r25370 - /trunk/specific_analyses/relax_disp/estimate_r2eff.py -- August 28, 2014 - 10:31

Author: tlinnet
Date: Thu Aug 28 10:31:22 2014
New Revision: 25370

URL: http://svn.gna.org/viewcvs/relax?rev=25370&view=rev
Log:
Tried to improve docstring for API documentation.

task #7822(https://gna.org/task/index.php?7822): Implement user function to 
estimate R2eff and associated errors for exponential curve fitting.

Modified:
    trunk/specific_analyses/relax_disp/estimate_r2eff.py

Modified: trunk/specific_analyses/relax_disp/estimate_r2eff.py
URL: 
http://svn.gna.org/viewcvs/relax/trunk/specific_analyses/relax_disp/estimate_r2eff.py?rev=25370&r1=25369&r2=25370&view=diff
==============================================================================
--- trunk/specific_analyses/relax_disp/estimate_r2eff.py        (original)
+++ trunk/specific_analyses/relax_disp/estimate_r2eff.py        Thu Aug 28 
10:31:22 2014
@@ -197,19 +197,19 @@
 
     If the minimisation uses the weighted least-squares function:
 
-        f_i = (Y(x, t_i) - y_i) / \sigma_i
-
-    then the covariance matrix above gives the statistical error on the 
best-fit parameters resulting from the Gaussian errors \sigma_i on the 
underlying data y_i.
-
-    This can be verified from the relation \delta f = J \delta c and the 
fact that the fluctuations in f from the data y_i are normalised by \sigma_i
-    and so satisfy <\delta f \delta f^T> = I.
+        f_i = (Y(x, t_i) - y_i) / sigma_i
+
+    then the covariance matrix above gives the statistical error on the 
best-fit parameters resulting from the Gaussian errors 'sigma_i' on the 
underlying data 'y_i'.
+
+    This can be verified from the relation 'd_f = J d_c' and the fact that 
the fluctuations in 'f from the data 'y_i' are normalised by 'sigma_i'
+    and so satisfy <d_f d_f^T> = I.
 
     For an unweighted least-squares function f_i = (Y(x, t_i) - y_i) the 
covariance matrix above should be multiplied by
     the variance of the residuals about the best-fit
 
-        \sigma^2 = \sum (y_i - Y(x, t_i))^2 / (n-p)
-
-    to give the variance-covariance matrix \sigma^2 C.
+        sigma^2 = sum ( (y_i - Y(x, t_i))^2 / (n-p) )
+
+    to give the variance-covariance matrix sigma^2 C.
     This estimates the statistical error on the best-fit parameters from the 
scatter of the underlying data.
 
     See: