var = np.load('../UU_sig.npy')[:290]
ell = np.load('../UU_ell.npy')[:290]
[x_quad, w] = ct.util.QuadratureRule('CC').get_rule(5, 6)
y_quad = np.load('../data_pressure_CC_quadrature_lev6.npy')[:, -1]
#coeffs = ct.chaos.PolyChaos().comp_coeffs(x_quad, y_quad, w, 9)
l2_err = np.zeros((6, 8))
for i in range(l2_err.shape[0]):
for j in range(l2_err.shape[1]):
Q = 2 + j
X_i = X[:50 * i + 40, :].copy()
Y_i = Y[:50 * i + 40, :].copy()
rbf = kp.RBF(X.shape[1], var[50 * i + 20], ell[50 * i + 20])
I = IntegralPosterior(X_i, Y_i, Q, rbf)
[m, C] = I.predict('L')
pol = ct.chaos.PolyBasis(5, Q, 'L')
P = pol(x_quad)
y_pred = np.dot(P, m)
diff = (y_quad - y_pred)**2
l2_err[i, j] = np.abs(np.sum(diff * w)) / np.sum(y_quad**2 * w)
print 'order :' + str(j)
print i
y_axis = [50 * i for i in range(6)]
x_axis = [2, 3, 4, 5, 6, 7, 8, 9]
np.save('./images/l2_err.npy', l2_err)
import scipy.stats as st
import sys
sys.path.insert(0, '../')
from GP_integral import *
import kernel_py as kp
import chaos_toolbox as ct
import matplotlib.pyplot as plt
X = np.load('X.npy')
Y = np.load('Y.npy')
Q = 5
var = np.load('sig_smooth.npy')[-1]
ell = np.load('ell_smooth.npy')[-2]
rbf = kp.RBF(X.shape[1], var, ell)
I = IntegralPosterior(X, Y, Q, rbf)
[m, C] = I.predict('L')
#v_all = I.v_all('L')
#print v_all
#np.save('coeffs/v_all.npy', v_all)
print m
plt.plot(m)
plt.show()
pol = ct.chaos.PolyBasis(2, Q, 'L')
xi = st.norm.rvs(size=(1000, 2))
P = pol(xi)
y = np.dot(P, m)
for i in range(XI.shape[0]):
print 'Taking initial sample : ' + str(i)
u = np.zeros((ny, nx))
v = np.zeros((ny, nx))
p = np.zeros((ny, nx))
b = np.zeros((ny, nx))
xi = 0.5 * (XI[i, :].copy() + 1.)
xi[-1] = 0.04 * xi[-1] + 0.01
u, v, p = cavity_flow(nt, u, v, dt, dx, dy, p, rho, xi)
YI[i, 0] = p[-2, -1]
print YI
kern = kp.RBF(dim, 1, 1)
gp = kp.GP(XI, YI, kern)
N_quad = 300
gp.optimize()
sig = np.zeros(N_quad + 1)
sig_noise = np.zeros(N_quad + 1)
ell = np.zeros(N_quad + 1)
sig[0] = gp._kern._var
sig_noise[0] = gp._noise_var
ell[0] = gp._kern._lengthscale[0]
kern._var = sig[0]
kern._lengthscale = [ell[0]] * dim
return y
X = 2 * st.uniform.rvs(size=(4, 2)) - 1.
Y = np.zeros((X.shape[0], 1))
N = 1000
T = 10.
for i in range(X.shape[0]):
y0 = np.zeros(3)
y0[0] = 1.
y0[1] = 0.1 * X[i, 0]
y0[2] = X[i, 1]
Y[i, 0] = RK4(y0, T, N)[1, -1] # + 0.1 * np.random.normal(size = (3,1))
kern = kp.RBF(2, 1, 1)
ker = gpy.kern.RBF(2, 1, 1)
m = gpy.models.GPRegression(X, Y, ker)
gp = kp.GP(X, Y, kern)
#x = np.linspace(-4., 4., 100).reshape(100,1)
x = np.linspace(-1, 1., 50)
y = np.linspace(-1, 1., 50)
xx, yy = np.meshgrid(x, y)
X_test = np.hstack(
[xx.flatten().reshape(2500, 1),
yy.flatten().reshape(2500, 1)])
f, var = gp.predict(X_test)