def sample(self, n=1):
left, right = self.low, self.high
mode = sqrt(left * right)
c = (mode - left) / (right - left)
loc = left
scale = right - left
return triang.rvs(c=c, loc=loc, scale=scale, size=n)
def sample(self, n=1): left, right = self.low, self.high mode = sqrt(left * right) c = (mode - left) / (right - left) loc = left scale = right - left return triang.rvs(c=c, loc=loc, scale=scale, size=n)
def generateToy():
np.random.seed(12345)
fig,ax = plt.subplots(4,sharex=True)
#fig,ax = plt.subplots(2)
powerlaw_arg = 2
triang_arg=0.7
n_samples = 500
#generate simple line with slope 1, from 0 to 1
frozen_powerlaw = powerlaw(powerlaw_arg) #powerlaw.pdf(x, a) = a * x**(a-1)
#generate triangle with peak at 0.7
frozen_triangle = triang(triang_arg) #up-sloping line from loc to (loc + c*scale) and then downsloping for (loc + c*scale) to (loc+scale).
frozen_uniform = uniform(0.2,0.5)
frozen_uniform2 = uniform(0.3,0.2)
x = np.linspace(0,1)
signal = np.random.normal(0.5, 0.1, n_samples/2)
data_frame = pd.DataFrame({'powerlaw':powerlaw.rvs(powerlaw_arg,size=n_samples),
'triangle':triang.rvs(triang_arg,size=n_samples),
'uniform':np.concatenate((uniform.rvs(0.2,0.5,size=n_samples/2),uniform.rvs(0.3,0.2,size=n_samples/2))),
'powerlaw_signal':np.concatenate((powerlaw.rvs(powerlaw_arg,size=n_samples/2),signal))})
ax[0].plot(x, frozen_powerlaw.pdf(x), 'k-', lw=2, label='powerlaw pdf')
hist(data_frame['powerlaw'],bins=100,normed=True,histtype='stepfilled',alpha=0.2,label='100 bins',ax=ax[0])
#hist(data_frame['powerlaw'],bins='blocks',fitness='poly_events',normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[0])
ax[0].legend(loc = 'best')
ax[1].plot(x, frozen_triangle.pdf(x), 'k-', lw=2, label='triangle pdf')
hist(data_frame['triangle'],bins=100,normed=True,histtype='stepfilled',alpha=0.2,label='100 bins',ax=ax[1])
hist(data_frame['triangle'],bins='blocks',fitness='poly_events',normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[1])
ax[1].legend(loc = 'best')
#ax[0].plot(x, frozen_powerlaw.pdf(x), 'k-', lw=2, label='powerlaw pdf')
hist(data_frame['powerlaw_signal'],bins=100,normed=True,histtype='stepfilled',alpha=0.2,label='100 bins',ax=ax[2])
#hist(data_frame['powerlaw_signal'],bins='blocks',normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[2])
ax[2].legend(loc = 'best')
ax[3].plot(x, frozen_uniform.pdf(x)+frozen_uniform2.pdf(x), 'k-', lw=2, label='uniform pdf')
hist(data_frame['uniform'],bins=100,normed=True,histtype='stepfilled',alpha=0.2,label='100 bins',ax=ax[3])
#hist(data_frame['uniform'],bins='blocks',fitness = 'poly_events',p0=0.05,normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[3])
ax[3].legend(loc = 'best')
plt.show()
fig.savefig('plots/toy_plots.png')
def sample(self): left, right, mode = self.low90, self.high90, self.geomean c = (mode - left) / (right - left) loc = left scale = right - left return triang.rvs(c=c, loc=loc, scale=scale)
fontweight='bold')
ax.set_ylabel("Count", fontweight='bold')
ax.set_xlabel("h, m", fontweight='bold')
# Skin will be uniformly distributed
skin_dist = uniform.rvs(loc=0, scale=10, size=n_trials, random_state=seed)
ax = sns.distplot(skin_dist, kde=False, ax=axs[1, 0])
axs[1, 0].set_title("Input distribution for skin damage \n", fontweight='bold')
ax.set_ylabel("Count", fontweight='bold')
ax.set_xlabel("S", fontweight='bold')
