Package lib :: Package dispersion :: Module lm63
[hide private]
[frames] | no frames]

Source Code for Module lib.dispersion.lm63

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2009 Sebastien Morin                                          # 
  4  # Copyright (C) 2013-2014 Edward d'Auvergne                                   # 
  5  #                                                                             # 
  6  # This file is part of the program relax (http://www.nmr-relax.com).          # 
  7  #                                                                             # 
  8  # This program is free software: you can redistribute it and/or modify        # 
  9  # it under the terms of the GNU General Public License as published by        # 
 10  # the Free Software Foundation, either version 3 of the License, or           # 
 11  # (at your option) any later version.                                         # 
 12  #                                                                             # 
 13  # This program is distributed in the hope that it will be useful,             # 
 14  # but WITHOUT ANY WARRANTY; without even the implied warranty of              # 
 15  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               # 
 16  # GNU General Public License for more details.                                # 
 17  #                                                                             # 
 18  # You should have received a copy of the GNU General Public License           # 
 19  # along with this program.  If not, see <http://www.gnu.org/licenses/>.       # 
 20  #                                                                             # 
 21  ############################################################################### 
 22   
 23  # Module docstring. 
 24  """The Luz and Meiboom (1963) 2-site fast exchange U{LM63<http://wiki.nmr-relax.com/LM63>} model. 
 25   
 26  Description 
 27  =========== 
 28   
 29  This module is for the function, gradient and Hessian of the U{LM63<http://wiki.nmr-relax.com/LM63>} model. 
 30   
 31   
 32  References 
 33  ========== 
 34   
 35  The model is named after the reference: 
 36   
 37      - Luz, S. and Meiboom S., (1963)  Nuclear Magnetic Resonance study of protolysis of trimethylammonium ion in aqueous solution - order of reaction with respect to solvent, I{J. Chem. Phys.}, B{39}, 366-370 (U{DOI: 10.1063/1.1734254<http://dx.doi.org/10.1063/1.1734254>}). 
 38   
 39   
 40  Equations 
 41  ========= 
 42   
 43  The equation used is:: 
 44   
 45                    phi_ex   /     4 * nu_cpmg         /     kex     \ \  
 46      R2eff = R20 + ------ * | 1 - -----------  * tanh | ----------- | | , 
 47                     kex     \         kex             \ 4 * nu_cpmg / / 
 48   
 49  where:: 
 50   
 51      phi_ex = pA * pB * delta_omega^2 , 
 52   
 53  kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, and delta_omega is the chemical shift difference between the two states. 
 54   
 55   
 56  Links 
 57  ===== 
 58   
 59  More information on the LM63 model can be found in the: 
 60   
 61      - U{relax wiki<http://wiki.nmr-relax.com/LM63>}, 
 62      - U{relax manual<http://www.nmr-relax.com/manual/LM63_2_site_fast_exchange_CPMG_model.html>}, 
 63      - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#LM63>}. 
 64  """ 
 65   
 66  # Python module imports. 
 67  from numpy import array, isfinite, sum, tanh 
 68   
 69   
70 -def r2eff_LM63(r20=None, phi_ex=None, kex=None, cpmg_frqs=None, back_calc=None, num_points=None):
71 """Calculate the R2eff values for the LM63 model. 72 73 See the module docstring for details. 74 75 76 @keyword r20: The R20 parameter value (R2 with no exchange). 77 @type r20: float 78 @keyword phi_ex: The phi_ex parameter value (pA * pB * delta_omega^2). 79 @type phi_ex: float 80 @keyword kex: The kex parameter value (the exchange rate in rad/s). 81 @type kex: float 82 @keyword cpmg_frqs: The CPMG nu1 frequencies. 83 @type cpmg_frqs: numpy rank-1 float array 84 @keyword back_calc: The array for holding the back calculated R2eff values. Each element corresponds to one of the CPMG nu1 frequencies. 85 @type back_calc: numpy rank-1 float array 86 @keyword num_points: The number of points on the dispersion curve, equal to the length of the cpmg_frqs and back_calc arguments. 87 @type num_points: int 88 """ 89 90 # Catch divide with zeros (to avoid pointless mathematical operations). 91 if kex == 0.0: 92 back_calc[:] = array([r20]*num_points) 93 return 94 95 # Catch zeros (to avoid pointless mathematical operations). 96 # This will result in no exchange, returning flat lines. 97 if phi_ex == 0.0: 98 back_calc[:] = array([r20]*num_points) 99 return 100 101 # Repetitive calculations (to speed up calculations). 102 rex = phi_ex / kex 103 kex_4 = 4.0 / kex 104 105 # Calculate R2eff. 106 R2eff = r20 + rex * (1.0 - kex_4 * cpmg_frqs * tanh(kex / (4.0 * cpmg_frqs))) 107 108 # Catch errors, taking a sum over array is the fastest way to check for 109 # +/- inf (infinity) and nan (not a number). 110 if not isfinite(sum(R2eff)): 111 R2eff = array([1e100]*num_points) 112 113 back_calc[:] = R2eff
114