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# -*- coding: utf-8 -*-
# Author: Vincent Dubourg <vincent.dubourg@gmail.com>
# (mostly translation, see implementation details)
# License: BSD 3 clause
"""
The built-in regression models submodule for the gaussian_process module.
"""
import numpy as np
def constant(x):
"""
Zero order polynomial (constant, p = 1) regression model.
x --> f(x) = 1
Parameters
----------
x : array_like
An array with shape (n_eval, n_features) giving the locations x at
which the regression model should be evaluated.
Returns
-------
f : array_like
An array with shape (n_eval, p) with the values of the regression
model.
"""
x = np.asarray(x, dtype=np.float64)
n_eval = x.shape[0]
f = np.ones([n_eval, 1])
return f
def linear(x):
"""
First order polynomial (linear, p = n+1) regression model.
x --> f(x) = [ 1, x_1, ..., x_n ].T
Parameters
----------
x : array_like
An array with shape (n_eval, n_features) giving the locations x at
which the regression model should be evaluated.
Returns
-------
f : array_like
An array with shape (n_eval, p) with the values of the regression
model.
"""
x = np.asarray(x, dtype=np.float64)
n_eval = x.shape[0]
f = np.hstack([np.ones([n_eval, 1]), x])
return f
def quadratic(x):
"""
Second order polynomial (quadratic, p = n*(n-1)/2+n+1) regression model.
x --> f(x) = [ 1, { x_i, i = 1,...,n }, { x_i * x_j, (i,j) = 1,...,n } ].T
i > j
Parameters
----------
x : array_like
An array with shape (n_eval, n_features) giving the locations x at
which the regression model should be evaluated.
Returns
-------
f : array_like
An array with shape (n_eval, p) with the values of the regression
model.
"""
x = np.asarray(x, dtype=np.float64)
n_eval, n_features = x.shape
f = np.hstack([np.ones([n_eval, 1]), x])
for k in range(n_features):
f = np.hstack([f, x[:, k, np.newaxis] * x[:, k:]])
return f
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