Added Besselfunction (#26785)

Added Besselfunction

Framework/PythonInterface/plugins/functions/Bessel.py

+# Mantid Repository : https://github.com/mantidproject/mantid
+#
+# Copyright © 2018 ISIS Rutherford Appleton Laboratory UKRI,
+#     NScD Oak Ridge National Laboratory, European Spallation Source
+#     & Institut Laue - Langevin
+# SPDX - License - Identifier: GPL - 3.0 +
+# pylint: disable=invalid-name, anomalous-backslash-in-string, attribute-defined-outside-init
+
+from mantid.api import IFunction1D, FunctionFactory
+import numpy as np
+from scipy import special as sp
+
+
+class Bessel(IFunction1D):
+
+    def category(self):
+        return "Muon"
+
+    def init(self):
+        self.declareParameter("A0", 1, 'Amplitude')
+        self.declareParameter("Phi", 0.1, 'Phase(rad)')
+        self.declareParameter("Nu", 0.1, 'Frequency(MHz)')
+
+    def function1D(self, x):
+        A0 = self.getParameterValue("A0")
+        Phi = self.getParameterValue("Phi")
+        Nu = self.getParameterValue("Nu")
+        return A0 * sp.j0(2 * np.pi * Nu * x + Phi)
+
+FunctionFactory.subscribe(Bessel)

Framework/PythonInterface/test/python/plugins/functions/BesselTest.py

+# Mantid Repository : https://github.com/mantidproject/mantid
+#
+# Copyright © 2018 ISIS Rutherford Appleton Laboratory UKRI,
+#     NScD Oak Ridge National Laboratory, European Spallation Source
+#     & Institut Laue - Langevin
+# SPDX - License - Identifier: GPL - 3.0 +
+from __future__ import (absolute_import, division, print_function)
+
+import unittest
+import numpy as np
+
+from MsdTestHelper import (is_registered, check_output, do_a_fit)
+
+
+class BesselTest(unittest.TestCase):
+
+	def test_function_has_been_registered(self):
+		status, msg = is_registered("Bessel")
+		if not status:
+			self.fail(msg)
+
+	def test_function_output(self):
+		input = [0.0, 4.0, 8.0, 12.0]
+		expected = [0.09900249722395764, -0.010116392139648565, -0.024891569859118595, -0.006976567202361606]
+		tolerance = 1.0e-05
+		status, output = check_output("Bessel", input, expected, tolerance, A0=0.1, Phi=0.2, Nu=0.2)
+		if not status:
+			msg = 'Computed output {} from input {} unequal to expected: {}'
+			self.fail(msg.format(*[str(i) for i in (output, input, expected)]))
+
+	def test_do_fit(self):
+		do_a_fit(np.arange(0.1, 16, 0.2), 'Bessel', guess=dict(A0=0.15, Phi=0.25, Nu=0.25), target=dict(A0=0.1, Phi=0.2, Nu=0.2), atol=0.01)
+
+if __name__ == '__main__':
+	unittest.main()

Framework/PythonInterface/test/python/plugins/functions/CMakeLists.txt

 # Tests for Fit functions
 
 set(TEST_PY_FILES
+    BesselTest.py
     DSFinterp1DFitTest.py
     EISFDiffSphereTest.py
     EISFDiffCylinderTest.py

docs/source/fitting/fitfunctions/Bessel.rst

+.. _func-Bessel:
+
+======
+Bessel
+======
+
+.. index:: Bessel
+
+Description
+-----------
+
+.. math:: A(t)=A_0J_0(2\pi\nu t+\phi)
+
+where,
+
+:math:`A_0` is the amplitude,
+
+:math:`\nu` is the frequency of oscillation (MHz),
+
+:math:`\phi` is the phase at :math:`t=0`,
+
+and :math:`J_0(x)` is the Bessel Function of the first kind, its expression is given by:
+
+.. math:: J_0(x)=\sum_{l=0}^{\infty}\frac{(-1)^l}{2^{2l}(l!)^2}x^{2l}.
+
+.. figure:: /images/Bessel.png
+   :alt: A plot of Bessel function.
+
+.. attributes::
+
+.. properties::
+
+References
+----------
+
+[1]  `Savici et al., PRB 66 (2002) <https://journals.aps.org/prb/pdf/10.1103/PhysRevB.66.014524>`_.
+
+.. categories::
+
+.. sourcelink::