Source code for MDAnalysis.analysis.waterdynamics

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# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
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"""
Water dynamics analysis --- :mod:`MDAnalysis.analysis.waterdynamics`
=======================================================================

:Author: Alejandro Bernardin
:Year: 2014-2015
:Copyright: GNU Public License v3

.. versionadded:: 0.11.0

This module provides functions to analize water dynamics trajectories and water interactions with other molecules.
The functions in this module are: water orientational relaxation (WOR) [Yeh1999]_, hydrogen bond lifetimes (HBL) [Rapaport1983]_,
angular distribution (AD) [Grigera1995]_, mean square displacement (MSD) [Brodka1994]_ and survival probability (SP) [Liu2004]_.

For more information about this type of analysis please refer to [Araya-Secchi2014]_ (water in a protein cavity) and [Milischuk2011]_ (water in a nanopore).

.. rubric:: References

.. [Rapaport1983] D.C. Rapaport (1983): Hydrogen bonds in water, Molecular Physics: An International
            Journal at the Interface Between Chemistry and Physics, 50:5, 1151-1162.

.. [Yeh1999] Yu-ling Yeh and Chung-Yuan Mou (1999).
             Orientational Relaxation Dynamics of Liquid Water Studied by Molecular Dynamics
             Simulation, J. Phys. Chem. B 1999, 103, 3699-3705.

.. [Grigera1995] Raul Grigera, Susana G. Kalko and Jorge Fischbarg (1995). Wall-Water Interface.
                  A Molecular Dynamics Study, Langmuir 1996,12,154-158

.. [Liu2004] Pu Liu, Edward Harder, and B. J. Berne (2004).On the Calculation of Diffusion Coefficients
             in Confined Fluids and Interfaces with an Application to the Liquid-Vapor Interface of
             Water, J. Phys. Chem. B 2004, 108, 6595-6602.

.. [Brodka1994] Aleksander Brodka (1994). Diffusion in restricted volume, Molecular Physics, 1994, Vol.
                82, No. 5, 1075-1078.

.. [Araya-Secchi2014] Araya-Secchi, R., Tomas Perez-Acle, Seung-gu Kang, Tien Huynh, Alejandro Bernardin, Yerko Escalona, Jose-Antonio Garate, Agustin D. Martinez,
                     Isaac E. Garcia, Juan C. Saez, Ruhong Zhou (2014). Characterization of a novel water pocket inside the human Cx26 hemichannel structure. Biophysical journal, 107(3), 599-612.

.. [Milischuk2011] Anatoli A. Milischuk and Branka M. Ladanyi. Structure and dynamics of water confined
                    in silica nanopores. J. Chem. Phys. 135, 174709 (2011); doi: 10.1063/1.3657408



.. examples

Examples
--------

HydrogenBondLifetimes
~~~~~~~~~~~~~~~~~~~~~

Analyzing hydrogen bond lifetimes (HBL) :class:`HydrogenBondLifetimes`, both continuos and intermittent. In this case we are analyzing
how residue 38 interact with a water sphere of radius 6.0 centered on the geometric center of protein and
residue 42. If the hydrogen bond lifetimes are very stable, we can assume that residue 38 is hydrophilic, on the other
hand, if the  are very unstable, we can assume that residue 38 is hydrophobic::

  import MDAnalysis
  from MDAnalysis.analysis.waterdynamics import HydrogenBondLifetimes as HBL

  u = MDAnalysis.Universe(pdb, trajectory)
  selection1 = "byres name OH2 and sphzone 6.0 protein and resid 42"
  selection2 = "resid 38"
  HBL_analysis = HBL(universe, selection1, selection2, 0, 2000, 30)
  HBL_analysis.run()
  i=0
  #now we print the data ready to graph. The first two columns are the HBLc vs t graph and
  #the second two columns are the HBLi vs t graph
  for HBLc, HBLi in HBL_analysis.timeseries:
        print i +" "+ HBLc +" "+ i +" "+ HBLi
        i+=1

where HBLc is the value for the continuos hydrogen bond lifetimes and HBLi is the value for the intermittent
hydrogen bond lifetime, t0 = 0, tf = 2000 and dtmax = 30. In this way we create 30 windows timestep
(30 values in x axis). The continuos hydrogen bond lifetimes should decay faster than intermittent.


WaterOrientationalRelaxation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Analyzing water orientational relaxation (WOR) :class:`WaterOrientationalRelaxation`. In this case we are analyzing "how fast" water molecules are rotating/changing direction. If WOR is very stable we can assume that water molecules are rotating/changing direction very slow, on the other hand, if WOR decay very fast, we can assume that water molecules are rotating/changing direction very fast::

  import MDAnalysis
  from MDAnalysis.analysis.waterdynamics import WaterOrientationalRelaxation as WOR

  u = MDAnalysis.Universe(pdb, trajectory)
  selection = "byres name OH2 and sphzone 6.0 protein and resid 42"
  WOR_analysis = WOR(universe, selection, 0, 1000, 20)
  WOR_analysis.run()
  i=0
  #now we print the data ready to graph. The first two columns are WOR_OH vs t graph,
  #the second two columns are WOR_HH vs t graph and the third two columns are WOR_dip vs t graph
  for WOR_OH, WOR_HH, WOR_dip in WOR_analysis.timeseries:
        print i +" "+ WOR_OH +" "+ i +" "+ WOR_HH +" "+ i +" "+ WOR_dip

where t0 = 0, tf = 1000 and dtmax = 20. In this way we create 20 windows timesteps (20 values in the x axis),
the first window is created with 1000 timestep average (1000/1), the second window is created with 500
timestep average(1000/2), the third window is created with 333 timestep average (1000/3) and so on.

AngularDistribution
~~~~~~~~~~~~~~~~~~~

