def fit(self, X, Y, Sigma):
"""
@brief the method whether the fitting magic happens
Parameters
----------
X : double array_like
An array with shape (n_samples, ) or (n_samples, n_dim) with the
input at which observations were made.
Y : double array_like
An array containing the observations f(X)
Sigma : double array_like
An array of shape (n_samples, ) containing the measurement errors
of Y, or a (n_samples, n_samples) covariance matrix of the data.
Returns
-------
gp : self
A fitted Gaussian Process model object awaiting data to perform
predictions.
"""
# set the observational data
self._set_data(X, Y, Sigma)
# calculate matrix of distances D between input X samples
D = tools.l1_distances(self.X)
self.D = D
# do the fitting
# Maximum Likelihood Estimation of the parameters
if self.verbose:
print("Performing Maximum Likelihood Estimation of the "
+ "autocorrelation parameters...")
self.theta, self.likelihood_function_value, par = self.optimize()
if np.isinf(self.likelihood_function_value):
raise Exception("Bad parameter region. Try increasing upper bound")
self.alpha = par['alpha']
self.L = par['L']
return self
def predict(self, Xstar):
"""
@brief evaluate the Gaussian Process model at X.
Parameters
----------
Xstar : array_like
An array with shape (n_eval, n_features) giving the point(s) at
which the prediction(s) should be made.
Returns
-------
y : array_like
An array with shape (n_eval, ) with the predicted value, f(x)
sigma : array_like
An array with shape (n_eval, ) with the standard deviation at x.
"""
n = len(Xstar)
# Check input shapes
if(np.shape(Xstar) == (n,)):
Xstar = np.reshape(Xstar, (n, 1))
n_eval, n_dim_Xstar = Xstar.shape
n_samples, n_dim_X = self.X.shape
# Run input checks
if n_dim_Xstar != n_dim_X:
raise ValueError(("The number of dimensions in Xstar "
"(Xstar.shape[1] = %d) "
"should match the sample size used for fit() "
"which is %d.") % (n_dim_Xstar, n_dim_X))
fmean = np.zeros(n)
fstd = np.zeros(n)
for i in range(n):
thisXstar = Xstar[i, :]
nstar = thisXstar.shape[0]
# Get pairwise componentwise L1-distances to the input training set
dx = tools.l1_distances(tools.array2d(thisXstar), self.X)
# the covariance vector between these distances and training set
kstar = self.covf.covfunc(self.theta, dx).T
kstar = kstar.flatten()
# the predictive mean
mean = np.dot(kstar.T, self.alpha)
# calculate predictive standard deviation
v = linalg.solve(self.L, kstar)
# now compute cov(Xstar, Xstar)
dxx = tools.l1_distances(tools.array2d(thisXstar))
covstar = self.covf.covfunc(self.theta, dxx).T
covstar = covstar.flatten()[0]
var = covstar - np.dot(v.T, v)
if (self.mu != None):
mean += self.mu(Xstar, *self.muargs)
if var < 0.: var = 0
fmean[i] = mean
fstd[i] = np.sqrt(var)
return fmean, fstd
def fit(self, X, Y, Sigma, batch_size=200, overlap=0.2):
"""
@brief the method whether the fitting magic happens
Parameters
----------
X : double array_like
An array with shape (n_samples, ) or (n_samples, n_dim) with the
input at which observations were made.
Y : double array_like
An array containing the observations f(X)
Sigma : double array_like
An array of shape (n_samples, ) containing the measurement errors
of Y, or a (n_samples, n_samples) covariance matrix of the data.
batch_size : double, optional
the width in points along the x-axis to fit one at a time
overlap : double, optional
the percentage of points to overlap between batches that are fit
Returns
-------
gp : self
A fitted Gaussian Process model object awaiting data to perform
predictions.
