def run():
# experimental data for z=Normal(12,2)
exp_x =np.array([5.04, 5.14, 4.78, 5.12, 5.11, 5.13, 4.97, 5.1 , 5.53, 5.09])
exp_y = np.array([3.33, 3.56, 2.94, 3.27, 3.54, 3.4 , 3.52, 3.63, 3.45, 3.19])
exp_data = np.array([-26.16, -18.39, -20.57, -45.24, -29.16, -22., -46.47, -3.15, -10.48, -16.88])
# measurement error
sigma = 0.1
# Create parameters. Pass experimental input data to
# non-calibration parameters.
x = puq.NormalParameter('x', 'x', mean=5, dev=0.2, caldata=exp_x)
y = puq.NormalParameter('y', 'y', mean=3.4, dev=0.25, caldata=exp_y)
z = puq.UniformParameter('z', 'z', min=5, max=20)
# set up host, uq and prog normally
host = puq.InteractiveHost()
uq = puq.Smolyak([x,y,z], level=2)
prog = puq.TestProgram('python model_1.py', desc='model_1 calibration')
# pass experimental results to Sweep
return puq.Sweep(uq, host, prog, caldata=exp_data, calerr=sigma)
def value(self):
value = self.w.value
if value == 'Exact':
return [self.name, self.label, self.w1.value]
if value == 'Gaussian':
return puq.NormalParameter(self.name,
self.label,
mean=self.w1.value,
dev=self.w2.value)
if value == 'Uniform':
return puq.UniformParameter(self.name,
self.label,
min=self.w1.value,
max=self.w2.value)
return None
import puq
import numpy as np
# Calibration example/test case
# Calibrate one parameter of a two parameter model
# QoI is 0.2. There is a known variable with a
# measurement error of .05
def model(x, y):
return y**2 + 17 * x
# The actual values of our parameters
real_y = puq.NormalParameter('y', 'y', mean=5, dev=0.1)
real_x = 0.2
# take some samples, run them through the model
# and add some noise
num_samples = 50
y_data = real_y.pdf.random(num_samples)
y_err = np.ones(len(y_data)) * 0.1 # [0.1, 0.1, 0.1,...]
y_data_noisy = y_data + y_err * np.random.randn(len(y_data)) # simulated noise
y_caldata = np.column_stack((y_data_noisy, y_err))
z_data = model(real_x, y_data)
z_err = np.ones(len(z_data))
z_data_noisy = z_data + z_err * np.random.randn(len(z_data)) # simulated noise
# prior for x. Caltype is 'D' because x is not a stochastic.
def model(x, y, z):
return x**2 + 0.75 * y**2 + 2 * y + x * y - 7 * z + 2
# experimental data for z=Normal(12,1)
exp_x = np.array([
5.29, 4.96, 5.3, 5.18, 4.93, 5.11, 4.98, 4.81, 5.27, 4.69, 5.06, 4.99,
4.87, 5.04, 5.15
])
exp_y = np.array([
3.51, 3.34, 3.45, 3.26, 3.45, 3.5, 3.37, 3.45, 3.42, 3.4, 3.2, 3.24, 3.39,
3.35, 3.4
])
exp_data = np.array([
-18.28, -24.23, -24.5, -24.13, -25.36, -17.2, -16.5, -24.87, -16.25,
-26.51, -12.3, -15.91, -27.96, -27.98, -34.41
])
# measurement error for exp_data
sigma = 0.1
# Create parameters. Pass experimental input data to
# non-calibration parameters.
x = puq.NormalParameter('x', 'x', mean=5, dev=0.2, caldata=exp_x)
y = puq.NormalParameter('y', 'y', mean=3.4, dev=0.1, caldata=exp_y)
z = puq.UniformParameter('z', 'z', min=5, max=20, caltype='S')
[x, y, calibrated_z], kpdf = puq.calibrate([x, y, z], exp_data, sigma, model)
print "Calibrated z is", calibrated_z
import puq
import numpy as np
import pylab
def model(x):
return (x-4)**3
# our real value of x
real_x = puq.NormalParameter('x', 'x', mean=5, dev=0.1)
# We take 25 samples of x
num_samples = 25
x_data = real_x.pdf.lhs(num_samples)
x_data.sort() # sort for easier plotting
# compute z using our x samples
z_data = model(x_data)
# add some 'measurement' noise
sigma = 0.1
z_data_noisy = z_data + sigma * np.random.randn(len(z_data))
# prior for x. All we assume is x is between 2 and 25
# caltype is 'S' because we want to calibrate
# mean and deviation of x
x = puq.UniformParameter('x', 'x', min=2, max=25, caltype='S')
# do calibration
[calibrated], kpdf = puq.calibrate([x], z_data_noisy, sigma, model)
print(calibrated)