np.set_printoptions(precision=1)
print "\nHow many locations per dimension?"
N = input("Enter: ")
print "\nWhich dimension?"
dim = input("Enter: ")
# Choose some hyperparameters for the Matern kernel
nu = 1.0
sigma = 1.0
rho = 1.0
# get and plot points
X = get_gppoints(N, dim)
def maternkernel(x, y, ORD=None, NU=nu, SIGMA=sigma, RHO=rho):
r = norm_diff(x, y, ORD)
return maternfunction(r, NU, SIGMA, RHO)
# build kernelmatrix
M = build_kernelmatrix(X, X, maternkernel)
# check condition number of matrix
print "\nCondition number of the kernel matrix:"
print "\tCond(K) =", np.linalg.cond(M)
print ""
def plotGP_mean(Minverse, data, kernelmatrix):
# extract info from data
approxpts = data[:, 0]
approxpts = np.reshape(approxpts, (len(approxpts), 1))
y = data[:, 1]
y = np.reshape(y, (len(y), 1))
# determine axis limits
xmin = np.min(approxpts)
xmax = np.max(approxpts)
ymin = np.min(y)
ymax = np.max(y)
newpts = np.linspace(xmin, xmax, 250)
newpts = np.reshape(newpts, (len(newpts), 1))
# build kernel approximation matrices on new pts
K = build_kernelmatrix(newpts, approxpts, kernelmatrix)
K2 = build_kernelmatrix(newpts, newpts, kernelmatrix)
# build approximation mean on newpts
coeff = Minverse.dot(y - np.mean(y))
approxmean = K.dot(coeff) + np.mean(y) * np.ones((len(newpts), 1))
# build approximation covariance on newpts
Knew = K2 - K.dot(Minv).dot(K.T)
# construct deviations
plusdev = approxmean[:, 0] + np.sqrt(Knew.diagonal())
minusdev = approxmean[:, 0] - np.sqrt(Knew.diagonal())
# plot mean
fig = plt.figure()
plt.plot(newpts[:, 0],
approxmean[:, 0],
'-',
linewidth=3,
color='darkblue')
# plot data
plt.plot(approxpts, y, 'o', markersize=10, color='darkslategray')
# plot deviation
# plt.fill_between(newpts[:,0], minusdev, plusdev, color = 'burlywood', alpha = 0.5)
plt.xlim((xmin - 0.1, xmax + 0.1))
plt.ylim((ymin - 1, ymax + 1))
# remove frame
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.gca().spines['bottom'].set_visible(False)
plt.gca().spines['left'].set_visible(False)
plt.tick_params(top='off',
bottom='off',
left='off',
right='off',
labelleft='off',
labelbottom='off') #plt.title("Confidence intervals")
# save figure
plt.savefig("firstdeviation")
return 0