def run_demo(args):
"""
@brief a Gaussian Process regression example using an input covariance
model. The demo divides the observations along the x-axis and computes in
parallel using mpi4py
"""
np.random.seed(1)
def f(x):
"""
@brief the function to predict.
"""
return x * np.sin(x)
# the inpute data points
X = np.linspace(0.1, 9.9, 500)
# make the observations with added noise
y = f(X).ravel()
dy = 0.5 + 1.0 * np.random.random(y.shape)
noise = np.random.normal(0, dy)
y += noise
# mesh the input space for evaluations of the prediction
x = np.linspace(-2, 12, 2*len(X))
# instanciate a Gaussian Process model, allowing all params to vary
gp = GaussianProcessMPI(theta0 = [0.5, 2.0, 1.0],
covfunction=args.covariance, verbose=True,
fixed=[False, False, False])
# fit to data using Maximum Likelihood Estimation of the parameters
gp.fit(X, y, dy)
# make the prediction on the meshed x-axis
y_pred, sigma = gp.predict(x)
if MPI.COMM_WORLD.Get_rank() == 0:
# plot the function, the prediction and the 95% confidence interval based on
# the standard deviation
fig = pl.figure()
pl.plot(x, f(x), 'r:', label=r'$f(x) = x \ \mathrm{sin}(x)$')
pl.errorbar(X.ravel(), y, dy, label='Observations')
pl.plot(x, y_pred, label='Prediction')
pl.fill(np.concatenate([x, x[::-1]]),
np.concatenate([y_pred - 1.9600 * sigma,
(y_pred + 1.9600 * sigma)[::-1]]),
alpha=.2, fc='DarkGoldenRod', ec="None", label='95% confidence interval')
pl.xlabel('$x$', fontsize=16)
pl.ylabel('$f(x)$', fontsize=16)
pl.ylim(-15, 20)
pl.legend(loc='upper left')
pl.show()
def run_demo(args):
"""
@brief a Gaussian Process regression example that fits several supernovae
spectra in parallel using mpi4pys
"""
myrank = comm.Get_rank()
nprocs = comm.Get_size()
# read in the relevant files in correct order
f1 = glob("../data/SN2011fe/11feM*")
f1.sort(reverse=True)
f2 = glob("../data/SN2011fe/11feP*")
f2.sort()
files = f1+f2
pl.ion()
for N, f in enumerate(files):
file_root = os.path.splitext(os.path.basename(f))[0]
time = float(file_root[-3:])/10.
if 'M' in file_root: time *= -1.
# load the data from inputdata.txt
X, Y, Yerr = np.loadtxt(f, unpack=True)
n_eval = len(X)
batch_size = args.batch_size
resolution = args.resolution
# instanciate a Gaussian Process model, allowing all params to vary
gp = GaussianProcessMPI(theta0 = [1e-13, 2.0, 1e-13],
covfunction=args.covariance, verbose=True,
fixed=[False, False, False])
xmin = np.amin(X)
xmax = np.amax(X)
nstar = len(X)*resolution
# mesh the input space for evaluations of the prediction
x = np.linspace(xmin, xmax, nstar)
# fit to data using Maximum Likelihood Estimation of the parameters
gp.fit(X, Y, Yerr, batch_size=200)
# make the prediction on the meshed x-axis
y_pred, sigma = gp.predict(x)
# plot if you are the master
if myrank == 0:
# plot the function, the prediction and the 95% confidence interval based on
# the standard deviation
pl.cla()
pl.plot(X, Y, label='Observations')
pl.plot(x, y_pred, label='Prediction')
pl.fill(np.concatenate([x, x[::-1]]),
np.concatenate([y_pred - 1.9600 * sigma,
(y_pred + 1.9600 * sigma)[::-1]]),
alpha=0.5, fc='DarkGoldenRod', ec="None",
label='95% confidence interval')
pl.xlabel(r'$\lambda \ (\AA)$', fontsize=16)
pl.ylabel('$\mathrm{Flux \ (erg/s/cm^2/\AA)}$', fontsize=16)
pl.legend(loc='upper right')
pl.title("SNe 2011fe %+.1f days relative to B-band max" %time)
pl.ylim(-0.2e-12, 1.2e-12)
pl.savefig("figures/SN11fe_mpi_%02d.png" %N)
pl.draw()
