def plot_r2_comp(name_site_combo,
dat_dir='./out_files/',
out_fig_dir='./out_figs/'):
"""Plot r2 of the three patterns separately for each community."""
models = ['asne', 'agsne', 'ssnt_0', 'ssnt_1']
model_names = ['ASNE', 'AGSNE', 'SSNT_N', 'SSNT_M']
patterns = ['rad', 'isd', 'sdr']
pattern_names = ['SAD', 'ISD', 'SDR']
col_list = ['b', '#787878', 'r']
symbol_list = ['o', 's', '*']
fig = plt.figure(figsize=(10.5, 3.5))
for i, pattern in enumerate(patterns):
r2_dic = {'asne': [], 'agsne': [], 'ssnt_0': [], 'ssnt_1': []}
r2_list = []
for j, model in enumerate(models):
for dat_name, site in name_site_combo:
pred_obs_model_pattern = wk.import_obs_pred_data(dat_dir +
dat_name +
'_obs_pred_' +
pattern +
'_' + model +
'.csv')
pred_obs_site = pred_obs_model_pattern[
pred_obs_model_pattern['site'] == site]
r2 = mtools.obs_pred_rsquare(np.log10(pred_obs_site['obs']),
np.log10(pred_obs_site['pred']))
r2_dic[model].append(r2)
r2_list.append(r2)
ax = plt.subplot(1, 3, i + 1)
for j in range(1, 4):
model = models[j]
plt.scatter(r2_dic['asne'],
r2_dic[model],
s=20,
marker=symbol_list[j - 1],
facecolors=col_list[j - 1],
edgecolors='none',
label=model_names[j])
min_val, max_val = min(r2_list), max(r2_list)
if min_val < 0: axis_min = 1.1 * min_val
else: axis_min = 0.9 * min_val
if max_val < 0: axis_max = 0.9 * max_val
else: axis_max = 1.1 * max_val
plt.plot([axis_min, axis_max], [axis_min, axis_max], 'k-')
plt.xlim(axis_min, axis_max)
plt.ylim(axis_min, axis_max)
ax.tick_params(axis='both', which='major', labelsize=6)
ax.set_xlabel(r'$R^2$ of ASNE', labelpad=4, size=10)
ax.set_ylabel(r'$R^2$ of the other models', labelpad=4, size=10)
ax.set_title(pattern_names[i], size=16)
if i == 0: ax.legend(loc=2, prop={'size': 10})
plt.subplots_adjust(left=0.08, wspace=0.3)
plt.tight_layout()
plt.savefig(out_fig_dir + 'r2_comp.png', dpi=400)
def bootstrap_SDR(name_site_combo, model, in_dir = './data/', out_dir = './out_files/', Niter = 200):
"""A general function of bootstrapping for ISD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to one file on disk for R^2.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
par_list = []
for sp in np.unique(dat_clean['sp']):
dat_sp = dat_clean[dat_clean['sp'] == sp]
n = len(dat_sp)
genus_sp = dat_sp['genus'][0]
m = len(np.unique(dat_clean[dat_clean['genus'] == genus_sp]['sp']))
par_list.append([m, n])
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_sdr_' + model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred']
obs = pred_obs[pred_obs['site'] == site]['obs']
out_list_rsquare = [dat_name, site, str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))]
iisd_agsne = mete_distributions.theta_agsne([G, S, N, E], [lambda1, beta, lambda3, agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3])
iisd_asne = mete_distributions.theta_epsilon(S, N, E)
dbh_scaled = np.array(dat_clean['dbh'] / min(dat_clean['dbh']))
iisd_ssnt_0 = ssnt_isd_bounded(1, N / (sum(dbh_scaled ** 1) - N))
iisd_ssnt_1 = ssnt_isd_bounded(2/3, N / (sum(dbh_scaled ** (2/3)) - N))
dist_for_model = {'ssnt_0': iisd_ssnt_0, 'ssnt_1': iisd_ssnt_1, 'asne': iisd_asne, 'agsne': iisd_agsne}
dist = dist_for_model[model]
for i in range(Niter):
if model in ['ssnt_0', 'ssnt_1']: obs_boot = np.array([np.mean((dist.rvs(par[1])) ** 2) for par in par_list]) # Here par[1] is n for each species
elif model == 'asne':
obs_boot = np.array([np.mean(np.array(dist.rvs(par[1], par[1]))) for par in par_list])
else:
obs_boot = np.array([np.mean(np.array(dist.rvs(par[1], par[1], par[0]))) for par in par_list])
out_list_rsquare.append(str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
wk.write_to_file(out_dir + 'SDR_bootstrap_' + model + '_rsquare.txt', ",".join(str(x) for x in out_list_rsquare))
def bootstrap_SAD(name_site_combo, model, in_dir = './data/', out_dir = './out_files/', Niter = 200):
"""A general function of bootstrapping for SAD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
