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).          # 
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 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