/
example_inv_murakami.py
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/
example_inv_murakami.py
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from __future__ import absolute_import
from __future__ import print_function
# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2015 by the BurnMan team, released under the GNU
# GPL v2 or later.
import sys
import numpy as np
import matplotlib.pyplot as plt
import burnman_path # adds the local burnman directory to the path
import burnman
from burnman import minerals
import pymc
import cProfile
import scipy.stats as sp
import matplotlib.mlab as mlab
assert burnman_path # silence pyflakes warning
if __name__ == "__main__":
seismic_model = burnman.seismic.PREM()
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(
['pressure', 'density', 'v_p', 'v_s', 'v_phi'], depths)
temperature = burnman.geotherm.brown_shankland(depths)
print("preparations done")
def calc_velocities(amount_pv, iron_pv, iron_fp):
pv = minerals.SLB_2011.mg_fe_perovskite([1.0 - iron_pv, iron_pv, 0.0])
fp = minerals.SLB_2011.ferropericlase([1.0 - iron_fp, iron_fp])
rock = burnman.Composite([pv, fp], [amount_pv, 1.0 - amount_pv])
mat_rho, mat_vp, mat_vs = rock.evaluate(
['density', 'v_p', 'v_s'], seis_p, temperature)
return mat_vp, mat_vs, mat_rho
def error(amount_pv, iron_pv, iron_fp):
mat_vp, mat_vs, mat_rho = calc_velocities(amount_pv, iron_pv, iron_fp)
vs_err = burnman.tools.math.l2(depths, mat_vs, seis_vs) / 1e9
vp_err = burnman.tools.math.l2(depths, mat_vp, seis_vp) / 1e9
den_err = burnman.tools.math.l2(depths, mat_rho, seis_rho) / 1e9
# print vs_err, vp_err, den_err
return vs_err + vp_err + den_err
# Priors on unknown parameters:
amount_pv = pymc.Uniform('amount_pv', lower=0.0, upper=1.0, value=0.5)
iron_pv = pymc.Uniform('iron_pv', lower=0.0, upper=1.0, value=0.5)
iron_fp = pymc.Uniform('iron_fp', lower=0.0, upper=1.0, value=0.5)
minerr = 1e100
@pymc.deterministic
def theta(amount_pv=amount_pv, iron_pv=iron_pv, iron_fp=iron_fp):
global minerr
try:
e = error(amount_pv, iron_pv, iron_fp)
if (e < minerr):
minerr = e
print("best fit", e, "values:", amount_pv, iron_pv, iron_fp)
return e
except ValueError:
return 1e20 # float("inf")
sig = 10.0
misfit = pymc.Normal('d', mu=theta, tau=1.0 / (
sig * sig), value=0, observed=True, trace=True)
model = [amount_pv, iron_pv, iron_fp, misfit]
things = ['amount_pv', 'iron_pv', 'iron_fp', 'misfit']
whattodo = ""
if len(sys.argv) < 3:
print("options:")
print("run <dbname>")
print("continue <dbname>")
print("plot <dbname1> <dbname2> ...")
print("show amount_pv iron_pv iron_fp")
else:
whattodo = sys.argv[1]
dbname = sys.argv[2]
if whattodo == "run":
S = pymc.MCMC(model, db='pickle', dbname=dbname)
S.sample(iter=400, burn=200, thin=1)
S.db.close()
if whattodo == "continue":
n_runs = 50
for l in range(0, n_runs):
db = pymc.database.pickle.load(dbname)
print("*** run=%d/%d, # samples: %d" %
(l, n_runs, db.trace('amount_pv').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)
toburn = 0
plot_idx = 1
for t in things:
if t == 'misfit':
continue
trace = []
print("trace:", t)
for filename in files:
db = pymc.database.pickle.load(filename)
dir(db)
newtrace = db.trace(t, chain=None).gettrace(
burn=toburn, chain=None)
if (trace != []):
trace = np.append(trace, newtrace)
else:
trace = newtrace
print(" adding ", newtrace.size, "burn = ", toburn)
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)
plt.subplot(2, len(things) / 2, plot_idx)
if plot_idx == 2:
n, bins, patches = plt.hist(
np.array(trace), 50, normed=1, facecolor='green', alpha=0.75)
