# -*- coding: utf-8 -*- # Author: Vincent Dubourg # (mostly translation, see implementation details) # License: BSD 3 clause """ The built-in correlation models submodule for the gaussian_process module. """ import numpy as np from ..utils import deprecated @deprecated("The function absolute_exponential of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def absolute_exponential(theta, d): """ Absolute exponential autocorrelation model. (Ornstein-Uhlenbeck stochastic process):: n theta, d --> r(theta, d) = exp( sum - theta_i * |d_i| ) i = 1 Parameters ---------- theta : array_like An array with shape 1 (isotropic) or n (anisotropic) giving the autocorrelation parameter(s). d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) containing the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.abs(np.asarray(d, dtype=np.float64)) if d.ndim > 1: n_features = d.shape[1] else: n_features = 1 if theta.size == 1: return np.exp(- theta[0] * np.sum(d, axis=1)) elif theta.size != n_features: raise ValueError("Length of theta must be 1 or %s" % n_features) else: return np.exp(- np.sum(theta.reshape(1, n_features) * d, axis=1)) @deprecated("The function squared_exponential of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def squared_exponential(theta, d): """ Squared exponential correlation model (Radial Basis Function). (Infinitely differentiable stochastic process, very smooth):: n theta, d --> r(theta, d) = exp( sum - theta_i * (d_i)^2 ) i = 1 Parameters ---------- theta : array_like An array with shape 1 (isotropic) or n (anisotropic) giving the autocorrelation parameter(s). d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) containing the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.asarray(d, dtype=np.float64) if d.ndim > 1: n_features = d.shape[1] else: n_features = 1 if theta.size == 1: return np.exp(-theta[0] * np.sum(d ** 2, axis=1)) elif theta.size != n_features: raise ValueError("Length of theta must be 1 or %s" % n_features) else: return np.exp(-np.sum(theta.reshape(1, n_features) * d ** 2, axis=1)) @deprecated("The function generalized_exponential of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def generalized_exponential(theta, d): """ Generalized exponential correlation model. (Useful when one does not know the smoothness of the function to be predicted.):: n theta, d --> r(theta, d) = exp( sum - theta_i * |d_i|^p ) i = 1 Parameters ---------- theta : array_like An array with shape 1+1 (isotropic) or n+1 (anisotropic) giving the autocorrelation parameter(s) (theta, p). d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) with the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.asarray(d, dtype=np.float64) if d.ndim > 1: n_features = d.shape[1] else: n_features = 1 lth = theta.size if n_features > 1 and lth == 2: theta = np.hstack([np.repeat(theta[0], n_features), theta[1]]) elif lth != n_features + 1: raise Exception("Length of theta must be 2 or %s" % (n_features + 1)) else: theta = theta.reshape(1, lth) td = theta[:, 0:-1].reshape(1, n_features) * np.abs(d) ** theta[:, -1] r = np.exp(- np.sum(td, 1)) return r @deprecated("The function pure_nugget of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def pure_nugget(theta, d): """ Spatial independence correlation model (pure nugget). (Useful when one wants to solve an ordinary least squares problem!):: n theta, d --> r(theta, d) = 1 if sum |d_i| == 0 i = 1 0 otherwise Parameters ---------- theta : array_like None. d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) with the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.asarray(d, dtype=np.float64) n_eval = d.shape[0] r = np.zeros(n_eval) r[np.all(d == 0., axis=1)] = 1. return r @deprecated("The function cubic of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def cubic(theta, d): """ Cubic correlation model:: theta, d --> r(theta, d) = n prod max(0, 1 - 3(theta_j*d_ij)^2 + 2(theta_j*d_ij)^3) , i = 1,...,m j = 1 Parameters ---------- theta : array_like An array with shape 1 (isotropic) or n (anisotropic) giving the autocorrelation parameter(s). d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) with the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.asarray(d, dtype=np.float64) if d.ndim > 1: n_features = d.shape[1] else: n_features = 1 lth = theta.size if lth == 1: td = np.abs(d) * theta elif lth != n_features: raise Exception("Length of theta must be 1 or " + str(n_features)) else: td = np.abs(d) * theta.reshape(1, n_features) np.clip(td, None, 1., out=td) ss = 1. - td ** 2. * (3. - 2. * td) r = np.prod(ss, 1) return r @deprecated("The function linear of correlation_models is " "deprecated in version 0.19.1 and will be removed in 0.22.") def linear(theta, d): """ Linear correlation model:: theta, d --> r(theta, d) = n prod max(0, 1 - theta_j*d_ij) , i = 1,...,m j = 1 Parameters ---------- theta : array_like An array with shape 1 (isotropic) or n (anisotropic) giving the autocorrelation parameter(s). d : array_like An array with shape (n_eval, n_features) giving the componentwise distances between locations x and x' at which the correlation model should be evaluated. Returns ------- r : array_like An array with shape (n_eval, ) with the values of the autocorrelation model. """ theta = np.asarray(theta, dtype=np.float64) d = np.asarray(d, dtype=np.float64) if d.ndim > 1: n_features = d.shape[1] else: n_features = 1 lth = theta.size if lth == 1: td = np.abs(d) * theta elif lth != n_features: raise Exception("Length of theta must be 1 or %s" % n_features) else: td = np.abs(d) * theta.reshape(1, n_features) np.clip(td, None, 1., out=td) ss = 1. - td r = np.prod(ss, 1) return r