Author: bugman
Date: Thu Nov 20 09:53:10 2014
New Revision: 26646
URL: http://svn.gna.org/viewcvs/relax?rev=26646&view=rev
Log:
More improvements for the align_tensor.matrix_angles user function description.
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=26646&r1=26645&r2=26646&view=diff
==============================================================================
--- trunk/user_functions/align_tensor.py (original)
+++ trunk/user_functions/align_tensor.py Thu Nov 20 09:53:10 2014
@@ -341,7 +341,7 @@
)
# Description.
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_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 mapped 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 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.")
@@ -351,7 +351,7 @@
uf.desc[-1].add_verbatim("""\
/ <A1 , A2> \
theta = arccos | ------------- | ,
- \ ||A1|| ||A2|| / \
+ \ ||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 spherical
tensor 5D basis set, the Am components are defined as")
uf.desc[-1].add_verbatim("""\
@@ -369,7 +369,9 @@
""")
uf.desc[-1].add_paragraph("and, for this complex notation, the angle is")
uf.desc[-1].add_verbatim("""\
- theta = arccos(Re(<A1|A2>) / (|A1|.|A2|)) , \
+ / Re(<A1|A2>) \
+ theta = arccos | ----------- | ,
+ \ |A1|.|A2| / \
""")
uf.desc[-1].add_paragraph("where the inner product is defined as")
uf.desc[-1].add_verbatim("""\
@@ -379,7 +381,13 @@
/__
m=-2,2 \
""")
-uf.desc[-1].add_paragraph("and where Am* = (-1)^m A-m, and the norm is defined
as |A1| = Re(sqrt(<A1|A1>)).")
+uf.desc[-1].add_paragraph("and where Am* = (-1)^m A-m, and the norm is defined
as |A1| = Re(sqrt(<A1|A1>)). For all other basis sets whereby the map is real
matrix -> real vector, the inter-tensor angle is defined as")
+uf.desc[-1].add_verbatim("""\
+ / <A1|A2> \
+ theta = arccos | --------- | ,
+ \ |A1|.|A2| / \
+""")
+uf.desc[-1].add_paragraph("where the inner product <A1|A2> is simply the
vector dot product and |A1| is the vector length.")
uf.backend = align_tensor.matrix_angles
uf.menu_text = "&matrix_angles"
uf.gui_icon = "oxygen.categories.applications-education"
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