def main():
print(
gv.ranseed(
(2050203335594632366, 8881439510219835677, 2605204918634240925)))
log_stdout('eg3a.out')
integ = vegas.Integrator(4 * [[0, 1]])
# adapt grid
training = integ(f(), nitn=10, neval=1000)
# evaluate multi-integrands
result = integ(f(), nitn=10, neval=5000)
print('I[0] =', result[0], ' I[1] =', result[1], ' I[2] =', result[2])
print('Q = %.2f\n' % result.Q)
print('<x> =', result[1] / result[0])
print('sigma_x**2 = <x**2> - <x>**2 =',
result[2] / result[0] - (result[1] / result[0])**2)
print('\ncorrelation matrix:\n', gv.evalcorr(result))
unlog_stdout()
r = gv.gvar(gv.mean(result), gv.sdev(result))
print(r[1] / r[0])
print((r[1] / r[0]).sdev / (result[1] / result[0]).sdev)
print(r[2] / r[0] - (r[1] / r[0])**2)
print(result.summary())
def main():
print(gv.ranseed((1814855126, 100213625, 262796317)))
log_stdout('eg3a.out')
integ = vegas.Integrator(4 * [[0, 1]])
# adapt grid
training = integ(f(), nitn=10, neval=2000)
# evaluate multi-integrands
result = integ(f(), nitn=10, neval=10000)
print('I[0] =', result[0], ' I[1] =', result[1], ' I[2] =', result[2])
print('Q = %.2f\n' % result.Q)
print('<x> =', result[1] / result[0])
print('sigma_x**2 = <x**2> - <x>**2 =',
result[2] / result[0] - (result[1] / result[0])**2)
print('\ncorrelation matrix:\n', gv.evalcorr(result))
unlog_stdout()
r = gv.gvar(gv.mean(result), gv.sdev(result))
print(r[1] / r[0])
print((r[1] / r[0]).sdev / (result[1] / result[0]).sdev)
print(r[2] / r[0] - (r[1] / r[0])**2)
print((r[2] / r[0] - (r[1] / r[0])**2).sdev /
(result[2] / result[0] - (result[1] / result[0])**2).sdev)
print(result.summary())
# do it again for a dictionary
print(gv.ranseed((1814855126, 100213625, 262796317)))
integ = vegas.Integrator(4 * [[0, 1]])
# adapt grid
training = integ(f(), nitn=10, neval=2000)
# evaluate the integrals
result = integ(fdict(), nitn=10, neval=10000)
log_stdout('eg3b.out')
print(result)
print('Q = %.2f\n' % result.Q)
print('<x> =', result['x'] / result['1'])
print('sigma_x**2 = <x**2> - <x>**2 =',
result['x**2'] / result['1'] - (result['x'] / result['1'])**2)
unlog_stdout()
def main():
np.random.seed(12)
log_stdout('eg6a.out')
itg = vegas.Integrator(dim * [[0, 1]], alpha=0.25)
nstrat = 5 * [12] + (dim - 5) * [1]
itg(f, nitn=15, nstrat=nstrat)
r = itg(f, nitn=5, nstrat=nstrat)
print(r.summary())
print('nstrat =', np.array(itg.nstrat))
unlog_stdout()
print()
log_stdout('eg6b.out')
itg = vegas.Integrator(dim * [[0, 1]], alpha=0.25)
neval = 2e6
itg(f, nitn=15, neval=neval)
r = itg(f, nitn=5, neval=neval)
