Author: bugman
Date: Wed Nov 19 17:33:51 2014
New Revision: 26627
URL: http://svn.gna.org/viewcvs/relax?rev=26627&view=rev
Log:
Editing of the description for the 'irreducible 5D' alignment tensor basis set.
This is for the align_tensor.matrix_angles and align_tensor.svd user functions.
All Sm element have
been converted to Am.
Modified:
trunk/pipe_control/align_tensor.py
trunk/user_functions/align_tensor.py
Modified: trunk/pipe_control/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/pipe_control/align_tensor.py?rev=26627&r1=26626&r2=26627&view=diff
==============================================================================
--- trunk/pipe_control/align_tensor.py (original)
+++ trunk/pipe_control/align_tensor.py Wed Nov 19 17:33:51 2014
@@ -889,7 +889,7 @@
The basis set defines how the angles are calculated:
- "matrix", the standard inter-matrix angle. The angle is calculated
via the Euclidean inner product of the alignment matrices in rank-2, 3D form
divided by the Frobenius norm ||A||_F of the matrices.
- - "irreducible 5D", the irreducible 5D basis set {S-2, S-1, S0, S1,
S2}.
+ - "irreducible 5D", the irreducible 5D basis set {A-2, A-1, A0, A1,
A2}.
- "unitary 5D", the unitary 5D basis set {Sxx, Syy, Sxy, Sxz, Syz}.
- "geometric 5D", the geometric 5D basis set {Szz, Sxxyy, Sxy, Sxz,
Syz}. This is also the Pales standard notation.
@@ -994,10 +994,10 @@
# Header printout.
if basis_set == 'matrix':
sys.stdout.write("Standard inter-tensor matrix angles in degress using
the Euclidean inner product divided by the Frobenius norms (theta =
arccos(<A1,A2>/(||A1||.||A2||)))")
+ elif basis_set == 'irreducible 5D':
+ sys.stdout.write("Inter-tensor vector angles in degrees for the
irreducible 5D vectors {A-2, A-1, A0, A1, A2}")
elif basis_set == 'unitary 9D':
sys.stdout.write("Inter-tensor vector angles in degrees for the
unitary 9D vectors {Sxx, Sxy, Sxz, Syx, Syy, Syz, Szx, Szy, Szz}")
- elif basis_set == 'irreducible 5D':
- sys.stdout.write("Inter-tensor vector angles in degrees for the
irreducible 5D vectors {S-2, S-1, S0, S1, S2}")
elif basis_set == 'unitary 5D':
sys.stdout.write("Inter-tensor vector angles in degrees for the
unitary 5D vectors {Sxx, Syy, Sxy, Sxz, Syz}")
elif basis_set == 'geometric 5D':
@@ -1679,13 +1679,13 @@
If the selected basis set is the default of 'irreducible 5D', the matrix
on which SVD will be performed will be::
- | S-2(1) S-1(1) S0(1) S1(1) S2(1) |
- | S-2(2) S-1(2) S0(2) S1(2) S2(2) |
- | S-2(3) S-1(3) S0(3) S1(3) S2(3) |
+ | A-2(1) A-1(1) A0(1) A1(1) A2(1) |
+ | A-2(2) A-1(2) A0(2) A1(2) A2(2) |
+ | A-2(3) A-1(3) A0(3) A1(3) A2(3) |
| . . . . . |
| . . . . . |
| . . . . . |
- | S-2(N) S-1(N) S0(N) S1(N) S2(N) |
+ | A-2(N) A-1(N) A0(N) A1(N) A2(N) |
If the selected basis set is 'unitary 9D', the matrix on which SVD will be
performed will be::
@@ -1717,18 +1717,18 @@
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |
- For the irreducible basis set, the Sm components are defined as::
+ For the irreducible basis set, the Am components are defined as::
/ 4pi \ 1/2
- S0 = | --- | Szz ,
+ A0 = | --- | Szz ,
\ 5 /
/ 8pi \ 1/2
- S+/-1 = +/- | --- | (Sxz +/- iSyz) ,
+ A+/-1 = +/- | --- | (Sxz +/- iSyz) ,
\ 15 /
/ 2pi \ 1/2
- S+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
+ A+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
\ 15 /
The relationships between the geometric and unitary basis sets are::
Modified: trunk/user_functions/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/user_functions/align_tensor.py?rev=26627&r1=26626&r2=26627&view=diff
==============================================================================
--- trunk/user_functions/align_tensor.py (original)
+++ trunk/user_functions/align_tensor.py Wed Nov 19 17:33:51 2014
@@ -307,7 +307,7 @@
