Add unit tests for numerical third derivative

Also renamed function to more pythonic style.
And added tests for function to extend range.

Author: GuiMacielPereira

src/mvesuvio/analysis_reduction.py

@@ -12,7 +12,7 @@
                             VesuvioThickness, Integration, Divide, Multiply, DeleteWorkspaces, \
                             CreateWorkspace
 
-from mvesuvio.util.analysis_helpers import numericalThirdDerivative, load_resolution, load_instrument_params, \
+from mvesuvio.util.analysis_helpers import numerical_third_derivative, load_resolution, load_instrument_params, \
                                             extend_range_of_array
 
 np.set_printoptions(suppress=True, precision=4, linewidth=200)
@@ -559,7 +559,7 @@ def _neutron_compton_profiles(self, pars):
         JOfY = scipy.special.voigt_profile(self._y_space_arrays[self._row_being_fit] - centers, total_gaussian_width, lorentzian_width)
 
         # Third derivative cuts edges of array by 6 indices
-        JOfY_third_derivative = numericalThirdDerivative(self._y_space_arrays[self._row_being_fit], JOfY)
+        JOfY_third_derivative = numerical_third_derivative(self._y_space_arrays[self._row_being_fit], JOfY)
 
         deltaQ = self._deltaQ[self._row_being_fit, 6: -6]
         E0 = self._E0[self._row_being_fit, 6: -6]

src/mvesuvio/util/analysis_helpers.py

@@ -237,7 +237,7 @@ def extractWS(ws):
     return ws.extractX(), ws.extractY(), ws.extractE()
 
 
-def numericalThirdDerivative(x, y):
+def numerical_third_derivative(x, y):
     k6 = (- y[:, 12:] + y[:, :-12]) * 1
     k5 = (+ y[:, 11:-1] - y[:, 1:-11]) * 24
     k4 = (- y[:, 10:-2] + y[:, 2:-10]) * 192

tests/unit/analysis/test_analysis_helpers.py

@@ -1,10 +1,11 @@
 import unittest
 import numpy as np
+import scipy
 import dill
 import numpy.testing as nptest
 from mock import MagicMock
 from mvesuvio.util.analysis_helpers import extractWS, _convert_dict_to_table,  \
-    fix_profile_parameters, calculate_h_ratio
+    fix_profile_parameters, calculate_h_ratio, extend_range_of_array, numerical_third_derivative
 from mantid.simpleapi import CreateWorkspace, DeleteWorkspace
 
 
@@ -126,5 +127,27 @@ def test_conversion_of_constraints(self):
         self.assertEqual(converted_constraints[1]['fun']([0, 0, 0, 2, 0, 0, 1]), 2-0.7234)
 
 
+    def test_extend_range_of_array_for_increasing_range(self):
+        x = np.arange(10)
+        x = np.vstack([x, 2*x])
+        x_extended = extend_range_of_array(x, 5)
+        np.testing.assert_array_equal(x_extended, np.vstack([np.arange(-5, 15, 1), np.arange(-10, 30, 2)]))
+
+
+    def test_extend_range_of_array_for_decreasing_range(self):
+        x = np.linspace(-5, 5, 21)
+        x = np.vstack([x, 2*x])
+        x_extended = extend_range_of_array(x, 5)
+        np.testing.assert_array_equal(x_extended, np.vstack([np.linspace(-7.5, 7.5, 31), np.linspace(-15, 15, 31)]))
+
+
+    def test_numerical_third_derivative(self):
+        x= np.linspace(-20, 20, 300)    # Workspaces are about 300 points of range
+        x = np.vstack([x, 2*x])
+        y = scipy.special.voigt_profile(x, 5, 5)
+        numerical_derivative = numerical_third_derivative(x, y)
+        expected_derivative = np.array([np.gradient(np.gradient(np.gradient(y_i, x_i), x_i), x_i)[6: -6] for y_i, x_i in zip(y, x) ])
+        np.testing.assert_allclose(numerical_derivative, expected_derivative, atol=1e-6)
+
 if __name__ == "__main__":
     unittest.main()