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


import numpy as np
from scipy import weave
from ...util.misc import param_to_array
from stationary import Stationary
from GPy.util.caching import Cache_this
from ...core.parameterization import variational
from psi_comp import ssrbf_psi_comp
from psi_comp.ssrbf_psi_gpucomp import PSICOMP_SSRBF

class RBF(Stationary):
    """
    Radial Basis Function kernel, aka squared-exponential, exponentiated quadratic or Gaussian kernel:

    .. math::

       k(r) = \sigma^2 \exp \\bigg(- \\frac{1}{2} r^2 \\bigg)

    """
    _support_GPU = True
    def __init__(self, input_dim, variance=1., lengthscale=None, ARD=False, active_dims=None, name='rbf', useGPU=False):
        super(RBF, self).__init__(input_dim, variance, lengthscale, ARD, active_dims, name, useGPU=useGPU)
        self.weave_options = {}
        self.group_spike_prob = False
        
        if self.useGPU:
            self.psicomp = PSICOMP_SSRBF()
            

    def K_of_r(self, r):
        return self.variance * np.exp(-0.5 * r**2)

    def dK_dr(self, r):
        return -r*self.K_of_r(r)

    #---------------------------------------#
    #             PSI statistics            #
    #---------------------------------------#

    def psi0(self, Z, variational_posterior):
        if self.useGPU:
            if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
                return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[0]
        else:
            return self.Kdiag(variational_posterior.mean)

    def psi1(self, Z, variational_posterior):
        if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
            if self.useGPU:
                return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[1]
            else:
                psi1, _, _, _, _, _, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
        else:
            _, _, _, psi1 = self._psi1computations(Z, variational_posterior)
        return psi1

    def psi2(self, Z, variational_posterior):
        if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
            if self.useGPU:
                return self.psicomp.psicomputations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)[2]
            else:
                psi2, _, _, _, _, _, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
        else:
            _, _, _, _, psi2 = self._psi2computations(Z, variational_posterior)
        return psi2

    def update_gradients_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
        # Spike-and-Slab GPLVM
        if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
            if self.useGPU:
                self.psicomp.update_gradients_expectations(dL_dpsi0, dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
            else:
                
                _, _dpsi1_dvariance, _, _, _, _, _dpsi1_dlengthscale = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
                _, _dpsi2_dvariance, _, _, _, _, _dpsi2_dlengthscale = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
    
                #contributions from psi0:
                self.variance.gradient = np.sum(dL_dpsi0)
    
                #from psi1
                self.variance.gradient += np.sum(dL_dpsi1 * _dpsi1_dvariance)
                if self.ARD:
                    self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
                else:
                    self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).sum()  
    
                #from psi2
                self.variance.gradient += (dL_dpsi2 * _dpsi2_dvariance).sum()
                if self.ARD:
                    self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
                else:
                    self.lengthscale.gradient += (dL_dpsi2[:,:,:,None] * _dpsi2_dlengthscale).sum()
                    
        elif isinstance(variational_posterior, variational.NormalPosterior):
            l2 = self.lengthscale**2
            if l2.size != self.input_dim:
                l2 = l2*np.ones(self.input_dim)

            #contributions from psi0:
            self.variance.gradient = np.sum(dL_dpsi0)
            self.lengthscale.gradient = 0.

            #from psi1
            denom, _, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
            d_length = psi1[:,:,None] * ((dist_sq - 1.)/(self.lengthscale*denom) +1./self.lengthscale)
            dpsi1_dlength = d_length * dL_dpsi1[:, :, None]
            if self.ARD:
                self.lengthscale.gradient += dpsi1_dlength.sum(0).sum(0)
            else:
                self.lengthscale.gradient += dpsi1_dlength.sum()
            self.variance.gradient += np.sum(dL_dpsi1 * psi1) / self.variance
            #from psi2
            S = variational_posterior.variance
            _, Zdist_sq, _, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
            if not self.ARD:
                self.lengthscale.gradient += self._weave_psi2_lengthscale_grads(dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2).sum()
            else:
                self.lengthscale.gradient += self._weave_psi2_lengthscale_grads(dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2)

            self.variance.gradient += 2.*np.sum(dL_dpsi2 * psi2)/self.variance

        else:
            raise ValueError, "unknown distriubtion received for psi-statistics"

    def gradients_Z_expectations(self, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
        # Spike-and-Slab GPLVM
        if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
            if self.useGPU:
                return self.psicomp.gradients_Z_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
            else:
                _, _, _, _, _, _dpsi1_dZ, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
                _, _, _, _, _, _dpsi2_dZ, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
    
                #psi1
                grad = (dL_dpsi1[:, :, None] * _dpsi1_dZ).sum(axis=0)
    