beta_ssnt = mete.get_beta(S, N, version = 'untruncated')
beta_asne = mete.get_beta(S, N)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
sad_agsne = mete_distributions.sad_agsne([G, S, N, E], [lambda1, beta, lambda3, agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3])
dist_for_model = {'ssnt_0': stats.logser(np.exp(-beta_ssnt)),
'ssnt_1': stats.logser(np.exp(-beta_ssnt)),
'asne': md.trunc_logser(np.exp(-beta_asne), N),
'agsne': sad_agsne}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_rad_' + model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred'][::-1]
obs = pred_obs[pred_obs['site'] == site]['obs'][::-1]
out_list_rsquare = [dat_name, site, str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))]
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [dat_name, site, str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))]
for i in range(Niter):
obs_boot = np.array(sorted(dist.rvs(S)))
cdf_boot = np.array([dist.cdf(x) for x in obs_boot])
emp_cdf_boot = mtools.get_emp_cdf(obs_boot)
out_list_rsquare.append(str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
out_list_ks.append(str(max(abs(emp_cdf_boot - np.array(cdf_boot)))))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_rsquare.txt', ",".join(str(x) for x in out_list_rsquare))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_ks.txt', ",".join(str(x) for x in out_list_ks))
def plot_r2_comp(name_site_combo, dat_dir = './out_files/', out_fig_dir = './out_figs/'):
"""Plot r2 of the three patterns separately for each community."""
models = ['asne', 'agsne', 'ssnt_0', 'ssnt_1']
model_names = ['ASNE', 'AGSNE', 'SSNT_N', 'SSNT_M']
patterns = ['rad', 'isd', 'sdr']
pattern_names = ['SAD', 'ISD', 'SDR']
col_list = ['b', '#787878', 'r']
symbol_list = ['o', 's', '*']
fig = plt.figure(figsize = (10.5, 3.5))
for i, pattern in enumerate(patterns):
r2_dic = {'asne':[], 'agsne':[], 'ssnt_0':[], 'ssnt_1':[]}
r2_list = []
for j, model in enumerate(models):
for dat_name, site in name_site_combo:
pred_obs_model_pattern = wk.import_obs_pred_data(dat_dir + dat_name + '_obs_pred_' + pattern + '_' + model + '.csv')
pred_obs_site = pred_obs_model_pattern[pred_obs_model_pattern['site'] == site]
r2 = mtools.obs_pred_rsquare(np.log10(pred_obs_site['obs']), np.log10(pred_obs_site['pred']))
r2_dic[model].append(r2)
r2_list.append(r2)
ax = plt.subplot(1, 3, i + 1)
for j in range(1, 4):
model = models[j]
plt.scatter(r2_dic['asne'], r2_dic[model], s = 20, marker = symbol_list[j - 1], facecolors = col_list[j - 1],
edgecolors = 'none', label = model_names[j])
min_val, max_val = min(r2_list), max(r2_list)
if min_val < 0: axis_min = 1.1 * min_val
else: axis_min = 0.9 * min_val
if max_val < 0: axis_max = 0.9 * max_val
else: axis_max= 1.1 * max_val
plt.plot([axis_min, axis_max], [axis_min, axis_max], 'k-')
plt.xlim(axis_min, axis_max)
plt.ylim(axis_min, axis_max)
ax.tick_params(axis = 'both', which = 'major', labelsize = 6)
ax.set_xlabel(r'$R^2$ of ASNE', labelpad = 4, size = 10)
ax.set_ylabel(r'$R^2$ of the other models', labelpad = 4, size = 10)
ax.set_title(pattern_names[i], size = 16)
if i == 0: ax.legend(loc = 2, prop = {'size': 10})
plt.subplots_adjust(left = 0.08, wspace = 0.3)
plt.tight_layout()
plt.savefig(out_fig_dir + 'r2_comp.png', dpi = 400)
def bootstrap_ISD(name_site_combo, model, in_dir = './data/', out_dir = './out_files/', Niter = 200):
"""A general function of bootstrapping for ISD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
isd_agsne = mete_distributions.psi_agsne([G, S, N, E], [lambda1, beta, lambda3, agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3])
isd_asne = mete_distributions.psi_epsilon_approx(S, N, E)
dbh_scaled = np.array(dat_clean['dbh'] / min(dat_clean['dbh']))
isd_ssnt_0 = ssnt_isd_bounded(1, N / (sum(dbh_scaled ** 1) - N))
isd_ssnt_1 = ssnt_isd_bounded(2/3, N / (sum(dbh_scaled ** (2/3)) - N))
