Module tp02

The Trott and Palmer (2002) 2-site exchange R1rho TP02 model.

Description

This module is for the function, gradient and Hessian of the TP02 model.

References

The model is named after the reference:

• Trott, O. and Palmer, 3rd, A. G. (2002). R1rho relaxation outside of the fast-exchange limit. J. Magn. Reson., 154(1), 157-160. (DOI: 10.1006/jmre.2001.2466).

Code origin

The code originates as the funTrottPalmer.m Matlab file from the sim_all.tar file attached to task #7712 (https://web.archive.org/web/https://gna.org/task/?7712). This is code from Nikolai Skrynnikov and Martin Tollinger.

Links to the copyright licensing agreements from all authors are:

• Nikolai Skrynnikov, http://article.gmane.org/gmane.science.nmr.relax.devel/4279,
• Martin Tollinger, http://article.gmane.org/gmane.science.nmr.relax.devel/4276.

Links

More information on the TP02 model can be found in the:

• relax wiki,
• relax manual,
• relaxation dispersion page of the relax website.

Functions

r1rho_TP02(r1rho_prime=None, omega=None, offset=None, pA=None, pB=None, dw=None, kex=None, R1=0.0, spin_lock_fields=None, spin_lock_fields2=None, back_calc=None, num_points=None)
Calculate the R1rho' values for the TP02 model.

Variables

__package__ = 'lib.dispersion'

Imports: abs, arctan2, array, isfinite, min, sin, sum

Function Details

r1rho_TP02(r1rho_prime=None, omega=None, offset=None, pA=None, pB=None, dw=None, kex=None, R1=0.0, spin_lock_fields=None, spin_lock_fields2=None, back_calc=None, num_points=None)

Calculate the R1rho' values for the TP02 model.

See the module docstring for details. This is the Trott and Palmer (2002) equation according to Korzhnev (J. Biomol. NMR (2003), 26, 39-48).

Parameters:

• r1rho_prime (float) - The R1rho_prime parameter value (R1rho with no exchange).
• omega (float) - The chemical shift for the spin in rad/s.
• offset (numpy rank-1 float array) - The spin-lock offsets for the data.
• 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.
• kex (float) - The kex parameter value (the exchange rate in rad/s).
• R1 (float) - The R1 relaxation rate.
• spin_lock_fields (numpy rank-1 float array) - The R1rho spin-lock field strengths (in rad.s^-1).
• spin_lock_fields2 (numpy rank-1 float array) - The R1rho spin-lock field strengths squared (in rad^2.s^-2). This is for speed.
• back_calc (numpy rank-1 float array) - The array for holding the back calculated R1rho values. Each element corresponds to the combination of offset and spin lock field.
• num_points (int) - The number of points on the dispersion curve, equal to the length of the spin_lock_fields and back_calc arguments.