Mantid enables Fit function objects to be produced in python. For example
g = Gaussian()
will make g into a Gaussian function with default values and
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
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:
gSigma = g["Sigma"]
g["Height"] = 1.5
One can also get and set function parameters and attributes, by dot operations, for example:
gSigma = g.Sigma
g.Height = 1.5
Composite functions can be created by means of the plus operation and individual functions can be accessed by array index operations. For example:
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.
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:
f1Sigma = spectrum["f1.Sigma"]
spectrum["f1.Height"] = 1.5
One can add a function by the +- operator or remove be the del function.
spectrum += Lorentzian(PeakCentre=3)
del spectrum[1]
Also available is the len function and iteration over the member functions:
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:
spectrum = CompositeFunctionWrapper(LinearBackground(), Gaussian(PeakCentre=1), Gaussian(PeakCentre=2))
P = ProductFunctionWrapper(ExpDecay(), Gaussian(Height=1,Sigma=0.2))
Multi-Domain functions can be constructed like this:
md_fun = MultiDomainFunction(Gaussian(PeakCentre=1, Sigma=0.1), Gaussian(PeakCentre=1, Sigma=0.2), ..., global=['Height'])
The parameters of functions can be tied or fixed like this:
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:
func.untie('f3.Sigma')
To tie all parameters of the same local name in a composite function, one can use TieAll:
func.tieAll('Sigma')
All members of the composite function must have this parameter (in this case Sigma). Similarly with fixing:
spectrum1.fixAll('FWHM')
Also parameters of a function can be fixed with fixAllParameters and unfixed with untieAllParameters.
c.fixAllParameters()
...
c.untieAllParameters()
One can set and remove constraints as follows:
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.
comp.constrainAll("Sigma < 1.8")
...
comp.unconstrainAll("Sigma")
One can evaluate functions:
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:
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.
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.
Category: Concepts