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PyReweighting-2D.py
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PyReweighting-2D.py
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#! /usr/bin/env python
## Required Software:
# Python: https://www.python.org/downloads/
# NumPy and SciPy: http://www.scipy.org/scipylib/download.html
# matplotlib: http://matplotlib.org/downloads.html
import math
import scipy
import scipy.stats as stats
import numpy as np
import sys
import matplotlib.pyplot as plt
import csv
from argparse import ArgumentParser
from scipy.optimize import curve_fit
## from scipy.optimize import *
print ("============================================================")
print ("PyReweighting: Python scripts used to reweight accelerated molecular dynamics simulations.")
print (" ")
print ("Authors: Yinglong Miao <[email protected]>")
print (" Bill Sinko <[email protected]>")
print ("\n\
Copyright <2014-2019> <Yinglong Miao and William Sinko> \n\
\n\
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \"PyReweighting\"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following citation: \n\
\n\
Miao Y, Sinko W, Pierce L, Bucher D, Walker RC, McCammon JA (2014) Improved reweighting of accelerated molecular dynamics simulations for free energy calculation. J Chemical Theory and Computation. 10(7): 2677-2689.")
print (" ")
###########MAIN
def main():
## Set control parameters
plt_figs = 0
args = cmdlineparse()
data=loadfiletoarray(args.input)
rows = len(data[:,0])
weights,dV = weightparse(rows, args)
if args.discX:
discX=float(args.discX)
else :
discX = 6
if args.discY:
discY=float(args.discY)
else :
discY = 6
if args.Xdim:
binsX= assignbins(args.Xdim, discX)
else:
max_data = discX * (int(np.amax(data[:,0])/discX) + 1)
min_data = discX * (int(np.amin(data[:,0])/discX) - 1)
binsX= assignbins([min_data,max_data], discX) ## Default bin size
if args.Ydim:
binsY= assignbins(args.Ydim, discY)
else:
max_data = discY * (int(np.amax(data[:,1])/discY) + 1)
min_data = discY * (int(np.amin(data[:,1])/discY) - 1)
binsY= assignbins([min_data,max_data], discY) ## Default bin size
## SET MAX ENERGY FOR ALL INFINITY VALUES
if args.Emax:
cb_max=float(args.Emax)
else :
cb_max = 8
## SET HISTOGRAM CUTOFF
if args.cutoff:
hist_min=int(args.cutoff)
else :
hist_min = 10 # minimum number of configurations in one bin
## SET ORDER of McLaurin series expansion
if args.order:
order=int(args.order)
else :
order = 10 # default
## SET TEMPERATURE
if args.T:
T=float(args.T)
else :
T = 300 # simulation temperature
beta = 1.0/(0.001987*T)
##REWEIGHTING
## SET flag for Gaussian fitting of deltaV
if args.fit:
fit=args.fit
else :
fit=False # simulation temperature
##REWEIGHTING
if args.job == "amdweight_CE":
hist2,newedgesX,newedgesY,c1,c2,c3 = reweight_CE(data,hist_min,binsX,discX,binsY,discY,dV,T,fit)
pmf = hist2pmf2D(hist2,hist_min,T)
c1 = -np.multiply(1.0/beta,c1)
c2 = -np.multiply(1.0/beta,c2)
c3 = -np.multiply(1.0/beta,c3)
c12 = np.add(c1,c2)
c123 = np.add(c12,c3)
pmf_c1 = np.add(pmf, c1)
print ("pmf_min-c1 = ", np.min(pmf_c1))
pmf_c1 = normalize2D(pmf_c1,cb_max)
pmf_c2 = np.add(pmf, c12)
print ("pmf_min-c2 = ", np.min(pmf_c2))
