/
example_inv_big_pv.py
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/
example_inv_big_pv.py
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import os, sys, numpy as np, matplotlib.pyplot as plt
#hack to allow scripts to be placed in subdirectories next to burnman:
if not os.path.exists('burnman') and os.path.exists('../burnman'):
sys.path.insert(1,os.path.abspath('..'))
import burnman
from burnman import minerals
from time import time
import pymc
import math
import cProfile
from scipy.stats import norm
import matplotlib.mlab as mlab
seismic_model = burnman.seismic.prem() # pick from .prem() .slow() .fast() (see code/seismic.py)
number_of_points = 10 #set on how many depth slices the computations should be done
depths = np.linspace(1000e3,2500e3, number_of_points)
seis_p, seis_rho, seis_vp, seis_vs, seis_vphi = seismic_model.evaluate_all_at(depths)
temperature = burnman.geotherm.brown_shankland(seis_p)
print "preparations done"
def calc_velocities(mg_pv_K,mg_pv_K_prime,mg_pv_G,mg_pv_G_prime,fe_pv_K,fe_pv_K_prime,fe_pv_G,fe_pv_G_prime):
method = 'slb3' #slb3|slb2|mgd3|mgd2
amount_perovskite = 0.95
rock = burnman.composite( [ ( minerals.SLB_2005.mg_fe_perovskite(0.1), amount_perovskite ),
(minerals.SLB_2005.ferropericlase(0.5), 1.0-amount_perovskite) ] )
mg_pv = rock.staticphases[0].mineral.base_materials[0]
fe_pv = rock.staticphases[0].mineral.base_materials[1]
mg_pv.params['K_0'] = mg_pv_K
mg_pv.params['Kprime_0'] = mg_pv_K_prime
mg_pv.params['G_0'] = mg_pv_G
mg_pv.params['Gprime_0'] = mg_pv_G_prime
fe_pv.params['K_0'] = fe_pv_K
fe_pv.params['Kprime_0'] = fe_pv_K_prime
fe_pv.params['G_0'] = fe_pv_G
fe_pv.params['Gprime_0'] = fe_pv_G_prime
rock.set_method(method)
mat_rho, mat_vp, mat_vs, mat_vphi, mat_K, mat_G = burnman.velocities_from_rock(rock,seis_p, temperature)
return mat_vp, mat_vs, mat_rho
def error(mg_pv_K,mg_pv_K_prime,mg_pv_G,mg_pv_G_prime,fe_pv_K,fe_pv_K_prime,fe_pv_G,fe_pv_G_prime):
mat_vp, mat_vs, mat_rho = calc_velocities(mg_pv_K,mg_pv_K_prime,mg_pv_G,mg_pv_G_prime,fe_pv_K,fe_pv_K_prime,fe_pv_G,fe_pv_G_prime)
vs_err = burnman.l2(depths, mat_vs, seis_vs)
vp_err = burnman.l2(depths, mat_vp, seis_vp)
den_err = burnman.l2(depths, mat_rho, seis_rho)
return vs_err #+ vp_err #+ den_err
# Priors on unknown parameters:
sigma = 10.0e9
prime_sigma = 0.1
mg_pv_K = pymc.Normal('mg_pv_K', mu=251.e9, tau=1./(sigma**2))
mg_pv_K_prime = pymc.Normal('mg_pv_K_prime', mu=4.1, tau=1./(prime_sigma**2))
mg_pv_G = pymc.Normal('mg_pv_G', mu=175.e9, tau=1./(sigma**2))
mg_pv_G_prime = pymc.Normal('mg_pv_G_prime', mu=1.8, tau=1./(prime_sigma**2))
fe_pv_K = pymc.Normal('fe_pv_K', mu=281.e9, tau=1./(sigma**2))
fe_pv_K_prime = pymc.Normal('fe_pv_K_prime', mu=4.1, tau=1./(prime_sigma**2))
fe_pv_G = pymc.Normal('fe_pv_G', mu=161.e9, tau=1./(sigma**2))
fe_pv_G_prime = pymc.Normal('fe_pv_G_prime', mu=1.57, tau=1./(prime_sigma**2))
minerr = 1e100
#(plot=False)
@pymc.deterministic
def theta(p1=mg_pv_K,p2=mg_pv_K_prime,p3=mg_pv_G,p4=mg_pv_G_prime,p5=fe_pv_K,p6=fe_pv_K_prime,p7=fe_pv_G,p8=fe_pv_G_prime):
global minerr
if (p1<0 or p2<0 or p3<0 or p4<0 or p5<0 or p6<0 or p7<0 or p8<0):
return 1e30
try:
e = error(p1,p2,p3,p4,p5,p6,p7,p8)
if (e<minerr):
minerr=e
print "best fit", e, "values:", p1,p2,p3,p4,p5,p6,p7,p8
return e
except ValueError:
return 1e20#float("inf")
sig = 1e-4
misfit = pymc.Normal('d',mu=theta,tau=1.0/(sig*sig),value=0,observed=True,trace=True)
model = [mg_pv_K,mg_pv_K_prime,mg_pv_G,mg_pv_G_prime,fe_pv_K,fe_pv_K_prime,fe_pv_G,fe_pv_G_prime,misfit]
things = ['mg_pv_K','mg_pv_K_prime','mg_pv_G','mg_pv_G_prime','fe_pv_K','fe_pv_K_prime','fe_pv_G','fe_pv_G_prime','misfit']
whattodo = ""
if len(sys.argv)<3:
print "options:"
print "run <dbname>"
print "continue <dbname>"
print "plot <dbname1> <dbname2> ..."
