Author: bugman
Date: Wed Nov 19 16:01:53 2014
New Revision: 26622
URL: http://svn.gna.org/viewcvs/relax?rev=26622&view=rev
Log:
Added the irreducible tensor notation of {A-2, A-1, A0, A1, A2} to the
alignment tensor object.
This follows from the definition of Sass et al, J. Am. Chem. Soc. 1999, 121,
2047-2055,
http://dx.doi.org/10.1021/ja983887w.
The equations of (2) were converted using Gaussian elimination to obtain a
reduced row echelon form,
so that the equations in terms of {A-2, A-1, A0, A1, A2} were derived. These
have been coded into
the alignment tensor object calc_Am2, calc_Am1, calc_A0, calc_A1 and calc_A2
methods respectively,
and the values can be obtained by accessing the Am2, Am1, A0, A1, and A2
objects.
To check that the implementation is correct, a unit test has been created to
compare the calculated
values with those determined using Pales.
Modified:
trunk/data_store/align_tensor.py
trunk/test_suite/unit_tests/_data_store/test_align_tensor.py
Modified: trunk/data_store/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/data_store/align_tensor.py?rev=26622&r1=26621&r2=26622&view=diff
==============================================================================
--- trunk/data_store/align_tensor.py (original)
+++ trunk/data_store/align_tensor.py Wed Nov 19 16:01:53 2014
@@ -23,9 +23,10 @@
"""The alignment tensor objects of the relax data store."""
# Python module imports.
-from re import search
+from math import pi, sqrt
from numpy import eye, float64, zeros
from numpy.linalg import det, eig, eigvals
+from re import search
# relax module imports.
from data_store.data_classes import Element
@@ -33,6 +34,12 @@
from lib.geometry.rotations import R_to_euler_zyz
from lib.errors import RelaxError
from lib.xml import fill_object_contents, xml_to_object
+
+
+# Constants (once off calculations for speed).
+fact_A2 = sqrt(2.0*pi / 15.0)
+fact_A1 = sqrt(8.0*pi / 15.0)
+fact_A0 = sqrt(4.0*pi / 5.0)
def calc_A(Axx, Ayy, Azz, Axy, Axz, Ayz):
@@ -396,6 +403,114 @@
return tensor_diag
+def calc_A0(Szz):
+ """Function for calculating the A0 irreducible component of the Saupe
order matrix.
+
+ The equation for calculating the parameter is::
+
+ / 4pi \ 1/2
+ A0 = | --- | Szz .
+ \ 5 /
+
+
+ @param Szz: The Szz component of the Saupe order matrix.
+ @type Szz: float
+ @return: The A0 irreducible component of the Saupe order matrix.
+ @rtype: float
+ """
+
+ # Calculate and return the A0 value.
+ return fact_A0 * Szz
+
+
+def calc_A1(Sxz, Syz):
+ """Function for calculating the A1 irreducible component of the Saupe
order matrix.
+
+ The equation for calculating the parameter is::
+
+ / 8pi \ 1/2
+ A1 = | --- | (Sxz + iSyz) .
+ \ 15 /
+
+
+ @param Sxz: The Sxz component of the Saupe order matrix.
+ @type Sxz: float
+ @param Syz: The Syz component of the Saupe order matrix.
+ @type Syz: float
+ @return: The A1 irreducible component of the Saupe order matrix.
+ @rtype: float
+ """
+
+ # Calculate and return the A1 value.
+ return fact_A1 * (Sxz + 1.j*Syz)
+
+
+def calc_A2(Sxx, Syy, Sxy):
+ """Function for calculating the A2 irreducible component of the Saupe
order matrix.
+
+ The equation for calculating the parameter is::
+
+ / 2pi \ 1/2
+ A2 = | --- | (Sxx - Syy + 2iSxy) .
+ \ 15 /
+
+
+ @param Sxx: The Sxx component of the Saupe order matrix.
+ @type Sxx: float
+ @param Syy: The Syy component of the Saupe order matrix.
+ @type Syy: float
+ @return: The A2 irreducible component of the Saupe order matrix.
+ @rtype: float
+ """
+
+ # Calculate and return the A2 value.
+ return fact_A2 * (Sxx - Syy + 2.j*Sxy)
+
+
+def calc_Am1(Sxz, Syz):
+ """Function for calculating the A-1 irreducible component of the Saupe
order matrix.
+
+ The equation for calculating the parameter is::
+
+ / 8pi \ 1/2
+ A-1 = - | --- | (Sxz - iSyz) .
+ \ 15 /
+
+
+ @param Sxz: The Sxz component of the Saupe order matrix.
+ @type Sxz: float
+ @param Syz: The Syz component of the Saupe order matrix.
+ @type Syz: float
+ @return: The A-1 irreducible component of the Saupe order matrix.
+ @rtype: float
+ """
+
+ # Calculate and return the A-1 value.
+ return -fact_A1 * (Sxz - 1.j*Syz)
+
+
+def calc_Am2(Sxx, Syy, Sxy):
+ """Function for calculating the A-2 irreducible component of the Saupe
order matrix.
+
+ The equation for calculating the parameter is::
+
+ / 2pi \ 1/2
+ A-2 = | --- | (Sxx - Syy - 2iSxy) ,
+ \ 15 /
+
+
+ @param Sxx: The Sxx component of the Saupe order matrix.
+ @type Sxx: float
+ @param Syy: The Syy component of the Saupe order matrix.
+ @type Syy: float
+ @return: The A-2 irreducible component of the Saupe order matrix.