Analyzing angular distribution (AD) :class:`AngularDistribution` for OH vector, HH vector and dipole vector. It returns
a line histogram with vector orientation preference. A straight line in the output graphic means no preferential
orientation in water molecules. In this case we are analyzing if water molecules have some orientational
preference, in this way we can see if water molecules are under an electric field or if they are interacting
with something (residue, protein, etc)::

  import MDAnalysis
  from MDAnalysis.analysis.waterdynamics import AngularDistribution as AD

  u = MDAnalysis.Universe(pdb, trajectory)
  selection = "byres name OH2 and sphzone 6.0 (protein and (resid 42 or resid 26) )"
  bins = 30
  AD_analysis = AD(universe,selection,bins)
  AD_analysis.run()
  #now we print data ready to graph. The first two columns are P(cos(theta)) vs cos(theta) for OH vector ,
  #the seconds two columns are P(cos(theta)) vs cos(theta) for HH vector and thirds two columns
  #are P(cos(theta)) vs cos(theta) for dipole vector
  for i in range(bins):
        print AD_analysis.graph[0][i] +" "+ AD_analysis.graph[1][i] +" "+ AD_analysis.graph[2][i]

where P(cos(theta)) is the angular distribution or angular probabilities.

MeanSquareDisplacement
~~~~~~~~~~~~~~~~~~~~~~
Analyzing mean square displacement (MSD):class:`MeanSquareDisplacement` for water molecules. In this case we are analyzing the average distance
that water molecules travels inside protein in XYZ direction (cylindric zone of radius 11[nm], Zmax 4.0[nm] and Zmin -8.0[nm]). A strong
rise mean a fast movement of water molecules, a weak rise mean slow movement of particles::

  import MDAnalysis
  from MDAnalysis.analysis.waterdynamics import MeanSquareDisplacement as MSD

  u = MDAnalysis.Universe(pdb, trajectory)
  selection = "byres name OH2 and cyzone 11.0 4.0 -8.0 protein"
  MSD_analysis = MSD(universe, selection, 0, 1000, 20)
  MSD_analysis.run()
  #now we print data ready to graph. The graph
  #represents MSD vs t
  i=0
  for msd in MSD_analysis.timeseries:
        print i +" "+ msd
        i += 1


SurvivalProbability
~~~~~~~~~~~~~~~~~~~
Analyzing survival probability (SP) :class:`SurvivalProbability` for water molecules. In this case we are analyzing how long water
molecules remain in a sphere of radius 12.3 centered in the geometrical center of resid 42, 26, 34 and 80.
A slow decay of SP means a long permanence time of water molecules in the zone, on the
other hand, a fast decay means a short permanence time::

  import MDAnalysis
  from MDAnalysis.analysis.waterdynamics import SurvivalProbability as SP

  u = MDAnalysis.Universe(pdb, trajectory)
  selection = "byres name OH2 and sphzone 12.3 (resid 42 or resid 26 or resid 34 or resid 80) "
  SP_analysis = SP(universe, selection, 0, 100, 20)
  SP_analysis.run()
  #now we print data ready to graph. The graph
  #represents SP vs t
  i=0
  for sp in SP_analysis.timeseries:
        print i +" "+ sp
        i += 1

