KaneAI - World’s First E2E Software Testing Agent.Book a Demo Join TestMu Conference
How to use d_exp2 method in fMBT

Best Python code snippet using fMBT_python
ssrbf_psi_comp.py
Source:ssrbf_psi_comp.py
1# Copyright (c) 2012, GPy authors (see AUTHORS.txt).2# Licensed under the BSD 3-clause license (see LICENSE.txt)3"""4The package for the psi statistics computation5"""6import numpy as np7try:8    from scipy import weave9    def _psicomputations(variance, lengthscale, Z, variational_posterior):10        """11        Z - MxQ12        mu - NxQ13        S - NxQ14        gamma - NxQ15        """16        # here are the "statistics" for psi0, psi1 and psi217        # Produced intermediate results:18        # _psi1                NxM19        mu = variational_posterior.mean20        S = variational_posterior.variance21        gamma = variational_posterior.binary_prob22        N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]23        l2 = np.square(lengthscale)24        log_denom1 = np.log(S/l2+1)25        log_denom2 = np.log(2*S/l2+1)26        log_gamma = np.log(gamma)27        log_gamma1 = np.log(1.-gamma)28        variance = float(variance)29        psi0 = np.empty(N)30        psi0[:] = variance31        psi1 = np.empty((N,M))32        psi2n = np.empty((N,M,M))33        from ....util.misc import param_to_array34        S = param_to_array(S)35        mu = param_to_array(mu)36        gamma = param_to_array(gamma)37        Z = param_to_array(Z)38        support_code = """39        #include <math.h>40        """41        code = """42        for(int n=0; n<N; n++) {43            for(int m1=0;m1<M;m1++) {44                double log_psi1=0;45                for(int m2=0;m2<=m1;m2++) {46                    double log_psi2_n=0;47                    for(int q=0;q<Q;q++) {48                        double Snq = S(n,q);49                        double lq = l2(q);50                        double Zm1q = Z(m1,q);51                        double Zm2q = Z(m2,q);52                        if(m2==0) {53                            // Compute Psi_154                            double muZ = mu(n,q)-Z(m1,q);55                            double psi1_exp1 = log_gamma(n,q) - (muZ*muZ/(Snq+lq) +log_denom1(n,q))/2.;56                            double psi1_exp2 = log_gamma1(n,q) -Zm1q*Zm1q/(2.*lq);57                            log_psi1 += (psi1_exp1>psi1_exp2)?psi1_exp1+log1p(exp(psi1_exp2-psi1_exp1)):psi1_exp2+log1p(exp(psi1_exp1-psi1_exp2));58                        }59                        // Compute Psi_260                        double muZhat = mu(n,q) - (Zm1q+Zm2q)/2.;61                        double Z2 = Zm1q*Zm1q+ Zm2q*Zm2q;62                        double dZ = Zm1q - Zm2q;63                        double psi2_exp1 = dZ*dZ/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q);64                        double psi2_exp2 = log_gamma1(n,q) - Z2/(2.*lq);65                        log_psi2_n += (psi2_exp1>psi2_exp2)?psi2_exp1+log1p(exp(psi2_exp2-psi2_exp1)):psi2_exp2+log1p(exp(psi2_exp1-psi2_exp2));66                    }67                    double exp_psi2_n = exp(log_psi2_n);68                    psi2n(n,m1,m2) = variance*variance*exp_psi2_n;69                    if(m1!=m2) { psi2n(n,m2,m1) = variance*variance*exp_psi2_n;}70                }71                psi1(n,m1) = variance*exp(log_psi1);72            }73        }74        """75        weave.inline(code, support_code=support_code, arg_names=['psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1'], type_converters=weave.converters.blitz)76        psi2 = psi2n.sum(axis=0)77        return psi0,psi1,psi2,psi2n78    from GPy.util.caching import Cacher79    psicomputations = Cacher(_psicomputations, limit=1)80    def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):81        ARD = (len(lengthscale)!=1)82        _,psi1,_,psi2n = psicomputations(variance, lengthscale, Z, variational_posterior)83        mu = variational_posterior.mean84        S = variational_posterior.variance85        gamma = variational_posterior.binary_prob86        N,M,Q = mu.shape[0],Z.shape[0],mu.shape[1]87        l2 = np.square(lengthscale)88        log_denom1 = np.log(S/l2+1)89        log_denom2 = np.log(2*S/l2+1)90        log_gamma = np.log(gamma)91        log_gamma1 = np.log(1.