r25317 - in /trunk/test_suite/shared_data/curve_fitting/numeric_gradient: Hessian.log Hessian.py -- August 26, 2014 - 19:38

Author: bugman
Date: Tue Aug 26 19:38:01 2014
New Revision: 25317

URL: http://svn.gna.org/viewcvs/relax?rev=25317&view=rev
Log:
Added a script and log file for calculating the numerical gradient for an 
exponential curve.

This uses the data at 
http://thread.gmane.org/gmane.science.nmr.relax.devel/6807/focus=6840 and
calculates the Hessian using the numdifftools.Hessian object construct and 
obtain the matrix, both
at the minimum and at a point away from the minimum.  The values will be used 
to construct a unit
test to check the C module implementation.


Added:
    trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.log
    trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.py
      - copied, changed from r25316, 
trunk/test_suite/shared_data/curve_fitting/numeric_gradient/integrate.py

Added: trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.log
URL: 
http://svn.gna.org/viewcvs/relax/trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.log?rev=25317&view=auto
==============================================================================
--- trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.log   
  (added)
+++ trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.log   
  Tue Aug 26 19:38:01 2014
@@ -0,0 +1,14 @@
+
+
+On-minimum:
+
+The Hessian at [1.0, 1000.0] is:
+[[  4.72548021e+03   6.00949488e-13]
+ [  6.00949488e-13   0.00000000e+00]]
+
+
+Off-minimum:
+
+The Hessian at [2.0, 500.0] is:
+[[ -4.11964848e+02   2.70730426e-09]
+ [  2.70730426e-09   0.00000000e+00]]

Copied: 
trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.py (from 
r25316, 
trunk/test_suite/shared_data/curve_fitting/numeric_gradient/integrate.py)
URL: 
http://svn.gna.org/viewcvs/relax/trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.py?p2=trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.py&p1=trunk/test_suite/shared_data/curve_fitting/numeric_gradient/integrate.py&r1=25316&r2=25317&rev=25317&view=diff
==============================================================================
--- trunk/test_suite/shared_data/curve_fitting/numeric_gradient/integrate.py  
  (original)
+++ trunk/test_suite/shared_data/curve_fitting/numeric_gradient/Hessian.py    
  Tue Aug 26 19:38:01 2014
@@ -3,13 +3,16 @@
 # Python module imports.
 from math import exp
 from numpy import array, float64
-from scipy.misc import derivative
+from numdifftools import Hessian
 
 
-def func_R(R):
+def func(params):
     """Calculate the chi-squared value."""
 
     global times, I, I0, errors
+
+    # Unpack the parameters.
+    R, IO = params
 
     # The intensities.
     back_calc = []
@@ -20,31 +23,6 @@
     chi2 = 0.0
     for i in range(len(times)):
         chi2 += (I[i] - back_calc[i])**2 / errors[i]**2
-
-    # Printout.
-    print("dR:  R=%f, I=%s, chi2=%f" % (R, back_calc, chi2))
-
-    # Return the value.
-    return chi2
-
-
-def func_I(I0):
-    """Calculate the chi-squared value."""
-
-    global times, I, R, errors
-
-    # The intensities.
-    back_calc = []
-    for i in range(len(times)):
-        back_calc.append(I0 * exp(-R*times[i]))
-
-    # The chi2.
-    chi2 = 0.0
-    for i in range(len(times)):
-        chi2 += (I[i] - back_calc[i])**2 / errors[i]**2
-
-    # Printout.
-    print("dI0: I0=%f, I=%s, chi2=%f" % (I0, back_calc, chi2))
 
     # Return the value.
     return chi2
@@ -63,16 +41,17 @@
 # The intensity errors.
 errors = [10.0, 10.0, 10.0, 10.0, 10.0]
 
-# The numeric gradient at the minimum.
+# Set up the Hessian function.
+d2func = Hessian(func)
+
+# The numeric Hessian at the minimum.
 print("\n\nOn-minimum:\n")
-grad_R = derivative(func_R, R, dx=1e-5, order=11)
-grad_I = derivative(func_I, I0, dx=1e-5, order=11)
-print("\nThe gradient at %s is:\n    %s" % ([R, I0], [grad_R, grad_I]))
+hess = d2func([R, I0])
+print("The Hessian at %s is:\n%s" % ([R, I0], hess))
 
-# The numeric gradient off the minimum.
+# The numeric Hessian off the minimum.
 print("\n\nOff-minimum:\n")
 R = 2.0
 I0 = 500.0
-grad_R = derivative(func_R, R, dx=1e-5, order=11)
-grad_I = derivative(func_I, I0, dx=1e-5, order=11)
-print("\nThe gradient at %s is:\n    %s" % ([R, I0], [grad_R, grad_I]))
+hess = d2func([R, I0])
+print("The Hessian at %s is:\n%s" % ([R, I0], hess))