.. Output

Output
------

HydrogenBondLifetimes
~~~~~~~~~~~~~~~~~~~~~
Hydrogen bond lifetimes (HBL) data is returned per window timestep, which is stored in
:attr:`HydrogenBondLifetimes.timeseries` (in all the following descriptions, # indicates comments that are not part of the output)::

    results = [
        [ # time t0
            <HBL_c>, <HBL_i>
        ],
        [ # time t1
            <HBL_c>, <HBL_i>
        ],
        ...
     ]

WaterOrientationalRelaxation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Water orientational relaxation (WOR) data is returned per window timestep, which is stored in
:attr:`WaterOrientationalRelaxation.timeseries`::

    results = [
        [ # time t0
            <WOR_OH>, <WOR_HH>, <WOR_dip>
        ],
        [ # time t1
            <WOR_OH>, <WOR_HH>, <WOR_dip>
        ],
        ...
     ]

AngularDistribution
~~~~~~~~~~~~~~~~~~~
Angular distribution (AD) data is returned per vector, which is stored in
:attr:`AngularDistribution.graph`. In fact, AngularDistribution returns a histogram::

    results = [
        [ # OH vector values
          # the values are order in this way: <x_axis  y_axis>
            <cos_theta0 ang_distr0>, <cos_theta1 ang_distr1>, ...
        ],
        [ # HH vector values
            <cos_theta0 ang_distr0>, <cos_theta1 ang_distr1>, ...
        ],
        [ # dip vector values
           <cos_theta0 ang_distr0>, <cos_theta1 ang_distr1>, ...
        ],
     ]

MeanSquareDisplacement
~~~~~~~~~~~~~~~~~~~~~~
Mean Square Displacement (MSD) data is returned in a list, which each element represents a MSD value in its respective
window timestep. Data is stored in :attr:`MeanSquareDisplacement.timeseries`::

    results = [
         #MSD values orders by window timestep
            <MSD_t0>, <MSD_t1>, ...
     ]

SurvivalProbability
~~~~~~~~~~~~~~~~~~~
Survival Probability (SP) data is returned in a list, which each element represents a SP value in its respective
window timestep. Data is stored in :attr:`SurvivalProbability.timeseries`::

    results = [
         # SP values order by window timestep
            <SP_t0>, <SP_t1>, ...
     ]



Classes
--------

.. autoclass:: HydrogenBondLifetimes
   :members:
   :inherited-members:

.. autoclass:: WaterOrientationalRelaxation
   :members:
   :inherited-members:

.. autoclass:: AngularDistribution
   :members:
   :inherited-members:

.. autoclass:: MeanSquareDisplacement
   :members:
   :inherited-members:

.. autoclass:: SurvivalProbability
   :members:
   :inherited-members:


"""

import MDAnalysis.analysis.hbonds
import numpy
import multiprocessing
import itertools

