Author: bugman
Date: Tue Jul 16 15:17:43 2013
New Revision: 20334
URL: http://svn.gna.org/viewcvs/relax?rev=20334&view=rev
Log:
Added the 'NS 2-site' R2eff calculating function to the relax library.
This is the model of the numerical solution for the 2-site Bloch-McConnell
equations. It originates
as optimization function number 1 from the fitting_main_kex.py script from
Mathilde Lescanne, Paul
Schanda, and Dominique Marion (see
http://thread.gmane.org/gmane.science.nmr.relax.devel/4138,
https://gna.org/task/?7712#comment2 and
https://gna.org/support/download.php?file_id=18262).
This commit follows step 3 of the relaxation dispersion model addition
tutorial
(http://thread.gmane.org/gmane.science.nmr.relax.devel/3907).
Added:
branches/relax_disp/lib/dispersion/ns_2site.py
- copied, changed from r20327,
branches/relax_disp/lib/dispersion/ns_2site_star.py
Modified:
branches/relax_disp/lib/dispersion/__init__.py
Modified: branches/relax_disp/lib/dispersion/__init__.py
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/lib/dispersion/__init__.py?rev=20334&r1=20333&r2=20334&view=diff
==============================================================================
--- branches/relax_disp/lib/dispersion/__init__.py (original)
+++ branches/relax_disp/lib/dispersion/__init__.py Tue Jul 16 15:17:43 2013
@@ -29,6 +29,7 @@
'lm63',
'm61',
'm61b',
+ 'ns_2site',
'ns_2site_star',
'ns_matrices',
'two_point'
Copied: branches/relax_disp/lib/dispersion/ns_2site.py (from r20327,
branches/relax_disp/lib/dispersion/ns_2site_star.py)
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/lib/dispersion/ns_2site.py?p2=branches/relax_disp/lib/dispersion/ns_2site.py&p1=branches/relax_disp/lib/dispersion/ns_2site_star.py&r1=20327&r2=20334&rev=20334&view=diff
==============================================================================
--- branches/relax_disp/lib/dispersion/ns_2site_star.py (original)
+++ branches/relax_disp/lib/dispersion/ns_2site.py Tue Jul 16 15:17:43 2013
@@ -23,44 +23,47 @@
# Module docstring.
"""This function performs a numerical fit of 2-site Bloch-McConnell
equations for CPMG-type experiments.
-The function uses an explicit matrix that contains relaxation, exchange and
chemical shift terms. It does the 180deg pulses in the CPMG train with
conjugate complex matrices. The approach of Bloch-McConnell can be found in
chapter 3.1 of Palmer, A. G. Chem Rev 2004, 104, 3623-3640. This function
was written, initially in MATLAB, in 2010.
+The function uses an explicit matrix that contains relaxation, exchange and
chemical shift terms. It does the 180deg pulses in the CPMG train. The
approach of Bloch-McConnell can be found in chapter 3.1 of Palmer, A. G. Chem
Rev 2004, 104, 3623-3640. This function was written, initially in MATLAB, in
2010.
-The code was submitted at
http://thread.gmane.org/gmane.science.nmr.relax.devel/4132 by Paul Schanda.
+This is the model of the numerical solution for the 2-site Bloch-McConnell
equations. It originates as optimization function number 1 from the
fitting_main_kex.py script from Mathilde Lescanne, Paul Schanda, and
Dominique Marion (see
http://thread.gmane.org/gmane.science.nmr.relax.devel/4138,
https://gna.org/task/?7712#comment2 and
https://gna.org/support/download.php?file_id=18262).
"""
# Dependency check module.
import dep_check
# Python module imports.
-from math import log
-from numpy import add, complex, conj, dot
-from numpy.linalg import matrix_power
+from math import fabs, log
if dep_check.scipy_module:
from scipy.linalg import expm
+# relax module imports.
+from lib.dispersion.ns_matrices import r180x_3d, rcpmg_3d
-def r2eff_ns_2site_star(Rr=None, Rex=None, RCS=None, R=None, M0=None,
r20a=None, r20b=None, fA=None, inv_tcpmg=None, tcp=None, back_calc=None,
num_points=None, power=None):
- """The 2-site numerical solution to the Bloch-McConnell equation using
complex conjugate matrices.
+
+def r2eff_ns_2site_star(M0=None, r10a=None, r10b=None, r20a=None, r20b=None,
pA=None, dw=None, k_AB=None, k_BA=None, inv_tcpmg=None, tcp=None,
back_calc=None, num_points=None, power=None):
+ """The 2-site numerical solution to the Bloch-McConnell equation.
This function calculates and stores the R2eff values.