print(r.summary())
print('nstrat =', np.array(itg.nstrat))
unlog_stdout()
print()
def main():
dim = 5
log_stdout('eg5a.out')
np.random.seed(123)
map = vegas.AdaptiveMap(dim * [(0, 1)])
itg = vegas.Integrator(map, alpha=0.1)
r = itg(f, neval=1e4, nitn=5)
print(r.summary())
unlog_stdout()
log_stdout('eg5b.out')
np.random.seed(1234567)
map = vegas.AdaptiveMap(dim * [(0, 1)])
x = np.concatenate([
np.random.normal(loc=0.45, scale=3 / 50, size=(1000, dim)),
np.random.normal(loc=0.7, scale=3 / 50, size=(1000, dim)),
])
map.adapt_to_samples(x, f, nitn=5)
itg = vegas.Integrator(map, alpha=0.1)
r = itg(f, neval=1e4, nitn=5)
print(r.summary())
unlog_stdout()
log_stdout('eg5c.out')
np.random.seed(123)
def smc(f, neval, dim):
" integrates f(y) over dim-dimensional unit hypercube "
y = np.random.uniform(0, 1, (neval, dim))
fy = f(y)
return (np.average(fy), np.std(fy) / neval**0.5)
def g(y):
jac = np.empty(y.shape[0], float)
x = np.empty(y.shape, float)
map.map(y, x, jac)
return jac * f(x)
# with map
r = smc(g, 50_000, dim)
print(' SMC + map:', f'{r[0]:.3f} +- {r[1]:.3f}')
# without map
r = smc(f, 50_000, dim)
print('SMC (no map):', f'{r[0]:.3f} +- {r[1]:.3f}')
])
# print (y)
print()
log_prior = BufferDict()
log_prior['log(a)'] = log(gvar(0.02, 0.02))
sqrt_prior = BufferDict()
sqrt_prior['sqrt(a)'] = sqrt(gvar(0.02, 0.02))
prior = BufferDict(a = gvar(0.02, 0.02))
unif_prior = BufferDict()
unif_prior['ga(a)'] = BufferDict.uniform('ga', 0, 0.04)
for p in [prior, log_prior, sqrt_prior, unif_prior]:
key = list(p.keys())[0].replace('(a)','_a')
log_stdout("eg6-{}.out".format(key))
def fcn(p, N=len(y)):
return N*[p['a']]
fit = nonlinear_fit(prior=p, fcn=fcn, data=(y))
print (fit)
print ("a =", fit.p['a'])
if DO_PLOT:
log_stdout('eg6-hist.out')
print(fit)
a = fit.p['a']
print('a =', a)
import matplotlib.pyplot as plt
fs = plt.rcParams['figure.figsize']
def main():
print(
gv.ranseed(
(5751754790502652836, 7676372623888309739, 7570829798026950508)))
integ = vegas.Integrator([[-1., 1.], [0., 1.], [0., 1.], [0., 1.]],
# analyzer=vegas.reporter(),
)
if SAVE_OUTPUT:
log_stdout('eg1a.out')
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
integ.map.show_grid(30,
axes=[(0, 1), (2, 3), (0, None), (None, 1), (2, 0),
(3, 0)],
shrink=False)
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1b.out')
result = integ(f, nitn=100, neval=1000)
print('larger nitn => %s Q = %.2f' % (result, result.Q))
result = integ(f, nitn=10, neval=1e4)
print('larger neval => %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1c.out')