                #psi2
                grad += (dL_dpsi2[:, :, :, None] * _dpsi2_dZ).sum(axis=0).sum(axis=1)
    
                return grad

        elif isinstance(variational_posterior, variational.NormalPosterior):
            l2 = self.lengthscale **2

            #psi1
            denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
            grad = np.einsum('ij,ij,ijk,ijk->jk', dL_dpsi1, psi1, dist, -1./(denom*l2))

            #psi2
            Zdist, Zdist_sq, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
            term1 = Zdist / l2 # M, M, Q
            S = variational_posterior.variance
            term2 = mudist / (2.*S[:,None,None,:] + l2) # N, M, M, Q

            grad += 2.*np.einsum('ijk,ijk,ijkl->kl', dL_dpsi2, psi2, term1[None,:,:,:] + term2)

            return grad
        else:
            raise ValueError, "unknown distriubtion received for psi-statistics"

    def gradients_qX_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
        # Spike-and-Slab GPLVM
        if isinstance(variational_posterior, variational.SpikeAndSlabPosterior):
            if self.useGPU:
                return self.psicomp.gradients_qX_expectations(dL_dpsi1, dL_dpsi2, self.variance, self.lengthscale, Z, variational_posterior)
            else:   
                ndata = variational_posterior.mean.shape[0]
    
                _, _, _dpsi1_dgamma, _dpsi1_dmu, _dpsi1_dS, _, _ = ssrbf_psi_comp._psi1computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
                _, _, _dpsi2_dgamma, _dpsi2_dmu, _dpsi2_dS, _, _ = ssrbf_psi_comp._psi2computations(self.variance, self.lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)
    
                #psi1
                grad_mu = (dL_dpsi1[:, :, None] * _dpsi1_dmu).sum(axis=1)
                grad_S = (dL_dpsi1[:, :, None] * _dpsi1_dS).sum(axis=1)
                grad_gamma = (dL_dpsi1[:,:,None] * _dpsi1_dgamma).sum(axis=1)
    
                #psi2
                grad_mu += (dL_dpsi2[:, :, :, None] * _dpsi2_dmu).reshape(ndata,-1,self.input_dim).sum(axis=1)
                grad_S += (dL_dpsi2[:, :, :, None] * _dpsi2_dS).reshape(ndata,-1,self.input_dim).sum(axis=1)
                grad_gamma += (dL_dpsi2[:,:,:, None] * _dpsi2_dgamma).reshape(ndata,-1,self.input_dim).sum(axis=1)
                
                if self.group_spike_prob:
                    grad_gamma[:] = grad_gamma.mean(axis=0)
    
                return grad_mu, grad_S, grad_gamma

        elif isinstance(variational_posterior, variational.NormalPosterior):

            l2 = self.lengthscale **2
            #psi1
            denom, dist, dist_sq, psi1 = self._psi1computations(Z, variational_posterior)
            tmp = psi1[:, :, None] / l2 / denom
            grad_mu = np.sum(dL_dpsi1[:, :, None] * tmp * dist, 1)
            grad_S = np.sum(dL_dpsi1[:, :, None] * 0.5 * tmp * (dist_sq - 1), 1)
            #psi2
            _, _, mudist, mudist_sq, psi2 = self._psi2computations(Z, variational_posterior)
            S = variational_posterior.variance
            tmp = psi2[:, :, :, None] / (2.*S[:,None,None,:] + l2)
            grad_mu += -2.*np.einsum('ijk,ijkl,ijkl->il', dL_dpsi2, tmp , mudist)
            grad_S += np.einsum('ijk,ijkl,ijkl->il', dL_dpsi2 , tmp , (2.*mudist_sq - 1))

        else:
            raise ValueError, "unknown distriubtion received for psi-statistics"

        return grad_mu, grad_S

    #---------------------------------------#
    #            Precomputations            #
    #---------------------------------------#

    @Cache_this(limit=1)
    def _psi1computations(self, Z, vp):
        mu, S = vp.mean, vp.variance
        l2 = self.lengthscale **2
        denom = S[:, None, :] / l2 + 1. # N,1,Q
        dist = Z[None, :, :] - mu[:, None, :] # N,M,Q
        dist_sq = np.square(dist) / l2 / denom # N,M,Q
        exponent = -0.5 * np.sum(dist_sq + np.log(denom), -1)#N,M
        psi1 = self.variance * np.exp(exponent) # N,M
        return denom, dist, dist_sq, psi1


    @Cache_this(limit=1, ignore_args=(0,))
    def _Z_distances(self, Z):
        Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q
        Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q
        return Zhat, Zdist

