kernel.py 8.8 KB
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import numpy as np
from abc import ABC, abstractmethod

from scipy.spatial.distance import pdist, cdist, squareform

class kernel(ABC):
    def __init__(self):
        self._theta = None

    @abstractmethod
    def kernel(self):
        pass

#    @abstractmethod
#    def kernel_vector(self):
#        pass

#    @abstractmethod
#    def kernel_matrix(self):
#        pass

    @abstractmethod
    def kernel_jacobian(self):
        pass

    @abstractmethod
    def kernel_hyperparameter_gradient(self):
        pass

    @property
    def theta(self):
        return self._theta

    @theta.setter
    def theta(self, theta):
        self._theta = theta
    
    def numerical_jacobian(self,x,y, dx=1.e-5):
        if np.ndim(y) == 1:
            y = y.reshape((1,-1))
        nx = len(x)
        ny = y.shape[0]
        f0 = self.kernel(x,y)
        f_jac = np.zeros((ny,nx))
        for i in range(nx):
            x_up = np.copy(x)
            x_down = np.copy(x)
            x_up[i] += 0.5*dx
            x_down[i] -= 0.5*dx
            
            f_up = self.kernel(x_up,y)
            f_down = self.kernel(x_down,y)
            f_jac[:,i] = (f_up - f_down)/dx
        return f_jac

    def numerical_hyperparameter_gradient(self,X, dx=1.e-5):
        N_data = X.shape[0]
        theta = np.copy(self.theta)
        N_hyper = len(theta)
        dK_dTheta = np.zeros((N_hyper, N_data, N_data))
        for i in range(N_hyper):
            theta_up = np.copy(theta)
            theta_down = np.copy(theta)
            theta_up[i] += 0.5*dx
            theta_down[i] -= 0.5*dx
            
            self.theta = theta_up
            K_up = self.kernel(X,X)
            self.theta = theta_down
            K_down = self.kernel(X,X)
            dK_dTheta[i,:,:] = (K_up - K_down)/dx
        return dK_dTheta


class gauss_kernel(kernel):
    def __init__(self, amplitude=10.0, length_scale=10.0, amplitude_bounds=(1e0, 1e3), length_scale_bounds=(1e-1, 1e1)):
        self.amplitude = amplitude
        self.length_scale = length_scale
        self.amplitude_bounds = amplitude_bounds
        self.length_scale_bounds = length_scale_bounds
        self._theta_bounds = [amplitude_bounds, length_scale_bounds]

    def __call__(self, X,Y, eval_gradient=False):
        pass
        
    def kernel(self, X,Y):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        if np.ndim(Y) == 1:
            Y = Y.reshape((1,-1))
        d = cdist(X / self.length_scale,
                  Y / self.length_scale, metric='sqeuclidean')
        K = self.amplitude * np.exp(-0.5 * d)
        return K
        
    def kernel_value(self, x,y):
        d = cdist(x.reshape(1,-1) / self.length_scale,
                  y.reshape(1,-1) / self.length_scale, metric='sqeuclidean')
        K = self.amplitude * np.exp(-0.5 * d)
        return K

    def kernel_vector(self, x,Y):
        d = cdist(x.reshape(1,-1) / self.length_scale,
                  Y / self.length_scale, metric='sqeuclidean')
        K = self.amplitude * np.exp(-0.5 * d)
        return K

    def kernel_matrix(self, X,Y=None):
        if Y is None:
            d = cdist(X / self.length_scale, X / self.length_scale, metric='sqeuclidean')
        else:
            d = cdist(X / self.length_scale, Y / self.length_scale, metric='sqeuclidean')
        K = self.amplitude * np.exp(-0.5 * d)
        return K

    def kernel_jacobian(self, X,Y):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        if np.ndim(Y) == 1:
            Y = Y.reshape((1,-1))
        K = self.kernel(X,Y).T
        dK_dd = -1./(2*self.length_scale**2)*K
        dd_df = 2*(X - Y)

        dk_df = np.multiply(dK_dd, dd_df)
        return dk_df

    @property
    def theta(self):
        self._theta = [self.amplitude, self.length_scale]
        return self._theta

