Module ns_cpmg_2site_3d
source code
The numerical fit of 2site BlochMcConnell equations for CPMGtype
experiments, the NS CPMG 2site 3D and NS
CPMG 2site 3D full models.
Description
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 BlochMcConnell can be found in chapter
3.1 of Palmer, A. G. Chem Rev 2004, 104, 36233640. This function was
written, initially in MATLAB, in 2010.
Code origin
This is the model of the numerical solution for the 2site
BlochMcConnell 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).
Links
More information on the NS CPMG 2site 3D model can be found in
the:
More information on the NS CPMG 2site 3D full model can be found in
the:

r2eff_ns_cpmg_2site_3D(r180x=None,
M0=None,
r10a=0.0,
r10b=0.0,
r20a=None,
r20b=None,
pA=None,
pB=None,
dw=None,
k_AB=None,
k_BA=None,
inv_tcpmg=None,
tcp=None,
back_calc=None,
num_points=None,
power=None)
The 2site numerical solution to the BlochMcConnell equation. 
source code



__package__ = ' lib.dispersion '

Imports:
log,
dot,
rcpmg_3d,
isNaN,
matrix_exponential
r2eff_ns_cpmg_2site_3D(r180x=None,
M0=None,
r10a=0.0,
r10b=0.0,
r20a=None,
r20b=None,
pA=None,
pB=None,
dw=None,
k_AB=None,
k_BA=None,
inv_tcpmg=None,
tcp=None,
back_calc=None,
num_points=None,
power=None)
 source code

The 2site numerical solution to the BlochMcConnell equation.
This function calculates and stores the R2eff values.
 Parameters:
r180x (numpy float64, rank2, 7D array)  The Xaxis pipulse propagator.
M0 (numpy float64, rank1, 7D array)  This is a vector that contains the initial magnetizations
corresponding to the A and B state transverse magnetizations.
r10a (float)  The R1 value for state A.
r10b (float)  The R1 value for state B.
r20a (float)  The R2 value for state A in the absence of exchange.
r20b (float)  The R2 value for state B in the absence of exchange.
pA (float)  The population of state A.
pB (float)  The population of state B.
dw (float)  The chemical exchange difference between states A and B in rad/s.
k_AB (float)  The rate of exchange from site A to B (rad/s).
k_BA (float)  The rate of exchange from site B to A (rad/s).
inv_tcpmg (float)  The inverse of the total duration of the CPMG element (in inverse
seconds).
tcp (numpy rank1 float array)  The tau_CPMG times (1 / 4.nu1).
back_calc (numpy rank1 float array)  The array for holding the back calculated R2eff values. Each
element corresponds to one of the CPMG nu1 frequencies.
num_points (int)  The number of points on the dispersion curve, equal to the length
of the tcp and back_calc arguments.
power (numpy int16, rank1 array)  The matrix exponential power array.
