrainAll("Sigma")
Evaluation
----------
One can evaluate functions:
.. code:: python
p = Polynomial(n=2, A0=0, A1=0.5, A2=0.5)
print p(1) # expect 1.0
print p(2) # expect 3.0
print p(3) # expect 6.0
print p([0,1,2,3]) # expect [ 0. 1. 3. 6.]
ws = CreateWorkspace(DataX=[0,1,2,3,4,5,6,7], DataY=[5,5,5,5,5,5,5])
print p(ws).readY(1) # expect [ 0.375 1.875 4.375 7.875 12.375 17.875 24.375]
One can use numpy arrays:
.. code:: python
import numpy as np
a = np.array([[0, 1,], [2, 3]])
p = Polynomial(n=4, A0=1, A1=1, A2=1, A3=1, A4=1)
print p(a)
# expect [[ 1. 5.]
# [ 31. 121.]]
Also one can put parameters into the function when evaluating.
.. code:: python
p = Polynomial(n=2)
print p([0,1,2,3], 0.0, 0.5, 0.5) #expect [ 0. 1. 3. 6.]
This enables one to fit the functions with ``scipy.optimize.curve_fit``.
Plotting
--------
Functions may be plotted by calling the plot method of the function.
This method can be called in any of the following manners:
.. code:: python
f.plot(xValues=[0,2,2.5,3,5]) # for these x-values
f.plot(workpace=ws) # for the x-values of workspace ws
f.plot(workspace=ws, workspaceIndex=i) # for x-values of workspace index i of ws
f.plot(startX=xmin, endX=xmax) # for 20 x-values between xmin and xmax
f.plot(startX=xmin, endX=xmax, nSteps=10) # for 10 x-values between xmin and xmax
f.plot(workspace=ws, startX=xmin, endX=xmax) # for x-values of ws between xmin & xmax
Owing to the way workspaces are named in python, only one plot can be shown at a time.
.. categories:: Concepts