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300 lines
9.9 KiB
Python
300 lines
9.9 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from kern import kern
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import parts
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def rbf(input_dim,variance=1., lengthscale=None,ARD=False):
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"""
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Construct an RBF kernel
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:param input_dim: dimensionality of the kernel, obligatory
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param ARD: Auto Relevance Determination (one lengthscale per dimension)
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:type ARD: Boolean
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"""
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part = parts.rbf.RBF(input_dim,variance,lengthscale,ARD)
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return kern(input_dim, [part])
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def linear(input_dim,variances=None,ARD=False):
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"""
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Construct a linear kernel.
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Arguments
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---------
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input_dimD (int), obligatory
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variances (np.ndarray)
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ARD (boolean)
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"""
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part = parts.linear.Linear(input_dim,variances,ARD)
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return kern(input_dim, [part])
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def white(input_dim,variance=1.):
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"""
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Construct a white kernel.
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Arguments
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---------
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input_dimD (int), obligatory
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variance (float)
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"""
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part = parts.white.White(input_dim,variance)
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return kern(input_dim, [part])
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def exponential(input_dim,variance=1., lengthscale=None, ARD=False):
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"""
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Construct an exponential kernel
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:param input_dim: dimensionality of the kernel, obligatory
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param ARD: Auto Relevance Determination (one lengthscale per dimension)
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:type ARD: Boolean
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"""
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part = parts.exponential.Exponential(input_dim,variance, lengthscale, ARD)
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return kern(input_dim, [part])
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def Matern32(input_dim,variance=1., lengthscale=None, ARD=False):
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"""
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Construct a Matern 3/2 kernel.
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:param input_dim: dimensionality of the kernel, obligatory
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param ARD: Auto Relevance Determination (one lengthscale per dimension)
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:type ARD: Boolean
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"""
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part = parts.Matern32.Matern32(input_dim,variance, lengthscale, ARD)
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return kern(input_dim, [part])
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def Matern52(input_dim, variance=1., lengthscale=None, ARD=False):
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"""
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Construct a Matern 5/2 kernel.
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:param input_dim: dimensionality of the kernel, obligatory
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param ARD: Auto Relevance Determination (one lengthscale per dimension)
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:type ARD: Boolean
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"""
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part = parts.Matern52.Matern52(input_dim, variance, lengthscale, ARD)
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return kern(input_dim, [part])
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def bias(input_dim, variance=1.):
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"""
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Construct a bias kernel.
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Arguments
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---------
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input_dim (int), obligatory
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variance (float)
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"""
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part = parts.bias.Bias(input_dim, variance)
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return kern(input_dim, [part])
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def finite_dimensional(input_dim, F, G, variances=1., weights=None):
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"""
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Construct a finite dimensional kernel.
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input_dim: int - the number of input dimensions
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F: np.array of functions with shape (n,) - the n basis functions
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G: np.array with shape (n,n) - the Gram matrix associated to F
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variances : np.ndarray with shape (n,)
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"""
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part = parts.finite_dimensional.FiniteDimensional(input_dim, F, G, variances, weights)
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return kern(input_dim, [part])
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def spline(input_dim, variance=1.):
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"""
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Construct a spline kernel.
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:param input_dim: Dimensionality of the kernel
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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"""
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part = parts.spline.Spline(input_dim, variance)
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return kern(input_dim, [part])
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def Brownian(input_dim, variance=1.):
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"""
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Construct a Brownian motion kernel.
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:param input_dim: Dimensionality of the kernel
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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"""
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part = parts.Brownian.Brownian(input_dim, variance)
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return kern(input_dim, [part])
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try:
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import sympy as sp
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from sympykern import spkern
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from sympy.parsing.sympy_parser import parse_expr
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sympy_available = True
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except ImportError:
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sympy_available = False
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if sympy_available:
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def rbf_sympy(input_dim, ARD=False, variance=1., lengthscale=1.):
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"""
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Radial Basis Function covariance.
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"""
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X = [sp.var('x%i' % i) for i in range(input_dim)]
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Z = [sp.var('z%i' % i) for i in range(input_dim)]
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rbf_variance = sp.var('rbf_variance',positive=True)
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if ARD:
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rbf_lengthscales = [sp.var('rbf_lengthscale_%i' % i, positive=True) for i in range(input_dim)]
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dist_string = ' + '.join(['(x%i-z%i)**2/rbf_lengthscale_%i**2' % (i, i, i) for i in range(input_dim)])
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dist = parse_expr(dist_string)
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f = rbf_variance*sp.exp(-dist/2.)