else:
whattodo = sys.argv[1]
dbname = sys.argv[2]
if whattodo=="run":
S = pymc.MCMC(model, db='pickle', dbname=dbname)
S.sample(iter=100, burn=0, thin=1)
S.db.close()
whattodo="continue"
if whattodo=="continue":
n_runs = 1000
for l in range(0,n_runs):
db = pymc.database.pickle.load(dbname)
print "*** run=%d/%d, # samples: %d" % (l, n_runs, db.trace('mg_pv_K').stats()['n'] )
S = pymc.MCMC(model, db=db)
S.sample(iter=500, burn=0, thin=1)
S.db.close()
if whattodo=="plot":
files=sys.argv[2:]
print "files:",files
b=10000
i=1
for t in things:
if t=='misfit':
continue
trace=[]
print "trace:",t
for filename in files:
db = pymc.database.pickle.load(filename)
newtrace=db.trace(t,chain=None).gettrace(burn=b,chain=None)
if (trace!=[]):
trace = np.append(trace, newtrace)
else:
trace=newtrace
print " adding ", newtrace.size, "burn = ",b
print " total size ", trace.size
print "mean = ", trace.mean()
for bin in [10,20,50,100]:
hist,bin_edges=np.histogram(trace,bins=bin)
a=np.argmax(hist)
print "maxlike = ", bin_edges[a], bin_edges[a+1], (bin_edges[a]+bin_edges[a+1])/2.0
(mu, sigma) = norm.fit(np.array(trace))
print "mu, sigma: %e %e" % (mu, sigma)
plt.subplot(2,len(things)/2,i)
n, bins, patches = plt.hist(np.array(trace), 60, normed=1, facecolor='green', alpha=0.75)
y = mlab.normpdf( bins, mu, sigma)
l = plt.plot(bins, y, 'r--', linewidth=2)
plt.title("%s, mean: %.3e, std dev.: %.3e" % (t,mu,sigma),fontsize='small')
#pymc.Matplot.histogram(np.array(trace),t,rows=2,columns=len(things)/2,num=i)
i=i+1
plt.savefig("output_figures/example_inv_big_pv.png")
plt.show()
if whattodo=="test":
db = pymc.database.pickle.load(dbname)
S = pymc.MCMC(model, db=db)
for t in things:
print db.trace(t).stats()
print "means:"
for t in things:
print t,"\t",db.trace(t).stats()['mean']
print "#samples: %d" % db.trace('mg_pv_K').stats()['n']
pymc.raftery_lewis(S, q=0.025, r=0.01)
b = 1
t = 1
scores = pymc.geweke(S, intervals=20)
pymc.Matplot.trace(db.trace('deviance',chain=None).gettrace(burn=1000,thin=t,chain=None),'deviance',rows=2,columns=9,num=1)
pymc.Matplot.trace(db.trace('mg_pv_K',chain=None).gettrace(thin=t,chain=None),'mg_pv_K',rows=2,columns=9,num=2)
pymc.Matplot.histogram(np.array(db.trace('mg_pv_K',chain=None).gettrace(burn=b,chain=None)),'mg_pv_K',rows=2,columns=9,num=11)
pymc.Matplot.trace(db.trace('mg_pv_K_prime',chain=None).gettrace(thin=t,chain=None),'mg_pv_K_prime',rows=2,columns=9,num=3)
pymc.Matplot.histogram(np.array(db.trace('mg_pv_K_prime',chain=None).gettrace(burn=b,chain=None)),'mg_pv_K_prime',rows=2,columns=9,num=12)
pymc.Matplot.trace(db.trace('mg_pv_G',chain=None).gettrace(thin=t,chain=None),'mg_pv_G',rows=2,columns=9,num=4)
pymc.Matplot.histogram(np.array(db.trace('mg_pv_G',chain=None).gettrace(burn=b,chain=None)),'mg_pv_G',rows=2,columns=9,num=13)
pymc.Matplot.trace(db.trace('mg_pv_G_prime',chain=None).gettrace(thin=t,chain=None),'mg_pv_G_prime',rows=2,columns=9,num=5)
