def inference(self, kern_r, kern_c, Xr, Xc, Zr, Zc, likelihood, Y, qU_mean ,qU_var_r, qU_var_c):
N, D, Mr, Mc, Qr, Qc = Y.shape[<NUM_LIT:0>], Y.shape[<NUM_LIT:1>], Zr.shape[<NUM_LIT:0>], Zc.shape[<NUM_LIT:0>], Zr.shape[<NUM_LIT:1>], Zc.shape[<NUM_LIT:1>]<EOL>uncertain_inputs_r = isinstance(Xr, VariationalPosterior)<EOL>uncertain_inputs_c = isinstance(Xc, VariationalPosterior)<EOL>uncertain_outputs = isinstance(Y, VariationalPosterior)<EOL>beta = <NUM_LIT:1.>/likelihood.variance<EOL>psi0_r, psi1_r, psi2_r = self.gatherPsiStat(kern_r, Xr, Zr, uncertain_inputs_r)<EOL>psi0_c, psi1_c, psi2_c = self.gatherPsiStat(kern_c, Xc, Zc, uncertain_inputs_c)<EOL>Kuu_r = kern_r.K(Zr).copy()<EOL>diag.add(Kuu_r, self.const_jitter)<EOL>Lr = jitchol(Kuu_r)<EOL>Kuu_c = kern_c.K(Zc).copy()<EOL>diag.add(Kuu_c, self.const_jitter)<EOL>Lc = jitchol(Kuu_c)<EOL>mu, Sr, Sc = qU_mean, qU_var_r, qU_var_c<EOL>LSr = jitchol(Sr)<EOL>LSc = jitchol(Sc)<EOL>LcInvMLrInvT = dtrtrs(Lc,dtrtrs(Lr,mu.T)[<NUM_LIT:0>].T)[<NUM_LIT:0>]<EOL>LcInvPsi2_cLcInvT = backsub_both_sides(Lc, psi2_c,'<STR_LIT:right>')<EOL>LrInvPsi2_rLrInvT = backsub_both_sides(Lr, psi2_r,'<STR_LIT:right>')<EOL>LcInvLSc = dtrtrs(Lc, LSc)[<NUM_LIT:0>]<EOL>LrInvLSr = dtrtrs(Lr, LSr)[<NUM_LIT:0>]<EOL>LcInvScLcInvT = tdot(LcInvLSc)<EOL>LrInvSrLrInvT = tdot(LrInvLSr)<EOL>LcInvPsi1_cT = dtrtrs(Lc, psi1_c.T)[<NUM_LIT:0>]<EOL>LrInvPsi1_rT = dtrtrs(Lr, psi1_r.T)[<NUM_LIT:0>]<EOL>tr_LrInvPsi2_rLrInvT_LrInvSrLrInvT = (LrInvPsi2_rLrInvT*LrInvSrLrInvT).sum()<EOL>tr_LcInvPsi2_cLcInvT_LcInvScLcInvT = (LcInvPsi2_cLcInvT*LcInvScLcInvT).sum()<EOL>tr_LrInvSrLrInvT = np.square(LrInvLSr).sum()<EOL>tr_LcInvScLcInvT = np.square(LcInvLSc).sum()<EOL>tr_LrInvPsi2_rLrInvT = np.trace(LrInvPsi2_rLrInvT)<EOL>tr_LcInvPsi2_cLcInvT = np.trace(LcInvPsi2_cLcInvT)<EOL>logL_A = - np.square(Y).sum()- (LcInvMLrInvT.T.dot(LcInvPsi2_cLcInvT).dot(LcInvMLrInvT)*LrInvPsi2_rLrInvT).sum()-  tr_LrInvPsi2_rLrInvT_LrInvSrLrInvT* tr_LcInvPsi2_cLcInvT_LcInvScLcInvT+ <NUM_LIT:2> * (Y * LcInvPsi1_cT.T.dot(LcInvMLrInvT).dot(LrInvPsi1_rT)).sum() - psi0_c * psi0_r+ tr_LrInvPsi2_rLrInvT * tr_LcInvPsi2_cLcInvT<EOL>logL = -N*D/<NUM_LIT>*(np.log(<NUM_LIT>*np.pi)-np.log(beta)) + beta/<NUM_LIT>* logL_A-Mc * (np.log(np.diag(Lr)).sum()-np.log(np.diag(LSr)).sum())  -Mr * (np.log(np.diag(Lc)).sum()-np.log(np.diag(LSc)).sum())- np.square(LcInvMLrInvT).sum()/<NUM_LIT> - tr_LrInvSrLrInvT * tr_LcInvScLcInvT/<NUM_LIT> + Mr*Mc/<NUM_LIT><EOL>tmp =  beta* LcInvPsi2_cLcInvT.dot(LcInvMLrInvT).dot(LrInvPsi2_rLrInvT).dot(LcInvMLrInvT.T)+ beta* tr_LrInvPsi2_rLrInvT_LrInvSrLrInvT * LcInvPsi2_cLcInvT.dot(LcInvScLcInvT)- beta* LcInvMLrInvT.dot(LrInvPsi1_rT).dot(Y.T).dot(LcInvPsi1_cT.T)- beta/<NUM_LIT> * tr_LrInvPsi2_rLrInvT* LcInvPsi2_cLcInvT - Mr/<NUM_LIT>*np.eye(Mc)+ tdot(LcInvMLrInvT)/<NUM_LIT> + tr_LrInvSrLrInvT/<NUM_LIT> * LcInvScLcInvT<EOL>dL_dKuu_c = backsub_both_sides(Lc, tmp, '<STR_LIT:left>')<EOL>dL_dKuu_c += dL_dKuu_c.T<EOL>dL_dKuu_c *= <NUM_LIT:0.5><EOL>tmp =  beta* LcInvMLrInvT.T.dot(LcInvPsi2_cLcInvT).dot(LcInvMLrInvT).dot(LrInvPsi2_rLrInvT)+ beta* tr_LcInvPsi2_cLcInvT_LcInvScLcInvT * LrInvPsi2_rLrInvT.dot(LrInvSrLrInvT)- beta* LrInvPsi1_rT.dot(Y.T).dot(LcInvPsi1_cT.T).dot(LcInvMLrInvT)- beta/<NUM_LIT> * tr_LcInvPsi2_cLcInvT * LrInvPsi2_rLrInvT - Mc/<NUM_LIT>*np.eye(Mr)+ tdot(LcInvMLrInvT.T)/<NUM_LIT> + tr_LcInvScLcInvT/<NUM_LIT> * LrInvSrLrInvT<EOL>dL_dKuu_r = backsub_both_sides(Lr, tmp, '<STR_LIT:left>')<EOL>dL_dKuu_r += dL_dKuu_r.T<EOL>dL_dKuu_r *= <NUM_LIT:0.5><EOL>dL_dthetaL = -D*N*beta/<NUM_LIT> - logL_A*beta*beta/<NUM_LIT><EOL>tmp = -beta * LcInvPsi2_cLcInvT.dot(LcInvMLrInvT).dot(LrInvPsi2_rLrInvT)+ beta* LcInvPsi1_cT.dot(Y).dot(LrInvPsi1_rT.T) - LcInvMLrInvT<EOL>dL_dqU_mean = dtrtrs(Lc, dtrtrs(Lr, tmp.T, trans=<NUM_LIT:1>)[<NUM_LIT:0>].T, trans=<NUM_LIT:1>)[<NUM_LIT:0>]<EOL>LScInv = dtrtri(LSc)<EOL>tmp = -beta/<NUM_LIT>*tr_LrInvPsi2_rLrInvT_LrInvSrLrInvT * LcInvPsi2_cLcInvT -tr_LrInvSrLrInvT/<NUM_LIT>*np.eye(Mc)<EOL>dL_dqU_var_c = backsub_both_sides(Lc, tmp, '<STR_LIT:left>') + tdot(LScInv.T) * Mr/<NUM_LIT><EOL>LSrInv = dtrtri(LSr)<EOL>tmp = -beta/<NUM_LIT>*tr_LcInvPsi2_cLcInvT_LcInvScLcInvT * LrInvPsi2_rLrInvT -tr_LcInvScLcInvT/<NUM_LIT>*np.eye(Mr)<EOL>dL_dqU_var_r = backsub_both_sides(Lr, tmp, '<STR_LIT:left>') + tdot(LSrInv.T) * Mc/<NUM_LIT><EOL>post = PosteriorMultioutput(LcInvMLrInvT=LcInvMLrInvT, LcInvScLcInvT=LcInvScLcInvT,<EOL>LrInvSrLrInvT=LrInvSrLrInvT, Lr=Lr, Lc=Lc, kern_r=kern_r, Xr=Xr, Zr=Zr)<EOL>dL_dpsi0_r = - psi0_c * beta/<NUM_LIT> * np.ones((D,))<EOL>dL_dpsi0_c = - psi0_r * beta/<NUM_LIT> * np.ones((N,))<EOL>dL_dpsi1_c = beta * dtrtrs(Lc, (Y.dot(LrInvPsi1_rT.T).dot(LcInvMLrInvT.T)).T, trans=<NUM_LIT:1>)[<NUM_LIT:0>].T<EOL>dL_dpsi1_r = beta * dtrtrs(Lr, (Y.T.dot(LcInvPsi1_cT.T).dot(LcInvMLrInvT)).T, trans=<NUM_LIT:1>)[<NUM_LIT:0>].T<EOL>tmp = beta/<NUM_LIT>*(-LcInvMLrInvT.dot(LrInvPsi2_rLrInvT).dot(LcInvMLrInvT.T) - tr_LrInvPsi2_rLrInvT_LrInvSrLrInvT * LcInvScLcInvT<EOL>+tr_LrInvPsi2_rLrInvT *np.eye(Mc))<EOL>dL_dpsi2_c = backsub_both_sides(Lc, tmp, '<STR_LIT:left>')<EOL>tmp = beta/<NUM_LIT>*(-LcInvMLrInvT.T.dot(LcInvPsi2_cLcInvT).dot(LcInvMLrInvT) - tr_LcInvPsi2_cLcInvT_LcInvScLcInvT * LrInvSrLrInvT<EOL>+tr_LcInvPsi2_cLcInvT *np.eye(Mr))<EOL>dL_dpsi2_r = backsub_both_sides(Lr, tmp, '<STR_LIT:left>')<EOL>if not uncertain_inputs_r:<EOL><INDENT>dL_dpsi1_r += psi1_r.dot(dL_dpsi2_r+dL_dpsi2_r.T)<EOL><DEDENT>if not uncertain_inputs_c:<EOL><INDENT>dL_dpsi1_c += psi1_c.dot(dL_dpsi2_c+dL_dpsi2_c.T)<EOL><DEDENT>grad_dict = {<EOL>'<STR_LIT>':dL_dthetaL,<EOL>'<STR_LIT>':dL_dqU_mean,<EOL>'<STR_LIT>':dL_dqU_var_c,<EOL>'<STR_LIT>':dL_dqU_var_r,<EOL>'<STR_LIT>': dL_dKuu_c,<EOL>'<STR_LIT>': dL_dKuu_r,<EOL>}<EOL>if uncertain_inputs_c:<EOL><INDENT>grad_dict['<STR_LIT>'] = dL_dpsi0_c<EOL>grad_dict['<STR_LIT>'] = dL_dpsi1_c<EOL>grad_dict['<STR_LIT>'] = dL_dpsi2_c<EOL><DEDENT>else:<EOL><INDENT>grad_dict['<STR_LIT>'] = dL_dpsi0_c<EOL>grad_dict['<STR_LIT>'] = dL_dpsi1_c<EOL><DEDENT>if uncertain_inputs_r:<EOL><INDENT>grad_dict['<STR_LIT>'] = dL_dpsi0_r<EOL>grad_dict['<STR_LIT>'] = dL_dpsi1_r<EOL>grad_dict['<STR_LIT>'] = dL_dpsi2_r<EOL><DEDENT>else:<EOL><INDENT>grad_dict['<STR_LIT>'] = dL_dpsi0_r<EOL>grad_dict['<STR_LIT>'] = dL_dpsi1_r<EOL><DEDENT>return post, logL, grad_dict<EOL>
The SVI-VarDTC inference