pmf_c2 = normalize2D(pmf_c2,cb_max)
pmf_c3 = np.add(pmf, c123)
print ("pmf_min-c3 = ", np.min(pmf_c3))
pmf_c3 = normalize2D(pmf_c3,cb_max)
elif args.job == "amdweight_MC":
n=order
MCweight=np.zeros(len(dV))
beta_dV=np.multiply(dV,beta)
for x in range(0,n+1):
MCweight=np.add(MCweight,(np.divide(np.power(beta_dV, x), float(scipy.misc.factorial(x)))))
weights=MCweight
hist2,newedgesX,newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=weights)
hist2=prephist(hist2,T,cb_max)
elif args.job == "amdweight":
hist2,newedgesX,newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=weights)
hist2=prephist(hist2,T,cb_max)
else :
hist2,newedgesX,newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=None)
hist2=prephist(hist2,T,cb_max)
##SAVE FREE ENERGY DATA INTO A FILE
if args.job == "amdweight_MC" or args.job == "amdweight" or args.job == "noweight" :
pmffile = 'pmf-'+str(args.input)+'.xvg'
output_pmf2D(pmffile,hist2,binsX,binsY)
if args.job == "amdweight_CE" :
hist2 = pmf_c1
pmffile = 'pmf-c1-'+str(args.input)+'.xvg'
output_pmf2D(pmffile,hist2,binsX,binsY)
hist2 = pmf_c3
pmffile = 'pmf-c3-'+str(args.input)+'.xvg'
output_pmf2D(pmffile,hist2,binsX,binsY)
hist2 = pmf_c2
pmffile = 'pmf-c2-'+str(args.input)+'.xvg'
output_pmf2D(pmffile,hist2,binsX,binsY)
if args.job == "histo" :
hist2,newedgesX,newedgesY = histo(data,hist_min,binsX,discX,binsY)
pmffile = 'histo-'+str(args.input)+'.xvg'
output_dV_anharm2D(pmffile,binsX,binsY,hist2)
if args.job == "amd_dV":
plt_figs = 0
hist2,newedgesX,newedgesY,binfX,binfY,dV_avg,dV_std,dV_anharm,dV_mat = reweight_dV(data,hist_min,binsX,binsY,discX,discY,dV,T)
pmffile = 'dV-hist-2D-'+str(args.input) + '.xvg'
output_dV(pmffile,dV)
alpha = anharm(dV)
print ("Anharmonicity of all dV = " + str(alpha))
pmffile = 'dV-anharm-2D-'+str(args.input)+'.xvg'
output_dV_anharm2D(pmffile,binsX,binsY,dV_anharm)
pmffile = 'dV-stat-2D-'+str(args.input)+'.xvg'
output_dV_stat2D(pmffile,binsX,binsY,dV_avg,dV_std,dV_anharm)
pmffile = 'dV-mat-2D-'+str(args.input)+'.xvg'
output_dV_mat2D(pmffile,binsX,binsY,hist2,dV_avg,dV_std,dV_anharm,dV_mat)
###PLOTTING FUNCTION FOR FREE ENERGY FIGURE
if plt_figs :
cbar_ticks=[0, cb_max*.25, cb_max*.5, cb_max*.75, 8.0]
plt.figure(2, figsize=(11,8.5))
extent = [newedgesX[0], newedgesX[-1], newedgesY[-1], newedgesY[0]]
print (extent)
plt.imshow(hist2.transpose(), extent=extent, interpolation='gaussian')
cb = plt.colorbar(ticks=cbar_ticks, format=('% .1f'), aspect=10) # grab the Colorbar instance
imaxes = plt.gca()
plt.sca(cb.ax)
plt.clim(vmin=0,vmax=8.0)
plt.yticks(fontsize=18)
plt.sca(imaxes)
axis=(min(binsX), max(binsX), min(binsY), max(binsY))
plt.axis(axis)
plt.xticks(size='18')
plt.yticks(size='18')
plt.xlabel('RC1',fontsize=18)
plt.ylabel('RC2',fontsize=18)
## plt.xlabel(r'$\phi$',fontsize=18)
## plt.ylabel(r'$\psi$',fontsize=18)
## plt.xlabel(r'$\chi$1',fontsize=18)
## plt.ylabel(r'$\chi$2',fontsize=18)
plt.savefig('2D_Free_energy_surface.png',bbox_inches=0)
print ("FIGURE SAVED 2D_Free_energy_surface.png")
###PLOTTING FUNCTION FOR WEIGHTS histogram
[hist, edges] = np.histogram(weights, bins=100)
width=np.absolute(np.subtract(edges[0], edges[1]))
plt.figure(1, figsize=(11,8.5))
