def main(client):
from model_specific_helpers import (get_example_site_vars,
make_param_filter_func,
make_weighted_cost_func,
make_param2res, make_param2res_2,
UnEstimatedParameters,
EstimatedParameters, Observables)
from general_helpers import (make_uniform_proposer,
make_multivariate_normal_proposer, mcmc,
make_feng_cost_func, plot_solutions)
# fixme:
# put the (relative or asolute) location of your data into a small file called 'config.json' and
# in my case the content looks like this:
# {"dataPath": "/home/data/yuanyuan"}
# DO NOT add the file to the repository. It is not only model- but also site specific.
# So you are likely to have one for every model on every computer
# you run this code on.
# (this example uses an absolute path starting with a '/'
with Path('config.json').open(mode='r') as f:
conf_dict = json.load(f)
dataPath = Path(conf_dict['dataPath'])
# fixme:
# Note that the function is imported from
# model_specific_helpers which means that you have to provide
# your version of this fuction which will most likely return different
# variables
npp, rh, clitter, csoil, cveg, cleaf, croot, cwood = get_example_site_vars(
dataPath)
# combine them to a single array which we will later use as input to the costfunction
#nyears=140
nyears = 10
tot_len = 12 * nyears
obs = np.stack([cleaf, croot, cwood, clitter, csoil, rh],
axis=1)[0:tot_len, :]
# leaf, root , wood, metabolic, structural, CWD, microbial, slow, passive
# fixme
c_min = np.array([
0.09, 0.09, 0.09, 0.01, 0.01, 1 / (2 * 365), 1 / (365 * 10),
1 / (60 * 365), 0.1 / (0.1 * 365), 0.06 / (0.137 * 365),
0.06 / (5 * 365), 0.06 / (222.22 * 365), clitter[0] / 100,
clitter[0] / 100, csoil[0] / 100, csoil[0] / 2
])
c_max = np.array([
1, 1, 0.21, 1, 1, 1 / (0.3 * 365), 1 / (0.8 * 365), 1 / 365,
1 / (365 * 0.1), 0.6 / (365 * 0.137), 0.6 / (365 * 5),
0.6 / (222.22 * 365), clitter[0], clitter[0], csoil[0] / 3, csoil[0]
])
# fixme
# this function is model specific: It discards parameter proposals
# where beta1 and beta2 add up to more than 0.99
isQualified = make_param_filter_func(c_max, c_min)
uniform_prop = make_uniform_proposer(
c_min,
c_max,
D=100.0, # this value
filter_func=isQualified)
cpa = UnEstimatedParameters(C_leaf_0=cleaf[0],
C_root_0=croot[0],
C_wood_0=cwood[0],
clitter_0=clitter[0],
csoil_0=csoil[0],
rh_0=rh[0],
npp=npp,
number_of_months=tot_len,
clay=0.2028,
silt=0.2808,
lig_wood=0.4,
f_wood2CWD=1,
f_metlit2mic=0.45)
param2res = make_param2res(cpa)
epa_0 = EstimatedParameters(
beta_leaf=0.15,
beta_root=0.2,
lig_leaf=0.15,
f_leaf2metlit=0.28,
f_root2metlit=0.6,
k_leaf=1 / 365,
k_root=1 / (365 * 5),
k_wood=1 / (365 * 40),
k_metlit=0.5 / (365 * 0.1),
k_mic=0.3 / (365 * 0.137),
k_slowsom=0.3 / (365 * 5),
k_passsom=0.3 / (222.22 * 365),
C_metlit_0=0.05,
CWD_0=0.1,
C_mic_0=1,
C_passom_0=5,
)
# it is sensible to use the same costfunction for both the demo and
# the formal run so we define it here for both
#costfunction=make_feng_cost_func(obs)
costfunction = make_weighted_cost_func(obs)
# Look for data from the demo run and use it to compute the covariance matrix if necessarry
demo_aa_path = dataPath.joinpath('cable_demo_da_aa.csv')
demo_aa_j_path = dataPath.joinpath('cable_demo_da_j_aa.csv')
if not demo_aa_path.exists():
print("Did not find demo run results. Will perform demo run")
C_demo, J_demo = mcmc(initial_parameters=epa_0,
proposer=uniform_prop,
param2res=param2res,
costfunction=costfunction,
nsimu=10000)
# save the parameters and costfunctionvalues for postprocessing
pd.DataFrame(C_demo).to_csv(demo_aa_path, sep=',')
pd.DataFrame(J_demo).to_csv(demo_aa_j_path, sep=',')
else:
print("""Found {p} from a previous demo run.
