Source Code for Module lib.dispersion.tap03

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2000-2001 Nikolai Skrynnikov                                  # 
  4  # Copyright (C) 2000-2001 Martin Tollinger                                    # 
  5  # Copyright (C) 2013-2014 Edward d'Auvergne                                   # 
  6  #                                                                             # 
  7  # This file is part of the program relax (http://www.nmr-relax.com).          # 
  8  #                                                                             # 
  9  # This program is free software: you can redistribute it and/or modify        # 
 10  # it under the terms of the GNU General Public License as published by        # 
 11  # the Free Software Foundation, either version 3 of the License, or           # 
 12  # (at your option) any later version.                                         # 
 13  #                                                                             # 
 14  # This program is distributed in the hope that it will be useful,             # 
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 16  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               # 
 17  # GNU General Public License for more details.                                # 
 18  #                                                                             # 
 19  # You should have received a copy of the GNU General Public License           # 
 20  # along with this program.  If not, see <http://www.gnu.org/licenses/>.       # 
 21  #                                                                             # 
 22  ############################################################################### 
 23   
 24  # Module docstring. 
 25  """The Trott, Abergel and Palmer (2003) off-resonance 2-site exchange R1rho U{TAP03<http://wiki.nmr-relax.com/TAP03>} model. 
 26   
 27  Description 
 28  =========== 
 29   
 30  This module is for the function, gradient and Hessian of the U{TAP03<http://wiki.nmr-relax.com/TAP03>} model. 
 31   
 32   
 33  References 
 34  ========== 
 35   
 36  The model is named after the reference: 
 37   
 38      - Trott, O., Abergel, D., and Palmer, A. (2003).  An average-magnetization analysis of R1rho relaxation outside of the fast exchange.  I{Mol. Phys.}, B{101}, 753-763.  (U{DOI: 10.1080/0026897021000054826<http://dx.doi.org/10.1080/0026897021000054826>}). 
 39   
 40   
 41  Code origin 
 42  =========== 
 43   
 44  The code was copied from the U{TP02<http://wiki.nmr-relax.com/TP02>} model (via the U{MP05<http://wiki.nmr-relax.com/MP05>} model), hence it originates as the funTrottPalmer.m Matlab file from the sim_all.tar file attached to task #7712 (U{https://web.archive.org/web/https://gna.org/task/?7712}).  This is code from Nikolai Skrynnikov and Martin Tollinger. 
 45   
 46  Links to the copyright licensing agreements from all authors are: 
 47   
 48      - Nikolai Skrynnikov, U{http://article.gmane.org/gmane.science.nmr.relax.devel/4279}, 
 49      - Martin Tollinger, U{http://article.gmane.org/gmane.science.nmr.relax.devel/4276}. 
 50   
 51   
 52  Links 
 53  ===== 
 54   
 55  More information on the TAP03 model can be found in the: 
 56   
 57      - U{relax wiki<http://wiki.nmr-relax.com/TAP03>}, 
 58      - U{relax manual<http://www.nmr-relax.com/manual/TAP03_2_site_exchange_R1_model.html>}, 
 59      - U{relaxation dispersion page of the relax website<http://www.nmr-relax.com/analyses/relaxation_dispersion.html#TAP03>}. 
 60  """ 
 61   
 62  # Python module imports. 
 63  from numpy import arctan2, array, isfinite, min, sin, sqrt, sum 
 64   
 65   
 66 -def r1rho_TAP03(r1rho_prime=None, omega=None, offset=None, pA=None, pB=None, dw=None, kex=None, R1=0.0, spin_lock_fields=None, spin_lock_fields2=None, back_calc=None, num_points=None): 
 67      """Calculate the R1rho' values for the TP02 model. 
 68   
 69      See the module docstring for details.  This is the Trott, Abergel and Palmer (2003) equation. 
 70   
 71   
 72      @keyword r1rho_prime:       The R1rho_prime parameter value (R1rho with no exchange). 
 73      @type r1rho_prime:          float 
 74      @keyword omega:             The chemical shift for the spin in rad/s. 
 75      @type omega:                float 
 76      @keyword offset:            The spin-lock offsets for the data. 
