solve the interpolation issue

This is a squashed version of #38534 into `ornl-next`

fix the doc and add release note

simply codes

Framework/PythonInterface/plugins/algorithms/WorkflowAlgorithms/InterpolateBackground.py

@@ -74,8 +74,8 @@ def PyExec(self):
         lowWS = mtd[self.low_ws]
         highWS = mtd[self.high_ws]
 
-        scalar = (self.interpo_temp - self.low_temp) / (self.high_temp - self.interpo_temp)
-        outputWS = lowWS + scalar * highWS - scalar * lowWS
+        scalar = (self.interpo_temp - self.low_temp) / (self.high_temp - self.low_temp)
+        outputWS = scalar * highWS + (1 - scalar) * lowWS
 
         output_ws_name = self.getProperty("OutputWorkspace").value
         RenameWorkspace(InputWorkspace=outputWS, OutputWorkspace=output_ws_name)

Framework/PythonInterface/test/python/plugins/algorithms/WorkflowAlgorithms/InterpolateBackgroundTest.py

@@ -6,6 +6,7 @@
 # SPDX - License - Identifier: GPL - 3.0 +
 
 import unittest
+import numpy as np
 from mantid.simpleapi import DeleteWorkspace, InterpolateBackground, CreateWorkspace, GroupWorkspaces
 
 
@@ -26,8 +27,9 @@ def test_nominal(self):
         self.ws1.getRun().addProperty("SampleTemp", "100", False)
         self.ws2.getRun().addProperty("SampleTemp", "400", False)
         outputWS = InterpolateBackground(self.wsGroup, self.interpo)
-        expected = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150]
-        self.assertListEqual(list(outputWS.readY(0)), expected)
+        expected = [8.33333333, 16.66666667, 25.0, 33.33333333, 41.66666667, 50.0, 58.33333333, 66.66666667, 75.0, 83.33333333]
+        tolerance = 1.0e-8
+        np.testing.assert_allclose(list(outputWS.readY(0)), expected, rtol=tolerance)
 
     def test_bad_input(self):
         # Test raises Runtime error if a workspace is missing SampleTemp property

docs/source/algorithms/InterpolateBackground-v1.rst

@@ -20,7 +20,8 @@ Below is the function used for the interpolation:
 
 .. math::
 
-	WS_{interpolated} = WS_{low} + (temp_{interpo} - temp_{low}) / (temp_{high} - temp_{interpo}) * (WS_{high} - WS_{low}),
+    factor = (temp_{interpo} - temp_{low}) / (temp_{high} - temp_{low})
+    WS_{interpolated} = WS_{high} * factor + WS_{low} * (1 - factor)
 
 where :math:`WS_{low}` and :math:`WS_{high}` are the workspaces containing the run data, :math:`temp_{low}` and
 :math:`temp_{high}` are the two extreme temperatures the empty containers were measured at, and
@@ -44,10 +45,10 @@ Usage
    ws1 = CreateWorkspace(dataX, dataY1)
    ws2 = CreateWorkspace(dataX, dataY2)
    wsGroup = GroupWorkspaces("ws1,ws2")
-   interpoTemp = "300"
+   interpoTemp = "200"
    # CreateWorkspace does not add the "SampleTemp" property so we need to add it here
    ws1.getRun().addProperty("SampleTemp", "100", False)
-   ws2.getRun().addProperty("SampleTemp", "400", False)
+   ws2.getRun().addProperty("SampleTemp", "300", False)
 
    # Perform the background interpolation
    outputWS = InterpolateBackground(wsGroup, interpoTemp)
@@ -59,7 +60,7 @@ Output:
 
 .. testoutput::
 
-   Interpolated Y values are: [3. 3. 3. 3. 3. 3. 3. 3. 3. 3.]
+   Interpolated Y values are: [1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5]
 
 
 .. categories::

docs/source/release/v6.12.0/Diffraction/Powder/Bugfixes/38534.rst

@@ -0,0 +1 @@
+- Fix the issue with the :ref:`InterpolateBackground <algm-InterpolateBackground>` algorithm.