def test_optim():
# TODO
ntrain = 128
xtrain = halton(ntrain, 2)
l = np.array([0.5, 0.5])
sigf = 1.0
sign = 1e-4
hyp = np.hstack([l, sigf, sign])
ytrain = np.sin(2 * xtrain[:, 0]) + np.cos(3 * xtrain[:, 1])
loghyp0 = np.log10(hyp)
def cost(loghyp):
h = 10**loghyp
val, jac = negative_log_likelihood_cholesky(h,
xtrain,
ytrain,
RBF,
eval_gradient=True,
log_scale_hyp=True)
return val, h * np.log(10.0) * jac
opt_res = minimize(cost,
loghyp0,
method='L-BFGS-B',
jac=True,
bounds=((-2, 2), (-2, 2), (-2, 2), (-4, 0)))
def test_fit_manual():
ntrain = 128
xtrain = halton(ntrain, 2)
l = np.array([0.5, 0.5])
sigf = 1.0
sign = 1e-4
hyp = np.hstack([l, sigf, sign])
ytrain = np.sin(2 * xtrain[:, 0]) + np.cos(3 * xtrain[:, 1])
Ky = RBF(xtrain, xtrain, hyp[:-2], *hyp[-2:])
L = np.linalg.cholesky(Ky)
alpha = solve_cholesky(L, ytrain)
n1test = 20
n2test = 20
ntest = n1test * n2test
Xtest = np.mgrid[0:1:1j * n1test, 0:1:1j * n2test]
xtest = Xtest.reshape([2, ntest]).T
KstarT = RBF(xtest, xtrain, l, 1, 0)
ymean = KstarT @ alpha
yref = np.sin(2 * xtest[:, 0]) + np.cos(3 * xtest[:, 1])
assert (np.allclose(ymean, yref, rtol=1e-3, atol=1e-3))
from profit.sur.backend.kernels import kern_sqexp
from profit.util.halton import halton
def f(x): return x*np.cos(10*x)
# Custom function to build GP matrix
def build_K(xa, xb, hyp, K):
for i in np.arange(len(xa)):
for j in np.arange(len(xb)):
K[i, j] = kern_sqexp(xa[i], xb[j], hyp[0])
noise_train = 0.01
#ntrain = 20
for ntrain in range(1, 31):
xtrain = halton(1, ntrain)
ftrain = f(xtrain)
np.random.seed(0)
ytrain = ftrain + noise_train*np.random.randn(ntrain, 1)
# GP regression with fixed kernel hyperparameters
hyp = [0.1, 1e-4] # l and sig_noise**2
K = np.empty((ntrain, ntrain)) # train-train
build_K(xtrain, xtrain, hyp, K) # writes inside K
Ky = K + hyp[-1]*np.eye(ntrain)
Kyinv = invert(Ky, 4, 1e-6) # using gp_functions.invert
ntest = 300
xtest = np.linspace(0, 1, ntest)
ftest = f(xtest)
from profit.sur.backend.kernels import kern_sqexp
from profit.util.halton import halton
def f(x): return x*np.cos(10*x)
# Custom function to build GP matrix
def build_K(xa, xb, hyp, K):
for i in np.arange(len(xa)):
for j in np.arange(len(xb)):
K[i, j] = kern_sqexp(xa[i], xb[j], hyp[0])
noise_train = 0.01
#ntrain = 20
for ntrain in range(1, 31):
xtrain = halton(ntrain, 1)
ftrain = f(xtrain)
np.random.seed(0)
ytrain = ftrain + noise_train*np.random.randn(ntrain, 1)
# GP regression with fixed kernel hyperparameters
hyp = [0.1, 1e-4] # l and sig_noise**2
K = np.empty((ntrain, ntrain)) # train-train
build_K(xtrain, xtrain, hyp, K) # writes inside K
Ky = K + hyp[-1]*np.eye(ntrain)
Kyinv = invert(Ky, 4, 1e-6) # using gp_functions.invert
ntest = 300
xtest = np.linspace(0, 1, ntest)
ftest = f(xtest)
import numpy as np
from func import (integrate_pendulum)
from param import Nm, N, dtsymp, qmin, qmax, pmin, pmax
from profit.util.halton import halton
# specify initial conditions (q0, p0)
method = 'all'
# samples = bluenoise(2, N, method, qmin, qmax, pmin, pmax)
samples = halton(N, 2) * np.array([qmax - qmin, pmax - pmin]) + np.array(
[qmin, pmin])
q = samples[:, 0]
p = samples[:, 1] * 1.5
t0 = 0.0 # starting time
t1 = dtsymp * Nm # end time
t = np.linspace(t0, t1, Nm) # integration points in time
#integrate pendulum to provide data
ysint = integrate_pendulum(q, p, t)
#%%
P = np.empty((N))
Q = np.empty((N))
for ik in range(0, N):
P[ik] = ysint[ik][1, -1]
Q[ik] = ysint[ik][0, -1]
zqtrain = Q - q
zptrain = p - P
import numpy as np from profit.util import halton from profit.sur.backend.gpfunc import * ndim = 1 ntrain = 10 xtrain = np.asfortranarray(halton.halton(ntrain, ndim)) K = np.empty((ntrain, ntrain), order='F') print(K.shape) print(xtrain.shape) print(ntrain) gpfunc.build_k_sqexp(xtrain, xtrain, K)