[docs]class HydrogenBondLifetimes(object): r""" This is a autocorrelation function that gives the "Hydrogen Bond Lifetimes" (HBL) proposed by D.C. Rapaport [Rapaport1983]_. From this function we can obtain the continuos and intermittent behavior of hydrogen bonds in time. A fast decay in these parameters indicate a fast change in HBs connectivity. A slow decay indicate very stables hydrogen bonds, like in ice. The HBL is also know as "Hydrogen Bond Population Relaxation" (HBPR). In the continuos case we have: .. math:: C_{HB}^c(\tau) = \frac{\sum_{ij}h_{ij}(t_0)h'_{ij}(t_0+\tau)}{\sum_{ij}h_{ij}(t_0)} where :math:`h'_{ij}(t_0+\tau)=1` if there is a H-bond between a pair :math:`ij` during time interval :math:`t_0+\tau` (continuos) and :math:`h'_{ij}(t_0+\tau)=0` otherwise. In the intermittent case we have: .. math:: C_{HB}^i(\tau) = \frac{\sum_{ij}h_{ij}(t_0)h_{ij}(t_0+\tau)}{\sum_{ij}h_{ij}(t_0)} where :math:`h_{ij}(t_0+\tau)=1` if there is a H-bond between a pair :math:`ij` at time :math:`t_0+\tau` (intermittent) and :math:`h_{ij}(t_0+\tau)=0` otherwise. .. versionadded:: 0.11.0 :Arguments: *universe* Universe object *selection1* Selection string for first selection [‘byres name OH2’] It could be any selection available in MDAnalysis, not just water. *selection2* Selection string to analize its HBL against selection1 *t0* Time where analysis begin *tf* Time where analysis end *dtmax* Maximum dt size, dtmax < tf or it will crash. *nproc* Number of processors to use, by default is 1. """ def __init__(self,universe ,selection1 ,selection2, t0 , tf , dtmax, nproc = 1): self.universe = universe self.selection1 = selection1 self.selection2 = selection2 self.t0 = t0 self.tf = tf - 1 self.dtmax = dtmax self.nproc = nproc self.timeseries = None def _getC_i(self,HBP,t0,t): """ This function give the intermitent Hydrogen Bond Lifetime C_i = <h(t0)h(t)>/<h(t0)> between t0 and t """ C_i = 0 for i in range(len(HBP[t0])): for j in range(len(HBP[t])): if (HBP[t0][i][0] == HBP[t][j][0] and HBP[t0][i][1] == HBP[t][j][1]): C_i += 1 break if len(HBP[t0]) == 0 : return 0.0 else: return float(C_i)/len(HBP[t0]) def _getC_c(self,HBP,t0,t): """ This function give the continous Hydrogen Bond Lifetime C_c = <h(t0)h'(t)>/<h(t0)> between t0 and t """ C_c = 0 dt = 1 begt0 = t0 HBP_cp = HBP HBP_t0 = HBP[t0] newHBP = [] if t0==t: return 1.0 while t0+dt <= t: for i in range(len(HBP_t0)): for j in range(len(HBP_cp[t0+dt])): if (HBP_t0[i][0] == HBP_cp[t0+dt][j][0] and HBP_t0[i][1] == HBP_cp[t0+dt][j][1]): newHBP.append(HBP_t0[i]) break C_c = len(newHBP) t0 += dt HBP_t0 = newHBP newHBP = [] if len(HBP[begt0]) == 0 : return 0 else: return C_c/float(len(HBP[begt0])) def _intervC_c(self,HBP,t0,tf,dt): """ This function gets all the data for the h(t0)h(t0+dt)', where t0 = 1,2,3,...,tf. This function give us one point of the final graphic HBL vs t """ a = 0 count = 0 for i in range(len(HBP)): if (t0+dt <= tf): if t0 == t0+dt: b = self._getC_c(HBP,t0,t0) break b = self._getC_c(HBP,t0,t0+dt) t0 += dt a += b count += 1 if count == 0: return 1.0 return a/count def _intervC_i(self,HBP,t0,tf,dt): """ This function gets all the data for the h(t0)h(t0+dt), where t0 = 1,2,3,...,tf. This function give us a point of the final graphic HBL vs t """ a = 0 count = 0 for i in range(len(HBP)): if (t0+dt <= tf ): b = self._getC_i(HBP,t0,t0+dt) t0 += dt a += b count += 1 return a/count def _finalGraphGetC_i(self,HBP,t0,tf,maxdt): """ This function gets the final data of the C_i graph. """ output = [] for dt in range(maxdt): a = self._intervC_i(HBP,t0,tf,dt) output.append(a) return output def _finalGraphGetC_c(self,HBP,t0,tf,maxdt): """ This function gets the final data of the C_c graph. """ output = [] for dt in range(maxdt): a = self._intervC_c(HBP,t0,tf,dt) output.append(a) return output def _getGraphics(self,HBP,t0,tf,maxdt): """ Function that join all the results into a graphics. """ a = [] cont = self._finalGraphGetC_c(HBP,t0,tf,maxdt) inte = self._finalGraphGetC_i(HBP,t0,tf,maxdt) for i in range(len(cont)): fix = [cont[i],inte[i]] a.append(fix) return a def _HBA(self, ts, conn, universe, selAtom1, selAtom2, quiet=True): """ Main function for calculate C_i and C_c in parallel. """ finalGetResidue1 = selAtom1 finalGetResidue2 = selAtom2 frame = ts.frame h = MDAnalysis.analysis.hbonds.HydrogenBondAnalysis(universe, finalGetResidue1, finalGetResidue2, distance=3.5, angle=120.0, start=frame-1, stop=frame) while True: try: h.run(quiet=quiet) break except: print "error" print "trying again" sys.stdout.flush() sys.stdout.flush() conn.send(h.timeseries[0]) conn.close()