desc_short = "basis set",
desc = "The basis set to operate with.",
wiz_element_type = "combo",
- wiz_combo_choices = ["Standard matrix angles via the Euclidean inner
product", "Irreducible 5D {S-2, S-1, S0, S1, S2}", "Unitary 9D {Sxx, Sxy, Sxz,
..., Szz}", "Unitary 5D {Sxx, Syy, Sxy, Sxz, Syz}", "Geometric 5D {Szz, Sxxyy,
Sxy, Sxz, Syz}"],
+ wiz_combo_choices = ["Standard matrix angles via the Euclidean inner
product", "Irreducible 5D {A-2, A-1, A0, A1, A2}", "Unitary 9D {Sxx, Sxy, Sxz,
..., Szz}", "Unitary 5D {Sxx, Syy, Sxy, Sxz, Syz}", "Geometric 5D {Szz, Sxxyy,
Sxy, Sxz, Syz}"],
wiz_combo_data = ["matrix", "irreducible 5D", "unitary 9D", "unitary 5D",
"geometric 5D"]
)
uf.add_keyarg(
@@ -324,7 +324,7 @@
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 5D basis sets,
the matrices are first converted to a 5D vector form and then then the
inter-vector angles, rather than inter-matrix angles, are calculated. The
angles are dependent upon the basis set:")
uf.desc[-1].add_item_list_element("'matrix'", "The standard inter-tensor
matrix angle. This is the default option. The angle is calculated via 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
angle for the irreducible 5D basis set {S-2, S-1, S0, S1, S2}.")
+uf.desc[-1].add_item_list_element("'irreducible 5D'", "The inter-tensor vector
angle for the irreducible 5D basis set {A-2, A-1, A0, A1, A2}.")
uf.desc[-1].add_item_list_element("'unitary 9D'", "The inter-tensor vector
angle for the unitary 9D basis set {Sxx, Sxy, Sxz, Syx, Syy, Syz, Szx, Szy,
Szz}.")
uf.desc[-1].add_item_list_element("'unitary 5D'", "The inter-tensor vector
angle for the unitary 5D basis set {Sxx, Syy, Sxy, Sxz, Syz}.")
uf.desc[-1].add_item_list_element("'geometric 5D'", "The inter-tensor vector
angle for the geometric 5D basis set {Szz, Sxxyy, Sxy, Sxz, Syz}. This is also
the Pales standard notation.")
@@ -334,18 +334,18 @@
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 basis set, the
Sm 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 basis set, the
Am components are defined as")
uf.desc[-1].add_verbatim("""\
/ 4pi \ 1/2
- S0 = | --- | Szz ,
+ A0 = | --- | Szz ,
\ 5 /
/ 8pi \ 1/2
- S+/-1 = +/- | --- | (Sxz +/- iSyz) ,
+ A+/-1 = +/- | --- | (Sxz +/- iSyz) ,
\ 15 /
/ 2pi \ 1/2
- S+/-2 = | --- | (Sxx - Syy +/- 2iSxy) ,
+ A+/-2 = | --- | (Sxx - Syy +/- 2iSxy) ,
\ 15 / \
""")
uf.desc[-1].add_paragraph("and, for this complex notation, the angle is")
@@ -356,11 +356,11 @@
uf.desc[-1].add_verbatim("""\
___
\ 1 2*
- <A1|A2> = > Sm . Sm ,
+ <A1|A2> = > Am . Am ,
/__
m=-2,2 \
""")
-uf.desc[-1].add_paragraph("and where Sm* = (-1)^m S-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>)).")
uf.desc[-1].add_paragraph("The inner product solution is a linear map and
thereby preserves angles, whereas the {Sxx, Syy, Sxy, Sxz, Syz} and {Szz,
Sxxyy, Sxy, Sxz, Syz} basis sets are non-linear maps which do not preserve
angles. Therefore the angles from all three basis sets will be different.")
uf.backend = align_tensor.matrix_angles
uf.menu_text = "&matrix_angles"
@@ -508,18 +508,18 @@
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |\
""")
-uf.desc[-1].add_paragraph("For the irreducible basis set, the Sm components
are defined as")
+uf.desc[-1].add_paragraph("For the irreducible basis set, the Am components
are defined as")
uf.desc[-1].add_verbatim("""\
/ 4pi \ 1/2
- S0 = | --- | Szz ,
+ A0 = | --- | Szz ,
\ 5 /
/ 8pi \ 1/2
- S+/-1 = +/- | --- | (Sxz +/- iSyz) ,
+ A+/-1 = +/- | --- | (Sxz +/- iSyz) ,
\ 15 /
/ 2pi \ 1/2
- S+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
+ A+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
\ 15 / \
""")
uf.desc[-1].add_paragraph("The relationships between the geometric and unitary
basis sets are")
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