-gamma)92        variance = float(variance)93        dvar = np.zeros(1)94        dmu = np.zeros((N,Q))95        dS = np.zeros((N,Q))96        dgamma = np.zeros((N,Q))97        dl = np.zeros(Q)98        dZ = np.zeros((M,Q))99        dvar += np.sum(dL_dpsi0)100        from ....util.misc import param_to_array101        S = param_to_array(S)102        mu = param_to_array(mu)103        gamma = param_to_array(gamma)104        Z = param_to_array(Z)105        support_code = """106        #include <math.h>107        """108        code = """109        for(int n=0; n<N; n++) {110            for(int m1=0;m1<M;m1++) {111                double log_psi1=0;112                for(int m2=0;m2<M;m2++) {113                    double log_psi2_n=0;114                    for(int q=0;q<Q;q++) {115                        double Snq = S(n,q);116                        double lq = l2(q);117                        double Zm1q = Z(m1,q);118                        double Zm2q = Z(m2,q);119                        double gnq = gamma(n,q);120                        double mu_nq = mu(n,q);121                        if(m2==0) {122                            // Compute Psi_1123                            double lpsi1 = psi1(n,m1)*dL_dpsi1(n,m1);124                            if(q==0) {dvar(0) += lpsi1/variance;}125                            double Zmu = Zm1q - mu_nq;126                            double denom = Snq+lq;127                            double Zmu2_denom = Zmu*Zmu/denom;128                            double exp1 = log_gamma(n,q)-(Zmu*Zmu/(Snq+lq)+log_denom1(n,q))/(2.);129                            double exp2 = log_gamma1(n,q)-Zm1q*Zm1q/(2.*lq);130                            double d_exp1,d_exp2;131                            if(exp1>exp2) {132                                d_exp1 = 1.;133                                d_exp2 = exp(exp2-exp1);134                            } else {135                                d_exp1 = exp(exp1-exp2);136                                d_exp2 = 1.;137                            }138                            double exp_sum = d_exp1+d_exp2;139                            dmu(n,q) += lpsi1*Zmu*d_exp1/(denom*exp_sum);140                            dS(n,q) += lpsi1*(Zmu2_denom-1.)*d_exp1/(denom*exp_sum)/2.;141                            dgamma(n,q) += lpsi1*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;142                            dl(q) += lpsi1*((Zmu2_denom+Snq/lq)/denom*d_exp1+Zm1q*Zm1q/(lq*lq)*d_exp2)/(2.*exp_sum);143                            dZ(m1,q) += lpsi1*(-Zmu/denom*d_exp1-Zm1q/lq*d_exp2)/exp_sum;144                        }145                        // Compute Psi_2146                        double lpsi2 = psi2n(n,m1,m2)*dL_dpsi2(m1,m2);147                        if(q==0) {dvar(0) += lpsi2*2/variance;}148                        double dZm1m2 = Zm1q - Zm2q;149                        double Z2 = Zm1q*Zm1q+Zm2q*Zm2q;150                        double muZhat =  mu_nq - (Zm1q + Zm2q)/2.;151                        double denom = 2.*Snq+lq;152                        double muZhat2_denom = muZhat*muZhat/denom;153                        double exp1 = dZm1m2*dZm1m2/(-4.*lq)-muZhat*muZhat/(2.*Snq+lq) - log_denom2(n,q)/2. + log_gamma(n,q);154                        double exp2 = log_gamma1(n,q) - Z2/(2.*lq);155                        double d_exp1,d_exp2;156                        if(exp1>exp2) {157                            d_exp1 = 1.;158                            d_exp2 = exp(exp2-exp1);159                        } else {160                            d_exp1 = exp(exp1-exp2);161                            d_exp2 = 1.;162                        }163                        double exp_sum = d_exp1+d_exp2;164                        dmu(n,q) += -2.*lpsi2*muZhat/denom*d_exp1/exp_sum;165                        dS(n,q) += lpsi2*(2.*muZhat2_denom-1.)/denom*d_exp1/exp_sum;166                        dgamma(n,q) += lpsi2*(d_exp1/gnq-d_exp2/(1.-gnq))/exp_sum;167                        dl(q) += lpsi2*(((Snq/lq+muZhat2_denom)/denom+dZm1m2*dZm1m2/(4.*lq*lq))*d_exp1+Z2/(2.*lq*lq)*d_exp2)/exp_sum;168                        dZ(m1,q) += 2.