+ @rtype: float
+ """
+
+ # Calculate and return the A-2 value.
+ return fact_A2 * (Sxx - Syy - 2.j*Sxy)
+
+
def calc_Sxx(Axx):
"""Function for calculating the Axx value.
@@ -905,6 +1020,12 @@
yield ('Sxxyy', ['Axx', 'Ayy'],
['Sxx', 'Syy'])
yield ('Szz', ['Axx', 'Ayy'],
['Sxx', 'Syy'])
+ yield ('Am2', ['Axx', 'Ayy', 'Axy'],
['Sxx', 'Syy', 'Sxy'])
+ yield ('Am1', ['Axy', 'Ayz'],
['Sxz', 'Syz'])
+ yield ('A0', ['Axx', 'Ayy'],
['Szz'])
+ yield ('A1', ['Axy', 'Ayz'],
['Sxz', 'Syz'])
+ yield ('A2', ['Axx', 'Ayy', 'Axy'],
['Sxx', 'Syy', 'Sxy'])
+
# Tertiary objects (dependant on the secondary objects).
yield ('Aa', ['Axx', 'Ayy', 'Axy', 'Axz', 'Ayz'],
['A_diag'])
yield ('Ar', ['Axx', 'Ayy', 'Axy', 'Axz', 'Ayz'],
['A_diag'])
Modified: trunk/test_suite/unit_tests/_data_store/test_align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/test_suite/unit_tests/_data_store/test_align_tensor.py?rev=26622&r1=26621&r2=26622&view=diff
==============================================================================
--- trunk/test_suite/unit_tests/_data_store/test_align_tensor.py
(original)
+++ trunk/test_suite/unit_tests/_data_store/test_align_tensor.py Wed
Nov 19 16:01:53 2014
@@ -98,6 +98,60 @@
# Test the matrices.
self.assertEqual(self.align_data.A_sim[0].tostring(),
tensor.tostring())
+
+
+ def test_irreducible_params(self):
+ """Test the irreducible parameters {A-2, A-1, A0, A1, A2}.
+
+ This is to test if the Pales results can be matched. The example
is::
+
+ DATA SAUPE_MATRIX S(zz) S(xx-yy) S(xy) S(xz)
S(yz)
+ DATA SAUPE -1.2856e-04 -5.6870e-04 -3.1704e-04
3.5099e-04 -1.7937e-04
+ DATA IRREDUCIBLE_REP A0 A1R A1I A2R
A2I
+ DATA IRREDUCIBLE -2.0380e-04 -4.5433e-04 -2.3218e-04
-3.6807e-04 4.1038e-04
+ DATA IRREDUCIBLE GENERAL_MAGNITUDE 1.0816e-03
+ """
+
+ # From Pales (S(zz) S(xx-yy) S(xy) S(xz) S(yz))
+ Azz = 2.0 / 3.0 * -1.2856e-04
+ Axxyy = 2.0 / 3.0 * -5.6870e-04
+ Axy = 2.0 / 3.0 * -3.1704e-04
+ Axz = 2.0 / 3.0 * 3.5099e-04
+ Ayz = 2.0 / 3.0 * -1.7937e-04
+
+ # Parameter conversion.
+ Axx = (Axxyy - Azz) / 2.0
+ Ayy = (-Axxyy - Azz) / 2.0
+
+ # Set the values.
+ self.align_data.set(param='Axx', value=Axx)
+ self.align_data.set(param='Ayy', value=Ayy)
+ self.align_data.set(param='Axy', value=Axy)
+ self.align_data.set(param='Axz', value=Axz)
+ self.align_data.set(param='Ayz', value=Ayz)
+
+ # Pales equivalent printout.
+ print("Pales output:\n")
+ print("DATA SAUPE_MATRIX S(zz) S(xx-yy) S(xy)
S(xz) S(yz)")
+ print("DATA SAUPE -1.2856e-04 -5.6870e-04 -3.1704e-04
3.5099e-04 -1.7937e-04")
+ print("")
+ print("DATA IRREDUCIBLE_REP A0 A1R A1I
A2R A2I ")
+ print("DATA IRREDUCIBLE -2.0380e-04 -4.5433e-04 -2.3218e-04
-3.6807e-04 4.1038e-04")
+ print("DATA IRREDUCIBLE GENERAL_MAGNITUDE 1.0816e-03")
+ print("")
+ print("Calculated values:\n")
+ print("A0: %15.4e" % self.align_data.A0.real)
+ print("A1: %15.4e %11.4ei" % (self.align_data.A1.real,
self.align_data.A1.imag))
+ print("Am1: %15.4e %11.4ei" % (self.align_data.Am1.real,
self.align_data.Am1.imag))
+ print("A2: %15.4e %11.4ei" % (self.align_data.A2.real,
self.align_data.A2.imag))
+ print("Am2: %15.4e %11.4ei" % (self.align_data.Am2.real,
self.align_data.Am2.imag))
+
+ # Check that the values match Pales (guessing that Pales is using
the negative indices).
+ self.assertAlmostEqual(self.align_data.A0, -2.0380e-04)
+ self.assertAlmostEqual(self.align_data.Am1.real, -4.5433e-04)
+ self.assertAlmostEqual(self.align_data.Am1.imag, -2.3218e-04)
+ self.assertAlmostEqual(self.align_data.Am2.real, -3.6807e-04)
+ self.assertAlmostEqual(self.align_data.Am2.imag, 4.1038e-04)
def test_set_Szz(self):
r26622 - in /trunk: data_store/align_tensor.py test_suite/unit_tests/_data_store/test_align_tensor.py