    @Cache_this(limit=1)
    def _psi2computations(self, Z, vp):
        mu, S = vp.mean, vp.variance

        N, Q = mu.shape
        M = Z.shape[0]

        #compute required distances
        Zhat, Zdist = self._Z_distances(Z)
        Zdist_sq = np.square(Zdist / self.lengthscale) # M,M,Q

        #allocate memory for the things we want to compute
        mudist = np.empty((N, M, M, Q))
        mudist_sq = np.empty((N, M, M, Q))
        psi2 = np.empty((N, M, M))

        l2 = self.lengthscale **2
        denom = (2.*S[:,None,None,:] / l2) + 1. # N,Q
        half_log_denom = 0.5 * np.log(denom[:,0,0,:])
        denom_l2 = denom[:,0,0,:]*l2

        variance_sq = float(np.square(self.variance))
        code = """
        double tmp, exponent_tmp;

        #pragma omp parallel for private(tmp, exponent_tmp)
        for (int n=0; n<N; n++)
        {
            for (int m=0; m<M; m++)
            {
                for (int mm=0; mm<(m+1); mm++)
                {
                    exponent_tmp = 0.0;
                    for (int q=0; q<Q; q++)
                    {
                        //compute mudist
                        tmp = mu(n,q) - Zhat(m,mm,q);
                        mudist(n,m,mm,q) = tmp;
                        mudist(n,mm,m,q) = tmp;

                        //now mudist_sq
                        tmp = tmp*tmp/denom_l2(n,q);
                        mudist_sq(n,m,mm,q) = tmp;
                        mudist_sq(n,mm,m,q) = tmp;

                        //now exponent
                        tmp = -Zdist_sq(m,mm,q) - tmp - half_log_denom(n,q);
                        exponent_tmp += tmp;
                    }
                    //compute psi2 by exponontiating
                    psi2(n,m,mm) = variance_sq * exp(exponent_tmp);
                    psi2(n,mm,m) = psi2(n,m,mm);
                }
            }
        }
        """

        support_code = """
        #include <omp.h>
        #include <math.h>
        """
        mu = param_to_array(mu)
        weave.inline(code, support_code=support_code, libraries=['gomp'],
                     arg_names=['N', 'M', 'Q', 'mu', 'Zhat', 'mudist_sq', 'mudist', 'denom_l2', 'Zdist_sq', 'half_log_denom', 'psi2', 'variance_sq'],
                     type_converters=weave.converters.blitz, **self.weave_options)

        return Zdist, Zdist_sq, mudist, mudist_sq, psi2

    def _weave_psi2_lengthscale_grads(self, dL_dpsi2, psi2, Zdist_sq, S, mudist_sq, l2):

        #here's the einsum equivalent, it's ~3 times slower
        #return 2.*np.einsum( 'ijk,ijk,ijkl,il->l', dL_dpsi2, psi2, Zdist_sq * (2.*S[:,None,None,:]/l2 + 1.) + mudist_sq + S[:, None, None, :] / l2, 1./(2.*S + l2))*self.lengthscale

        result = np.zeros(self.input_dim)
        code = """
        double tmp;
        for(int q=0; q<Q; q++)
        {
            tmp = 0.0;
            #pragma omp parallel for reduction(+:tmp)
            for(int n=0; n<N; n++)
            {
                for(int m=0; m<M; m++)
                {
                    //diag terms
                    tmp += dL_dpsi2(n,m,m) * psi2(n,m,m) * (Zdist_sq(m,m,q) * (2.0*S(n,q)/l2(q) + 1.0) + mudist_sq(n,m,m,q) + S(n,q)/l2(q)) / (2.0*S(n,q) + l2(q)) ;

                    //off-diag terms
                    for(int mm=0; mm<m; mm++)
                    {
                        tmp += 2.0 * dL_dpsi2(n,m,mm) * psi2(n,m,mm) * (Zdist_sq(m,mm,q) * (2.0*S(n,q)/l2(q) + 1.0) + mudist_sq(n,m,mm,q) + S(n,q)/l2(q)) / (2.0*S(n,q) + l2(q)) ;
                    }
                }
            }
            result(q) = tmp;
        }

        """
        support_code = """
        #include <omp.h>
        #include <math.h>
        """
        N,Q = S.shape
        M = psi2.shape[-1]

        S = param_to_array(S)
        weave.inline(code, support_code=support_code, libraries=['gomp'],
                     arg_names=['psi2', 'dL_dpsi2', 'N', 'M', 'Q', 'mudist_sq', 'l2', 'Zdist_sq', 'S', 'result'],
                     type_converters=weave.converters.blitz, **self.weave_options)

        return 2.*result*self.lengthscale