Author: bugman
Date: Thu Nov 20 09:15:37 2014
New Revision: 26643
URL: http://svn.gna.org/viewcvs/relax?rev=26643&view=rev
Log:
Expanded the 'irreducible 5D' text in the align_tensor.matrix_angles and
align_tensor.svd user functions.
This now explains that these are the coefficients for the spherical harmonic
decomposition.
Modified:
trunk/user_functions/align_tensor.py
Modified: trunk/user_functions/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/user_functions/align_tensor.py?rev=26643&r1=26642&r2=26643&view=diff
==============================================================================
--- trunk/user_functions/align_tensor.py (original)
+++ trunk/user_functions/align_tensor.py Thu Nov 20 09:15:37 2014
@@ -343,7 +343,7 @@
uf.desc.append(Desc_container())
uf.desc[-1].add_paragraph("This will calculate the inter-matrix angles between
all loaded alignment tensors for the current data pipe. For the vector basis
sets, the matrices are first converted to vector form and then then the
inter-vector angles rather than inter-matrix angles are calculated. The angles
are dependent upon the basis set - linear maps produce identical results
whereas non-linear maps result in different angles. The basis set can be one
of:")
uf.desc[-1].add_item_list_element("'matrix'", "The standard inter-matrix
angles. This default option is a linear map, hence angles are preserved. The
angle is calculated via the arccos of the Euclidean inner product of the
alignment matrices in rank-2, 3D form divided by the Frobenius norm ||A||_F of
the matrices.")
-uf.desc[-1].add_item_list_element("'irreducible 5D'", "The inter-tensor vector
angles for the irreducible 5D basis set {A-2, A-1, A0, A1, A2}. This is a
linear map, hence angles are preserved.")
+uf.desc[-1].add_item_list_element("'irreducible 5D'", "The inter-tensor vector
angles for the irreducible spherical tensor 5D basis set {A-2, A-1, A0, A1,
A2}. This is a linear map, hence angles are preserved. These are the
spherical harmonic decomposition coefficients.")
uf.desc[-1].add_item_list_element("'unitary 9D'", "The inter-tensor vector
angles for the unitary 9D basis set {Sxx, Sxy, Sxz, Syx, Syy, Syz, Szx, Szy,
Szz}. This is a linear map, hence angles are preserved.")
uf.desc[-1].add_item_list_element("'unitary 5D'", "The inter-tensor vector
angles for the unitary 5D basis set {Sxx, Syy, Sxy, Sxz, Syz}. This is a
non-linear map, hence angles are not preserved.")
uf.desc[-1].add_item_list_element("'geometric 5D'", "The inter-tensor vector
angles for the geometric 5D basis set {Szz, Sxxyy, Sxy, Sxz, Syz}. This is a
non-linear map, hence angles are not preserved. This is also the Pales
standard notation.")
@@ -353,7 +353,7 @@
theta = arccos | ------------- | ,
\ ||A1|| ||A2|| / \
""")
-uf.desc[-1].add_paragraph("where <a,b> is the Euclidean inner product and
||a|| is the Frobenius norm of the matrix. For the irreducible 5D basis set,
the Am components are defined as")
+uf.desc[-1].add_paragraph("where <a,b> is the Euclidean inner product and
||a|| is the Frobenius norm of the matrix. For the irreducible spherical
tensor 5D basis set, the Am components are defined as")
uf.desc[-1].add_verbatim("""\
/ 4pi \ 1/2
A0 = | --- | Szz ,
@@ -491,7 +491,7 @@
# Description.
uf.desc.append(Desc_container())
uf.desc[-1].add_paragraph("This will perform a singular value decomposition
for all alignment tensors and calculate the condition number. The singular
values and condition number are dependent on the basis set - linear maps
produce identical results whereas non-linear maps result in different values.
The basis set can be one of:")
-uf.desc[-1].add_item_list_element("'irreducible 5D'", "The irreducible 5D
basis set {A-2, A-1, A0, A1, A2}. This is a linear map, hence angles, singular
values, and condition number are preserved.")
+uf.desc[-1].add_item_list_element("'irreducible 5D'", "The irreducible
spherical tensor 5D basis set {A-2, A-1, A0, A1, A2}. This is a linear map,
hence angles, singular values, and condition number are preserved. These are
the spherical harmonic decomposition coefficients.")
uf.desc[-1].add_item_list_element("'unitary 9D'", "The unitary 9D basis set
{Sxx, Sxy, Sxz, Syx, Syy, Syz, Szx, Szy, Szz}. This is a linear map, hence
angles, singular values, and condition number are preserved.")
uf.desc[-1].add_item_list_element("'unitary 5D'", "The unitary 5D basis set
{Sxx, Syy, Sxy, Sxz, Syz}. This is a non-linear map, hence angles, singular
values, and condition number are not preserved.")
uf.desc[-1].add_item_list_element("'geometric 5D'", "The geometric 5D basis
set {Szz, Sxxyy, Sxy, Sxz, Syz}. This is a non-linear map, hence angles,
singular values, and condition number are not preserved. This is also the
Pales standard notation.")
@@ -535,7 +535,7 @@
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |\
""")
-uf.desc[-1].add_paragraph("For the irreducible basis set, the Am components
are defined as")
+uf.desc[-1].add_paragraph("For the irreducible spherical tensor basis set, the
Am components are defined as")
uf.desc[-1].add_verbatim("""\
/ 4pi \ 1/2
A0 = | --- | Szz ,
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