# Source code for gemseo.mlearning.regression.linreg

# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
#
# This program 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 this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

# Contributors:
#    INITIAL AUTHORS - initial API and implementation and/or initial
#                         documentation
#        :author: Francois Gallard, Matthias De Lozzo
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
r"""The linear model algorithm for regression.

The linear regression surrogate discipline expresses the model output
as a weighted sum of the model inputs:

.. math::

y = w_0 + w_1x_1 + w_2x_2 + ... + w_dx_d
+ \alpha \left( \lambda \|w\|_2 + (1-\lambda) \|w\|_1 \right),

where the coefficients :math:(w_1, w_2, ..., w_d) and the intercept
:math:w_0 are estimated by least square regression. They are are easily
accessible via the arguments *coefficients* and *intercept*.

The penalty level :math:\alpha is a non-negative parameter intended to
prevent overfitting, while the penalty ratio :math:\lambda\in [0, 1]
expresses the ratio between :math:\ell_2- and :math:\ell_1-regularization.
When :math:\lambda=1, there is no :math:\ell_1-regularization, and a Ridge
regression is performed. When :math:\lambda=0, there is no
:math:\ell_2-regularization, and a Lasso regression is performed. For
:math:\lambda between 0 and 1, an elastic net regression is performed.

One may also choose not to penalize the regression at all, by setting
:math:\alpha=0. In this case, a simple least squares regression is performed.

This concept is implemented through the :class:.LinearRegression class which
inherits from the :class:.MLRegressionAlgo class.

Dependence
----------
The linear model relies on the LinearRegression, Ridge, Lasso and ElasticNet
classes of the scikit-learn library <https://scikit-learn.org/stable/modules/
linear_model.html>_.
"""
from __future__ import division, unicode_literals

import logging
from typing import Dict, Iterable, Optional, Union

from numpy import array, ndarray, repeat, zeros
from sklearn.linear_model import ElasticNet, Lasso
from sklearn.linear_model import LinearRegression as LinReg
from sklearn.linear_model import Ridge

from gemseo.core.dataset import Dataset
from gemseo.mlearning.core.ml_algo import DataType, TransformerType
from gemseo.mlearning.regression.regression import MLRegressionAlgo
from gemseo.mlearning.transform.dimension_reduction.dimension_reduction import (
DimensionReduction,
)
from gemseo.utils.data_conversion import DataConversion

LOGGER = logging.getLogger(__name__)

[docs]class LinearRegression(MLRegressionAlgo):
"""Linear regression."""

LIBRARY = "scikit-learn"
ABBR = "LinReg"

def __init__(
self,
data,  # type: Dataset
transformer=None,  # type: Optional[TransformerType]
input_names=None,  # type: Optional[Iterable[str]]
output_names=None,  # type: Optional[Iterable[str]]
fit_intercept=True,  # type: bool
penalty_level=0.0,  # type: float
l2_penalty_ratio=1.0,  # type: float
**parameters  # type: Optional[Union[float,int,str,bool]]
):  # type: (...) ->None
"""
Args:
fit_intercept: Whether to fit the intercept.
penalty_level: The penalty level greater or equal to 0.
If 0, there is no penalty.
l2_penalty_ratio: The penalty ratio related to the l2 regularization.
If 1, use the Ridge penalty.
If 0, use the Lasso penalty.
Between 0 and 1, use the ElasticNet penalty.
**parameters: The parameters of the machine learning algorithm.
"""
super(LinearRegression, self).__init__(
data,
transformer=transformer,
input_names=input_names,
output_names=output_names,
fit_intercept=fit_intercept,
penalty_level=penalty_level,
l2_penalty_ratio=l2_penalty_ratio,
**parameters
)
if "degree" in parameters:
del parameters["degree"]

if penalty_level == 0.0:
self.algo = LinReg(
normalize=False, copy_X=False, fit_intercept=fit_intercept, **parameters
)
else:
if l2_penalty_ratio == 1.0:
self.algo = Ridge(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters
)
elif l2_penalty_ratio == 0.0:
self.algo = Lasso(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
**parameters
)
else:
self.algo = ElasticNet(
normalize=False,
copy_X=False,
fit_intercept=fit_intercept,
alpha=penalty_level,
l1_ratio=1 - l2_penalty_ratio,
**parameters
)

def _fit(
self,
input_data,  # type: ndarray
output_data,  # type: ndarray
):  # type: (...) -> None
self.algo.fit(input_data, output_data)

def _predict(
self,
input_data,  # type: ndarray
):  # type: (...) -> ndarray
return self.algo.predict(input_data)

def _predict_jacobian(
self,
input_data,  # type: ndarray
):  # type: (...) -> ndarray
n_samples = input_data.shape[0]
return repeat(self.algo.coef_[None], n_samples, axis=0)

@property
def coefficients(self):  # type: (...) ->ndarray
"""The regression coefficients of the linear model."""
return self.algo.coef_

@property
def intercept(self):  # type: (...) ->ndarray
"""The regression intercepts of the linear model."""
if self.parameters["fit_intercept"]:
intercept = self.algo.intercept_
else:
intercept = zeros(self.algo.coef_.shape[0])
return intercept

[docs]    def get_coefficients(
self,
as_dict=True,  # type: bool
):  # type: (...) -> DataType
"""Return the regression coefficients of the linear model.

Args:
as_dict: If True, return the coefficients as a dictionary.
Otherwise, return the coefficients as a numpy.array

Returns:
The regression coefficients of the linear model.

Raises:
ValueError: If the coefficients are required as a dictionary
even though the transformers change the variables dimensions.
"""
coefficients = self.coefficients
if as_dict:
if any(
[
isinstance(transformer, DimensionReduction)
for _, transformer in self.transformer.items()
]
):
raise ValueError(
"Coefficients are only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the variables."
)
coefficients = self.__convert_array_to_dict(coefficients)
return coefficients

[docs]    def get_intercept(
self,
as_dict=True,  # type:bool
):  # type: (...) -> DataType
"""Return the regression intercepts of the linear model.

Args:
as_dict: If True, return the intercepts as a dictionary.
Otherwise, return the intercepts as a numpy.array

Returns:
The regression intercepts of the linear model.

Raises:
ValueError: If the coefficients are required as a dictionary
even though the transformers change the variables dimensions.
"""
intercept = self.intercept
if as_dict:
if Dataset.OUTPUT_GROUP in self.transformer:
raise ValueError(
"Intercept is only representable in dictionary "
"form if the transformers do not change the "
"dimensions of the output variables."
)
varsizes = self.learning_set.sizes
intercept = DataConversion.array_to_dict(
intercept, self.output_names, varsizes
)
intercept = {key: list(val) for key, val in intercept.items()}
return intercept

def __convert_array_to_dict(
self,
data,  # type:ndarray
):  # type: (...) -> Dict[str,ndarray]
"""Convert a data array into a dictionary.

Args:
data: The data to be converted.

Returns:
The converted data.
"""
varsizes = self.learning_set.sizes
data = [
DataConversion.array_to_dict(row, self.input_names, varsizes)
for row in data
]
data = [{key: list(val) for key, val in element.items()} for element in data]
data = DataConversion.array_to_dict(array(data), self.output_names, varsizes)
data = {key: list(val) for key, val in data.items()}
return data