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MetropolisCalculations.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Jun 11 14:57:11 2020
@author: mtd
"""
from numpy import empty,mean,exp,putmask,log,any
from scipy.stats import lognorm
import time
from CalcDelta import CalcDelta
from CalcADelta import CalcADelta
from CalcB import CalcB
from logninvstat import logninvstat
from CalcLklhd import CalcLklhd
def MetropolisCalculations(Prior,D,Obs,jmp,C,R,DAll,AllObs,nOpt,DebugMode):
[Delta,DeltaA,B,C,thetauA0,thetauna,thetaux1,thetauq,R]=InitializeMetropolis(D,C,Prior,R)
if DebugMode:
C.N=int(C.N/10)
C.Nburn=int(C.Nburn/10)
jmp.stdA0=0.1*mean(thetauA0)
jmp.stdna=0.01*mean(thetauna)
jmp.stdx1=0.1*mean(thetaux1)
# set target acceptance rates to 0.25 since all quantities are vectors (length D.nR)
jmp.target1=0.25
jmp.target2=0.25
jmp.target3=0.25
jmp.stdA0s=empty((C.N))
jmp.stdnas=empty((C.N))
jmp.stdx1s=empty((C.N))
meanA0=Prior.meanA0
covA0=Prior.stdA0/meanA0
vA0=(covA0*meanA0)**2
[muA0,sigmaA0]=logninvstat(meanA0,vA0)
#%%
meanna=Prior.meanna
covna=Prior.stdna/meanna
vna=(covna*Prior.meanna)**2
[muna,sigmana] = logninvstat(meanna,vna)
meanx1=Prior.meanx1
covx1=Prior.stdx1/meanx1
vx1=(covx1*Prior.meanx1)**2
[mux1,sigmax1] = logninvstat(-Prior.meanx1,vx1)
pu1=lognorm.pdf(thetauA0,sigmaA0,0,exp(muA0))
pu2=lognorm.pdf(thetauna,sigmana,0,exp(muna))
if nOpt<5:
pu3=lognorm.pdf(-thetaux1,sigmax1,0,exp(mux1))
elif nOpt==5:
pu3=lognorm.pdf(thetaux1,sigmax1,0,exp(mux1))
fu=CalcLklhd(Obs,AllObs,thetauA0,thetauna,thetaux1,D,Prior,Delta,DeltaA,B,thetauq,nOpt)
C.n_a1=0
C.n_a2=0
C.n_a3=0
C.Like=empty((C.N))
C.LogLike=empty((C.N))
#%%
tic=time.process_time()
for i in range(0,C.N):
if i%1000==0:
print("Iteration #", i+1, "/", C.N, ".")
if i<C.N*.2 and i>0 and i%100==0:
jmp.stdA0=mean(jmp.stdA0s[0:i-1] )/jmp.target1*(C.n_a1/i)
jmp.stdna=mean(jmp.stdnas[0:i-1] )/jmp.target2*(C.n_a2/i)
jmp.stdx1=mean(jmp.stdx1s[0:i-1] )/jmp.target3*(C.n_a3/i)
jmp.stdA0s[i]=jmp.stdA0
jmp.stdnas[i]=jmp.stdna
jmp.stdx1s[i]=jmp.stdx1
#A0
thetavA0=thetauA0+jmp.stdA0*R.z1[:,i]
thetavA0[thetavA0<jmp.A0min.reshape((D.nR,))]=putmask(thetavA0,thetavA0<jmp.A0min,jmp.A0min)
pv1=lognorm.pdf(thetavA0,sigmaA0,0,exp(muA0))
fv=CalcLklhd(Obs,AllObs,thetavA0,thetauna,thetaux1,D,Prior,Delta,DeltaA,B,thetauq,nOpt)
MetRatio=exp(fv-fu)*exp(sum(log(pv1))-sum(log(pu1)))
if MetRatio > R.u1[i]:
C.n_a1=C.n_a1+1
thetauA0=thetavA0; fu=fv;pu1=pv1 # update u->v
C.thetaA0[:,i]=thetauA0.T
#na
thetavna=thetauna+jmp.stdna*R.z2[:,i]
thetavna[thetavna<jmp.nmin]=putmask(thetavna,thetavna<jmp.nmin,jmp.nmin)
pv2=lognorm.pdf(thetavna,sigmana,0,exp(muna))
fv=CalcLklhd(Obs,AllObs,thetauA0,thetavna,thetaux1,D,Prior,Delta,DeltaA,B,thetauq,nOpt)
MetRatio=exp(fv-fu)*exp(sum(log(pv2))-sum(log(pu2)))
if MetRatio > R.u2[i]:
C.n_a2=C.n_a2+1
thetauna=thetavna; fu=fv; pu2=pv2;
C.thetana[:,i]=thetauna.T
#x1
thetavx1=thetaux1+jmp.stdx1*R.z3[:,i]
if nOpt<5:
pv3=lognorm.pdf(-thetavx1,sigmax1,0,exp(mux1))
elif nOpt==5:
pv3=lognorm.pdf(thetavx1,sigmax1,0,exp(mux1))
fv=CalcLklhd(Obs,AllObs,thetauA0,thetauna,thetavx1,D,Prior,Delta,DeltaA,B,thetauq,nOpt)
if any(pv3==0):
MetRatio=0
else:
MetRatio=exp(fv-fu)*exp(sum(log(pv3))-sum(log(pu3)))
if MetRatio > R.u3[i]:
C.n_a3=C.n_a3+1
thetaux1=thetavx1; fu=fv; pu3=pv3;
C.thetax1[:,i]=thetaux1.T
C.Like[i]=exp(fu)
C.LogLike[i]=fu
toc=time.process_time(); print('McFLI MCMC Time: %.2fs' %(toc-tic))
print('A0: Acceptance rate =',(C.n_a1/C.N*100), ' pct.')
print('na: Acceptance rate =', (C.n_a2/C.N*100), ' pct.')
print('x1 Acceptance rate =', (C.n_a3/C.N*100), ' pct.')
#%%
return C
def InitializeMetropolis(D,C,P,R):
from numpy.random import seed,rand,randn
Delta=CalcDelta(D.nR,D.nt,D.L)
DeltaA=CalcADelta(D.nR,D.nt)
B=CalcB(D.nR,D.nt)
C.thetaA0=empty((D.nR,C.N))
C.thetaA0[:,0]=P.meanA0
thetauA0=C.thetaA0[:,0]
C.thetana=empty((D.nR,C.N))
C.thetana[:,0]=P.meanna
thetauna=C.thetana[:,0]
C.thetax1=empty((D.nR,C.N))
C.thetax1[:,0]=P.meanx1
thetaux1=C.thetax1[:,0]
thetauq=[]
seed([R.Seed])
R.z1=randn(D.nR,C.N)
R.z2=randn(D.nR,C.N)
R.z3=randn(D.nR,C.N)
R.u1=rand(C.N,1)
R.u2=rand(C.N,1)
R.u3=rand(C.N,1)
return Delta,DeltaA,B,C,thetauA0,thetauna,thetaux1,thetauq,R