Re #11617. Added algorithm description.

Code/Mantid/docs/source/algorithms/CalculateChiSquared-v1.rst

@@ -10,35 +10,79 @@
 Description
 -----------
 
-TODO: Enter a full rst-markup description of your algorithm here.
+Calculates a measure of the goodness of a fit in four ways.
 
+The ChiSquared property returns the sum of squares of differences between the calculated and measured values:
+
+:math:`\chi_{1}^{2} = \sum_{i} (y_i - f_i)^2`
+
+where :math:`y_i` and :math:`f_i` are the measured and calculated values at i-th point.
+
+The ChiSquaredDividedByDOF is ChiSquared divided by the number of degrees of freedom (DOF):
+
+:math:`\chi_{2}^{2} = \frac{1}{DOF}\sum_{i} (y_i - f_i)^2`
+
+:math:`DOF = N_d - N_p` where :math:`N_d` is the number of data points used in fitting and :math:`N_p`
+is the number of free (not fixed or tied) parameters of the function.
+
+The ChiSquaredWeighted property sums the squares of the differences divided by the data errors:
+
+:math:`\chi_{3}^{2} = \sum_{i} \left(\frac{y_i - f_i}{\sigma_i}\right)^2`
+
+Finally, ChiSquaredWeightedDividedByDOF is
+
+:math:`\chi_{4}^{2} = \chi_{3}^{2} / DOF`
 
 Usage
 -----
-..  Try not to use files in your examples,
-    but if you cannot avoid it then the (small) files must be added to
-    autotestdata\UsageData and the following tag unindented
-    .. include:: ../usagedata-note.txt
-
 **Example - CalculateChiSquared**
 
 .. testcode:: CalculateChiSquaredExample
 
-   # Create a host workspace
-   ws = CreateWorkspace(DataX=range(0,3), DataY=(0,2))
-   or
-   ws = CreateSampleWorkspace()
+    import numpy as np
+
+    # Create a data set
+    x = np.linspace(0,1,10)
+    y = 1.0 + 2.0 * x
+    e = np.sqrt(y)
+    ws = CreateWorkspace(DataX=x, DataY=y, DataE=e)
+
+    # Define a function
+    func = 'name=LinearBackground,A0=1.1,A1=1.9'
+
+    # Calculate the chi squared
+    chi2,chi2dof,chi2W,chi2Wdof = CalculateChiSquared(func,ws)
+
+    print 'Chi squared is %s' % chi2
+    print 'Chi squared / DOF is %s' % chi2dof
+    print 'Chi squared weighted is %s' % chi2W
+    print 'Chi squared weighted / DOF is %s' % chi2Wdof
+    print 
+
+    # Define a function that models the data exactly
+    func = 'name=LinearBackground,A0=1.0,A1=2.0'
 
-   wsOut = CalculateChiSquared()
+    # Calculate the chi squared
+    chi2,chi2dof,chi2W,chi2Wdof = CalculateChiSquared(func,ws)
 
-   # Print the result
-   print "The output workspace has %i spectra" % wsOut.getNumberHistograms()
+    print 'Chi squared is %s' % chi2
+    print 'Chi squared / DOF is %s' % chi2dof
+    print 'Chi squared weighted is %s' % chi2W
+    print 'Chi squared weighted / DOF is %s' % chi2Wdof
 
 Output:
 
 .. testoutput:: CalculateChiSquaredExample
 
-  The output workspace has ?? spectra
+    Chi squared is 0.0351851851852
+    Chi squared / DOF is 0.00439814814815
+    Chi squared weighted is 0.0266028783977
+    Chi squared weighted / DOF is 0.00332535979971
 
+    Chi squared is 0.0
+    Chi squared / DOF is 0.0
+    Chi squared weighted is 0.0
+    Chi squared weighted / DOF is 0.0
+
 .. categories::