# Reservoir pressure will be use the triangular distribution
# See https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.triang.html
pres_dist = triang.rvs(c=0.5,
loc=2750,
scale=500,
size=n_trials,
random_state=seed)
ax = sns.distplot(pres_dist, kde=False, ax=axs[1, 1])
axs[1, 1].set_title("Input distribution for reservoir pressure \n",
fontweight='bold')
ax.set_ylabel("Count", fontweight='bold')
ax.set_xlabel("P, psia", fontweight='bold')
plt.tight_layout()
plt.show()
# Custom function for performing PROSPER calculation
def calc_OPR(OpenServe, k, h, S, P):
DoSet(OpenServe, "PROSPER.SIN.IPR.Single.ResPerm", k)
def sample(self):
left, right, mode = self.low90, self.high90, self.geomean
c = (mode - left) / (right - left)
loc = left
scale = right - left
return triang.rvs(c=c, loc=loc, scale=scale)
# Generate three Bernoulli random numbers print(bernoulli.rvs(p, size=3)) # [0 1 0] # Poisson lmda = 2 x = 5 print(poisson.pmf(x, lmda)) print(poisson.cdf(x, lmda)) print(poisson.rvs(lmda, size=3)) # Uniform a = 3 b = 10 x = 10 print(uniform.pdf(x, loc=a, scale=(b - a))) # = 1 / 7 print(uniform.cdf(x, loc=a, scale=(b - a))) # = 1.0 print(uniform.rvs(loc=3, scale=(b - a), size=3)) # Exponential mu = 2 x = 2 print(expon.pdf(x, scale=(1 / mu))) print(expon.cdf(x, scale=(1 / mu))) print(expon.rvs(scale=(1 / mu), size=3)) # Triangular a = 1 b = 10 c = 7 print(triang.rvs(c, loc=a, scale=(b - a), size=3))
def distribution_compared_individual(data, sample_size= 10000):
'''
This function works to compare the degree distribution at the individual and group mean level to
a number of standard distribution: Uniform, Normal, Gamma, Exponential, Poisson, Triangular,
LogNormal, and Weibull. Further, the comparison is made using a one-way
Kolmogorov-Smirnov test for goodness of fit and a p-value is computed at the individual
and group level.
params:
sample size = number of random values to generate per distribution test--default val = 10000
data = list of degree distributions
'''
from scipy import stats
from scipy.stats import uniform, norm, gamma, expon, poisson, triang, lognorm, weibull_min
import numpy as np
from numpy.random import weibull
#####################################
#####################################
# Individual level comparison
for jj, ll in zip(graphs['Subject'], graphs['Degree_dist']):
path = jj[0]
deg_dist = ll
centered_deg_mean = np.asarray(deg_dist) - np.mean(deg_dist)
data_uniform = uniform.rvs(size=sample_size, loc = np.min(centered_deg_mean), scale=np.max(centered_deg_mean))
data_normal = norm.rvs(size=sample_size,loc=np.median(centered_deg_mean),scale=1)
data_gamma = gamma.rvs(a=5, size= sample_size)
data_expon = expon.rvs(scale=1,loc= np.median(centered_deg_mean),size= sample_size)
mu=3
data_poisson = poisson.rvs(mu=mu, size= sample_size)
c= 0.158
data_triang = triang.rvs(c=c, size = sample_size)
s = 0.954
data_lognorm = lognorm.rvs(s=s, size = sample_size)
a = 5.0
data_weibull = np.random.weibull(a = a, size = sample_size)
Distributions = [data_uniform, data_normal, data_gamma, data_expon, data_poisson, data_triang, data_lognorm, data_weibull]
dist_names = ['Uniform', 'Normal', 'Gamma', 'Exponential', 'Poisson', 'Triangular', 'LogNormal', 'Weibull']
uniform_test = list(['Uniform:', stats.kstest(centered_deg_mean, data_uniform)])
normal_test = list(['Normal', stats.kstest(centered_deg_mean, data_normal)])
gamma_test = list(['Gamma', stats.kstest(centered_deg_mean, data_gamma)])
