Source Code for Module lib.dispersion.m61

  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 Meiboom (1961) 2-site fast exchange R1rho U{M61<http://wiki.nmr-relax.com/M61>} model. 
 25   
 26  Description 
 27  =========== 
 28   
 29  This module is for the function, gradient and Hessian of the U{M61<http://wiki.nmr-relax.com/M61>} model. 
 30   
 31   
 32  References 
 33  ========== 
 34   
 35  The model is named after the reference: 
 36   
 37      - Meiboom S. (1961).  Nuclear magnetic resonance study of the proton transfer in water.  I{J. Chem. Phys.}, B{34}, 375-388.  (U{DOI: 10.1063/1.1700960<http://dx.doi.org/10.1063/1.1700960>}). 
 38   
 39   
 40  Equations 
 41  ========= 
 42   
 43  The equation used is:: 
 44   
 45                         phi_ex * kex 
 46      R1rho = R1rho' + ----------------- , 
 47                       kex^2 + omega_1^2 
 48   
 49  where:: 
 50   
 51      phi_ex = pA * pB * delta_omega^2 , 
 52   
 53  R1rho' is the R1rho value in the absence of exchange, kex is the chemical exchange rate constant, pA and pB are the populations of states A and B, delta_omega is the chemical shift difference between the two states, and omega_1 is the spin-lock field strength. 
 54   
 55   
 56  Links 
 57  ===== 
 58   
 59  More information on the M61 model can be found in the: 
 60   
 61      - U{relax wiki<http://wiki.nmr-relax.com/M61>}, 
 62      - U{relax manual<http://www.nmr-relax.com/manual/M61_2_site_fast_exchange_R1_model.html>}, 
 63      - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#M61>}. 
 64  """ 
 65   
 66  # Python module imports. 
 67  from numpy import abs, array, isfinite, min, sum 
 68   
 69   
 70 -def r1rho_M61(r1rho_prime=None, phi_ex=None, kex=None, spin_lock_fields2=None, back_calc=None, num_points=None): 
 71      """Calculate the R2eff values for the M61 model. 
 72   
 73      See the module docstring for details. 
 74   
 75   
 76      @keyword r1rho_prime:       The R1rho_prime parameter value (R1rho with no exchange). 
 77      @type r1rho_prime:          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 spin_lock_fields2: The R1rho spin-lock field strengths squared (in rad^2.s^-2). 
 83      @type spin_lock_fields2:    numpy rank-1 float array 
 84      @keyword back_calc:         The array for holding the back calculated R1rho values.  Each element corresponds to the combination of spin lock field. 
 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 spin_lock_fields and back_calc arguments. 
 87      @type num_points:           int 
 88      """ 
 89   
 90      # Repetitive calculations (to speed up calculations). 
 91      kex2 = kex**2 
 92   
 93      # The numerator. 
 94      numer = phi_ex * kex 
 95   
 96      # Catch zeros (to avoid pointless mathematical operations). 
 97      # This will result in no exchange, returning flat lines. 
 98      if numer == 0.0: 
 99          back_calc[:] = array([r1rho_prime]*num_points) 
100          return 
101   
102      # Denominator. 
103      denom = kex2 + spin_lock_fields2 
104   
105      # Catch math domain error of dividing with 0. 
106      # This is when denom=0. 
107      if min(abs(denom)) == 0: 
108          back_calc[:] = array([1e100]*num_points) 
109          return 
110   
111      # R1rho calculation. 
112      R1rho = r1rho_prime + numer / denom 
113   
114      # Catch errors, taking a sum over array is the fastest way to check for 
115      # +/- inf (infinity) and nan (not a number). 
116      if not isfinite(sum(R1rho)): 
117          R1rho = array([1e100]*num_points) 
118   
119      back_calc[:] = R1rho 
120