Feature/concurrent regression

examples/plot_functional_regression.py

@@ -0,0 +1,89 @@
+"""
+Functional Linear Regression with multivariate covariates.
+==========================================================
+
+This example explores the use of the linear regression with
+multivariate (scalar) covariates and functional response.
+
+"""
+
+# Author: Rafael Hidalgo Alejo
+# License: MIT
+
+import numpy as np
+import pandas as pd
+from sklearn.preprocessing import OneHotEncoder
+
+import skfda
+from skfda.ml.regression import LinearRegression
+from skfda.representation.basis import FDataBasis, FourierBasis
+
+# %%
+# In this example, we will demonstrate the use of the Linear Regression with
+# functional response and multivariate covariates using the
+# :func:`weather <skfda.datasets.fetch_weather>` dataset.
+# It is possible to divide the weather stations into four groups:
+# Atlantic, Pacific, Continental and Artic.
+# There are a total of 35 stations in this dataset.
+
+X_weather, y_weather = skfda.datasets.fetch_weather(
+    return_X_y=True, as_frame=True,
+)
+fd = X_weather.iloc[:, 0].values
+
+# %%
+# The main goal is knowing about the effect of stations' geographic location
+# on the shape of the temperature curves.
+# So we will have a model with a functional response, the temperature curve,
+# and five covariates. The first one is the intercept (all entries equal to 1)
+# and it shows the contribution of the Canadian mean temperature. The remaining
+# covariates use one-hot encoding, with 1 if that weather station is in the
+# corresponding climate zone and 0 otherwise.
+
+# We first create the one-hot encoding of the climates.
+
+enc = OneHotEncoder(handle_unknown='ignore')
+enc.fit([['Atlantic'], ['Continental'], ['Pacific']])
+X = np.array(y_weather).reshape(-1, 1)
+X = enc.transform(X).toarray()
+
+# %%
+# Then, we construct a dataframe with each covariate in a different column and
+# the temperature curves (responses).
+
+X_df = pd.DataFrame(X)
+
+y_basis = FourierBasis(n_basis=65)
+y_fd = fd.coordinates[0].to_basis(y_basis)
+
+# %%
+# An intercept term is incorporated.
+# All functional coefficients will have the same basis as the response.
+
+funct_reg = LinearRegression(fit_intercept=True)
+funct_reg.fit(X_df, y_fd)
+
+# %%
+# The regression coefficients are shown below. The first one is the intercept
+# coefficient, corresponding to Canadian mean temperature.
+
+funct_reg.intercept_.plot()
+funct_reg.coef_[0].plot()
+funct_reg.coef_[1].plot()
+funct_reg.coef_[2].plot()
+
+# %%
+# Finally, it is shown a panel with the prediction for all climate zones.
+
+predictions = []
+
+predictions.append(funct_reg.predict([[0, 1, 0, 0]])[0])
+predictions.append(funct_reg.predict([[0, 0, 1, 0]])[0])
+predictions.append(funct_reg.predict([[0, 0, 0, 1]])[0])
+
+predictions_conc = FDataBasis.concatenate(*predictions)
+
+predictions_conc.argument_names = ('day',)
+predictions_conc.coordinate_names = ('temperature (ºC)',)
+
+predictions_conc.plot()

skfda/misc/_math.py

@@ -12,7 +12,7 @@
 import numpy as np
 import scipy.integrate
 
-from .._utils import nquad_vec
+from .._utils import _same_domain, nquad_vec
 from ..representation import FData, FDataBasis, FDataGrid
 from ..representation.basis import Basis
 from ..typing._base import DomainRange
@@ -243,6 +243,7 @@
     Args:
         arg1: First sample.
         arg2: Second sample.
+        kwargs: Additional parameters for the function.
 
     Returns:
         Vector with the inner products of each pair of samples.
@@ -388,10 +389,17 @@
     arg2: Union[FDataBasis, Basis],
     *,
     _matrix: bool = False,
+    _domain_range: Optional[DomainRange] = None,
     inner_product_matrix: Optional[NDArrayFloat] = None,
     force_numerical: bool = False,
 ) -> NDArrayFloat:
 
+    if not _same_domain(arg1, arg2):
+        raise ValueError("Both Objects should have the same domain_range")
+
+    if _domain_range and not np.array_equal(arg1.domain_range, _domain_range):
+        raise ValueError("_domain_range should be the same as arg objects")
+
     if isinstance(arg1, Basis):
         arg1 = arg1.to_basis()
 
@@ -479,8 +487,15 @@
     def integrand(*args: NDArrayFloat) -> NDArrayFloat:  # noqa: WPS430
         f_args = np.asarray(args)
 
-        f1 = arg1(f_args)[:, 0, :]
-        f2 = arg2(f_args)[:, 0, :]
+        try:
+            f1 = arg1(f_args)[:, 0, :]
+        except Exception:
+            f1 = arg1(f_args)
+
+        try:
+            f2 = arg2(f_args)[:, 0, :]
+        except Exception:
+            f2 = arg2(f_args)
 
         if _matrix:
             ret = np.einsum('n...,m...->nm...', f1, f2)

skfda/ml/regression/_coefficients.py

@@ -157,8 +157,12 @@ def coefficient_info_from_covariate(
 def _coefficient_info_from_covariate_ndarray(  # type: ignore[misc]
     X: NDArrayFloat,
     y: NDArrayFloat,
+    basis: Basis = None,
     **_: Any,
 ) -> CoefficientInfo[NDArrayFloat]:
+    if basis:
+        return CoefficientInfoNdarray(basis=basis)
+
     return CoefficientInfoNdarray(basis=np.identity(X.shape[1], dtype=X.dtype))