# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)


from kernpart import kernpart
import numpy as np

class linear_ARD(kernpart):
    """
    Linear ARD kernel

    :param D: the number of input dimensions
    :type D: int
    :param variances: ARD variances
    :type variances: None|np.ndarray
    """

    def __init__(self,D,variances=None):
        self.D = D
        if variances is not None:
            assert variances.shape==(self.D,)
        else:
            variances = np.ones(self.D)
        self.Nparam = int(self.D)
        self.name = 'linear'
        self.set_param(variances)

    def get_param(self):
        return self.variances

    def set_param(self,x):
        assert x.size==(self.Nparam)
        self.variances = x

    def get_param_names(self):
        if self.D==1:
            return ['variance']
        else:
            return ['variance_%i'%i for i in range(self.variances.size)]

    def K(self,X,X2,target):
        XX = X*np.sqrt(self.variances)
        XX2 = X2*np.sqrt(self.variances)
        target += np.dot(XX, XX2.T)

    def Kdiag(self,X,target):
        np.add(target,np.sum(self.variances*np.square(X),-1),target)

    def dK_dtheta(self,partial,X,X2,target):
        product = X[:,None,:]*X2[None,:,:]
        target += (partial[:,:,None]*product).sum(0).sum(0)

    def dK_dX(self,partial,X,X2,target):
        target += (((X2[:, None, :] * self.variances)) * partial[:,:, None]).sum(0)

    def psi0(self,Z,mu,S,target):
        expected = np.square(mu) + S
        np.add(target,np.sum(self.variances*expected),target)

    def dpsi0_dtheta(self,Z,mu,S,target):
        expected = np.square(mu) + S
        return -2.*np.sum(expected,0)

    def dpsi0_dmuS(self,Z,mu,S,target_mu,target_S):
        np.add(target_mu,2*mu*self.variances,target_mu)
        np.add(target_S,self.variances,target_S)

    def dpsi0_dZ(self,Z,mu,S,target):
        pass

    def psi1(self,Z,mu,S,target):
        """the variance, it does nothing"""
        self.K(mu,Z,target)

    def dpsi1_dtheta(self,Z,mu,S,target):
        """the variance, it does nothing"""
        self.dK_dtheta(mu,Z,target)

    def dpsi1_dmuS(self,Z,mu,S,target_mu,target_S):
        """Do nothing for S, it does not affect psi1"""
        np.add(target_mu,Z/self.variances2,target_mu)

    def dpsi1_dZ(self,Z,mu,S,target):
        self.dK_dX(mu,Z,target)

    def psi2(self,Z,mu,S,target):
        """Think N,M,M,Q """
        mu2_S = np.square(mu)+S# N,Q,
        ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
        psi2 = ZZ*np.square(self.variances)*mu2_S
        np.add(target, psi2.sum(-1),target) # M,M

    def dpsi2_dtheta(self,Z,mu,S,target):
        mu2_S = np.square(mu)+S# N,Q,
        ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
        target += 2.*ZZ*mu2_S*self.variances

    def dpsi2_dmuS(self,Z,mu,S,target_mu,target_S):
        """Think N,M,M,Q """
        mu2_S = np.sum(np.square(mu)+S,0)# Q,
        ZZ = Z[:,None,:]*Z[None,:,:] # M,M,Q
        tmp = ZZ*np.square(self.variances) # M,M,Q
        np.add(target_mu, tmp*2.*mu[:,None,None,:],target_mu) #N,M,M,Q
        np.add(target_S, tmp, target_S) #N,M,M,Q

    def dpsi2_dZ(self,Z,mu,S,target):
        mu2_S = np.sum(np.square(mu)+S,0)# Q,
        target += Z[:,None,:]*np.square(self.variances)*mu2_S