Author: bugman
Date: Wed Nov 19 17:29:26 2014
New Revision: 26626
URL: http://svn.gna.org/viewcvs/relax?rev=26626&view=rev
Log:
Added the 'irreducible 5D' basis set option to the align_tensor.svd user
function.
This is for the inter-tensor vector angle for the irreducible 5D basis set
{A-2, A-1, A0, A1, A2}.
Its results match that of the 'unitary 9D' basis set.
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=26626&r1=26625&r2=26626&view=diff
==============================================================================
--- trunk/pipe_control/align_tensor.py (original)
+++ trunk/pipe_control/align_tensor.py Wed Nov 19 17:29:26 2014
@@ -1667,24 +1667,35 @@
raise RelaxNoTensorError('alignment', tensor)
-def svd(basis_set='unitary 9D', tensors=None):
+def svd(basis_set='irreducible 5D', tensors=None):
"""Calculate the singular values of all the loaded tensors.
The basis set can be set to one of:
- 'unitary 9D', the unitary 9D basis set {Sxx, Sxy, Sxz, Syx, Syy, Syz,
Szx, Szy, Szz}. The is the only basis set which is a linear map, hence angles
are preserved.
- '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.
-
- If the selected basis set is the default of 'unitary 9D', the matrix on
which SVD will be performed will be::
-
- | Sxx1 Sxy1 Sxz1 Syx1 Syy1 Syz1 Szx1 Szy1 Szz1 |
- | Sxx2 Sxy2 Sxz2 Syx2 Syy2 Syz2 Szx2 Szy2 Szz2 |
- | Sxx3 Sxy3 Sxz3 Syx3 Syy3 Syz3 Szx3 Szy3 Szz3 |
- | . . . . . . . . . |
- | . . . . . . . . . |
- | . . . . . . . . . |
- | SxxN SxyN SxzN SyxN SyyN SyzN SzxN SzyN SzzN |
+ - 'irreducible 5D', the irreducible 5D basis set {A-2, A-1, A0, A1,
A2}. This is a linear map, hence angles are preserved.
+ - 'unitary 9D', the unitary 9D basis set {Sxx, Sxy, Sxz, Syx, Syy,
Syz, Szx, Szy, Szz}. This is a linear map, hence angles are preserved.
+ - 'unitary 5D', the unitary 5D basis set {Sxx, Syy, Sxy, Sxz, Syz}.
This is a non-linear map, hence angles are not preserved.
+ - 'geometric 5D', 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.
+
+ 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) |
+ | . . . . . |
+ | . . . . . |
+ | . . . . . |
+ | S-2(N) S-1(N) S0(N) S1(N) S2(N) |
+
+ If the selected basis set is 'unitary 9D', the matrix on which SVD will be
performed will be::
+
+ | Sxx1 Sxy1 Sxz1 Syx1 Syy1 Syz1 Szx1 Szy1 Szz1 |
+ | Sxx2 Sxy2 Sxz2 Syx2 Syy2 Syz2 Szx2 Szy2 Szz2 |
+ | Sxx3 Sxy3 Sxz3 Syx3 Syy3 Syz3 Szx3 Szy3 Szz3 |
+ | . . . . . . . . . |
+ | . . . . . . . . . |
+ | . . . . . . . . . |
+ | SxxN SxyN SxzN SyxN SyyN SyzN SzxN SzyN SzzN |
Otherwise if the selected basis set is 'unitary 5D', the matrix for SVD
is::
@@ -1706,6 +1717,20 @@
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |
+ For the irreducible basis set, the Sm components are defined as::
+
+ / 4pi \ 1/2
+ S0 = | --- | Szz ,
+ \ 5 /
+
+ / 8pi \ 1/2
+ S+/-1 = +/- | --- | (Sxz +/- iSyz) ,
+ \ 15 /
+
+ / 2pi \ 1/2
+ S+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
+ \ 15 /
+
The relationships between the geometric and unitary basis sets are::
Szz = - Sxx - Syy,
@@ -1714,14 +1739,14 @@
The SVD values and condition number are dependant upon the basis set
chosen.
- @param basis_set: The basis set to use for the SVD. This can be one of
'unitary 9D', 'unitary 5D' or 'geometric 5D'.
+ @param basis_set: The basis set to use for the SVD. This can be one of
"irreducible 5D", "unitary 9D", "unitary 5D" or "geometric 5D".
@type basis_set: str
@param tensors: The list of alignment tensor IDs to calculate
inter-matrix angles between. If None, all tensors will be used.
@type tensors: None or list of str
"""
# Argument check.
- allowed = ['unitary 9D', 'unitary 5D', 'geometric 5D']
+ allowed = ['irreducible 5D', 'unitary 9D', 'unitary 5D', 'geometric 5D']
if basis_set not in allowed:
raise RelaxError("The basis set of '%s' is not one of %s." %
(basis_set, allowed))
@@ -1739,6 +1764,8 @@
# Create the matrix to apply SVD on.
if basis_set in ['unitary 9D']:
matrix = zeros((tensor_num, 9), float64)
+ elif basis_set in ['irreducible 5D']:
+ matrix = zeros((tensor_num, 5), complex128)
else:
matrix = zeros((tensor_num, 5), float64)
@@ -1749,8 +1776,16 @@
if tensors and tensor.name not in tensors:
continue
+ # 5D irreducible basis set.
