Update to basics doc

docs/basics.rst

@@ -45,8 +45,63 @@ SALib provides several sensitivity analysis methods, such as Sobol, Morris,
 and FAST.  There are many factors that determine which method is appropriate
 for a specific application, which we will discuss later.  However, for now, just
 remember that regardless of which method you choose, you need to use only two
-functions: :code:`sample` and :code:`analyze`.
+functions: :code:`sample` and :code:`analyze`.  To demonstrate the use of SALib,
+we will walk you through a simple example.
 
+An Example
+----------
+In this example, we will perform a Sobol' sensitivity analysis of the Ishigami 
+function, shown below.  The Ishigami function is commonly used to test 
+uncertainty and sensitivity analysis methods because it exhibits strong 
+nonlinearity and nonmonotonicity.
+
+.. math::
+
+    f(x) = sin(x_1) + a sin^2(X_2) + b x_3^4*sin(x_1)
+    
+Importing SALib
+~~~~~~~~~~~~~~~
+
+The first step is the import the necessary libraries.  In SALib, the
+:code:`sample` and :code:`analyze` functions are stored in separate
+Python modules.  For example, below we import the :code:`saltelli` sample
+function and the :code:`sobol` analyze function.  We also import the Ishigami
+function, which is provided as a test function within SALib.  Lastly, we
+import :code:`numpy`, as it is used by SALib to store the model inputs and
+outputs in a matrix.
+
+.. code:: python
+
+    from SALib.sample import saltelli
+    from SALib.analyze import sobol
+    from SALib.test_functions import Ishigami
+    import numpy as np
+    
+Defining the Model Inputs
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+.. code:: python
+
+    # Define the model inputs
+    problem = {
+        'num_vars': 3, 
+        'names': ['x1', 'x2', 'x3'], 
+        'bounds': [[-3.14159265359, 3.14159265359], 
+                   [-3.14159265359, 3.14159265359], 
+                   [-3.14159265359, 3.14159265359]]
+    }
+
+    # Generate samples
+    param_values = saltelli.sample(problem, 1000, calc_second_order=True)
+
+    # Run model (example)
+    Y = Ishigami.evaluate(param_values)
+
+    # Perform analysis
+    Si = sobol.analyze(problem, Y, print_to_console=False)
+
+    # Print the first-order sensitivity indices
+    print Si['S1']
 
 .. autofunction:: SALib.analyze.fast.analyze
 

docs/conf.py

@@ -106,7 +106,7 @@ def __getattr__(cls, name):
 
 # If true, the current module name will be prepended to all description
 # unit titles (such as .. function::).
-#add_module_names = True
+add_module_names = False
 
 # If true, sectionauthor and moduleauthor directives will be shown in the
 # output. They are ignored by default.