def test_calculateEV_norm(mean=0.0, moment=2):
# calculate moments of a normal distribution
def fFn(x):
return abs(scipy.real(scipy.power(x, moment)))
gridArray = scipy.linspace(-10, 10, 500)
fArray = fFn(gridArray)
sdRange = scipy.linspace(0.1, 2.0, 100)
t1 = time.time()
result1 = [calculateEV_montecarlo(fFn, scipy.stats.norm(loc=mean, scale=sd)) for sd in sdRange]
t2 = time.time()
result2 = [calculateEV_integrate(fFn, scipy.stats.norm(loc=mean, scale=sd)) for sd in sdRange]
t3 = time.time()
result3 = [calculateEV_grid(gridArray, fFn, scipy.stats.norm(loc=mean, scale=sd), zOffset=0.0, leftK=fArray[0], rightK=fArray[-1]) for sd in sdRange]
t4 = time.time()
result4 = [_myfuncs.mycalcEV_grid(gridArray, fArray, _myfuncs.NormalCDFObj(mean, sd),
_myfuncs.NormalPDFObj(mean, sd), 0.0, fArray[0], fArray[-1]) for sd in sdRange]
t5 = time.time()
print("montecarlo: %f" % (t2-t1))
print("integrate: %f" % (t3-t2))
print("grid: %f" % (t4-t3))
print("c++ grid: %f" % (t5-t4))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result1)
plt.title("monte carlo")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result2)
plt.title("integrate")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result3)
plt.title("grid")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result4)
plt.title("c++ grid")
def test_calculateEV_lognorm(mean=0.0, moment=2):
# calculate moments of a lognormal distribution
def fFn(x):
#return abs(scipy.real(scipy.power(x, moment)))
return scipy.real(-(1.0/x))
#gridArray = scipy.linspace(0.001, 20, 1000)
sdRange = scipy.linspace(0.1, 1.5, 100)
t1 = time.time()
result1 = []
for sd in sdRange:
rv = scipy.stats.lognorm(sd, scale=scipy.exp(mean))
EV = calculateEV_montecarlo(fFn, rv)
result1.append(EV)
t2 = time.time()
result2 = [calculateEV_integrate(fFn, scipy.stats.lognorm(sd, scale=scipy.exp(mean))) for sd in sdRange]
t3 = time.time()
result3 = []
for sd in sdRange:
rv = scipy.stats.lognorm(sd, scale=scipy.exp(mean))
x = rv.ppf(scipy.linspace(0, 1, 200))[1:-1]
y = fFn(x)
EV = calculateEV_grid(x, fFn, rv, zOffset=0.0, leftK=y[0], rightK=y[-1], fArray=y)
result3.append(EV)
t4 = time.time()
result4 = []
for sd in sdRange:
rv = scipy.stats.lognorm(sd, scale=scipy.exp(mean))
x = rv.ppf(scipy.linspace(0, 1, 200))[1:-1]
y = fFn(x)
result4.append(_myfuncs.mycalcEV_grid(x, y, _myfuncs.LognormalCDFObj(mean, sd),
_myfuncs.LognormalPDFObj(mean, sd), 0.0, y[0], y[-1]))
t5 = time.time()
result5 = []
x = scipy.linspace(0, 20, 1000)
y = fFn(x)
for sd in sdRange:
rv = scipy.stats.lognorm(sd, scale=scipy.exp(mean))
pdf_x = rv.ppf(scipy.linspace(0, 1, 1000))[1:-1]
pdf_y = rv.pdf(pdf_x)
result5.append(_myfuncs.mycalcEV_grid2(x, y, pdf_x, pdf_y))
t6 = time.time()
result6 = []
x = scipy.linspace(0, 20, 1000)[1:-1]
y = fFn(x)
for sd in sdRange:
rv = scipy.stats.lognorm(sd, scale=scipy.exp(mean))
EV = calculateEV_montecarlo2(x, y, rv)
result6.append(EV)
t7 = time.time()
result7 = []
x = scipy.linspace(0, 20, 1000)[1:-1]
y = fFn(x)
for sd in sdRange:
EV = calculateEV_lognorm(x, y, lambda x: x, mean, sd)
result7.append(EV)
t8 = time.time()
result8 = []
x = scipy.linspace(0, 20, 1000)[1:-1]
y = fFn(x)
for sd in sdRange:
EV = _myfuncs.lognormal_EV_lininterp(x, y, mean, sd)
result8.append(EV)
t9 = time.time()
print("montecarlo: %f" % (t2-t1))
print("integrate: %f" % (t3-t2))
print("grid with CDF/PDF: %f" % (t4-t3))
print("c++ grid with CDF/PDF: %f" % (t5-t4))
print("c++ grid 2: %f" % (t6-t5))
print("monte carlo 2: %f" % (t7-t6))
print("partial exp: %f" % (t8-t7))
print("c++ partial exp: %f" % (t9-t8))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result1)
plt.title("monte carlo")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result2)
plt.title("integrate")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result3)
plt.title("grid")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result4)
plt.title("c++ grid")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result5)
plt.title("c++ grid 2")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result6)
plt.title("monte carlo 2")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result7)
plt.title("partial exp")
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(sdRange, result8)
plt.title("c++ partial exp")