# integ.set(map=[[-2., .4, .6, 2.], [0, .4, .6, 2.], [0,.4, .6, 2.], [0.,.4, .6, 2.]])
# integ.set(map=[[-2., 2.], [0, 2.], [0, 2.], [0., 2.]])
integ = vegas.Integrator([[-2., 2.], [0, 2.], [0, 2.], [0., 2.]], )
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1c1.out')
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1d.out')
integ(f, nitn=7, neval=1000)
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1e.out')
integ = vegas.Integrator([[-1, 1]] + 3 * [[0, 1]])
integ(f, nitn=10, neval=1000)
def g(x):
return x[0] * f(x)
result = integ(g, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1f.out')
# integ(f_sphere, nitn=10, neval=400000, alpha=0.25)
# result = integ(f_sphere, nitn=10, neval=400000, alpha=0.25, beta=0.75)#, analyzer=vegas.reporter(5))
integ(f_sphere, nitn=10, neval=1000, alpha=0.5)
result = integ(f_sphere, nitn=10, neval=1000,
alpha=0.5) #, analyzer=vegas.reporter(5))
# print(integ.settings())
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1g.out')
integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
result = integ(f_sphere, nitn=10, neval=1000, adapt=False) # alpha=0.1)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1h.out')
integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
result = integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
# log_stdout('eg1h.out')
integ = vegas.Integrator(4 * [[0, 1]])
integ(f2, nitn=10, neval=4e4)
result = integ(f2, nitn=10, neval=4e4,
beta=0.75) # , analyzer=vegas.reporter())
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
integ.map.show_grid(70)
print(integ(f2, nitn=10, neval=4e4, beta=0.).summary())
def main():
### 1) least-squares fit to the data
x = np.array([
0.2, 0.4, 0.6, 0.8, 1.,
1.2, 1.4, 1.6, 1.8, 2.,
2.2, 2.4, 2.6, 2.8, 3.,
3.2, 3.4, 3.6, 3.8
])
y = gv.gvar([
'0.38(20)', '2.89(20)', '0.85(20)', '0.59(20)', '2.88(20)',
'1.44(20)', '0.73(20)', '1.23(20)', '1.68(20)', '1.36(20)',
'1.51(20)', '1.73(20)', '2.16(20)', '1.85(20)', '2.00(20)',
'2.11(20)', '2.75(20)', '0.86(20)', '2.73(20)'
])
prior = make_prior()
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=fitfcn)
if LSQFIT_ONLY:
log_stdout('case-outliers-lsq.out')
elif not MULTI_W:
log_stdout('case-outliers.out')
print(fit)
# plot data
plt.errorbar(x, gv.mean(y), gv.sdev(y), fmt='o', c='b')
# plot fit function
xline = np.linspace(x[0], x[-1], 100)
yline = fitfcn(xline, fit.p)
plt.plot(xline, gv.mean(yline), 'k:')
# yp = gv.mean(yline) + gv.sdev(yline)
# ym = gv.mean(yline) - gv.sdev(yline)
# plt.fill_between(xline, yp, ym, color='0.8')
plt.xlabel('x')
plt.ylabel('y')
plt.savefig('case-outliers1.png', bbox_inches='tight')
if LSQFIT_ONLY:
return
### 2) Bayesian integral with modified PDF
pdf = ModifiedPDF(data=(x, y), fcn=fitfcn, prior=prior)
# integrator for expectation values with modified PDF
expval = vegas.PDFIntegrator(fit.p, pdf=pdf)
# adapt integrator to pdf
expval(neval=1000, nitn=15)
# evaluate expectation value of g(p)
def g(p):
w = p['w']
c = p['c']
return dict(w=[w, w**2], mean=c, outer=np.outer(c,c))
results = expval(g, neval=1000, nitn=15, adapt=False)
print(results.summary())
# expval.map.show_grid(15)
if MULTI_W:
log_stdout('case-outliers-multi.out')
# parameters c[i]
mean = results['mean']
cov = results['outer'] - np.outer(mean, mean)
c = mean + gv.gvar(np.zeros(mean.shape), gv.mean(cov))
print('c =', c)
print(
'corr(c) =',
np.array2string(gv.evalcorr(c), prefix=10 * ' '),
'\n',
)
# parameter w
wmean, w2mean = results['w']
wsdev = gv.mean(w2mean - wmean ** 2) ** 0.5
w = wmean + gv.gvar(np.zeros(np.shape(wmean)), wsdev)
print('w =', w, '\n')
# Bayes Factor
print('logBF =', np.log(results.pdfnorm))
sys.stdout = STDOUT
if MULTI_W:
return
# add new fit to plot
yline = fitfcn(xline, dict(c=c))
plt.plot(xline, gv.mean(yline), 'r--')
yp = gv.mean(yline) + gv.sdev(yline)