exponential_test = list(['Exponential', stats.kstest(centered_deg_mean, data_expon)])
poisson_test = list(['Poisson', stats.kstest(centered_deg_mean, data_poisson)])
triang_test = list(['Triang', stats.kstest(centered_deg_mean, data_triang)])
lognormal_test = list(['Lognormal', stats.kstest(centered_deg_mean, data_lognorm)])
weibull_test = list(['Weibull', stats.kstest(centered_deg_mean, data_weibull)])
for ii, kk in zip(Distributions, dist_names):
sns.set_context('talk')
ax = sns.histplot(ii,
bins = 50,
kde= True,
color = 'skyblue')
#hist_kws={'linewidth':15, 'alpha':1})
ax.set(title= kk + ' Sample Degree Distribution', ylabel = 'Frequency')
aj = sns.histplot(centered_deg_mean,
bins= 50,
kde=True,
color='forestgreen')
plt.savefig( path + '/reports/' + kk + ' Sample Degree Distribution.png')
plt.clf()
ks_test_results_individual= [uniform_test, normal_test, gamma_test, exponential_test, poisson_test,
triang_test, lognormal_test, weibull_test]
with open(path + '/reports/' +'ks_test_results' + jj[0] +'.txt', 'w') as filehandle:
for listitem in ks_test_results_individual:
filehandle.write('%s\n' % listitem)
return
def generateToy():
np.random.seed(12345)
fig, ax = plt.subplots(4, sharex=True)
#fig,ax = plt.subplots(2)
powerlaw_arg = 2
triang_arg = 0.7
n_samples = 500
#generate simple line with slope 1, from 0 to 1
frozen_powerlaw = powerlaw(
powerlaw_arg) #powerlaw.pdf(x, a) = a * x**(a-1)
#generate triangle with peak at 0.7
frozen_triangle = triang(
triang_arg
) #up-sloping line from loc to (loc + c*scale) and then downsloping for (loc + c*scale) to (loc+scale).
frozen_uniform = uniform(0.2, 0.5)
frozen_uniform2 = uniform(0.3, 0.2)
x = np.linspace(0, 1)
signal = np.random.normal(0.5, 0.1, n_samples / 2)
data_frame = pd.DataFrame({
'powerlaw':
powerlaw.rvs(powerlaw_arg, size=n_samples),
'triangle':
triang.rvs(triang_arg, size=n_samples),
'uniform':
np.concatenate((uniform.rvs(0.2, 0.5, size=n_samples / 2),
uniform.rvs(0.3, 0.2, size=n_samples / 2))),
'powerlaw_signal':
np.concatenate((powerlaw.rvs(powerlaw_arg,
size=n_samples / 2), signal))
})
ax[0].plot(x, frozen_powerlaw.pdf(x), 'k-', lw=2, label='powerlaw pdf')
hist(data_frame['powerlaw'],
bins=100,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='100 bins',
ax=ax[0])
#hist(data_frame['powerlaw'],bins='blocks',fitness='poly_events',normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[0])
ax[0].legend(loc='best')
ax[1].plot(x, frozen_triangle.pdf(x), 'k-', lw=2, label='triangle pdf')
hist(data_frame['triangle'],
bins=100,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='100 bins',
ax=ax[1])
hist(data_frame['triangle'],
bins='blocks',
fitness='poly_events',
normed=True,
histtype='stepfilled',
alpha=0.2,
label='b blocks',
ax=ax[1])
ax[1].legend(loc='best')
#ax[0].plot(x, frozen_powerlaw.pdf(x), 'k-', lw=2, label='powerlaw pdf')
hist(data_frame['powerlaw_signal'],
bins=100,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='100 bins',
ax=ax[2])
#hist(data_frame['powerlaw_signal'],bins='blocks',normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[2])
ax[2].legend(loc='best')
ax[3].plot(x,
frozen_uniform.pdf(x) + frozen_uniform2.pdf(x),
'k-',
lw=2,
label='uniform pdf')
hist(data_frame['uniform'],
bins=100,
normed=True,
histtype='stepfilled',
alpha=0.2,
label='100 bins',
ax=ax[3])
