Add doc for function background

.github/workflows/build_docs.yml

@@ -23,7 +23,7 @@ jobs:
     - name: Set up Python 
       uses: actions/setup-python@v4
       with:
-        python-version: '3.11' 
+        python-version: '3.10' 
     - name: Build docs
       run: |
         # create an x11 display because otherwise MATLAB refuses to export live scripts...
@@ -48,7 +48,7 @@ jobs:
         wget https://github.com/jgm/pandoc/releases/download/3.6.2/pandoc-3.6.2-1-amd64.deb
         sudo apt install -y ./pandoc-3.6.2-1-amd64.deb
 
-        pip install matlabengine==24.1.*
+        pip install matlabengine==9.14.*
         pip install -r requirements.txt
         python build_docs.py
     - name: Checkout gh-pages

source/_static/custom.css

@@ -47,10 +47,6 @@ html[data-theme=dark] {
   margin: 0;
 }
 
-#rat{
-  margin-bottom: 1.5em;
-}
-
 .sd-card-header{
   font-weight: 550;
 }

source/advanced/backgroundFunctions.rst

@@ -0,0 +1,60 @@
+====================
+Function Backgrounds
+====================
+
+RAT supports function backgrounds, which use a custom function to describe the background for the experiment. 
+
+
+The signature for background functions is shown in the code snippet below. The first argument `xdata` is a vector containing the q points over the simulation range, 
+which should incorporate the q values of the supplied data and the second argument `params` is a vector containing the background parameters associated with the background, 
+up to 5 can be related to a specific function background. The function should return an array with the background value for each of the input simulation points.
+
+.. tab-set-code::
+    .. code-block:: MATLAB
+
+        function background = backgroundFunction(xdata, params)
+
+            background = zeros(numel(xdata), 1);
+
+        end
+
+    .. code-block:: Python
+
+        import numpy as np
+
+
+        def background_function(xdata, params):
+
+            background = np.zeros(len(xdata))
+            return background
+
+To define a function background, add the custom function, associated background parameters, then create the background as shown below 
+
+.. tab-set-code::
+    .. code-block:: MATLAB
+
+        % Add the function background
+        % Add the function to custom files, and its parameters to background
+        % parameters
+        problem.addCustomFile('Back Fun','backgroundFunction.m','matlab',pwd);
+
+        problem.addBackgroundParam('Fn Ao',5e-7, 8e-6, 5e-5);
+        problem.addBackgroundParam('Fn k',40, 70, 90);
+        problem.addBackgroundParam('Fn Const',1e-7, 8e-6, 1e-5);
+
+        % Add the Background
+        problem.addBackground('Func Background','function','Back Fun','Fn Ao','Fn k','Fn Const');
+
+    .. code-block:: Python
+
+        problem.custom_files.append(name="Back Fun", filename="background_function.py", language="python")
+
+        problem.background_parameters.append(name="Fn Ao", min=5e-7, value=8e-6, max=5e-5)
+        problem.background_parameters.append(name="Fn k", min=40, value=70, max=90)
+        problem.background_parameters.append(name="Fn Const", min=1e-7, value=8e-6, max=1e-5)
+
+        problem.backgrounds.append(name="Func Background", type="function", source="Back Func", value_1="Fn Ao", value_2="Fn k", value_3="Fn Const")
+
+
+An example of using Python and Matlab custom models can be found in examples folder. Look at DSPCScriptWithFunctionBackground.m and 
+DSPC_function_background.py in Matlab and Python respectively.

source/advanced/index.rst

@@ -12,6 +12,7 @@ In this section we discuss some advanced features of the toolbox:-
    resampling
    parallelisation
    customLanguages
+   backgroundFunctions
    events