dist_for_model = {'ssnt_0': isd_ssnt_0, 'ssnt_1': isd_ssnt_1, 'asne': isd_asne, 'agsne': isd_agsne}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_isd_' + model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred']
obs = pred_obs[pred_obs['site'] == site]['obs']
out_list_rsquare = [dat_name, site, str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))]
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt', ",".join(str(x) for x in out_list_rsquare), new_line = False)
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [dat_name, site, str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))]
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt', ",".join(str(x) for x in out_list_ks), new_line = False)
num_pools = 8 # Assuming that 8 pools are to be created
for i in xrange(Niter):
obs_boot = []
cdf_boot = []
while len(obs_boot) < N:
pool = multiprocessing.Pool(num_pools)
out_sample = pool.map(wk.generate_isd_sample, [dist for j in xrange(num_pools)])
for combo in out_sample:
cdf_sublist, sample_sublist = combo
obs_boot.extend(sample_sublist)
cdf_boot.extend(cdf_sublist)
pool.close()
pool.join()
if model in ['asne', 'agsne']: obs_boot = np.sort(obs_boot[:N]) ** 0.5 # Convert to diameter
else: obs_boot = np.sort(obs_boot[:N])
sample_rsquare = mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))
sample_ks = max(abs(emp_cdf - np.sort(cdf_boot[:N])))
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt', "".join([',', str(sample_rsquare)]), new_line = False)
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt', "".join([',', str(sample_ks)]), new_line = False)
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt', '\t')
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt', '\t')
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt', ",".join(str(x) for x in out_list_ks))
def bootstrap_SDR(name_site_combo,
model,
in_dir='./data/',
out_dir='./out_files/',
Niter=200):
"""A general function of bootstrapping for ISD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to one file on disk for R^2.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
par_list = []
for sp in np.unique(dat_clean['sp']):
dat_sp = dat_clean[dat_clean['sp'] == sp]
n = len(dat_sp)
genus_sp = dat_sp['genus'][0]
m = len(np.unique(dat_clean[dat_clean['genus'] == genus_sp]['sp']))
par_list.append([m, n])
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_sdr_' +
model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred']
obs = pred_obs[pred_obs['site'] == site]['obs']
out_list_rsquare = [
dat_name, site,
str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))
]
iisd_agsne = mete_distributions.theta_agsne([G, S, N, E], [
lambda1, beta, lambda3,
agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3
])
iisd_asne = mete_distributions.theta_epsilon(S, N, E)
dbh_scaled = np.array(dat_clean['dbh'] / min(dat_clean['dbh']))
iisd_ssnt_0 = ssnt_isd_bounded(1, N / (sum(dbh_scaled**1) - N))
iisd_ssnt_1 = ssnt_isd_bounded(2 / 3, N / (sum(dbh_scaled**(2 / 3)) - N))
dist_for_model = {
'ssnt_0': iisd_ssnt_0,
'ssnt_1': iisd_ssnt_1,
'asne': iisd_asne,
'agsne': iisd_agsne
}
dist = dist_for_model[model]
for i in range(Niter):
if model in ['ssnt_0', 'ssnt_1']:
obs_boot = np.array([
np.mean((dist.rvs(par[1]))**2) for par in par_list
]) # Here par[1] is n for each species
elif model == 'asne':
obs_boot = np.array([
np.mean(np.array(dist.rvs(par[1], par[1]))) for par in par_list
])
else:
obs_boot = np.array([
np.mean(np.array(dist.rvs(par[1], par[1], par[0])))
for par in par_list
])
out_list_rsquare.append(
str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
wk.write_to_file(out_dir + 'SDR_bootstrap_' + model + '_rsquare.txt',
",".join(str(x) for x in out_list_rsquare))
def bootstrap_ISD(name_site_combo,
model,
in_dir='./data/',
out_dir='./out_files/',
Niter=200):