ym = gv.mean(yline) - gv.sdev(yline)
plt.fill_between(xline, yp, ym, color='r', alpha=0.2)
plt.savefig('case-outliers2.png', bbox_inches='tight')
import numpy as np
import gvar
RMAX = (2 * 0.5**2)**0.5
def fcn(x):
dx2 = 0.0
for d in range(2):
dx2 += (x[d] - 0.5)**2
I = np.exp(-dx2)
# add I to appropriate bin in dI
dI = np.zeros(5, dtype=float)
dr = RMAX / len(dI)
j = int(dx2**0.5 / dr)
dI[j] = I
return dict(I=I, dI=dI)
log_stdout('eg4.out')
integ = vegas.Integrator(2 * [(0, 1)])
# results returned in a dictionary
result = integ(fcn)
print(result.summary())
print(' I =', result['I'])
print('dI/I =', result['dI'] / result['I'])
print('sum(dI/I) =', sum(result['dI']) / result['I'])
# print(gvar.evalcorr(result['dI'] / result['I']))
import numpy as np
from outputsplitter import log_stdout
def f(x):
return x[0] * x[1] ** 2
m = vegas.AdaptiveMap([[0, 1], [0, 1]], ninc=5)
ny = 1000
y = np.random.uniform(0., 1., (ny, 2)) # 1000 random y's
x = np.empty(y.shape, float) # work space
jac = np.empty(y.shape[0], float)
f2 = np.empty(y.shape[0], float)
log_stdout('eg2a.out')
print('initial grid:')
print m.settings()
for itn in range(5): # 20 iterations to adapt
m.map(y, x, jac) # compute x's and jac
for j in range(ny): # compute training data
f2[j] = (jac[j] * f(x[j])) ** 2
m.add_training_data(y, f2) # adapt
m.adapt(alpha=1.5)
print('iteration %d:' % itn)
print(m.settings())
def main():
print(gv.ranseed(
(5751754790502652836, 7676372623888309739, 7570829798026950508)
))
integ = vegas.Integrator(
[[-1., 1.], [0., 1.], [0., 1.], [0., 1.]],
# analyzer=vegas.reporter(),
)
if SAVE_OUTPUT:
log_stdout('eg1a.out')
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
integ.map.show_grid(
30,
axes=[(0, 1), (2, 3), (0, None), (None, 1), (2, 0), (3, 0)],
shrink=False
)
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1b.out')
result = integ(f, nitn=100, neval=1000 )
print('larger nitn => %s Q = %.2f' % (result, result.Q))
result = integ(f, nitn=10, neval=1e4)
print('larger neval => %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1c.out')
# integ.set(map=[[-2., .4, .6, 2.], [0, .4, .6, 2.], [0,.4, .6, 2.], [0.,.4, .6, 2.]])
# integ.set(map=[[-2., 2.], [0, 2.], [0, 2.], [0., 2.]])
integ = vegas.Integrator(
[[-2., 2.], [0, 2.], [0, 2.], [0., 2.]],
)
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1c1.out')
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1d.out')
integ(f, nitn=7, neval=1000)
result = integ(f, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1e.out')
integ = vegas.Integrator([[-1,1]] + 3 * [[0, 1]])
integ(f, nitn=10, neval=1000)
def g(x):
return x[0] * f(x)
result = integ(g, nitn=10, neval=1000)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1f.out')
# integ(f_sphere, nitn=10, neval=400000, alpha=0.25)
# result = integ(f_sphere, nitn=10, neval=400000, alpha=0.25, beta=0.75)#, analyzer=vegas.reporter(5))
integ(f_sphere, nitn=10, neval=1000, alpha=0.5)
result = integ(f_sphere, nitn=10, neval=1000, alpha=0.5)#, analyzer=vegas.reporter(5))
# print(integ.settings())
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1g.out')
integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
result = integ(f_sphere, nitn=10, neval=1000, adapt=False) # alpha=0.1)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
log_stdout('eg1h.out')
integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
result = integ(f_sphere, nitn=10, neval=1000, alpha=0.1)
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
if SAVE_OUTPUT:
unlog_stdout()
# log_stdout('eg1h.out')
integ = vegas.Integrator(4 * [[0, 1]])
integ(f2, nitn=10, neval=4e4)
result = integ(f2, nitn=10, neval=4e4, beta=0.75) # , analyzer=vegas.reporter())
print(result.summary())
print('result = %s Q = %.2f' % (result, result.Q))
integ.map.show_grid(70)
print(integ(f2, nitn=10, neval=4e4, beta=0.).summary())