Tutorial on learning in canonical tensor format.
'''
import tensap
# %% Function to approximate
CHOICE = 2
if CHOICE == 1:
ORDER = 5
X = tensap.RandomVector(tensap.NormalRandomVariable(), ORDER)
def fun(x):
return 1 / (10 + x[:, 0] + 0.5 * x[:, 1])**2
elif CHOICE == 2:
fun, X = tensap.multivariate_functions_benchmark('borehole')
ORDER = X.size
# %% Approximation basis
DEGREE = 8
BASES = [
tensap.PolynomialFunctionalBasis(X_TRAIN.orthonormal_polynomials(),
range(DEGREE + 1))
for X_TRAIN in X.random_variables
]
BASES = tensap.FunctionalBases(BASES)
# %% Training and test samples
NUM_TRAIN = 1000
X_TRAIN = X.random(NUM_TRAIN)
Y_TRAIN = fun(X_TRAIN)
You should have received a copy of the GNU Lesser General Public License
along with tensap. If not, see <https://www.gnu.org/licenses/>.
'''
import sys
import numpy as np
sys.path.insert(0, './../../../')
import tensap
# %% Choice of the function to approximate
CHOICE = 2
if CHOICE == 1:
print('Henon-Heiles')
D = 5
FUN, X = tensap.multivariate_functions_benchmark('henon_heiles', D)
DEGREE = 4
BASES = [tensap.PolynomialFunctionalBasis(x.orthonormal_polynomials(),
range(DEGREE+1)) for
x in X.random_variables]
elif CHOICE == 2:
print('Anisotropic function')
D = 6
X = tensap.RandomVector(tensap.UniformRandomVariable(-1, 1), D)
def FUN(x):
return 1/(10 + 2*x[:, 0] + x[:, 2] + 2*x[:, 3] - x[:, 4])**2
DEGREE = 13