"""A general function of bootstrapping for ISD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
isd_agsne = mete_distributions.psi_agsne([G, S, N, E], [
lambda1, beta, lambda3,
agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3
])
isd_asne = mete_distributions.psi_epsilon_approx(S, N, E)
dbh_scaled = np.array(dat_clean['dbh'] / min(dat_clean['dbh']))
isd_ssnt_0 = ssnt_isd_bounded(1, N / (sum(dbh_scaled**1) - N))
isd_ssnt_1 = ssnt_isd_bounded(2 / 3, N / (sum(dbh_scaled**(2 / 3)) - N))
dist_for_model = {
'ssnt_0': isd_ssnt_0,
'ssnt_1': isd_ssnt_1,
'asne': isd_asne,
'agsne': isd_agsne
}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_isd_' +
model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred']
obs = pred_obs[pred_obs['site'] == site]['obs']
out_list_rsquare = [
dat_name, site,
str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))
]
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt',
",".join(str(x) for x in out_list_rsquare),
new_line=False)
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [
dat_name, site,
str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))
]
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt',
",".join(str(x) for x in out_list_ks),
new_line=False)
num_pools = 8 # Assuming that 8 pools are to be created
for i in xrange(Niter):
obs_boot = []
cdf_boot = []
while len(obs_boot) < N:
pool = multiprocessing.Pool(num_pools)
out_sample = pool.map(wk.generate_isd_sample,
[dist for j in xrange(num_pools)])
for combo in out_sample:
cdf_sublist, sample_sublist = combo
obs_boot.extend(sample_sublist)
cdf_boot.extend(cdf_sublist)
pool.close()
pool.join()
if model in ['asne', 'agsne']:
obs_boot = np.sort(obs_boot[:N])**0.5 # Convert to diameter
else:
obs_boot = np.sort(obs_boot[:N])
sample_rsquare = mtools.obs_pred_rsquare(np.log10(obs_boot),
np.log10(pred))
sample_ks = max(abs(emp_cdf - np.sort(cdf_boot[:N])))
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt',
"".join([',', str(sample_rsquare)]),
new_line=False)
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt',
"".join([',', str(sample_ks)]),
new_line=False)
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_rsquare.txt', '\t')
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt', '\t')
wk.write_to_file(out_dir + 'ISD_bootstrap_' + model + '_ks.txt',
",".join(str(x) for x in out_list_ks))
def bootstrap_SAD(name_site_combo,
model,
in_dir='./data/',
out_dir='./out_files/',
Niter=200):
"""A general function of bootstrapping for SAD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
beta_ssnt = mete.get_beta(S, N, version='untruncated')
beta_asne = mete.get_beta(S, N)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
sad_agsne = mete_distributions.sad_agsne([G, S, N, E], [
lambda1, beta, lambda3,
agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3
])
dist_for_model = {
'ssnt_0': stats.logser(np.exp(-beta_ssnt)),
'ssnt_1': stats.logser(np.exp(-beta_ssnt)),
'asne': md.trunc_logser(np.exp(-beta_asne), N),
'agsne': sad_agsne
}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_rad_' +
model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred'][::-1]
obs = pred_obs[pred_obs['site'] == site]['obs'][::-1]
out_list_rsquare = [
dat_name, site,
str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))
]
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [
dat_name, site,
str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))
]
for i in range(Niter):
obs_boot = np.array(sorted(dist.rvs(S)))
cdf_boot = np.array([dist.cdf(x) for x in obs_boot])
emp_cdf_boot = mtools.get_emp_cdf(obs_boot)
out_list_rsquare.append(
str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
out_list_ks.append(str(max(abs(emp_cdf_boot - np.array(cdf_boot)))))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_rsquare.txt',
",".join(str(x) for x in out_list_rsquare))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_ks.txt',
",".join(str(x) for x in out_list_ks))