+ if basis_set == 'irreducible 5D':
+ matrix[i, 0] = tensor.Am2
+ matrix[i, 1] = tensor.Am1
+ matrix[i, 2] = tensor.A0
+ matrix[i, 3] = tensor.A1
+ matrix[i, 4] = tensor.A2
+
# 5D unitary basis set.
- if basis_set == 'unitary 9D':
+ elif basis_set == 'unitary 9D':
matrix[i, 0] = tensor.Sxx
matrix[i, 1] = tensor.Sxy
matrix[i, 2] = tensor.Sxz
@@ -1790,7 +1825,9 @@
cdp.align_tensors.cond_num = s[0] / s[-1]
# Print out.
- if basis_set == 'unitary 9D':
+ if basis_set == 'irreducible 5D':
+ sys.stdout.write("SVD for the irreducible 5D vectors {A-2, A-1, A0,
A1, A2}.\n")
+ elif basis_set == 'unitary 9D':
sys.stdout.write("SVD for the unitary 9D vectors {Sxx, Sxy, Sxz, Syx,
Syy, Syz, Szx, Szy, Szz}.\n")
elif basis_set == 'unitary 5D':
sys.stdout.write("SVD for the unitary 5D vectors {Sxx, Syy, Sxy, Sxz,
Syz}.\n")
Modified: trunk/user_functions/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/user_functions/align_tensor.py?rev=26626&r1=26625&r2=26626&view=diff
==============================================================================
--- trunk/user_functions/align_tensor.py (original)
+++ trunk/user_functions/align_tensor.py Wed Nov 19 17:29:26 2014
@@ -443,13 +443,13 @@
uf.display = True
uf.add_keyarg(
name = "basis_set",
- default = "unitary 9D",
+ default = "irreducible 5D",
py_type = "str",
desc_short = "basis set",
desc = "The basis set to operate with.",
wiz_element_type = "combo",
- wiz_combo_choices = ["Unitary 9D {Sxx, Sxy, Sxz, ..., Szz}", "Unitary 5D
{Sxx, Syy, Sxy, Sxz, Syz}", "Geometric 5D {Szz, Sxxyy, Sxy, Sxz, Syz}"],
- wiz_combo_data = ["unitary 9D", "unitary 5D", "geometric 5D"]
+ wiz_combo_choices = ["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 = ["irreducible 5D", "unitary 9D", "unitary 5D", "geometric
5D"]
)
uf.add_keyarg(
name = "tensors",
@@ -464,10 +464,21 @@
# Description.
uf.desc.append(Desc_container())
uf.desc[-1].add_paragraph("This will perform a singular value decomposition of
all tensors loaded for the current data pipe. The values are highly dependent
on the chosen basis set. This can be one of:")
-uf.desc[-1].add_item_list_element("'unitary 9D'", "The unitary 9D basis set
{Sxx, Sxy, Sxz, Syx, Syy, Syz, Szx, Szy, Szz}. The is the only basis set which
is a linear map, hence angles are preserved.")
-uf.desc[-1].add_item_list_element("'unitary 5D'", "The unitary 5D basis set
{Sxx, Syy, Sxy, Sxz, Syz}.")
-uf.desc[-1].add_item_list_element("'geometric 5D'", "The geometric 5D basis
set {Szz, Sxxyy, Sxy, Sxz, Syz}. This is also the Pales standard notation.")
-uf.desc[-1].add_paragraph("If the selected basis set is the default of
'unitary 9D', the matrix on which SVD will be performed will be:")
+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 numbers are preserved.")
+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 numbers 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 numbers 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 numbers are not preserved. This is also the
Pales standard notation.")
+uf.desc[-1].add_paragraph("If the selected basis set is the default of
'irreducible 5D', the matrix on which SVD will be performed will be:")
+uf.desc[-1].add_verbatim("""\
+ | 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) |
+ | . . . . . |
+ | . . . . . |
+ | . . . . . |
+ | A-2(N) A-1(N) A0(N) A1(N) A2(N) |\
+""")
+uf.desc[-1].add_paragraph("If the selected basis set is 'unitary 9D', the
matrix on which SVD will be performed will be:")
uf.desc[-1].add_verbatim("""\
| Sxx1 Sxy1 Sxz1 Syx1 Syy1 Syz1 Szx1 Szy1 Szz1 |
| Sxx2 Sxy2 Sxz2 Syx2 Syy2 Syz2 Szx2 Szy2 Szz2 |
@@ -497,7 +508,21 @@
| . . . . . |
| SzzN SxxyyN SxyN SxzN SyzN |\
""")
-uf.desc[-1].add_paragraph("The relationships between the geometric and unitary
basis sets are:")
+uf.desc[-1].add_paragraph("For the irreducible basis set, the Sm components
are defined as")
+uf.desc[-1].add_verbatim("""\
+ / 4pi \ 1/2
+ S0 = | --- | Szz ,
+ \ 5 /
+
+ / 8pi \ 1/2
+ S+/-1 = +/- | --- | (Sxz +/- iSyz) ,
+ \ 15 /
+
+ / 2pi \ 1/2
+ S+/-2 = | --- | (Sxx - Syy +/- 2iSxy) .
+ \ 15 / \
+""")
+uf.desc[-1].add_paragraph("The relationships between the geometric and unitary
basis sets are")
uf.desc[-1].add_verbatim("""\
Szz = - Sxx - Syy,
Sxxyy = Sxx - Syy.\
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