*lpsi2*((muZhat/denom-dZm1m2/(2*lq))*d_exp1-Zm1q/lq*d_exp2)/exp_sum;169                    }170                }171            }172        }173        """174        weave.inline(code, support_code=support_code, arg_names=['dL_dpsi1','dL_dpsi2','psi1','psi2n','N','M','Q','variance','l2','Z','mu','S','gamma','log_denom1','log_denom2','log_gamma','log_gamma1','dvar','dl','dmu','dS','dgamma','dZ'], type_converters=weave.converters.blitz)175        dl *= 2.*lengthscale176        if not ARD:177            dl = dl.sum()178        return dvar, dl, dZ, dmu, dS, dgamma179except:180    def psicomputations(variance, lengthscale, Z, variational_posterior):181        """182        Z - MxQ183        mu - NxQ184        S - NxQ185        gamma - NxQ186        """187        # here are the "statistics" for psi0, psi1 and psi2188        # Produced intermediate results:189        # _psi1                NxM190        mu = variational_posterior.mean191        S = variational_posterior.variance192        gamma = variational_posterior.binary_prob193        psi0 = np.empty(mu.shape[0])194        psi0[:] = variance195        psi1 = _psi1computations(variance, lengthscale, Z, mu, S, gamma)196        psi2 = _psi2computations(variance, lengthscale, Z, mu, S, gamma)197        return psi0, psi1, psi2198    def _psi1computations(variance, lengthscale, Z, mu, S, gamma):199        """200        Z - MxQ201        mu - NxQ202        S - NxQ203        gamma - NxQ204        """205        # here are the "statistics" for psi1206        # Produced intermediate results:207        # _psi1                NxM208        lengthscale2 = np.square(lengthscale)209        # psi1210        _psi1_denom = S[:, None, :] / lengthscale2 + 1.  # Nx1xQ211        _psi1_denom_sqrt = np.sqrt(_psi1_denom) #Nx1xQ212        _psi1_dist = Z[None, :, :] - mu[:, None, :]  # NxMxQ213        _psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom) # NxMxQ214        _psi1_common = gamma[:,None,:] / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #Nx1xQ215        _psi1_exponent1 = np.log(gamma[:,None,:]) - (_psi1_dist_sq + np.log(_psi1_denom))/2. # NxMxQ216        _psi1_exponent2 = np.log(1.-gamma[:,None,:]) - (np.square(Z[None,:,:])/lengthscale2)/2. # NxMxQ217        _psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)218        _psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ219        _psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM220        _psi1 = variance * np.exp(_psi1_exp_sum) # NxM221        return _psi1222    def _psi2computations(variance, lengthscale, Z, mu, S, gamma):223        """224        Z - MxQ225        mu - NxQ226        S - NxQ227        gamma - NxQ228        """229        # here are the "statistics" for psi2230        # Produced intermediate results:231        # _psi2                MxM232        lengthscale2 = np.square(lengthscale)233        _psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q234        _psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q235        _psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q236        _psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ237        # psi2238        _psi2_denom = 2.*S[:, None, None, :] / lengthscale2 + 1. # Nx1x1xQ239        _psi2_denom_sqrt = np.sqrt(_psi2_denom)240        _psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q241        _psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom)242        _psi2_common = gamma[:,None,None,:]/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # Nx1x1xQ243        _psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom)+np.log(gamma[:,None,None,:]) #N,M,M,Q244        _psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ245        _psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)246        _psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))247        _psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM248        _psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM249        return _psi2250    def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, lengthscale, Z, variational_posterior):251        ARD = (len(lengthscale)!