 77      @type offset:               numpy rank-1 float array 
 78      @keyword pA:                The population of state A. 
 79      @type pA:                   float 
 80      @keyword pB:                The population of state B. 
 81      @type pB:                   float 
 82      @keyword dw:                The chemical exchange difference between states A and B in rad/s. 
 83      @type dw:                   float 
 84      @keyword kex:               The kex parameter value (the exchange rate in rad/s). 
 85      @type kex:                  float 
 86      @keyword R1:                The R1 relaxation rate. 
 87      @type R1:                   float 
 88      @keyword spin_lock_fields:  The R1rho spin-lock field strengths (in rad.s^-1). 
 89      @type spin_lock_fields:     numpy rank-1 float array 
 90      @keyword spin_lock_fields2: The R1rho spin-lock field strengths squared (in rad^2.s^-2).  This is for speed. 
 91      @type spin_lock_fields2:    numpy rank-1 float array 
 92      @keyword back_calc:         The array for holding the back calculated R1rho values.  Each element corresponds to the combination of offset and spin lock field. 
 93      @type back_calc:            numpy rank-1 float array 
 94      @keyword num_points:        The number of points on the dispersion curve, equal to the length of the spin_lock_fields and back_calc arguments. 
 95      @type num_points:           int 
 96      """ 
 97   
 98      # Repetitive calculations (to speed up calculations). 
 99      Wa = omega                  # Larmor frequency [s^-1]. 
100      Wb = omega + dw             # Larmor frequency [s^-1]. 
101      kex2 = kex**2 
102      W = pA*Wa + pB*Wb           # Pop-averaged Larmor frequency [s^-1]. 
103   
104      # The numerator. 
105      phi_ex = pA * pB * dw**2 
106      numer = phi_ex * kex 
107   
108      # The factors. 
109      da = Wa - offset    # Offset of spin-lock from A. 
110      db = Wb - offset    # Offset of spin-lock from B. 
111      d = W - offset      # Offset of spin-lock from pop-average. 
112   
113      # The gamma factor. 
114      sigma = pB*da + pA*db 
115      sigma2 = sigma**2 
116   
117      gamma = 1.0 + phi_ex*(sigma2 - kex2 + spin_lock_fields2) / (sigma2 + kex2 + spin_lock_fields2)**2 
118   
119      # Bad gamma. 
120      if min(gamma) < 0.0: 
121          back_calc[:] = array([1e100]*num_points) 
122          return 
123   
124      # Special omega values. 
125      waeff2 = gamma*spin_lock_fields2 + da**2     # Effective field at A. 
126      wbeff2 = gamma*spin_lock_fields2 + db**2     # Effective field at B. 
127      weff2 = gamma*spin_lock_fields2 + d**2       # Effective field at pop-average. 
128   
129      # The rotating frame flip angle. 
130      theta = arctan2(spin_lock_fields, d) 
131      hat_theta = arctan2(sqrt(gamma)*spin_lock_fields, d) 
132   
133      # Repetitive calculations (to speed up calculations). 
134      sin_theta2 = sin(theta)**2 
135      hat_sin_theta2 = sin(hat_theta)**2 
136      R1_cos_theta2 = R1 * (1.0 - sin_theta2) 
137      R1rho_prime_sin_theta2 = r1rho_prime * sin_theta2 
138   
139      # Catch zeros (to avoid pointless mathematical operations). 
140      # This will result in no exchange, returning flat lines. 
141      if numer == 0.0: 
142          back_calc[:] = R1_cos_theta2 + R1rho_prime_sin_theta2 
143          return 
144   
145      # Denominator. 
146      denom = waeff2*wbeff2/weff2 + kex2 - 2.0*hat_sin_theta2*phi_ex + (1.0 - gamma)*spin_lock_fields2 
147    
148      # R1rho calculation. 
149      R1rho = R1_cos_theta2 + R1rho_prime_sin_theta2 + hat_sin_theta2 * numer / denom / gamma 
150   
151      # Catch errors, taking a sum over array is the fastest way to check for 
152      # +/- inf (infinity) and nan (not a number). 
153      if not isfinite(sum(R1rho)): 
154          R1rho = array([1e100]*num_points) 
155   
156      back_calc[:] = R1rho 
157