X = sp.gumbel_l.fit(np.array(trace))
print(X)
dist = sp.gumbel_l(X[0], X[1])
x = np.array(bins)
y = dist.pdf(x)
print(y)
plt.plot(x, y, 'k--', linewidth=2)
X = sp.norm.fit(np.array(trace))
print(X)
dist = sp.norm(X[0], X[1])
x = np.array(bins)
y = dist.pdf(x)
plt.plot(x, y, 'r--', linewidth=2)
X = sp.genextreme.fit(np.array(trace))
print(X)
dist = sp.genextreme(X[0], X[1], X[2])
x = np.array(bins)
y = dist.pdf(x)
plt.plot(x, y, 'b--', linewidth=2)
plt.title("%s" % (t), fontsize='small')
elif plot_idx == 3:
n, bins, patches = plt.hist(
np.array(trace), 50, normed=1, facecolor='green', alpha=0.75)
X = sp.expon.fit(np.array(trace), floc=0)
print(X)
dist = sp.expon(X[0], X[1])
print(bins)
print(dist.pdf(np.array(bins)))
plt.plot(bins, dist.pdf(np.array(bins)), 'r--', linewidth=2)
plt.title("%s, mu: %.3e, sigma: %.3e" %
(t, mu, sigma), fontsize='small')
else:
(mu, sigma) = sp.norm.fit(np.array(trace))
print("mu, sigma: %e %e" % (mu, sigma))
n, bins, patches = plt.hist(
np.array(trace), 50, 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')
plot_idx += 1
plt.savefig("output_figures/example_inv_murakami.png")
plt.show()
if whattodo == "misfittest":
for a in np.linspace(0.4, 0.8, 10):
for b in np.linspace(0.05, 0.2, 5):
for c in np.linspace(0, 0.2, 5):
mat_vp, mat_vs, mat_rho = calc_velocities(a, b, c)
misfit = error(a, b, c)
print("misfit: %s " % misfit)
if misfit < 25:
plt.subplot(2, 2, 1)
plt.plot(
seis_p / 1.e9, mat_vs / 1.e3, color='r', linestyle='-',
marker='x', markerfacecolor='r', markersize=4)
plt.subplot(2, 2, 2)
plt.plot(
seis_p / 1.e9, mat_vp / 1.e3, color='r', linestyle='-',
marker='x', markerfacecolor='r', markersize=4)
plt.subplot(2, 2, 3)
plt.plot(
seis_p / 1.e9, mat_rho / 1.e3, color='r', linestyle='-',
marker='x', markerfacecolor='r', markersize=4, label='model 1')
plt.subplot(2, 2, 1)
plt.plot(seis_p / 1.e9, seis_vs / 1.e3, color='k', linestyle='-',
marker='o', markerfacecolor='None', markersize=6)
plt.ylim([4, 8])
plt.title("Vs (km/s)")
# plot Vp
plt.subplot(2, 2, 2)
plt.plot(seis_p / 1.e9, seis_vp / 1.e3, color='k', linestyle='-',
marker='o', 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, seis_rho / 1.e3, color='k', linestyle='-',
marker='o', markerfacecolor='k', markersize=4, label='ref')
plt.title("density ($\cdot 10^3$ kg/m^$3$)")
plt.legend(loc='upper left')
plt.ylim([4, 8])
plt.savefig("output_figures/example_inv_murakami_2.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])
misfit = error(values[0], values[1], values[2])
print("misfit: %s " % misfit)
plt.suptitle('misfit %.3e, amount_pv=%.4f, iron_pv=%.4f, iron_fp=%.4f' %
(misfit, values[0], values[1], values[2]))
plt.subplot(2, 2, 1)
plt.plot(seis_p / 1.e9, mat_vs / 1.e3, color='r', linestyle='-',
marker='x', markerfacecolor='r', markersize=4)
plt.plot(seis_p / 1.e9, seis_vs / 1.e3, color='k', linestyle='-',
marker='o', markerfacecolor='None', markersize=6)
plt.ylim([4, 8])
plt.title("Vs (km/s)")
# plot Vp
plt.subplot(2, 2, 2)
plt.plot(seis_p / 1.e9, mat_vp / 1.e3, color='r', linestyle='-',
marker='x', markerfacecolor='r', markersize=4)
plt.plot(seis_p / 1.e9, seis_vp / 1.e3, color='k', linestyle='-',
marker='o', 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='x', markerfacecolor='r', markersize=4, label='model 1')
plt.plot(seis_p / 1.e9, seis_rho / 1.e3, color='k', linestyle='-',
marker='o', markerfacecolor='k', markersize=4, label='ref')
plt.title("density ($\cdot 10^3$ kg/m$^3$)")
plt.legend(loc='upper left')
plt.ylim([4, 8])
plt.savefig("output_figures/example_inv_murakami_2.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)]")