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else:
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rbf_lengthscale = sp.var('rbf_lengthscale',positive=True)
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dist_string = ' + '.join(['(x%i-z%i)**2' % (i, i) for i in range(input_dim)])
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dist = parse_expr(dist_string)
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f = rbf_variance*sp.exp(-dist/(2*rbf_lengthscale**2))
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return kern(input_dim, [spkern(input_dim, f)])
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def sympykern(input_dim, k):
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"""
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A kernel from a symbolic sympy representation
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"""
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return kern(input_dim, [spkern(input_dim, k)])
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del sympy_available
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def periodic_exponential(input_dim=1, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
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"""
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Construct an periodic exponential kernel
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:param input_dim: dimensionality, only defined for input_dim=1
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param period: the period
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:type period: float
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:param n_freq: the number of frequencies considered for the periodic subspace
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:type n_freq: int
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"""
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part = parts.periodic_exponential.PeriodicExponential(input_dim, variance, lengthscale, period, n_freq, lower, upper)
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return kern(input_dim, [part])
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def periodic_Matern32(input_dim, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
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"""
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Construct a periodic Matern 3/2 kernel.
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:param input_dim: dimensionality, only defined for input_dim=1
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param period: the period
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:type period: float
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:param n_freq: the number of frequencies considered for the periodic subspace
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:type n_freq: int
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"""
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part = parts.periodic_Matern32.PeriodicMatern32(input_dim, variance, lengthscale, period, n_freq, lower, upper)
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return kern(input_dim, [part])
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def periodic_Matern52(input_dim, variance=1., lengthscale=None, period=2 * np.pi, n_freq=10, lower=0., upper=4 * np.pi):
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"""
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Construct a periodic Matern 5/2 kernel.
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:param input_dim: dimensionality, only defined for input_dim=1
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:type input_dim: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param period: the period
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:type period: float
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:param n_freq: the number of frequencies considered for the periodic subspace
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:type n_freq: int
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"""
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part = parts.periodic_Matern52part(input_dim, variance, lengthscale, period, n_freq, lower, upper)
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return kern(input_dim, [part])
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def prod(k1,k2,tensor=False):
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"""
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Construct a product kernel over input_dim from two kernels over input_dim
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:param k1, k2: the kernels to multiply
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:type k1, k2: kernpart
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:rtype: kernel object
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"""
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part = parts.prodpart(k1,k2,tensor)
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return kern(part.input_dim, [part])
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def symmetric(k):
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"""
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Construct a symmetrical kernel from an existing kernel
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"""
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k_ = k.copy()
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k_.parts = [symmetric.Symmetric(p) for p in k.parts]
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return k_
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def coregionalise(Nout,R=1, W=None, kappa=None):
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p = parts.coregionalise.Coregionalise(Nout,R,W,kappa)
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return kern(1,[p])
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def rational_quadratic(input_dim, variance=1., lengthscale=1., power=1.):
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"""
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Construct rational quadratic kernel.
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:param input_dim: the number of input dimensions
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:type input_dim: int (input_dim=1 is the only value currently supported)
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:param variance: the variance :math:`\sigma^2`
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:type variance: float
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:param lengthscale: the lengthscale :math:`\ell`
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:type lengthscale: float
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:rtype: kern object
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"""
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part = parts.rational_quadratic.RationalQuadratic(input_dim, variance, lengthscale, power)
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return kern(input_dim, [part])
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def fixed(input_dim, K, variance=1.):
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"""
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Construct a Fixed effect kernel.
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Arguments
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---------
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input_dim (int), obligatory
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K (np.array), obligatory
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variance (float)
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"""
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part = parts.fixed.Fixed(input_dim, K, variance)
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return kern(input_dim, [part])
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def rbfcos(input_dim, variance=1., frequencies=None, bandwidths=None, ARD=False):
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"""
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construct a rbfcos kernel
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"""
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part = parts.rbfcos.RBFCos(input_dim, variance, frequencies, bandwidths, ARD)
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return kern(input_dim, [part])
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def independent_outputs(k):
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"""
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Construct a kernel with independent outputs from an existing kernel
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"""
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for sl in k.input_slices:
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assert (sl.start is None) and (sl.stop is None), "cannot adjust input slices! (TODO)"
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parts = [independent_outputs.IndependentOutputs(p) for p in k.parts]
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return kern(k.input_dim+1,parts)
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