[docs] def run(self, **kwargs): """ Analyze trajectory and produce timeseries """ h_list = [] i = 0 if (self.nproc > 1): while i < len(self.universe.trajectory): jobs = [] k=i for j in range(self.nproc): #start print "ts=",i+1 if i >= len(self.universe.trajectory): break conn_parent, conn_child = multiprocessing.Pipe(False) while True: try: #new thread jobs.append( (multiprocessing.Process( target=self._HBA, args=(self.universe.trajectory[i], conn_child, self.universe, self.selection1, self.selection2,)), conn_parent)) break except: print "error in jobs.append" jobs[j][0].start() i = i + 1 for j in range(self.nproc): if k >= len(self.universe.trajectory): break rec01 = jobs[j][1] received = rec01.recv() h_list.append(received) jobs[j][0].join() k += 1 self.timeseries = self._getGraphics( h_list , 0 , self.tf-1 , self.dtmax ) else: h_list = MDAnalysis.analysis.hbonds.HydrogenBondAnalysis(self.universe, self.selection1, self.selection2,distance=3.5, angle=120.0) h_list.run(**kwargs) self.timeseries = self._getGraphics(h_list.timeseries, self.t0, self.tf, self.dtmax)
[docs]class WaterOrientationalRelaxation(object): r""" Function to evaluate the Water Orientational Relaxation proposed by Yu-ling Yeh and Chung-Yuan Mou [Yeh1999_]. WaterOrientationalRelaxation indicates "how fast" water molecules are rotating or changing direction. This is a time correlation function given by: .. math:: C_{\hat u}(\tau)=\langle \mathit{P}_2[\mathbf{\hat{u}}(t_0)\cdot\mathbf{\hat{u}}(t_0+\tau)]\rangle where :math:`P_2=(3x^2-1)/2` is the second-order Legendre polynomial and :math:`\hat{u}` is a unit vector along HH, OH or dipole vector. .. versionadded:: 0.11.0 :Arguments: *universe* Universe object *selection* Selection string, only models with 3 atoms molecules are allowed (TIP3, TIP3P, etc) *t0* Time where analysis begin *tf* Time where analysis end *dtmax* Maximum dt size window, dtmax < tf or it will crash. """ def __init__(self,universe,selection,t0,tf,dtmax,nproc=1): self.universe = universe self.selection = selection self.t0 = t0 self.tf = tf self.dtmax= dtmax self.nproc = nproc self.timeseries = None def _repeatedIndex(self,selection,dt,totalFrames): """ Indicate the comparation between all the t+dt. The results is a list of list with all the repeated index per frame (or time). Ex: dt=1, so compare frames (1,2),(2,3),(3,4)... Ex: dt=2, so compare frames (1,3),(3,5),(5,7)... Ex: dt=3, so compare frames (1,4),(4,7),(7,10)... """ rep=[] for i in range(int(round( (totalFrames-1)/float(dt) ) ) ): if ( dt*i+dt < totalFrames ): rep.append(self._sameMolecTandDT(selection,dt*i,(dt*i)+dt)) return rep def _getOneDeltaPoint(self,universe, repInd, i ,t0, dt): """ Give one point to promediate and get one point of the graphic C_vect vs t Ex: t0=1 and tau=1 so calculate the t0-tau=1-2 intervale. Ex: t0=5 and tau=3 so calcultate the t0-tau=5-8 intervale. i = come from getMeanOnePoint (named j) (int) """ valOH = 0 valHH = 0 valdip= 0 n = 0 for j in range(len(repInd[i])/3): begj = 3*j universe.trajectory[t0] Ot0 = repInd[i][begj] H1t0 = repInd[i][begj+1] H2t0 = repInd[i][begj+2] OHVector0 = H1t0.position - Ot0.position HHVector0 = H1t0.position-H2t0.position dipVector0 = ((H1t0.position + H2t0.position)*0.5)-Ot0.position universe.trajectory[t0+dt] Otp = repInd[i][begj] H1tp = repInd[i][begj+1] H2tp = repInd[i][begj+2] OHVectorp = H1tp.position- Otp.position HHVectorp = H1tp.position - H2tp.position dipVectorp = ((H1tp.position + H2tp.position)*0.5)-Otp.position normOHVector0 = numpy.linalg.norm(OHVector0) normOHVectorp = numpy.linalg.norm(OHVectorp) normHHVector0 = numpy.linalg.norm(HHVector0) normHHVectorp = numpy.linalg.norm(HHVectorp) normdipVector0 = numpy.linalg.norm(dipVector0) normdipVectorp = numpy.linalg.norm(dipVectorp) unitOHVector0 = [OHVector0[0]/normOHVector0,OHVector0[1]/normOHVector0,OHVector0[2]/normOHVector0] unitOHVectorp = [OHVectorp[0]/normOHVectorp,OHVectorp[1]/normOHVectorp,OHVectorp[2]/normOHVectorp] unitHHVector0 = [HHVector0[0]/normHHVector0,HHVector0[1]/normHHVector0,HHVector0[2]/normHHVector0] unitHHVectorp = [HHVectorp[0]/normHHVectorp,HHVectorp[1]/normHHVectorp,HHVectorp[2]/normHHVectorp] unitdipVector0 = [dipVector0[0]/normdipVector0,dipVector0[1]/normdipVector0,dipVector0[2]/normdipVector0] unitdipVectorp = [dipVectorp[0]/normdipVectorp,dipVectorp[1]/normdipVectorp,dipVectorp[2]/normdipVectorp] valOH += self.lg2(numpy.dot(unitOHVector0,unitOHVectorp)) valHH += self.lg2(numpy.dot(unitHHVector0,unitHHVectorp)) valdip += self.lg2(numpy.dot(unitdipVector0,unitdipVectorp)) n += 1 valOH = valOH/n valHH = valHH/n valdip = valdip/n return (valOH,valHH,valdip) def _getMeanOnePoint(self,universe,selection1,selection_str,dt,totalFrames): """ This function get one point of the graphic C_OH vs t. It uses the _getOneDeltaPoint() function to calculate the average. """ repInd = self._repeatedIndex(selection1,dt,totalFrames) sumsdt = 0 n = 0.0 sumDeltaOH = 0.0 sumDeltaHH = 0.0 sumDeltadip = 0.0 valOHList = [] valHHList = [] valdipList = [] for j in range(totalFrames/dt-1): a = self._getOneDeltaPoint(universe,repInd,j,sumsdt,dt) sumDeltaOH += a[0] sumDeltaHH += a[1] sumDeltadip += a[2] valOHList.append(a[0]) valHHList.append(a[1]) valdipList.append(a[2]) sumsdt += dt n += 1 return (sumDeltaOH/n,sumDeltaHH/n,sumDeltadip/n) def _sameMolecTandDT(self,selection,t0d,tf): """ Compare the molecules in the t0d selection and the t0d+dt selection and select only the particles that are repeated in both frame. This is to consider only the molecules that remains in the selection after the dt time has elapsed. The result is a list with the indexs of the atoms. """ a = set(selection[t0d]) b = set(selection[tf]) sort = sorted(list(a.intersection(b))) return sort def _selection_serial(self,universe,selection_str): selection = [] for ts in universe.trajectory: selection.append(universe.select_atoms(selection_str)) print ts.frame return selection # Second Legendre polynomial lg2 = lambda self,x : (3*x*x - 1)/2
[docs] def run(self,**kwargs): """ Analyze trajectory and produce timeseries """ #All the selection to an array, this way is faster than selecting later. if self.nproc==1: selection_out = self._selection_serial(self.universe,self.selection) else: #selection_out = self._selection_parallel(self.universe,self.selection,self.nproc) #parallel selection to be implemented selection_out = self._selection_serial(self.universe,self.selection) self.timeseries = [] for dt in list(range(1,self.dtmax+1)): output = self._getMeanOnePoint(self.universe,selection_out,self.selection,dt,self.tf) self.timeseries.append(output)
[docs]class AngularDistribution(object): r""" The angular distribution function (AD) is defined as the distribution probability of the cosine of the :math:`\theta` angle formed by the OH vector, HH vector or dipolar vector of water molecules and a vector :math:`\hat n` parallel to chosen axis (z is the default value). The cosine is define as :math:`\cos \theta = \hat u \cdot \hat n`, where :math:`\hat u` is OH, HH or dipole vector. It creates a histogram and returns a list of lists, see Output_. The AD is also know as Angular Probability (AP). .. versionadded:: 0.11.0 :Arguments: *universe* Universe object *selection* Selection string to evaluate its angular distribution [‘byres name OH2’] *bins* Number of bins to create the histogram by means of numpy.histogram_ [40] *axis* Axis to create angle with the vector (HH, OH or dipole) and calculate cosine theta ['z']. Options: 'x', 'y', 'z' .. _numpy.histogram: http://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html """ def __init__(self,universe,selection_str,bins=40,nproc=1,axis="z"): self.universe = universe self.selection_str = selection_str self.bins = bins self.nproc = nproc self.axis = axis self.graph = None def _getCosTheta(self,universe,selection,axis): valOH = [] valHH = [] valdip= [] i = 0 while i <= (len(selection)-1): universe.trajectory[i] line = selection[ i ].positions Ot0 = line[::3] H1t0 = line[1::3] H2t0 = line[2::3] OHVector0 = H1t0 - Ot0 HHVector0 = H1t0 - H2t0 dipVector0 = (H1t0 + H2t0)*0.5 - Ot0 unitOHVector0 = OHVector0/numpy.linalg.norm(OHVector0, axis = 1)[:,None] unitHHVector0 = HHVector0/numpy.linalg.norm(HHVector0, axis = 1)[:,None] unitdipVector0 = dipVector0/numpy.linalg.norm(dipVector0, axis = 1)[:,None] j=0 while j < len(line)/3: if axis == "z": valOH.append(unitOHVector0[j][2]) valHH.append(unitHHVector0[j][2]) valdip.append(unitdipVector0[j][2]) elif axis == "x": valOH.append(unitOHVector0[j][0]) valHH.append(unitHHVector0[j][0]) valdip.append(unitdipVector0[j][0]) elif axis == "y": valOH.append(unitOHVector0[j][1]) valHH.append(unitHHVector0[j][1]) valdip.append(unitdipVector0[j][1]) j += 1 i += 1 return (valOH,valHH,valdip) def _getHistogram(self,universe,selection,bins,axis): """ This function gets a normalized histogram of the cos(theta) values. It return a list of list. """ a = self._getCosTheta(universe,selection,axis) cosThetaOH = a[0] cosThetaHH = a[1] cosThetadip = a[2] lencosThetaOH = len(cosThetaOH) lencosThetaHH = len(cosThetaHH) lencosThetadip = len(cosThetadip) histInterval = bins histcosThetaOH = numpy.histogram(cosThetaOH,histInterval, normed = True) histcosThetaHH = numpy.histogram(cosThetaHH,histInterval, normed = True) histcosThetadip = numpy.histogram(cosThetadip,histInterval, normed = True) return (histcosThetaOH,histcosThetaHH,histcosThetadip) def _hist2column(self,aList): """ This function transform from the histogram format to a column format. """ a = [] for x in itertools.izip_longest(*aList, fillvalue="."): a.append(" ".join(str(i) for i in x)) return a
[docs] def run(self,**kwargs): """ Function to evaluate the angular distribution of cos(theta) """ if self.nproc ==1: selection = self._selection_serial(self.universe,self.selection_str) else: #not implemented yet #selection = self._selection_parallel(self.universe,self.selection_str,self.nproc) selection = self._selection_serial(self.universe,self.selection_str) self.graph = [] output=self._getHistogram(self.universe,selection,self.bins,self.axis) #this is to format the exit of the file #maybe this output could be improved listOH = [list(output[0][1]),list(output[0][0])] listHH = [list(output[1][1]),list(output[1][0])] listdip = [list(output[2][1]),list(output[2][0])] self.graph.append(self._hist2column(listOH)) self.graph.append(self._hist2column(listHH)) self.graph.append(self._hist2column(listdip))
def _selection_serial(self,universe,selection_str): selection = [] for ts in universe.trajectory: selection.append(universe.select_atoms(selection_str)) print ts.frame return selection
[docs]class MeanSquareDisplacement(object): r""" Function to evaluate the Mean Square Displacement (MSD_). The MSD gives the average distance that particles travels. The MSD is given by: .. math:: \langle\Delta r(t)^2\rangle = 2nDt where :math:`r(t)` is the position of particle in time :math:`t`, :math:`\Delta r(t)` is the displacement after time lag :math:`t`, :math:`n` is the dimensionality, in this case :math:`n=3`, :math:`D` is the diffusion coefficient and :math:`t` is the time. .. _MSD: http://en.wikipedia.org/wiki/Mean_squared_displacement .. versionadded:: 0.11.0 :Arguments: *universe* Universe object *selection* Selection string *t0* Time where analysis begin *tf* Time where analysis end *dtmax* Maximum dt size window, dtmax < tf or it will crash. """ def __init__(self,universe,selection,t0,tf,dtmax,nproc=1): self.universe = universe self.selection = selection self.t0 = t0 self.tf = tf self.dtmax= dtmax self.nproc = nproc self.timeseries = None def _repeatedIndex(self,selection,dt,totalFrames): """ Indicate the comparation between all the t+dt. The results is a list of list with all the repeated index per frame (or time). Ex: dt=1, so compare frames (1,2),(2,3),(3,4)... Ex: dt=2, so compare frames (1,3),(3,5),(5,7)... Ex: dt=3, so compare frames (1,4),(4,7),(7,10)... """ rep=[] for i in range(int(round( (totalFrames-1)/float(dt) ) ) ): if ( dt*i+dt < totalFrames ): rep.append(self._sameMolecTandDT(selection,dt*i,(dt*i)+dt)) return rep def _getOneDeltaPoint(self,universe, repInd, i ,t0, dt): """ Give one point to promediate and get one point of the grapic C_vect vs t Ex: t0=1 and dt=1 so calculate the t0-dt=1-2 intervale. Ex: t0=5 and dt=3 so calcultate the t0-dt=5-8 intervale i = come from getMeanOnePoint (named j) (int) """ valO = 0 n = 0 for j in range(len(repInd[i])/3): begj = 3*j universe.trajectory[t0] #Plus zero is to avoid 0to be equal to 0tp Ot0 = repInd[i][begj].position + 0 universe.trajectory[t0+dt] #Plus zero is to avoid 0to be equal to 0tp Otp = repInd[i][begj].position + 0 #position oxygen OVector = Ot0 - Otp #here it is the difference with waterdynamics.WaterOrientationalRelaxation valO += numpy.dot(OVector, OVector) n += 1 valO = valO/n return (valO) def _getMeanOnePoint(self,universe,selection1,selection_str,dt,totalFrames): """ This function get one point of the graphic C_OH vs t. It's uses the _getOneDeltaPoint() function to calculate the average. """ repInd = self._repeatedIndex(selection1,dt,totalFrames) sumsdt = 0 n = 0.0 sumDeltaO = 0.0 valOList = [] for j in range(totalFrames/dt-1): a = self._getOneDeltaPoint(universe,repInd,j,sumsdt,dt) print "a=",a sumDeltaO += a valOList.append(a) sumsdt += dt n += 1 return (sumDeltaO/n) def _sameMolecTandDT(self,selection,t0d,tf): """ Compare the molecules in the t0d selection and the t0d+dt selection and select only the particles that are repeated in both frame. This is to consider only the molecules that remains in the selection after the dt time has elapsed. The result is a list with the indexs of the atoms. """ a = set(selection[t0d]) b = set(selection[tf]) sort = sorted(list(a.intersection(b))) return sort def _selection_serial(self,universe,selection_str): selection = [] for ts in universe.trajectory: selection.append(universe.select_atoms(selection_str)) print ts.frame return selection
[docs] def run(self,**kwargs): """ Analyze trajectory and produce timeseries """ #All the selection to an array, this way is faster than selecting later. if self.nproc==1: selection_out = self._selection_serial(self.universe,self.selection) else: #parallel not yet implemented #selection = selection_parallel(universe,selection_str,nproc) selection_out = self._selection_serial(self.universe,self.selection) self.timeseries = [] for dt in list(range(1,self.dtmax+1)): output = self._getMeanOnePoint(self.universe,selection_out,self.selection,dt,self.tf) self.timeseries.append(output)
[docs]class SurvivalProbability(object): r""" Function to evaluate the Survival Probability (SP). The SP gives the probability for a group of particles to remain in certain region. The SP is given by: .. math:: P(\tau) = \frac1T \sum_{t=1}^T \frac{N(t,t+\tau)}{N(t)} where :math:`T` is the maximum time of simulation, :math:`\tau` is the timestep and :math:`N` the number of particles in certain time. .. versionadded:: 0.11.0 :Arguments: *universe* Universe object *selection* Selection string, any selection is allowed, with this selection you define the region/zone where to analize, i.e.: "selection_a" and "zone" (see SP examples_ ) *t0* Time where analysis begin *tf* Time where analysis end *dtmax* Maximum dt size window, dtmax < tf or it will crash """ def __init__(self,universe,selection,t0,tf,dtmax,nproc=1): self.universe = universe self.selection = selection self.t0 = t0 self.tf = tf self.dtmax= dtmax self.nproc = nproc self.timeseries = None def _getOneDeltaPoint(self,selection, totalFrames, t0, tau): """ Give one point to promediate and get one point of the graphic C_vect vs t Ex: t0=1 and tau=1 so calculate the t0-tau=1-2 intervale. Ex: t0=5 and tau=3 so calcultate the t0-tau=5-8 intervale. """ Ntau = self._NumPart_tau(selection, totalFrames, t0, tau) Nt = float(self._NumPart(selection,t0)) return Ntau/Nt def _getMeanOnePoint(self,universe,selection1,selection_str,wint,totalFrames): """ This function get one point of the graphic P(t) vs t. It uses the _getOneDeltaPoint() function to calculate the average. """ n = 0.0 sumDeltaP = 0.0 for frame in range(totalFrames-wint): #This "try" is to avoid a division by zero when there is no particles in time t0, #this happens in very small selection regions. try: a = self._getOneDeltaPoint(selection1,totalFrames ,frame, wint) except ZeroDivisionError: continue sumDeltaP += a n += 1 return sumDeltaP/n def _NumPart_tau(self,selection, totalFrames, t0,tau): """ Compare the molecules in t0 selection and t0+tau selection and select only the particles that remaing from t0 to t0+tau. It returns the number of remaining particles. """ a = set(selection[t0]) i=0 while (t0+i) < t0+tau and (t0+i) < totalFrames: b = set(selection[t0+i]) a = a.intersection(b) i += 1 return len(a) def _NumPart(self, selection, t): return len(selection[t]) def _selection_serial(self,universe,selection_str): selection = [] for ts in universe.trajectory: selection.append(universe.select_atoms(selection_str)) print ts.frame return selection
[docs] def run(self,**kwargs): """ Analyze trajectory and produce timeseries """ #All the selection to an array, this way is faster than selecting later. if self.nproc==1: selection_out = self._selection_serial(self.universe, self.selection) else: #selection = selection_parallel(universe,selection_str,nproc) #parallel selection to be implemented selection_out = self._selection_serial(self.universe, self.selection) self.timeseries = [] for dt in list(range(1,self.dtmax+1)): output = self._getMeanOnePoint(self.universe, selection_out, self.selection, dt, self.tf) self.timeseries.append(output)