    @theta.setter
    def theta(self, theta):
        self._theta = theta
        self.amplitude = self._theta[0]
        self.length_scale = self._theta[1]

    def dK_da(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d = cdist(X / self.length_scale,
                  X / self.length_scale, metric='sqeuclidean')
        dK_da = np.exp(-0.5 * d)
        return dK_da
        
    def dK_dl(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d = cdist(X / self.length_scale,
                  X / self.length_scale, metric='sqeuclidean')
        dK_dl = self.amplitude * d/self.length_scale * np.exp(-0.5 * d)
        return dK_dl

    def kernel_hyperparameter_gradient(self, X):
        return np.array([self.dK_da(X), self.dK_dl(X)])
    

class double_gauss_kernel(kernel):
    def __init__(self, amplitude=10., amplitude_bounds=(1e0,1e3),
                 length_scale1=10.0, length_scale1_bounds=(1e0, 1e3),
                 length_scale2=10.0, length_scale2_bounds=(1e0, 1e3),
                 weight=0.01, weight_bounds=(0.01,0.01),
                 noise=3e-3, noise_bounds=(3e-3,3e-3)):
        self.amplitude = amplitude
        self.length_scale1 = length_scale1
        self.length_scale2 = length_scale2
        self.weight = weight

        self.amplitude_bounds = amplitude_bounds
        self.length_scale1_bounds = length_scale1_bounds
        self.length_scale2_bounds = length_scale2_bounds
        self.weight_bounds = weight_bounds

        self._theta_bounds = [amplitude_bounds, length_scale1_bounds, length_scale2_bounds, weight_bounds]

    def __call__(self, X,Y, eval_gradient=False):
        pass
        
    def kernel(self, X,Y):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        if np.ndim(Y) == 1:
            Y = Y.reshape((1,-1))
        d1 = cdist(X / self.length_scale1,
                  Y / self.length_scale1, metric='sqeuclidean')
        d2 = cdist(X / self.length_scale2,
                  Y / self.length_scale2, metric='sqeuclidean')
        K = self.amplitude * (np.exp(-0.5 * d1) + self.weight*np.exp(-0.5 * d2))
        return K

    def kernel_vector(self, x,Y):
        d = cdist(x.reshape(1,-1) / self.length_scale,
                  Y / self.length_scale, metric='sqeuclidean')
        K = np.exp(-0.5 * d)
        return K

    def kernel_matrix(self, X,Y=None):
        if Y is None:
            d = cdist(X / self.length_scale, X / self.length_scale, metric='sqeuclidean')
        else:
            d = cdist(X / self.length_scale, Y / self.length_scale, metric='sqeuclidean')
        K = np.exp(-0.5 * d)
        return K

    def kernel_jacobian(self, X,Y):
        """ Jacobian of the kernel with respect to X
        """
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        if np.ndim(Y) == 1:
            Y = Y.reshape((1,-1))
        d1 = cdist(X / self.length_scale1,
                   Y / self.length_scale1, metric='sqeuclidean')
        d2 = cdist(X / self.length_scale2,
                   Y / self.length_scale2, metric='sqeuclidean')
        dK1_dd1 = -1/(2*self.length_scale1**2) * np.exp(-0.5 * d1)
        dK2_dd2 = -1/(2*self.length_scale2**2) * np.exp(-0.5 * d2)
        dK_dd = self.amplitude * (dK1_dd1 + self.weight*dK2_dd2)
        dd_df = 2*(X - Y)

        dk_df = np.multiply(dK_dd.T, dd_df)
        return dk_df

    @property
    def theta(self):
        self._theta = [self.amplitude, self.length_scale1, self.length_scale2, self.weight]
        return self._theta

    @theta.setter
    def theta(self, theta):
        self._theta = theta
        self.amplitude = self._theta[0]
        self.length_scale1 = self._theta[1]
        self.length_scale2 = self._theta[2]
        self.weight = self._theta[3]

    def dK_da(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d1 = cdist(X / self.length_scale1,
                   X / self.length_scale1, metric='sqeuclidean')
        d2 = cdist(X / self.length_scale2,
                   X / self.length_scale2, metric='sqeuclidean')
        dK_da = np.exp(-0.5 * d1) + self.weight*np.exp(-0.5 * d2)
        return dK_da
        
    def dK_dl1(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d1 = cdist(X / self.length_scale1,
                   X / self.length_scale1, metric='sqeuclidean')
        dK_dl1 = self.amplitude*d1/self.length_scale1*np.exp(-0.5 * d1)
        return dK_dl1

    def dK_dl2(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d2 = cdist(X / self.length_scale2,
                   X / self.length_scale2, metric='sqeuclidean')
        dK_dl2 = self.amplitude*self.weight*d2/self.length_scale2*np.exp(-0.5 * d2)
        return dK_dl2

    def dK_dw(self, X):
        if np.ndim(X) == 1:
            X = X.reshape((1,-1))
        d2 = cdist(X / self.length_scale2,
                   X / self.length_scale2, metric='sqeuclidean')
        dK_dl2 = self.amplitude*np.exp(-0.5 * d2)
        return dK_dl2

    def kernel_hyperparameter_gradient(self, X):
        return np.array([self.dK_da(X), self.dK_dl1(X), self.dK_dl2(X), self.dK_dw(X)])