Author: bugman
Date: Fri Jul 25 11:19:15 2008
New Revision: 6967
URL: http://svn.gna.org/viewcvs/relax?rev=6967&view=rev
Log:
Wrote the average_rdc_tensor_dDij_dAmn() function.
This calculates the ensemble averaged RDC gradient element for the Amn
partial derivative.
Modified:
branches/rdc_analysis/maths_fns/n_state_model.py
branches/rdc_analysis/maths_fns/rdc.py
Modified: branches/rdc_analysis/maths_fns/n_state_model.py
URL:
http://svn.gna.org/viewcvs/relax/branches/rdc_analysis/maths_fns/n_state_model.py?rev=6967&r1=6966&r2=6967&view=diff
==============================================================================
--- branches/rdc_analysis/maths_fns/n_state_model.py (original)
+++ branches/rdc_analysis/maths_fns/n_state_model.py Fri Jul 25 11:19:15 2008
@@ -388,8 +388,8 @@
- i, the index over alignments,
- j, the index over spin systems,
- c, the index over the N-states (or over the structures),
- - n, the index over the first dimension of the alignment tensor
n = {x, y, z},
- - m, the index over the second dimension of the alignment tensor
m = {x, y, z}.
+ - m, the index over the first dimension of the alignment tensor
m = {x, y, z}.
+ - n, the index over the second dimension of the alignment tensor
n = {x, y, z},
Equations
Modified: branches/rdc_analysis/maths_fns/rdc.py
URL:
http://svn.gna.org/viewcvs/relax/branches/rdc_analysis/maths_fns/rdc.py?rev=6967&r1=6966&r2=6967&view=diff
==============================================================================
--- branches/rdc_analysis/maths_fns/rdc.py (original)
+++ branches/rdc_analysis/maths_fns/rdc.py Fri Jul 25 11:19:15 2008
@@ -27,7 +27,7 @@
from numpy import dot, sum
-def average_rdc_5D(vect, K, A, weights=None):
+def ave_rdc_5D(vect, K, A, weights=None):
"""Calculate the average RDC for an ensemble set of XH bond vectors,
using the 5D notation.
This function calculates the average RDC for a set of XH bond vectors
from a structural
@@ -87,7 +87,7 @@
return val
-def average_rdc_tensor(vect, K, A, weights=None):
+def ave_rdc_tensor(vect, K, A, weights=None):
"""Calculate the average RDC for an ensemble set of XH bond vectors,
using the 3D tensor.
This function calculates the average RDC for a set of XH bond vectors
from a structural
@@ -146,3 +146,67 @@
# Return the average RDC.
return val
+
+
+def ave_rdc_tensor_dDij_dAmn(dj, vect, N, dAi_dAmn, weights=None):
+ """Calculate the ensemble average RDC gradient element for Amn, using
the 3D tensor.
+
+ This function calculates the average RDC gradient for a set of XH bond
vectors from a structural
+ ensemble, using the 3D tensorial form of the alignment tensor. The
formula for this ensemble
+ average RDC gradient element is::
+
+ _N_
+ dDij(theta) \ T dAi
+ ----------- = dj > pc . mu_jc . ---- . mu_jc,
+ dAmn /__ dAmn
+ c=1
+
+ where:
+ - i is the alignment tensor index,
+ - j is the index over spins,
+ - m, the index over the first dimension of the alignment tensor m =
{x, y, z}.
+ - n, the index over the second dimension of the alignment tensor n =
{x, y, z},
+ - c is the index over the states or multiple structures,
+ - theta is the parameter vector,
+ - Amn is the matrix element of the alignment tensor,
+ - dj is the dipolar constant for spin j,
+ - N is the total number of states or structures,
+ - pc is the population probability or weight associated with state c
(equally weighted to
+ 1/N if weights are not provided),
+ - mu_jc is the unit vector corresponding to spin j and state c,
+ - dAi/dAmn is the partial derivative of the alignment tensor with
respect to element Amn.
+
+
+ @param dj: The dipolar constant for spin j.
+ @type dj: float
+ @param vect: The unit XH bond vector matrix. The first dimension
corresponds to the
+ structural index, the second dimension is the
coordinates of the unit
+ vector.
+ @type vect: numpy matrix
+ @param N: The total number of structures.
+ @type N: int
+ @param dAi_dAmn: The alignment tensor derivative with respect to
parameter Amn.
+ @type dAi_dAmn: numpy rank-2 3D tensor
+ @param weights: The weights for each member of the ensemble. The
last weight is assumed to
+ be missing, and is calculated by this function.
Hence the length should be
+ one less than N.
+ @type weights: numpy rank-1 array
+ @return: The average RDC gradient element.
+ @rtype: float
+ """
+
+ # Initial back-calculated RDC gradient.
+ grad = 0.0
+
+ # The populations.
+ if weights == None:
+ pc = 1.0 / N
+ else:
+ weights.append(1.0 - sum(weights, axis=0))
+
+ # Back-calculate the RDC gradient element.
+ for c in xrange(N):
+ grad = grad + pc * dot(vect[c], dot(dAi_dAmn, vect[c]))
+
+ # Return the average RDC gradient element.
+ return dj * grad
r6967 - in /branches/rdc_analysis/maths_fns: n_state_model.py rdc.py