pymc.Matplot.histogram(np.array(db.trace('mg_pv_G_prime',chain=None).gettrace(burn=b,chain=None)),'mg_pv_G_prime',rows=2,columns=9,num=14)
pymc.Matplot.trace(db.trace('fe_pv_K',chain=None).gettrace(thin=t,chain=None),'fe_pv_K',rows=2,columns=9,num=6)
pymc.Matplot.histogram(np.array(db.trace('fe_pv_K',chain=None).gettrace(burn=b,chain=None)),'fe_pv_K',rows=2,columns=9,num=15)
pymc.Matplot.trace(db.trace('fe_pv_K_prime',chain=None).gettrace(thin=t,chain=None),'fe_pv_K_prime',rows=2,columns=9,num=7)
pymc.Matplot.histogram(np.array(db.trace('fe_pv_K_prime',chain=None).gettrace(burn=b,chain=None)),'fe_pv_K_prime',rows=2,columns=9,num=16)
pymc.Matplot.trace(db.trace('fe_pv_G',chain=None).gettrace(thin=t,chain=None),'fe_pv_G',rows=2,columns=9,num=8)
pymc.Matplot.histogram(np.array(db.trace('fe_pv_G',chain=None).gettrace(burn=b,chain=None)),'fe_pv_G',rows=2,columns=9,num=17)
pymc.Matplot.trace(db.trace('fe_pv_G_prime',chain=None).gettrace(thin=t,chain=None),'fe_pv_G_prime',rows=2,columns=9,num=9)
pymc.Matplot.histogram(np.array(db.trace('fe_pv_G_prime',chain=None).gettrace(burn=b,chain=None)),'fe_pv_G_prime',rows=2,columns=9,num=18)
plt.show()
if whattodo=="show":
values = [float(i) for i in sys.argv[2:]]
mat_vp, mat_vs, mat_rho = calc_velocities(values[0], values[1], values[2], values[3], values[4], values[5], values[6], values[7])
plt.subplot(2,2,1)
plt.plot(seis_p/1.e9,mat_vs/1.e3,color='r',linestyle='-',marker='^',markerfacecolor='r',markersize=4)
plt.plot(seis_p/1.e9,seis_vs/1.e3,color='k',linestyle='-',marker='v',markerfacecolor='k',markersize=4)
plt.ylim([4, 8])
plt.title("Vs (km/s)")
# plot Vphi
plt.subplot(2,2,2)
plt.plot(seis_p/1.e9,mat_vp/1.e3,color='r',linestyle='-',marker='^',markerfacecolor='r',markersize=4)
plt.plot(seis_p/1.e9,seis_vp/1.e3,color='k',linestyle='-',marker='v',markerfacecolor='k',markersize=4)
plt.ylim([10, 14])
plt.title("Vp (km/s)")
# plot density
plt.subplot(2,2,3)
plt.plot(seis_p/1.e9,mat_rho/1.e3,color='r',linestyle='-',marker='^',markerfacecolor='r',markersize=4,label='model 1')
plt.plot(seis_p/1.e9,seis_rho/1.e3,color='k',linestyle='-',marker='v',markerfacecolor='k',markersize=4,label='ref')
plt.title("density (kg/m^3)")
plt.legend(loc='upper left')
plt.ylim([4, 8])
plt.savefig("output_figures/example_inv_big_pv_show.png")
plt.show()
if whattodo=="profile2":
#run with:
#python -m cProfile -o output.pstats example_inv_big_pv.py profile2 1
#gprof2dot.py -f pstats output.pstats | dot -Tpng -o output.png
[error(235.654790318e9, 3.87724833477, 165.45907725e9, 1.61618366689, 273.888690109e9, 4.38543140228, 306.635371217e9, 1.42610871557) for i in range(0,10)]
if whattodo=="profile":
#just run normally
cProfile.run("[error(235.654790318e9, 3.87724833477, 165.45907725e9, 1.61618366689, 273.888690109e9, 4.38543140228, 306.635371217e9, 1.42610871557) for i in range(0,10)]")