plt.bar(edges[:100], hist, width=width, log=True)
plt.yscale('log') ###if typerror is thrown delete .matplotlib/fontList.cache file
plt.xticks(fontsize='18')
plt.yticks(fontsize='18')
plt.savefig('weights.png',bbox_inches=0)
print ("FIGURE SAVED weights.png")
print (" ")
print ("END")
def cmdlineparse():
parser = ArgumentParser(description="command line arguments")
parser.add_argument("-input", dest="input", required=True, help="2D input file", metavar="<2D input file>")
parser.add_argument("-job", dest="job", required=True, help="Reweighting method to use: <noweight>, <weighthist>, <amd_time>, <amd_dV>, <amdweight>, <amdweight_MC>, <amdweight_CE>", metavar="<Job type reweighting method>")
parser.add_argument("-weight", dest="weight", required=False, help="weight file", metavar="<weight file>")
parser.add_argument("-Xdim", dest="Xdim", required=False, nargs="+", help="Xdimensions", metavar="<Xmin Xmax >")
parser.add_argument("-Ydim", dest="Ydim", required=False, nargs="+", help="Ydimension", metavar="<Ymin Ymax >")
parser.add_argument("-discX", dest="discX", required=False, help="Discretization size in X dimension", metavar="<discretization-X>")
parser.add_argument("-discY", dest="discY", required=False, help="Discretization size in Y dimension", metavar="<discretization-Y>")
parser.add_argument("-cutoff", dest="cutoff", required=False, help="histogram cutoff", metavar="<cutoff>")
parser.add_argument("-T", dest="T", required=False, help="Temperature", metavar="<Temperature>")
parser.add_argument("-Emax", dest="Emax", required=False, help="Maximum free energy", metavar="<Emax>")
parser.add_argument("-fit", dest="fit", required=False, help="Fit deltaV distribution", metavar="<fit>")
parser.add_argument("-order", dest="order", required=False, help="Order of Maclaurin series", metavar="<order>")
args=parser.parse_args()
return args
def loadfiletoarray(file):
loaded=np.loadtxt(file, usecols=[0,1])
print ("DATA LOADED: "+file)
return loaded
def weightparse(rows, args):
if args.job == "weighthist":
data=np.loadtxt(args.weight)
weights=data[:,0]
dV = np.zeros(rows)
elif args.job == "amd_time" or args.job == "amd_dV" or args.job == "amdweight" or args.job == "amdweight_MC" or args.job == "amdweight_CE" :
data=np.loadtxt(args.weight)
weights = np.exp(data[:,0])
dV = data[:,2]
elif args.job == "noweight" or args.job == "histo":
weights = np.zeros(rows)
weights = weights + 1
dV = np.zeros(rows)
else:
print ("ERROR JOBTYPE"+ args.job+ " NOT RECOGNIZED")
del data
del weights
del dV
return weights,dV
def histo(data,hist_min,binsX,discX,binsY,discY):
hist2, newedgesX, newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=None)
return hist2,newedgesX,newedgesY
def assignbins(dim, disc):
minimum=float(dim[0])
maximum=float(dim[1])
bins =np.arange(minimum,(maximum+disc),disc)
return bins
def normalize2D(pmf,cb_max):
pmf=pmf-np.min(pmf) ## zero value to lowest energy state
temphist=pmf
#set infinity free energy values to is cb_max
for jy in range(len(temphist[0,:])):
for jx in range(len(temphist[:,0])):
if np.isinf(temphist[jx,jy]):
temphist[jx,jy]=cb_max
return temphist
def prephist(hist2,T,cb_max):
hist2=np.add(hist2,0.000000000000000001) ###so that distrib