"""
nprocs = comm.Get_size()
myrank = comm.Get_rank()
nbatches = max(1, len(X)/batch_size)
self.nbatches = nbatches
n_samples = len(X)
self.fits = []
self.xbounds = []
# do given batch of the fit based on rank
for k in range(myrank, nbatches, nprocs):
batch_from = k * batch_size
batch_to = min([(k + 1) * batch_size + 1, n_samples + 1])
if k == nbatches-1: batch_to = len(X)
# keep track of the x bounds
xmin = np.amin(X[batch_from:batch_to])
xmax = np.amax(X[batch_from:batch_to])
self.xbounds.append((xmin, xmax))
batch_to += overlap*batch_size
batch_from -= overlap*batch_size
if batch_from < 0: batch_from = 0
X_cut = X[batch_from:batch_to]
Y_cut = Y[batch_from:batch_to]
Sigma_cut = Sigma[batch_from:batch_to]
# set the observational data
self._set_data(X_cut, Y_cut, Sigma_cut)
# calculate matrix of distances D between input X samples
D = tools.l1_distances(self.X)
self.D = D
# do the fitting
# Maximum Likelihood Estimation of the parameters
if self.verbose:
print("Performing Maximum Likelihood Estimation of the "
+ "autocorrelation parameters...")
self.theta, self.likelihood_function_value, par = self.optimize()
if np.isinf(self.likelihood_function_value):
raise Exception("Bad parameter region. Try increasing upper bound")
self.alpha = par['alpha']
self.L = par['L']
self.fits.append(copy.deepcopy(self))
return self
def predict(self, Xstar):
"""
@brief evaluate the Gaussian Process model at X.
Parameters
----------
Xstar : array_like
An array with shape (n_eval, n_features) giving the point(s) at
which the prediction(s) should be made.
Returns
-------
y : array_like
An array with shape (n_eval, ) with the Best Linear Unbiased
Prediction at x.
sigma : array_like
An array with shape (n_eval, ) with the standard deviation at x.
"""
nprocs = comm.Get_size()
myrank = comm.Get_rank()
data_pred = [] # the predicted data
# do given batch of the fit based on rank
cnt = 0
for k in range(myrank, self.nbatches, nprocs):
# trim Xstar
inds = np.where((Xstar>=self.xbounds[cnt][0])*(Xstar<=self.xbounds[cnt][1]))
Xstar_cut = Xstar[inds]
# check for Xstar outside fitting X range
if k == 0:
inds = np.where(Xstar < self.xbounds[cnt][0])
Xstar_cut = np.append(Xstar[inds], Xstar_cut)
if k == self.nbatches-1:
inds = np.where(Xstar > self.xbounds[cnt][1])
Xstar_cut = np.append(Xstar_cut, Xstar[inds])
n = len(Xstar_cut)
# Check input shapes
if(np.shape(Xstar_cut) == (n,)):
Xstar_cut = np.reshape(Xstar_cut, (n, 1))
n_eval, n_dim_Xstar = Xstar_cut.shape
n_samples, n_dim_X = self.X.shape
# Run input checks
if n_dim_Xstar != n_dim_X:
raise ValueError(("The number of dimensions in Xstar "
"(Xstar.shape[1] = %d) "
"should match the sample size used for fit() "
"which is %d.") % (n_dim_Xstar, n_dim_X))
# get the right fit
fit = self.fits[cnt]
fmean = np.zeros(n)
fstd = np.zeros(n)
for i in range(n):
thisXstar = Xstar_cut[i, :]
nstar = thisXstar.shape[0]
# Get pairwise componentwise L1-distances to the input training set
dx = tools.l1_distances(tools.array2d(thisXstar), fit.X)
# the covariance vector between these distances and training set
kstar = self.covf.covfunc(fit.theta, dx).T
kstar = kstar.flatten()
# the predictive mean
mean = np.dot(kstar.T, fit.alpha)
# calculate predictive standard deviation
v = linalg.solve(fit.L, kstar)
# now compute cov(Xstar, Xstar)
dxx = tools.l1_distances(tools.array2d(thisXstar))
covstar = self.covf.covfunc(fit.theta, dxx).T
covstar = covstar.flatten()[0]
var = covstar - np.dot(v.T, v)
if (self.mu != None):
mean += self.mu(Xstar, *self.muargs)
if var < 0.: var = 0
fmean[i] = mean
fstd[i] = np.sqrt(var)
cnt += 1
# save the predictions
data_pred.append((k, Xstar_cut, fmean, fstd))
# gather the reconstructed data to the master
data_pred = comm.gather(data_pred, root=0)
# the master combines and returns
if myrank == 0:
x_rec, y_rec, yerr_rec = self._combine_data(data_pred)
return y_rec, yerr_rec
else:
return None, None
