Source Code for Module lib.dispersion.m61b

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2009 Sebastien Morin                                          # 
  4  # Copyright (C) 2013-2014 Edward d'Auvergne                                   # 
  5  # Copyright (C) 2014 Troels E. Linnet                                         # 
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  7  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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 23   
 24  # Module docstring. 
 25  """The Meiboom (1961) 2-site on-resonance skewed population R1rho U{M61 skew<http://wiki.nmr-relax.com/M61_skew>} model. 
 26   
 27  Description 
 28  =========== 
 29   
 30  This module is for the function, gradient and Hessian of the U{M61 skew<http://wiki.nmr-relax.com/M61_skew>} model. 
 31   
 32   
 33  References 
 34  ========== 
 35   
 36  The model is named after the reference: 
 37   
 38      - 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>}). 
 39   
 40   
 41  Equations 
 42  ========= 
 43   
 44  The equation used is:: 
 45   
 46                             pA^2.pB.delta_omega^2.kex 
 47      R1rho = R1rho' + -------------------------------------- , 
 48                       kex^2 + pA^2.delta_omega^2 + omega_1^2 
 49   
 50  where 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 = omega_e is the effective field in the rotating frame. 
 51   
 52   
 53  Links 
 54  ===== 
 55   
 56  More information on the M61 skew model can be found in the: 
 57   
 58      - U{relax wiki<http://wiki.nmr-relax.com/M61_skew>}, 
 59      - U{relax manual<http://www.nmr-relax.com/manual/The_M61_skew_2_site_fast_exchange_R1_rho_model.html>}, 
 60      - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#M61_skew>}. 
 61  """ 
 62   
 63  # Python module imports. 
 64  from numpy import any, isfinite, min, sum 
 65  from numpy.ma import fix_invalid, masked_where 
 66   
 67   
 68 -def r1rho_M61b(r1rho_prime=None, pA=None, dw=None, kex=None, spin_lock_fields2=None, back_calc=None): 
 69      """Calculate the R1rho values for the M61 skew model. 
 70   
 71      See the module docstring for details. 
 72   
 73   
 74      @keyword r1rho_prime:       The R1rho_prime parameter value (R1rho with no exchange). 
 75      @type r1rho_prime:          numpy float array of rank [NE][NS][NM][NO][ND] 
 76      @keyword pA:                The population of state A. 
 77      @type pA:                   float 
 78      @keyword dw:                The chemical exchange difference between states A and B in rad/s. 
 79      @type dw:                   numpy float array of rank [NE][NS][NM][NO][ND] 
 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 float array of rank [NE][NS][NM][NO][ND] 
 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 float array of rank [NE][NS][NM][NO][ND] 
 86      """ 
 87   
 88      # Flag to tell if values should be replaced if numer is zero. 
 89      t_numer_zero = False 
 90      t_denom_zero = False 
 91   
 92      # The B population. 
 93      pB = 1.0 - pA 
 94   
 95      # Repetitive calculations (to speed up calculations). 
 96      pA2dw2 = pA**2 * dw**2 
 97      kex2_pA2dw2 = kex**2 + pA2dw2 
 98   
 99      # The numerator. 
100      numer = pA2dw2 * pB * kex 
101   
102      # Catch zeros (to avoid pointless mathematical operations). 
103      # This will result in no exchange, returning flat lines. 
104      if min(numer) == 0.0: 
105          t_numer_zero = True 
106          mask_numer_zero = masked_where(numer == 0.0, numer) 
107   
108      # Denominator. 
109      denom = kex2_pA2dw2 + spin_lock_fields2 
110   
111      # Catch math domain error of dividing with 0. 
112      # This is when denom = 0. 
113      mask_denom_zero = denom == 0.0 
114      if any(mask_denom_zero): 
115          t_denom_zero = True 
116          denom[mask_denom_zero] = 1.0 
117   
118      # R1rho calculation. 
119      back_calc[:] = r1rho_prime + numer / denom 
120   
121      # Replace data in array. 
122      # If numer is zero. 
123      if t_numer_zero: 
124          back_calc[mask_numer_zero.mask] = r1rho_prime[mask_numer_zero.mask] 
125   
126      # If denom is zero. 
127      if t_denom_zero: 
128          back_calc[mask_denom_zero] = 1e100 
129   
130      # Catch errors, taking a sum over array is the fastest way to check for 
131      # +/- inf (infinity) and nan (not a number). 
132      if not isfinite(sum(back_calc)): 
133          # Replaces nan, inf, etc. with fill value. 
134          fix_invalid(back_calc, copy=False, fill_value=1e100) 
135