hist2=(0.001987*T)*np.log(hist2) ####Convert to free energy in Kcal/mol
hist2=np.max(hist2)-hist2 ## zero value to lowest energy state
temphist2=hist2
#set infinity free energy values to is cb_max
for jy in range(len(temphist2[0,:])):
for jx in range(len(temphist2[:,0])):
if np.isinf(temphist2[jx,jy]):
temphist2[jx,jy]=cb_max
return temphist2
# memory usage is much reduced with multidimensional list for dV_mat; pretty fast ~ O(N)
def reweight_CE(data,hist_min,binsX,discX,binsY,discY,dV,T,fit):
hist2, newedgesX, newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=None)
beta = 1.0/(0.001987*T)
nf = len(data[:,0])
nbinsX = len(hist2[:,0])
nbinsY = len(hist2[0,:])
c1 = np.zeros((nbinsX,nbinsY))
c2 = np.zeros((nbinsX,nbinsY))
c3 = np.zeros((nbinsX,nbinsY))
binfX = np.zeros(nf) # array for storing assigned bin of each frame
binfY = np.zeros(nf) # array for storing assigned bin of each frame
nA = np.zeros((nbinsX,nbinsY),dtype=np.int) # nA is equivalent to hist here
dV_avg = np.zeros((nbinsX,nbinsY))
dV_avg2 = np.zeros((nbinsX,nbinsY))
dV_avg3 = np.zeros((nbinsX,nbinsY))
dV_std = np.zeros((nbinsX,nbinsY))
dV_avg_all=np.average(dV)
dV_std_all=np.std(dV)
print ('dV all: avg = ', dV_avg_all, 'std = ', dV_std_all)
dV_mat = [[[[] for i in range(1)] for i in range(nbinsY)] for i in range(nbinsX)]
for i in range(len(data[:,0])):
jx = int((data[i,0]-binsX[0])/discX)
jy = int((data[i,1]-binsY[0])/discY)
if jx < nbinsX and jy < nbinsY :
binfX[i] = jx
binfY[i] = jy
dV_mat[jx][jy].append(dV[i])
nA[jx,jy] = nA[jx,jy]+1
for jx in range(nbinsX):
for jy in range(nbinsY):
if nA[jx,jy]>=hist_min :
num = int(nA[jx,jy])
atemp = np.asarray(dV_mat[jx][jy][1:num+1])
atemp2 = np.power(atemp,2)
atemp3 = np.power(atemp,3)
dV_avg[jx,jy] = np.average(atemp)
dV_std[jx,jy]=np.std(atemp)
dV_avg2[jx,jy]=np.average(atemp2)
dV_avg3[jx,jy]=np.average(atemp3)
del atemp
del atemp2
del atemp3
c1[jx,jy] = beta*dV_avg[jx,jy]
c2[jx,jy] = 0.5*beta**2*dV_std[jx,jy]**2
c3[jx,jy] = (1.0/6.0)*beta**3*(dV_avg3[jx,jy]-3.0*dV_avg2[jx,jy]*dV_avg[jx,jy]+2.0*dV_avg[jx,jy]**3)
del dV_mat
del dV_avg
del dV_avg2
del dV_avg3
del dV_std
return hist2,newedgesX,newedgesY,c1,c2,c3
def reweight_dV(data,hist_min,binsX,binsY,discX,discY,dV,T):
hist2, newedgesX, newedgesY = np.histogram2d(data[:,0], data[:,1], bins = (binsX, binsY), weights=None)
nf = len(data[:,0])
nbinsX = len(hist2[:,0])
nbinsY = len(hist2[0,:])
binfX = np.zeros(nf) # array for storing assigned bin of each frame
binfY = np.zeros(nf) # array for storing assigned bin of each frame
nA = np.zeros((nbinsX,nbinsY),dtype=np.int) # nA is equivalent to hist here
dV_avg = np.zeros((nbinsX,nbinsY))
dV_std = np.zeros((nbinsX,nbinsY))
dV_anharm = np.zeros((nbinsX,nbinsY))
dV_mat = [[[[] for i in range(1)] for i in range(nbinsY)] for i in range(nbinsX)]
for i in range(len(data[:,0])):
jx = int((data[i,0]-binsX[0])/discX)
jy = int((data[i,1]-binsY[0])/discY)
if jx < nbinsX and jy < nbinsY :
binfX[i] = jx
binfY[i] = jy
dV_mat[jx][jy].append(dV[i])
nA[jx,jy] = nA[jx,jy]+1
for jx in range(nbinsX):
for jy in range(nbinsY):
dV_anharm[jx,jy] = 100
if nA[jx,jy]>=hist_min :
num = int(nA[jx,jy])
atemp = np.asarray(dV_mat[jx][jy][1:num+1])