If you also want to recreate the demo output then move the file!
""".format(p=demo_aa_path))
C_demo = pd.read_csv(demo_aa_path).to_numpy()
J_demo = pd.read_csv(demo_aa_j_path).to_numpy()
# build a new proposer based on a multivariate_normal distribution using the
# estimated covariance of the previous run if available first we check how many
# accepted parameters we got
# and then use part of them to compute a covariance matrix for the
# formal run
covv = np.cov(C_demo[:, int(C_demo.shape[1] / 10):])
normal_prop = make_multivariate_normal_proposer(covv=covv,
filter_func=isQualified)
# Look for data from the formal run and use it for postprocessing
#formal_aa_path = dataPath.joinpath('cable_formal_da_aa.csv')
#formal_aa_j_path = dataPath.joinpath('cable_formal_da_j_aa.csv')
#if not formal_aa_path.exists():
# print("Did not find results. Will perform formal run")
# C_formal, J_formal = mcmc(
# initial_parameters=epa_0,
# proposer=normal_prop,
# param2res=param2res,
# costfunction=costfunction,
# nsimu=100
# )
# pd.DataFrame(C_formal).to_csv(formal_aa_path,sep=',')
# pd.DataFrame(J_formal).to_csv(formal_aa_j_path,sep=',')
#else:
# print("""Found {p} from a previous demo run.
# If you also want recreate the output then move the file!
# """.format(p = formal_aa_path))
#C_formal = pd.read_csv(formal_aa_path).to_numpy()
#J_formal = pd.read_csv(formal_aa_j_path).to_numpy()
#define parallel mcmc wrapper
def parallel_mcmc(_):
return (mcmc(initial_parameters=epa_0,
proposer=normal_prop,
param2res=param2res,
costfunction=costfunction,
nsimu=20000))
print("before map")
print("Client: ", client)
#run 10 chains
[[c_form1, j_form1], [c_form2, j_form2], [c_form3, j_form3],
[c_form4, j_form4], [c_form5, j_form5], [c_form6, j_form6],
[c_form7, j_form7], [c_form8, j_form8], [c_form9, j_form9],
[c_form10,
j_form10]] = client.gather(client.map(parallel_mcmc, range(0, 10)))
print("after map")
print("Client: ", client)
#print chain5 output as test
formal_c_path = dataPath.joinpath('chain5_pmcmc_c.csv')
formal_j_path = dataPath.joinpath('chain5_pmcmc_j.csv')
pd.DataFrame(c_form5).to_csv(formal_c_path, sep=',')
pd.DataFrame(j_form5).to_csv(formal_j_path, sep=',')
#use output csv file for post processing
C_formal = pd.read_csv(formal_c_path).to_numpy()
J_formal = pd.read_csv(formal_j_path).to_numpy()
# POSTPROCESSING
#
# The 'solution' of the inverse problem is actually the (joint) posterior
# probability distribution of the parameters, which we approximate by the
# histogram consisting of the mcmc generated samples.
# This joint distribution contains as much information as all its (infinitly
# many) projections to curves through the parameter space combined.
# Unfortunately, for this very reason, a joint distribution of more than two
# parameters is very difficult to visualize in its entirity.
# to do:
# a) make a movie of color coded samples of the a priori distribution of the parameters.
# b) -"- of the a posteriory distribution -'-
# Therefore the following visualizations have to be considered with caution:
# 1.
# The (usual) histograms of the values of a SINGLE parameters can be very
# misleading since e.g. we can not see that certain parameter combination only
# occure together. In fact this decomposition is only appropriate for
# INDEPENDENT distributions of parameters in which case the joint distribution
# would be the product of the distributions of the single parameters. This is
# however not even to be expected if our prior probability distribution can be
# decomposed in this way. (Due to the fact that the Metropolis Hastings Alg. does not
# produce independent samples )
df = pd.DataFrame({
name: C_formal[:, i]
for i, name in enumerate(EstimatedParameters._fields)
})
subplots = df.hist()
fig = subplots[0, 0].figure
fig.set_figwidth(15)
fig.set_figheight(15)
fig.savefig('histograms.pdf')
