# Copyright (c) 2020, Anthony Nouy, Erwan Grelier
# This file is part of tensap (tensor approximation package).

# tensap is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.

# tensap is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.

# You should have received a copy of the GNU Lesser General Public License
# along with tensap.  If not, see <https://www.gnu.org/licenses/>.

"""
Tutorial on learning in tree-based tensor format.

"""

from time import time
import numpy as np
import tensap


# %% Creating a function providing the entries of a tensor
ORDER = 5
N = 10
SIZE = np.full(ORDER, N)

def fun(i):
    return (
        np.cos(i[:, 0] / SIZE[0])
        + 1 / (1 + (i[:, 1] / SIZE[1]) ** 2 + (i[:, 2] / SIZE[2]) ** 4)
        + i[:, 2] / SIZE[2]
    )

X = tensap.random_multi_indices(SIZE)


# %% Approximation basis
USE_POLYBASES = True
if USE_POLYBASES:
    BASES = [
        tensap.PolynomialFunctionalBasis(x.orthonormal_polynomials(), range(SIZE[i]))
        for i, x in enumerate(X.random_variables)
    ]
else:
    BASES = [
        tensap.DeltaFunctionalBasis(values=range(SIZE[i]))
        for i, x in enumerate(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)

NUM_TEST = 10000
X_TEST = X.random(NUM_TEST)
Y_TEST = fun(X_TEST)

# %% Tree-based tensor format
# Tensor format
# 1 - Random tree and active nodes
# 2 - Tensor-Train
# 3 - Hierarchial Tensor-Train
# 4 - Binary tree
CHOICE = 3
if CHOICE == 1:
    print("Random tree with active nodes")
    ARITY = [2, 4]
    TREE = tensap.DimensionTree.random(ORDER, ARITY)
    IS_ACTIVE_NODE = np.full(TREE.nb_nodes, True)
    SOLVER = tensap.TreeBasedTensorLearning(
        TREE, IS_ACTIVE_NODE, tensap.SquareLossFunction()
    )
elif CHOICE == 2:
    print("Tensor-train format")
    SOLVER = tensap.TreeBasedTensorLearning.tensor_train(
        ORDER, tensap.SquareLossFunction()
    )
elif CHOICE == 3:
    print("Tensor Train Tucker")
    SOLVER = tensap.TreeBasedTensorLearning.tensor_train_tucker(
        ORDER, tensap.SquareLossFunction()
    )
elif CHOICE == 4:
    print("Binary tree")
    TREE = tensap.DimensionTree.balanced(ORDER)
    IS_ACTIVE_NODE = np.full(TREE.nb_nodes, True)
    SOLVER = tensap.TreeBasedTensorLearning(
        TREE, IS_ACTIVE_NODE, tensap.SquareLossFunction()
    )
else:
    raise NotImplementedError("Not implemented.")

# %% Random shuffling of the dimensions associated to the leaves
RANDOMIZE = False
if RANDOMIZE:
    SOLVER.tree.dim2ind = np.random.permutation(SOLVER.tree.dim2ind)
    SOLVER.tree = SOLVER.tree.update_dims_from_leaves()

# %% Learning in tree-based tensor format
SOLVER.bases = BASES
SOLVER.bases_eval = BASES.eval(X_TRAIN)
SOLVER.training_data = [None, Y_TRAIN]

SOLVER.tolerance["on_stagnation"] = 1e-6
SOLVER.tolerance["on_error"] = 1e-6

SOLVER.initialization_type = "canonical"

SOLVER.linear_model_learning.regularization = False
SOLVER.linear_model_learning.basis_adaptation = USE_POLYBASES
SOLVER.linear_model_learning.error_estimation = True

SOLVER.test_error = True
SOLVER.test_data = [X_TEST, Y_TEST]
# SOLVER.bases_eval_test = BASES.eval(X_TEST)

SOLVER.rank_adaptation = True
SOLVER.rank_adaptation_options["max_iterations"] = 10
SOLVER.rank_adaptation_options["theta"] = 0.8
SOLVER.rank_adaptation_options["early_stopping"] = True
SOLVER.rank_adaptation_options["early_stopping_factor"] = 10

SOLVER.tree_adaptation = False
SOLVER.tree_adaptation_options["max_iterations"] = 1e2
# SOLVER.tree_adaptation_options['force_rank_adaptation'] = True

SOLVER.alternating_minimization_parameters["stagnation"] = 1e-10
SOLVER.alternating_minimization_parameters["max_iterations"] = 5

SOLVER.display = True
SOLVER.alternating_minimization_parameters["display"] = False

SOLVER.model_selection = True
SOLVER.model_selection_options["type"] = "test_error"

# DMRG (inner rank adaptation)
DMRG = False
if DMRG:
    # Rank of the initialization
    SOLVER.rank = 3
    # Type of rank adaptation: can be 'dmrg' to perform classical DMRG (using
    # a truncation of the factor to adapt the rank) or 'dmrg_low_rank' to learn
    # the factor using a rank-adaptive learning
    # algorithm
    SOLVER.rank_adaptation_options["type"] = "dmrg_low_rank"
    # Maximum alpha-rank for all the nodes of the tree
    SOLVER.rank_adaptation_options["max_rank"] = 10
    # If True: perform an alternating minimization with fixed tree and ranks
    # after the rank adaptation using DMRG
    SOLVER.rank_adaptation_options["post_alternating_minimization"] = False
    # Model selection type when type is 'dmrg_low_rank': can be 'cv_error' to
    # use a cross-validation estimator of the error or 'test_error' to use
    # the error on a test sample
    SOLVER.rank_adaptation_options["model_selection_type"] = "cv_error"

T0 = time()
F, OUTPUT = SOLVER.solve()
T1 = time()
print(T1 - T0)

# %% Displays
TEST_ERROR = SOLVER.loss_function.test_error(F, [X_TEST, Y_TEST])
print("Ranks: %s" % F.tensor.ranks)
print("Loo error = %2.5e" % OUTPUT["error"])
print("Test error = %2.5e" % TEST_ERROR)

F.tensor.plot(title="Active nodes")
F.tensor.tree.plot_dims(title="Dimensions associated to the leaf nodes")
F.tensor.tree.plot_with_labels_at_nodes(
    F.tensor.representation_rank, title="Representation ranks"
)
