Author: bugman
Date: Wed Nov 19 16:40:12 2014
New Revision: 26625
URL: http://svn.gna.org/viewcvs/relax?rev=26625&view=rev
Log:
Added the 'irreducible 5D' basis set option to the align_tensor.matrix_angles
user function.
This is for the inter-tensor vector angle for the irreducible 5D basis set
{S-2, S-1, S0, S1, S2}.
Its results match that of the standard tensor angle as well as the 'unitary 9D'
basis sets.
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=26625&r1=26624&r2=26625&view=diff
==============================================================================
--- trunk/pipe_control/align_tensor.py (original)
+++ trunk/pipe_control/align_tensor.py Wed Nov 19 16:40:12 2014
@@ -25,7 +25,7 @@
# Python module imports.
from copy import deepcopy
from math import acos, pi, sqrt
-from numpy import arccos, dot, float64, inner, linalg, zeros
+from numpy import arccos, complex128, dot, float64, inner, linalg, zeros
from numpy.linalg import norm
import sys
from warnings import warn
@@ -35,6 +35,7 @@
from lib.alignment.alignment_tensor import calc_chi_tensor, kappa
from lib.errors import RelaxError, RelaxNoTensorError, RelaxTensorError,
RelaxUnknownParamCombError, RelaxUnknownParamError
from lib.geometry.angles import wrap_angles
+from lib.geometry.vectors import vector_angle_complex_conjugate
from lib.io import write_data
from lib.text.sectioning import section, subsection
from lib.warnings import RelaxWarning
@@ -888,18 +889,19 @@
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}.
- "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.
- @param basis_set: The basis set to use for calculating the inter-matrix
angles. It can be one of "matrix", "unitary 5D", or "geometric 5D".
+ @param basis_set: The basis set to use for calculating the inter-matrix
angles. It can be one of "matrix", "irreducible 5D", "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 = ['matrix', 'unitary 9D', 'unitary 5D', 'geometric 5D']
+ allowed = ['matrix', 'unitary 9D', 'irreducible 5D', '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))
@@ -921,6 +923,9 @@
matrix = zeros((tensor_num, 9), float64)
elif basis_set in ['unitary 5D', 'geometric 5D']:
matrix = zeros((tensor_num, 5), float64)
+ elif basis_set in ['irreducible 5D']:
+ matrix = zeros((tensor_num, 5), complex128)
+ matrix_conj = zeros((tensor_num, 5), complex128)
# Loop over the tensors.
i = 0
@@ -953,6 +958,21 @@
matrix[i, 3] = tensor.Sxz
matrix[i, 4] = tensor.Syz
+ # 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
+
+ # The (-1)^mS-m conjugate.
+ matrix_conj[i, 0] = tensor.A2
+ matrix_conj[i, 1] = -tensor.A1
+ matrix_conj[i, 2] = tensor.A0
+ matrix_conj[i, 3] = -tensor.Am1
+ matrix_conj[i, 4] = tensor.Am2
+
# 5D geometric basis set.
elif basis_set == 'geometric 5D':
matrix[i, 0] = tensor.Szz
@@ -976,6 +996,8 @@
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 == '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':
@@ -1014,6 +1036,10 @@
# The angle.
theta = arccos(delta)
+
+ # The irreducible complex conjugate angles.
+ if basis_set in ['irreducible 5D']:
+ theta = vector_angle_complex_conjugate(v1=matrix[i],
v2=matrix[j], v1_conj=matrix_conj[i], v2_conj=matrix_conj[j])
# The full matrix angle.
elif basis_set in ['matrix']:
Modified: trunk/user_functions/align_tensor.py
URL:
http://svn.gna.org/viewcvs/relax/trunk/user_functions/align_tensor.py?rev=26625&r1=26624&r2=26625&view=diff
==============================================================================
--- trunk/user_functions/align_tensor.py (original)
+++ trunk/user_functions/align_tensor.py Wed Nov 19 16:40:12 2014
@@ -307,8 +307,8 @@
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", "Unitary 9D {Sxx, Sxy, Sxz, ..., Szz}", "Unitary 5D {Sxx, Syy, Sxy,
Sxz, Syz}", "Geometric 5D {Szz, Sxxyy, Sxy, Sxz, Syz}"],
- wiz_combo_data = ["matrix", "unitary 9D", "unitary 5D", "geometric 5D"]
+ 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_data = ["matrix", "irreducible 5D", "unitary 9D", "unitary 5D",
"geometric 5D"]
)
uf.add_keyarg(
name = "tensors",
@@ -324,16 +324,43 @@
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("'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.")
-uf.desc[-1].add_paragraph("The full matrix angle via the Euclidean inner
product is defined as:")
-uf.desc[-1].add_verbatim("""
+uf.desc[-1].add_paragraph("The full matrix angle via the Euclidean inner
product is defined as")
+uf.desc[-1].add_verbatim("""\
/ <A1 , A2> \
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.")
+ \ ||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_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("and, for this complex notation, the angle is")
+uf.desc[-1].add_verbatim("""\
+ theta = arccos(Re(<A1|A2>) / (|A1|.|A2|)) , \
+""")
+uf.desc[-1].add_paragraph("where the inner product is defined as")
+uf.desc[-1].add_verbatim("""\
+ ___
+ \ 1 2*
+ <A1|A2> = > Sm . Sm ,
+ /__
+ 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("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"
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