dV_avg[jx,jy] = np.average(atemp)
dV_std[jx,jy]=np.std(atemp)
dV_anharm[jx,jy] = anharm(atemp)
del atemp
return hist2,newedgesX,newedgesY,binfX,binfY,dV_avg,dV_std,dV_anharm,dV_mat
## Convert histogram to free energy in Kcal/mol
def hist2pmf2D(hist,hist_min,T):
nbinsX = len(hist[:,0])
nbinsY = len(hist[0,:])
pmf = np.zeros((nbinsX,nbinsY))
pmf_min = 100
for jx in range(len(hist[:,0])):
for jy in range(len(hist[0,:])):
if hist[jx,jy]>=hist_min :
pmf[jx,jy]=-(0.001987*T)*np.log(hist[jx,jy])
if pmf_min > pmf[jx,jy] :
pmf_min=pmf[jx,jy]
## pmf=pmf-pmf_min ## zero value to lowest energy state
return pmf
def output_pmf2D(pmffile,hist,binsX,binsY):
fpmf = open(pmffile, 'w')
strpmf='#RC1\tRC2\tPMF(kcal/mol)\n\n@ xaxis label \"RC1\"\n@ yaxis label \"RC2\"\n@TYPE xy\n'
fpmf.write(strpmf)
for jx in range(len(hist[:,0])):
for jy in range(len(hist[0,:])):
strpmf=str(binsX[jx]) + ' \t' + str(binsY[jy]) + ' \t' + str(hist[jx,jy]) + '\n'
fpmf.write(strpmf)
fpmf.closed
return fpmf
def output_dV(pmffile,dV):
fpmf = open(pmffile, 'w')
strpmf='#dV \tp(dV) \n\n@ xaxis label \"dV\"\n@ yaxis label \"p(dV)\"\n@TYPE xy\n'
hist_dV, bin_dV = np.histogram(dV, bins=50)
for k in range(len(hist_dV)):
strpmf=strpmf + str(bin_dV[k]) + ' \t' + str(hist_dV[k]) + ' \n'
fpmf.write(strpmf)
fpmf.closed
return fpmf
def output_dV_anharm2D(pmffile,binsX,binsY,dV_anharm):
fpmf = open(pmffile, 'w')
strpmf='#RC \tdV_anharm \tError\n\n@ xaxis label \"RC\"\n@ yaxis label \"dV_anmarm\"\n@TYPE xy\n'
fpmf.write(strpmf)
for jx in range(len(dV_anharm[:,0])):
for jy in range(len(dV_anharm[0,:])):
strpmf=str(binsX[jx]) + ' \t' + str(binsY[jy]) + ' \t' + str(dV_anharm[jx,jy]) + '\n'
fpmf.write(strpmf)
fpmf.closed
return fpmf
def output_dV_stat2D(pmffile,binsX,binsY,dV_avg,dV_std,dV_anharm):
fpmf = open(pmffile, 'w')
strpmf='#RC \tdV_avg(kcal/mol) \tError\n\n@ xaxis label \"RC\"\n@ yaxis label \"dV(kcal/mol)\"\n@TYPE xydy\n'
fpmf.write(strpmf)
for jx in range(len(dV_anharm[:,0])):
for jy in range(len(dV_anharm[0,:])):
strpmf=str(binsX[jx]) + ' \t' + str(binsY[jy]) + ' \t' + str(dV_avg[jx,jy]) + ' \t' + str(dV_std[jx,jy]) + ' \t' + str(dV_anharm[jx,jy]) + '\n'
fpmf.write(strpmf)
fpmf.closed
return fpmf
def output_dV_mat2D(pmffile,binsX,binsY,hist,dV_avg,dV_std,dV_anharm,dV_mat):
fpmf = open(pmffile, 'w')
strpmf='#RC \tNf \tdV_avg \tdV_std \tdV_ij \n\n@ xaxis label \"RC\"\n@ yaxis label \"dV(kcal/mol)\"\n@TYPE xy\n'
fpmf.write(strpmf)
for jx in range(len(hist[:,0])):
for jy in range(len(hist[0,:])):
nf_j = int(hist[jx,jy])
strpmf=str(binsX[jx]) + ' \t' + str(binsY[jy]) + ' \t' + str(hist[jx,jy]) + ' \t' + str(dV_avg[jx,jy]) + ' \t' + str(dV_std[jx,jy]) + ' \t' + str(dV_anharm[jx,jy])
strpmf=strpmf + ' \t' + str(dV_mat[jx][jy][1:nf_j+1])
strpmf=strpmf + '\n'
fpmf.write(strpmf)
fpmf.closed
return fpmf
def anharm(data):
var=np.var(data)
hist, edges=np.histogram(data, 50, normed=True)
hist=np.add(hist,0.000000000000000001) ###so that distrib
dx=edges[1]-edges[0]
S1=-1*np.trapz(np.multiply(hist, np.log(hist)),dx=dx)
S2=0.5*np.log(2.00*np.pi*np.exp(1.0)*var+0.000000000000000001)
alpha=S2-S1
if np.isinf(alpha):
alpha = 100
return alpha
if __name__ == '__main__':
main()