- @keyword Rr: The matrix that contains only the R2 relaxation
terms ("Redfield relaxation", i.e. non-exchange broadening).
- @type Rr: numpy complex64, rank-2, 2D array
- @keyword Rex: The matrix that contains the exchange terms
between the two states A and B.
- @type Rex: numpy complex64, rank-2, 2D array
- @keyword RCS: The matrix that contains the chemical shift
evolution. It works here only with X magnetization, and the complex notation
allows to evolve in the transverse plane (x, y).
- @type RCS: numpy complex64, rank-2, 2D array
- @keyword R: The matrix that contains all the contributions
to the evolution, i.e. relaxation, exchange and chemical shift evolution.
- @type R: numpy complex64, rank-2, 2D array
@keyword M0: This is a vector that contains the initial
magnetizations corresponding to the A and B state transverse magnetizations.
@type M0: numpy float64, rank-1, 2D array
+ @keyword r10a: The R1 value for state A.
+ @type r10a: float
+ @keyword r10b: The R1 value for state B.
+ @type r10b: float
@keyword r20a: The R2 value for state A in the absence of
exchange.
@type r20a: float
@keyword r20b: The R2 value for state B in the absence of
exchange.
@type r20b: float
- @keyword fA: The frequency of state A.
- @type fA: float
+ @keyword pA: The population of state A.
+ @type pA: float
+ @keyword dw: The chemical exchange difference between states
A and B in rad/s.
+ @type dw: float
+ @keyword k_AB: The rate of exchange from site A to B (rad/s).
+ @type k_AB: float
+ @keyword k_BA: The rate of exchange from site B to A (rad/s).
+ @type k_BA: float
@keyword inv_tcpmg: The inverse of the total duration of the CPMG
element (in inverse seconds).
@type inv_tcpmg: float
@keyword tcp: The tau_CPMG times (1 / 4.nu1).
@@ -73,36 +76,25 @@
@type power: numpy int16, rank-1 array
"""
- # The matrix that contains only the R2 relaxation terms ("Redfield
relaxation", i.e. non-exchange broadening).
- Rr[0, 0] = -r20a
- Rr[1, 1] = -r20b
-
- # The matrix that contains the chemical shift evolution. It works here
only with X magnetization, and the complex notation allows to evolve in the
transverse plane (x, y).
- RCS[1, 1] = complex(0.0, -fA)
-
# The matrix R that contains all the contributions to the evolution,
i.e. relaxation, exchange and chemical shift evolution.
- add(Rr, Rex, out=R)
- add(R, RCS, out=R)
-
- # This is the complex conjugate of the above. It allows the chemical
shift to run in the other direction, i.e. it is used to evolve the shift
after a 180 deg pulse. The factor of 2 is to minimise the number of
multiplications for the prop_2 matrix calculation.
- cR2 = conj(R) * 2.0
+ R = rcpmg_3d(R1A=r10a, R1B=r10b, R2A=r20a, R2B=r20b, df=dw, k_AB=k_AB,
k_BA=k_BA)
# Loop over the time points, back calculating the R2eff values.
for i in range(num_points):
+ # Initial magnetisation.
+ Mint = M0
+
# This matrix is a propagator that will evolve the magnetization
with the matrix R for a delay tcp.
- expm_R_tcp = expm(R*tcp[i])
+ Rexpo = expm(R*tcp[i])
- # This is the propagator for an element of [delay tcp; 180 deg
pulse; 2 times delay tcp; 180 deg pulse; delay tau], i.e. for 2 times
tau-180-tau.
- prop_2 = dot(dot(expm_R_tcp, expm(cR2*tcp[i])), expm_R_tcp)
-
- # Now create the total propagator that will evolve the magnetization
under the CPMG train, i.e. it applies the above tau-180-tau-tau-180-tau so
many times as required for the CPMG frequency under consideration.
- prop_total = matrix_power(prop_2, power[i])
-
- # Now we apply the above propagator to the initial magnetization
vector - resulting in the magnetization that remains after the full CPMG
pulse train. It is called M of t (t is the time after the CPMG train).
- Moft = dot(prop_total, M0)
+ # Loop over the CPMG elements.
+ for j in range(2*power[i]):
+ Mint = Rexpo * Mint
+ Mint = r180x_3d(0.0) * Mint
+ Mint = Rexpo * Mint
# The next lines calculate the R2eff using a two-point
approximation, i.e. assuming that the decay is mono-exponential.
- Mgx = Moft[0].real / M0[0]
+ Mgx = fabs((Mint[1])/pA)
if Mgx == 0.0:
back_calc[i] = 1e99
else:
r20334 - in /branches/relax_disp/lib/dispersion: __init__.py ns_2site.py