Package lib :: Package dispersion :: Module lm63_3site
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Module lm63_3site

source code

The Luz and Meiboom (1963) 3-site fast exchange LM63 3-site model.

Description

This module is for the function, gradient and Hessian of the LM63 3-site model.

References

The model is named after the reference:

Equations

The equation used is:

                  _3_
                  \    phi_ex_i   /     4 * nu_cpmg         /     ki      \ \ 
   R2eff = R20 +   >   -------- * | 1 - -----------  * tanh | ----------- | | .
                  /__     ki      \         ki              \ 4 * nu_cpmg / /
                  i=2

For deconvoluting the parameters, see the relax user manual or the reference:

Links

More information on the LM63 3-site model can be found in the:

Functions [hide private]
 
r2eff_LM63_3site(r20=None, phi_ex_B=None, phi_ex_C=None, kB=None, kC=None, cpmg_frqs=None, back_calc=None)
Calculate the R2eff values for the LM63 3-site model.
source code
Variables [hide private]
  __package__ = 'lib.dispersion'

Imports: fabs, min, tanh, isfinite, sum, fix_invalid, masked_where


Function Details [hide private]

r2eff_LM63_3site(r20=None, phi_ex_B=None, phi_ex_C=None, kB=None, kC=None, cpmg_frqs=None, back_calc=None)

source code 

Calculate the R2eff values for the LM63 3-site model.

See the module docstring for details.

Parameters:
  • r20 (numpy float array of rank [NS][NM][NO][ND]) - The R20 parameter value (R2 with no exchange).
  • phi_ex_B (numpy float array of rank [NS][NM][NO][ND]) - The fast exchange factor between sites A and B (ppm^2)
  • phi_ex_C (numpy float array of rank [NE][NS][NM][NO][ND]) - The fast exchange factor between sites A and C (ppm^2)
  • kB (float) - Approximate chemical exchange rate constant between sites A and B (the exchange rate in rad/s).
  • kC (float) - Approximate chemical exchange rate constant between sites A and C (the exchange rate in rad/s).
  • cpmg_frqs (numpy float array of rank [NE][NS][NM][NO][ND]) - The CPMG nu1 frequencies.
  • back_calc (numpy float array of rank [NE][NS][NM][NO][ND]) - The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies.