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normalmodes.py
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"""Contains the classes that deal with the normal mode representation.
Copyright (C) 2013, Joshua More and Michele Ceriotti
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http.//www.gnu.org/licenses/>.
Deals with the normal mode transformation, including the complications
introduced by PA-CMD when the bead masses are rescaled. Also deals with
the change in the dynamics introduced by this mass-scaling, and has its
own functions to calculate the kinetic energy, and the exact propagator
in the normal mode representation under the ring polymer Hamiltonian.
Classes:
NormalModes: Deals with the normal mode transformation in RPMD and PA-CMD.
"""
import numpy as np
from ipi.utils.depend import *
from ipi.utils import units
from ipi.utils import nmtransform
from ipi.utils.messages import verbosity, warning, info
__all__ = [ "NormalModes" ]
class NormalModes(dobject):
""" A helper class to manipulate the path NM.
Normal-modes transformation, determination of path frequencies,
dynamical mass matrix change, etc.
Attributes:
natoms: The number of atoms.
nbeads: The number of beads.
beads: The beads object for which the normal mode transformation should
be done.
ensemble: The ensemble object, specifying the temperature to hold the
system to.
transform: A nm_trans object that contains the functions that are
required for the normal mode transformation.
Depend objects:
mode: A string specifying how the bead masses are chosen.
transform_method: A string specifying how to do the normal mode
transformation.
nm_freqs: An array that specifies how the normal mode frequencies
of the ring polymers are to be calculated, and thus how the
bead masses should be chosen.
qnm: The bead positions in the normal mode representation. Depends on
beads.q.
pnm: The bead momenta in the normal mode representation. Depends on
beads.p.
omegan: The effective vibrational frequency for the interaction
between the replicas. Depends on the simulation temperature.
omegan2: omegan**2.
omegak: The normal mode frequencies for the free ring polymer.
Depends on omegan.
prop_pq: An array holding the exact normal mode propagator for the
free ring polymer, using mass scaled coordinates.
See J. Chem. Phys. 133, 124101 (2010). Depends on the bead masses
and the timestep.
nm_factor: An array of dynamical mass factors associated with each of
the normal modes. Depends on nm_freqs and mode.
dynm3: An array that gives the dynamical masses of individual atoms in the
normal modes representation. Depends on nm_factor and beads.m3.
dynomegak: The scaled vibrational frequencies. Depends on nm_factor and
omegak.
kins: A list of the kinetic energy for each normal mode, as
calculated in the normal mode representation, using the
dynamical mass factors. Depends on beads.sm3, beads.p and nm_factor.
kin: The total kinetic energy, as calculated in the normal mode
representation, using the dynamical mass factors.
kstress: The kinetic stress tensor, as calculated in the normal mode
representation, using the dynamical mass factors. Depends on
beads.sm3, beads.p and nm_factor.
"""
def __init__(self, mode="rpmd", transform_method="fft", freqs=None):
"""Initializes NormalModes.
Sets the options for the normal mode transform.
Args:
mode: A string specifying how to calculate the bead masses.
transform_method: A string specifying how to do the normal mode
transformation.
freqs: A list of data used to calculate the dynamical mass factors.
"""
if freqs is None:
freqs = []
dset(self,"mode", depend_value(name='mode', value=mode))
dset(self,"transform_method",
depend_value(name='transform_method', value=transform_method))
dset(self,"nm_freqs",
depend_array(name="nm_freqs",value=np.asarray(freqs, float) ) )
def bind(self, beads, ensemble):
""" Initializes the normal modes object and binds to beads and ensemble.
Do all the work down here as we need a full-formed necklace and ensemble
to know how this should be done.
Args:
beads: A beads object to be bound.
ensemble: An ensemble object to be bound.
"""
self.nbeads = beads.nbeads
self.natoms = beads.natoms
# stores a reference to the bound beads and ensemble objects
self.beads = beads
self.ensemble = ensemble
# sets up what's necessary to perform nm transformation.
if self.transform_method == "fft":
self.transform = nmtransform.nm_fft(nbeads=self.nbeads, natoms=self.natoms)
elif self.transform_method == "matrix":
self.transform = nmtransform.nm_trans(nbeads=self.nbeads)
# creates arrays to store normal modes representation of the path.
# must do a lot of piping to create "ex post" a synchronization between the beads and the nm
sync_q = synchronizer()
sync_p = synchronizer()
dset(self,"qnm",
depend_array(name="qnm",
value=np.zeros((self.nbeads,3*self.natoms), float),
func={"q": (lambda : self.transform.b2nm(depstrip(self.beads.q)) ) },
synchro=sync_q ) )
dset(self,"pnm",
depend_array(name="pnm",
value=np.zeros((self.nbeads,3*self.natoms), float),
func={"p": (lambda : self.transform.b2nm(depstrip(self.beads.p)) ) },
synchro=sync_p ) )
# must overwrite the functions
dget(self.beads, "q")._func = { "qnm": (lambda : self.transform.nm2b(depstrip(self.qnm)) ) }
dget(self.beads, "p")._func = { "pnm": (lambda : self.transform.nm2b(depstrip(self.pnm)) ) }
dget(self.beads, "q").add_synchro(sync_q)
dget(self.beads, "p").add_synchro(sync_p)
# also within the "atomic" interface to beads
for b in range(self.nbeads):
dget(self.beads._blist[b],"q")._func = { "qnm": (lambda : self.transform.nm2b(depstrip(self.qnm)) ) }
dget(self.beads._blist[b],"p")._func = { "pnm": (lambda : self.transform.nm2b(depstrip(self.pnm)) ) }
dget(self.beads._blist[b],"q").add_synchro(sync_q)
dget(self.beads._blist[b],"p").add_synchro(sync_p)
# finally, we mark the beads as those containing the set positions
dget(self.beads, "q").update_man()
dget(self.beads, "p").update_man()
# create path-frequencies related properties
dset(self,"omegan",
depend_value(name='omegan', func=self.get_omegan,
dependencies=[dget(self.ensemble,"temp")]) )
dset(self,"omegan2", depend_value(name='omegan2',func=self.get_omegan2,
dependencies=[dget(self,"omegan")]) )
dset(self,"omegak", depend_array(name='omegak',
value=np.zeros(self.beads.nbeads,float),
func=self.get_omegak, dependencies=[dget(self,"omegan")]) )
# sets up "dynamical" masses -- mass-scalings to give the correct RPMD/CMD dynamics
dset(self,"nm_factor", depend_array(name="nmm",
value=np.zeros(self.nbeads, float), func=self.get_nmm,
dependencies=[dget(self,"nm_freqs"), dget(self,"mode") ]) )
dset(self,"dynm3", depend_array(name="dm3",
value=np.zeros((self.nbeads,3*self.natoms), float),func=self.get_dynm3,
dependencies=[dget(self,"nm_factor"), dget(self.beads, "m3")] ) )
dset(self,"dynomegak", depend_array(name="dynomegak",
value=np.zeros(self.nbeads, float), func=self.get_dynwk,
dependencies=[dget(self,"nm_factor"), dget(self,"omegak") ]) )
dset(self,"prop_pq",
depend_array(name='prop_pq',value=np.zeros((self.beads.nbeads,2,2)),
func=self.get_prop_pq,
dependencies=[dget(self,"omegak"), dget(self,"nm_factor"), dget(self.ensemble,"dt")]) )
# if the mass matrix is not the RPMD one, the MD kinetic energy can't be
# obtained in the bead representation because the masses are all mixed up
dset(self,"kins",
depend_array(name="kins",value=np.zeros(self.nbeads, float),
func=self.get_kins,
dependencies=[dget(self,"pnm"), dget(self.beads,"sm3"), dget(self, "nm_factor") ] ))
dset(self,"kin",
depend_value(name="kin", func=self.get_kin,
dependencies=[dget(self,"kins")] ))
dset(self,"kstress",
depend_array(name="kstress",value=np.zeros((3,3), float),
func=self.get_kstress,
dependencies=[dget(self,"pnm"), dget(self.beads,"sm3"), dget(self, "nm_factor") ] ))
def get_omegan(self):
"""Returns the effective vibrational frequency for the interaction
between replicas.
"""
return self.ensemble.temp*self.nbeads*units.Constants.kb/units.Constants.hbar
def get_omegan2(self):
"""Returns omegan**2."""
return self.omegan**2
def get_omegak(self):
"""Gets the normal mode frequencies.
Returns:
A list of the normal mode frequencies for the free ring polymer.
The first element is the centroid frequency (0.0).
"""
return 2*self.omegan*np.array([np.sin(k*np.pi/self.nbeads) for k in range(self.nbeads)])
def get_dynwk(self):
"""Gets the dynamical normal mode frequencies.
Returns:
A list of the scaled normal mode frequencies for the free ring polymer.
The first element is the centroid frequency (0.0).
"""
return self.omegak/np.sqrt(self.nm_factor)
def get_prop_pq(self):
"""Gets the normal mode propagator matrix.
Note the special treatment for the centroid normal mode, which is
propagated using the standard velocity Verlet algorithm as required.
Note that both the normal mode positions and momenta are propagated
using this matrix.
Returns:
An array of the form (nbeads, 2, 2). Each 2*2 array prop_pq[i,:,:]
gives the exact propagator for the i-th normal mode of the
ring polymer.
"""
dt = self.ensemble.dt
pqk = np.zeros((self.nbeads,2,2), float)
pqk[0] = np.array([[1,0], [dt,1]])
for b in range(1, self.nbeads):
sk = np.sqrt(self.nm_factor[b]) # NOTE THAT THE PROPAGATOR USES MASS-SCALED MOMENTA!
dtomegak = self.omegak[b]*dt/sk
c = np.cos(dtomegak)
s = np.sin(dtomegak)
pqk[b,0,0] = c
pqk[b,1,1] = c
pqk[b,0,1] = -s*self.omegak[b]*sk
pqk[b,1,0] = s/(self.omegak[b]*sk)
return pqk
def get_nmm(self):
"""Returns dynamical mass factors, i.e. the scaling of normal mode
masses that determine the path dynamics (but not statics)."""
# also checks that the frequencies and the mode given in init are
# consistent with the beads and ensemble
dmf = np.zeros(self.nbeads,float)
dmf[:] = 1.0
if self.mode == "rpmd":
if len(self.nm_freqs) > 0:
warning("nm.frequencies will be ignored for RPMD mode.", verbosity.low)
elif self.mode == "manual":
if len(self.nm_freqs) != self.nbeads-1:
raise ValueError("Manual path mode requires (nbeads-1) frequencies, one for each internal mode of the path.")
for b in range(1, self.nbeads):
sk = self.omegak[b]/self.nm_freqs[b-1]
dmf[b] = sk**2
elif self.mode == "pa-cmd":
if len(self.nm_freqs) > 1:
warning("Only the first element in nm.frequencies will be considered for PA-CMD mode.", verbosity.low)
if len(self.nm_freqs) == 0:
raise ValueError("PA-CMD mode requires the target frequency of all the internal modes.")
for b in range(1, self.nbeads):
sk = self.omegak[b]/self.nm_freqs[0]
info(" ".join(["NM FACTOR", str(b), str(sk), str(self.omegak[b]), str(self.nm_freqs[0])]), verbosity.medium)
dmf[b] = sk**2
elif self.mode == "wmax-cmd":
if len(self.nm_freqs) > 2:
warning("Only the first two element in nm.frequencies will be considered for WMAX-CMD mode.", verbosity.low)
if len(self.nm_freqs) < 2:
raise ValueError("WMAX-CMD mode requires [wmax, wtarget]. The normal modes will be scaled such that the first internal mode is at frequency wtarget and all the normal modes coincide at frequency wmax.")
wmax = self.nm_freqs[0]
wt = self.nm_freqs[1]
for b in range(1, self.nbeads):
sk = 1.0/np.sqrt((wt)**2*(1+(wmax/self.omegak[1])**2)/(wmax**2+(self.omegak[b])**2))
dmf[b] = sk**2
return dmf
def get_dynm3(self):
"""Returns an array with the dynamical masses of individual atoms in the normal modes representation."""
dm3 = np.zeros(self.beads.m3.shape,float)
for b in range(self.nbeads):
dm3[b] = self.beads.m3[b]*self.nm_factor[b]
return dm3
def free_qstep(self):
"""Exact normal mode propagator for the free ring polymer.
Note that the propagator works in mass scaled coordinates, so that the
propagator matrix can be determined independently from the particular
atom masses, and so the same propagator will work for all the atoms in
the system. All the ring polymers are propagated at the same time by a
matrix multiplication.
Also note that the centroid coordinate is propagated in qcstep, so is
not altered here.
"""
if self.nbeads == 1:
pass
else:
pq = np.zeros((2,self.natoms*3),float)
sm = depstrip(self.beads.sm3)[0]
prop_pq = depstrip(self.prop_pq)
for k in range(1,self.nbeads):
pq[0,:] = depstrip(self.pnm)[k]/sm
pq[1,:] = depstrip(self.qnm)[k]*sm
pq = np.dot(prop_pq[k],pq)
self.qnm[k] = pq[1,:]/sm
self.pnm[k] = pq[0,:]*sm
def get_kins(self):
"""Gets the MD kinetic energy for all the normal modes.
Returns:
A list of the kinetic energy for each NM.
"""
kmd = np.zeros(self.nbeads,float)
sm = depstrip(self.beads.sm3[0])
pnm = depstrip(self.pnm)
nmf = depstrip(self.nm_factor)
# computes the MD ke in the normal modes representation, to properly account for CMD mass scaling
for b in range(self.nbeads):
sp = pnm[b]/sm # mass-scaled momentum of b-th NM
kmd[b] = np.dot(sp,sp)*0.5/nmf[b] # include the partially adiabatic CMD mass scaling
return kmd
def get_kin(self):
"""Gets the total MD kinetic energy.
Note that this does not correspond to the quantum kinetic energy estimate
for the system.
Returns:
The sum of the kinetic energy of each NM in the path.
"""
return self.kins.sum()
def get_kstress(self):
"""Calculates the total MD kinetic stress tensor.
Note that this does not correspond to the quantum kinetic stress tensor
estimate for the system.
Returns:
The sum of the MD kinetic stress tensor contributions from each NM.
"""
kmd = np.zeros((3,3),float)
sm = depstrip(self.beads.sm3[0])
pnm = depstrip(self.pnm)
nmf = depstrip(self.nm_factor)
for b in range(self.nbeads):
sp = pnm[b]/sm # mass-scaled momentum of b-th NM
for i in range(3):
for j in range(3):
# computes the outer product of the p of various normal modes
# singling out Cartesian components to build the tensor
# also takes care of the possibility of having non-RPMD masses
kmd[i,j] += np.dot(sp[i:3*self.natoms:3],sp[j:3*self.natoms:3])/nmf[b]
return kmd

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