# As the next best thing we can create a matrix of plots containing all
# projections to possible parameter tuples
# (like the pairs plot in the R package FME) but 16x16 plots are too much for one page..
# However the plot shows that we are dealing with a lot of colinearity for this parameter set
subplots = pd.plotting.scatter_matrix(df)
fig = subplots[0, 0].figure
fig.set_figwidth(15)
fig.set_figheight(15)
fig.savefig('scatter_matrix.pdf')
# 2.
# another way to get an idea of the quality of the parameter estimation is
# to plot trajectories.
# A possible aggregation of this histogram to a singe parameter
# vector is the mean which is an estimator of the expected value of the
# desired distribution.
sol_mean = param2res(np.mean(C_formal, axis=1))
fig = plt.figure()
plot_solutions(fig,
times=range(sol_mean.shape[0]),
var_names=Observables._fields,
tup=(sol_mean, obs),
names=('mean', 'obs'))
fig.savefig('solutions.pdf')
0.06 / (222.22 * 365), clitter[0] / 100, clitter[0] / 100, csoil[0] / 100,
csoil[0] / 2
])
c_max = np.array([
1, 1, 0.21, 1, 1, 1 / (0.3 * 365), 1 / (0.8 * 365), 1 / 365,
1 / (365 * 0.1), 0.6 / (365 * 0.137), 0.6 / (365 * 5),
0.6 / (222.22 * 365), clitter[0], clitter[0], csoil[0] / 3, csoil[0]
])
# fixme
# this function is model specific: It discards parameter proposals
# where beta1 and beta2 add up to more than 0.99
isQualified = make_param_filter_func(c_max, c_min)
uniform_prop = make_uniform_proposer(
c_min,
c_max,
D=100.0, # this value
filter_func=isQualified)
cpa = UnEstimatedParameters(C_leaf_0=cleaf[0],
C_root_0=croot[0],
C_wood_0=cwood[0],
clitter_0=clitter[0],
csoil_0=csoil[0],
rh_0=rh[0],
npp=npp,
number_of_months=tot_len,
clay=0.2028,
silt=0.2808,
lig_wood=0.4,
f_wood2CWD=1,
# forward run with median, max likelihood, and min J parameter sets
sol_median_autostep = param2res(np.median(C_autostep, axis=1))
sol_likelihood_autostep = param2res(max_likelihood_autostep)
sol_min_J_autostep = param2res(
C_autostep[:, np.where(J_autostep[1] == np.min(J_autostep[1]))])
# export solutions
pd.DataFrame(sol_median_autostep).to_csv(
dataPath.joinpath('sol_median_autostep.csv'), sep=',')
pd.DataFrame(sol_likelihood_autostep).to_csv(
dataPath.joinpath('sol_likelihood_autostep.csv'), sep=',')
pd.DataFrame(sol_min_J_autostep).to_csv(
dataPath.joinpath('sol_min_J_autostep.csv'), sep=',')
# Demo MCMC: with a uniform proposer and fixed step
uniform_prop = make_uniform_proposer(c_min,
c_max,
D=240,
filter_func=isQualified)
C_demo, J_demo = mcmc(
initial_parameters=epa_0,
proposer=uniform_prop,
param2res=param2res,
# costfunction=make_weighted_cost_func(obs)
costfunction=make_feng_cost_func(obs),
nsimu=10000)
# save the parameters and cost function values for postprocessing
pd.DataFrame(C_demo).to_csv(dataPath.joinpath('OCN_v2_demo_da_aa.csv'),
sep=',')
pd.DataFrame(J_demo).to_csv(dataPath.joinpath('OCN_v2_demo_da_j_aa.csv'),
sep=',')
def test_mcmc(self):
dataPath = self.dataPath
npp, rh, clitter, csoil, cveg, cleaf, croot, cwood = get_example_site_vars(
dataPath)
nyears = 10
tot_len = 12 * nyears
obs = np.stack([cleaf, croot, cwood, clitter, csoil, rh],
axis=1)[0:tot_len, :]
c_min = np.array([
0.09, 0.09, 0.09, 0.01, 0.01, 1 / (2 * 365), 1 / (365 * 10),
1 / (60 * 365), 0.1 / (0.1 * 365), 0.06 / (0.137 * 365),
0.06 / (5 * 365), 0.06 / (222.22 * 365), clitter[0] / 100,
clitter[0] / 100, csoil[0] / 100, csoil[0] / 2
