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EISFDiffSphere.py
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EISFDiffSphere.py
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#pylint: disable=no-init,invalid-name
"""
@author Jose Borreguero, ORNL
@date December 05, 2017
Copyright © 2007-8 ISIS Rutherford Appleton Laboratory,
NScD Oak Ridge National Laboratory & European Spallation Source
This file is part of Mantid.
Mantid 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.
Mantid 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.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
File change history is stored at: <https://github.com/mantidproject/mantid>
Code Documentation is available at: <http://doxygen.mantidproject.org>
"""
from __future__ import (absolute_import, division, print_function)
import numpy as np
try:
from scipy.special import spherical_jn
def j1(z): return spherical_jn(1, z)
def j1d(z): return spherical_jn(1, z, derivative=True)
except ImportError:
# spherical_jn removed from scipy >= 1.0.0
from scipy.special import sph_jn
def j1(z): return sph_jn(1, z)[0][1]
def j1d(z): return sph_jn(1, z)[1][1]
from mantid.api import IFunction1D, FunctionFactory
class EISFDiffSphere(IFunction1D):
r"""Models the elastic incoherent scattering intensity of a particle
undergoing diffusion but confined to a spherical volume
"""
vecbessel = np.vectorize(lambda z: j1(z) / z)
def category(self):
return 'QuasiElastic'
def init(self):
# Active fitting parameters
self.declareParameter('A', 1.0, 'Amplitude')
self.declareParameter('R', 1.0, 'Sphere radius, inverse units of Q.')
def function1D(self, xvals):
r"""Calculate the intensities
Parameters
----------
xvals : sequence of floats
The domain where to evaluate the function
jacobian: 2D array
partial derivative of the function with respect to the fitting
parameters evaluated at the domain.
Returns
-------
numpy.ndarray
Function values
"""
zs = self.getParameterValue('R') * np.asarray(xvals)
return self.getParameterValue('A') * np.square(3 * self.vecbessel(zs))
def functionDeriv1D(self, xvals, jacobian):
r"""Calculate the partial derivatives
Parameters
----------
xvals : sequence of floats
The domain where to evaluate the function
jacobian: 2D array
partial derivatives of the function with respect to the fitting
parameters, evaluated at the domain.
"""
amplitude = self.getParameterValue('A')
radius = self.getParameterValue('R')
i = 0
for x in xvals:
z = radius * x
j = j1(z)/z
jacobian.set(i, 0, np.square(3 * j))
jacobian.set(i,1, amplitude * 2 * 9 * j * (j1d(z) - j) / radius)
i += 1
# Required to have Mantid recognise the new function
FunctionFactory.subscribe(EISFDiffSphere)