#hist(data_frame['uniform'],bins='blocks',fitness = 'poly_events',p0=0.05,normed=True,histtype='stepfilled',alpha=0.2,label='b blocks',ax=ax[3])
ax[3].legend(loc='best')
plt.show()
fig.savefig('plots/toy_plots.png')
x = np.linspace(triang.ppf(0.01, c),
triang.ppf(0.99, c), 100)
ax.plot(x, triang.pdf(x, c),
'r-', lw=5, alpha=0.6, label='triang pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = triang(c)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = triang.ppf([0.001, 0.5, 0.999], c)
np.allclose([0.001, 0.5, 0.999], triang.cdf(vals, c))
# True
# Generate random numbers:
r = triang.rvs(c, size=1000)
# And compare the histogram:
ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
def distribution_compared_group(data, sample_size=10000, reports_path='.'):
'''
This function works to compare the degree distribution at the individual and group mean level to
a number of standard distribution: Uniform, Normal, Gamma, Exponential, Poisson, Triangular,
LogNormal, and Weibull. Further, the comparison is made using a one-way
Kolmogorov-Smirnov test for goodness of fit and a p-value is computed at the individual
and group level.
params:
sample size = number of random values to generate per distribution test--default val = 10000
data = list of degree distributions
'''
from scipy import stats
from scipy.stats import uniform, norm, gamma, expon, poisson, triang, lognorm, weibull_min
import numpy as np
from numpy.random import weibull
import os
import statistics
#####################################
# Group level comparison
group_deg_mean = []
for jj in data['Degree_dist']:
group_deg_mean.append(statistics.mean(jj))
group_deg_array = np.array(group_deg_mean)
group_centered_deg_mean = group_deg_array - np.mean(group_deg_array)
data_uniform = uniform.rvs(size=sample_size,
loc=np.min(group_centered_deg_mean),
scale=np.max(group_centered_deg_mean))
data_normal = norm.rvs(size=sample_size,
loc=np.median(group_centered_deg_mean),
scale=1)
data_gamma = gamma.rvs(a=5, size=sample_size)
data_expon = expon.rvs(scale=1,
loc=np.median(group_centered_deg_mean),
size=sample_size)
mu = 3
data_poisson = poisson.rvs(mu=mu, size=sample_size)
c = 0.158
data_triang = triang.rvs(c=c, size=sample_size)
s = 0.954
data_lognorm = lognorm.rvs(s=s, size=sample_size)
a = 5.0
data_weibull = np.random.weibull(a=a, size=sample_size)
Distributions = [
data_uniform, data_normal, data_gamma, data_expon, data_poisson,
data_triang, data_lognorm, data_weibull
]
dist_names = [
'Uniform', 'Normal', 'Gamma', 'Exponential', 'Poisson', 'Triangular',
'LogNormal', 'Weibull'
]
group_uniform = [
'Uniform:',
stats.kstest(group_centered_deg_mean, data_uniform)
]
group_normal = [
'Normal', stats.kstest(group_centered_deg_mean, data_normal)
]
group_gamma = ['Gamma', stats.kstest(group_centered_deg_mean, data_gamma)]
group_exponential = [
'Exponential',
stats.kstest(group_centered_deg_mean, data_expon)
]
group_poisson = [
'Poisson',
stats.kstest(group_centered_deg_mean, data_poisson)
]
group_traing = [
'Triang', stats.kstest(group_centered_deg_mean, data_triang)
]
group_lognormal = [
'Lognormal',
stats.kstest(group_centered_deg_mean, data_lognorm)
]
group_weibull = [
'Weibull',
stats.kstest(group_centered_deg_mean, data_weibull)
]
for ii, jj in zip(Distributions, dist_names):
sns.set_context('talk')
ax = sns.histplot(ii, bins=50, kde=True, color='skyblue')
#hist_kws={'linewidth':15, 'alpha':1})
ax.set(title=jj + ' Sample Degree Distribution', ylabel='Frequency')