])
c_max = np.array([
1, 1, 0.21, 1, 1, 1 / (0.3 * 365), 1 / (0.8 * 365), 1 / 365,
1 / (365 * 0.1), 0.6 / (365 * 0.137), 0.6 / (365 * 5),
0.6 / (222.22 * 365), clitter[0], clitter[0], csoil[0] / 3,
csoil[0]
])
isQualified = make_param_filter_func(c_max, c_min)
uniform_prop = make_uniform_proposer(
c_min,
c_max,
#D=10.0,
D=20.0,
filter_func=isQualified)
cpa = UnEstimatedParameters(C_leaf_0=cleaf[0],
C_root_0=croot[0],
C_wood_0=cwood[0],
clitter_0=clitter[0],
csoil_0=csoil[0],
rh_0=rh[0],
npp=npp,
number_of_months=tot_len,
clay=0.2028,
silt=0.2808,
lig_wood=0.4,
f_wood2CWD=1,
f_metlit2mic=0.45)
param2res = make_param2res(
cpa
) #pa=[beta1,beta2, lig_leaf, f41,f42, kleaf,kroot,kwood,kmet,kmic, kslow,kpass, cmet_init, cstr_init, cmic_init, cpassive_init ]
# pa= [0.15, 0.2,0.15,0.28, 0.6, 1/365, 1/(365*5), 1/(365*40), 0.5/(365*0.1), 0.3/(365*0.137), 0.3/(365*5), 0.3/(222.22*365), 0.05, 0.1, 1, 5]
epa_0 = EstimatedParameters(
beta_leaf=0.15,
beta_root=0.2,
lig_leaf=0.15,
f_leaf2metlit=0.28,
f_root2metlit=0.6,
k_leaf=1 / 365,
k_root=1 / (365 * 5),
k_wood=1 / (365 * 40),
k_metlit=0.5 / (365 * 0.1),
k_mic=0.3 / (365 * 0.137),
k_slowsom=0.3 / (365 * 5),
k_passsom=0.3 / (222.22 * 365),
C_metlit_0=0.05,
C_CWD_0=0.1,
C_mic_0=1,
C_passom_0=5,
)
# save the parameters and costfunctionvalues for postprocessing
demo_aa_path = Path('cable_demo_da_aa.csv')
demo_aa_j_path = Path('cable_demo_da_j_aa.csv')
if not demo_aa_path.exists():
print("did not find demo run results. Will perform demo run")
nsimu_demo = 200
C_demo, J_demo = mcmc(
initial_parameters=epa_0,
proposer=uniform_prop,
param2res=param2res,
#costfunction=make_weighted_cost_func(obs)
#costfunction=make_feng_cost_func(obs),
costfunction=make_jon_cost_func(obs),
nsimu=nsimu_demo)
# save the parameters and costfunctionvalues for postprocessing
pd.DataFrame(C_demo).to_csv(demo_aa_path, sep=',')
pd.DataFrame(J_demo).to_csv(demo_aa_j_path, sep=',')
else:
print("""Found {p} from a previous demo run.
If you also want to recreate the demo output move the file!
""".format(p=demo_aa_path))
C_demo = pd.read_csv(demo_aa_path).to_numpy()
J_demo = pd.read_csv(demo_aa_j_path).to_numpy()
# build a new proposer based on a multivariate_normal distribution using the estimated covariance of the previous run if available
# parameter values of the previous run
# first we check how many accepted parameters we got
n_accept = C_demo.shape[1]
# and then use part of them to compute a covariance matrix for the
# formal run
covv = np.cov(C_demo[:, int(n_accept / 10):])
normal_prop = make_multivariate_normal_proposer(
covv=covv, filter_func=isQualified)
C_formal, J_formal = mcmc(
initial_parameters=epa_0,
proposer=normal_prop,
param2res=param2res,
#costfunction=make_weighted_cost_func(obs)
#costfunction=make_feng_cost_func(obs),
costfunction=make_jon_cost_func(obs),
nsimu=200)
# save the parameters and costfunctionvalues for postprocessing
formal_aa_path = Path('cable_formal_da_aa.csv')
formal_aa_j_path = Path('cable_formal_da_j_aa.csv')
pd.DataFrame(C_formal).to_csv(formal_aa_path, sep=',')
pd.DataFrame(J_formal).to_csv(formal_aa_j_path, sep=',')
sol_mean = param2res(np.mean(C_formal, axis=1))
fig = plt.figure()
plot_solutions(fig,
times=range(sol_mean.shape[0]),
var_names=Observables._fields,
tup=(sol_mean, obs),
names=('mean', 'obs'))
fig.savefig('solutions.pdf')