aj = sns.histplot(group_centered_deg_mean,
bins=50,
kde=True,
color='forestgreen')
plt.savefig(reports_path + '/' + jj +
' Sample Degree Distribution.png')
plt.clf()
ks_test_results_group = [
group_uniform, group_normal, group_gamma, group_exponential,
group_poisson, group_traing, group_lognormal, group_weibull
]
with open(reports_path + '/' + 'ks_test_results_group.txt',
'w') as filehandle:
for listitem in ks_test_results_group:
filehandle.write('%s\n' % listitem)
return ks_test_results_group
for x in range(0, random.randint(0, 6) ): S[Z[x]]=0 FC, FA, r, sC, sA, z1, z2=S File2.write( "@NAME:SCAFFOLDS VERSION:0.4.1 FORMAT:TEXT CONCATENATED\n") File2.write( "@NAME LENGTH\n") File2.write( "scaffold_1 100000\n") File2.write( "@END_TABLE\n") File2.write( "@NAME:GENOTYPES VERSION:0.4.1 FORMAT:TEXT CONCATENATED INDEXED\n") File2.write( "@SCFNAME POS MN_FREQ Sample_1 Sample_2\n") for x in range(0, MAX): P=0 while(P<MINP or P>MAXP): P = round(triang.rvs(0.1), 2) Q=1-P td=random.random() mmmm, Mmmm, MMmm, mmMm, MmMm, MMMm, mmMM, MmMM, MMMM=getMs(P, S) if( min([mmmm, Mmmm, MMmm, mmMm, MmMm, MMMm, mmMM, MmMM, MMMM])<-0.0001): skipped+=1 continue Mmmm+=mmmm MMmm+=Mmmm mmMm+=MMmm MmMm+=mmMm
def WeightedRandom(sel, M, N, total, dist):
if dist == "no":
if sel == "exp":
rand = []
expvar = M
ctr = 100
final = (-float(M)) / math.log(0.05)
while ctr < total and expvar > final:
expvar = expvar - 500
ctr += 100
if expvar < final:
expvar = final
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(expon.rvs(scale=expvar)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(expon.rvs(scale=expvar))
if rand[i] < 0:
rand[i] = -rand[i]
elif sel == "filter":
rand = []
epscale = M
ctr = 100
while ctr < total and epscale != 1000:
epscale = epscale - 500
ctr += 100
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(gennorm.rvs(5, scale=epscale)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(gennorm.rvs(5, scale=epscale))
if rand[i] < 0:
rand[i] = -rand[i]
elif sel == "triang":
rand = []
triscale = M * 2
ctr = 100
final = M
while ctr < total and triscale > M:
triscale = triscale - 1000
ctr += 100
if triscale <= M:
triscale = M + int(round(M / 5))
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(triang.rvs(0, loc=0, scale=triscale)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(triang.rvs(0, loc=0, scale=triscale))
if rand[i] < 0:
rand[i] = -rand[i]
else:
if sel == "exp":
rand = []
expvar = (-float(M)) / math.log(0.05)
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(expon.rvs(scale=expvar)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(expon.rvs(scale=expvar))
if rand[i] < 0:
rand[i] = -rand[i]
elif sel == "filter":
rand = []
epscale = M / 5
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(gennorm.rvs(5, scale=epscale)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(gennorm.rvs(5, scale=epscale))
if rand[i] < 0:
rand[i] = -rand[i]
elif sel == "triang":
rand = []
triscale = M + int(round(M / 10))
if total < 0:
for i in range(0, N):
rand.append(random.randint(0, M - 1))
while rand.count(rand[i]) > 1:
rand[i] = random.randint(0, M - 1)
else:
for i in range(0, N):
rand.append(int(triang.rvs(0, loc=0, scale=triscale)))
if rand[i] < 0:
rand[i] = -rand[i]
while rand[i] >= M or rand.count(rand[i]) > 1:
rand[i] = int(triang.rvs(0, loc=0, scale=triscale))
if rand[i] < 0:
rand[i] = -rand[i]
return rand