=1)252        dvar_psi1, dl_psi1, dZ_psi1, dmu_psi1, dS_psi1, dgamma_psi1 = _psi1compDer(dL_dpsi1, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)253        dvar_psi2, dl_psi2, dZ_psi2, dmu_psi2, dS_psi2, dgamma_psi2 = _psi2compDer(dL_dpsi2, variance, lengthscale, Z, variational_posterior.mean, variational_posterior.variance, variational_posterior.binary_prob)254        dL_dvar = np.sum(dL_dpsi0) + dvar_psi1 + dvar_psi2255        dL_dlengscale = dl_psi1 + dl_psi2256        if not ARD:257            dL_dlengscale = dL_dlengscale.sum()258        dL_dgamma = dgamma_psi1 + dgamma_psi2259        dL_dmu = dmu_psi1 + dmu_psi2260        dL_dS = dS_psi1 + dS_psi2261        dL_dZ = dZ_psi1 + dZ_psi2262        return dL_dvar, dL_dlengscale, dL_dZ, dL_dmu, dL_dS, dL_dgamma263    def _psi1compDer(dL_dpsi1, variance, lengthscale, Z, mu, S, gamma):264        """265        dL_dpsi1 - NxM266        Z - MxQ267        mu - NxQ268        S - NxQ269        gamma - NxQ270        """271        # here are the "statistics" for psi1272        # Produced intermediate results: dL_dparams w.r.t. psi1273        # _dL_dvariance     1274        # _dL_dlengthscale  Q275        # _dL_dZ            MxQ276        # _dL_dgamma        NxQ277        # _dL_dmu           NxQ278        # _dL_dS            NxQ279        lengthscale2 = np.square(lengthscale)280        # psi1281        _psi1_denom = S / lengthscale2 + 1.  # NxQ282        _psi1_denom_sqrt = np.sqrt(_psi1_denom) #NxQ283        _psi1_dist = Z[None, :, :] - mu[:, None, :]  # NxMxQ284        _psi1_dist_sq = np.square(_psi1_dist) / (lengthscale2 * _psi1_denom[:,None,:]) # NxMxQ285        _psi1_common = gamma / (lengthscale2*_psi1_denom*_psi1_denom_sqrt) #NxQ286        _psi1_exponent1 = np.log(gamma[:,None,:]) -0.5 * (_psi1_dist_sq + np.log(_psi1_denom[:, None,:])) # NxMxQ287        _psi1_exponent2 = np.log(1.-gamma[:,None,:]) -0.5 * (np.square(Z[None,:,:])/lengthscale2) # NxMxQ288        _psi1_exponent_max = np.maximum(_psi1_exponent1,_psi1_exponent2)289        _psi1_exponent = _psi1_exponent_max+np.log(np.exp(_psi1_exponent1-_psi1_exponent_max) + np.exp(_psi1_exponent2-_psi1_exponent_max)) #NxMxQ290        _psi1_exp_sum = _psi1_exponent.sum(axis=-1) #NxM291        _psi1_exp_dist_sq = np.exp(-0.5*_psi1_dist_sq) # NxMxQ292        _psi1_exp_Z = np.exp(-0.5*np.square(Z[None,:,:])/lengthscale2) # 1xMxQ293        _psi1_q = variance * np.exp(_psi1_exp_sum[:,:,None] - _psi1_exponent) # NxMxQ294        _psi1 = variance * np.exp(_psi1_exp_sum) # NxM295        _dL_dvariance = np.einsum('nm,nm->',dL_dpsi1, _psi1)/variance # 1296        _dL_dgamma = np.einsum('nm,nmq,nmq->nq',dL_dpsi1, _psi1_q, (_psi1_exp_dist_sq/_psi1_denom_sqrt[:,None,:]-_psi1_exp_Z)) # NxQ297        _dL_dmu = np.einsum('nm, nmq, nmq, nmq, nq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_dist,_psi1_common)  # NxQ298        _dL_dS = np.einsum('nm,nmq,nmq,nq,nmq->nq',dL_dpsi1,_psi1_q,_psi1_exp_dist_sq,_psi1_common,(_psi1_dist_sq-1.))/2.  # NxQ299        _dL_dZ = np.einsum('nm,nmq,nmq->mq',dL_dpsi1,_psi1_q, (- _psi1_common[:,None,:] * _psi1_dist * _psi1_exp_dist_sq - (1-gamma[:,None,:])/lengthscale2*Z[None,:,:]*_psi1_exp_Z))300        _dL_dlengthscale = lengthscale* np.einsum('nm,nmq,nmq->q',dL_dpsi1,_psi1_q,(_psi1_common[:,None,:]*(S[:,None,:]/lengthscale2+_psi1_dist_sq)*_psi1_exp_dist_sq + (1-gamma[:,None,:])*np.square(Z[None,:,:]/lengthscale2)*_psi1_exp_Z))301        return _dL_dvariance, _dL_dlengthscale, _dL_dZ, _dL_dmu, _dL_dS, _dL_dgamma302    def _psi2compDer(dL_dpsi2, variance, lengthscale, Z, mu, S, gamma):303        """304        Z - MxQ305        mu - NxQ306        S - NxQ307        gamma - NxQ308        dL_dpsi2 - MxM309        """310        # here are the "statistics" for psi2311        # Produced the derivatives w.r.t. psi2:312        # _dL_dvariance      1313        # _dL_dlengthscale   Q314        # _dL_dZ             MxQ315        # _dL_dgamma         NxQ316        # _dL_dmu            NxQ317        # _dL_dS             NxQ318        lengthscale2 = np.square(lengthscale)319        _psi2_Zhat = 0.5 * (Z[:, None, :] + Z[None, :, :]) # M,M,Q320        _psi2_Zdist = 0.5 * (Z[:, None, :] - Z[None, :, :]) # M,M,Q321        _psi2_Zdist_sq = np.square(_psi2_Zdist / lengthscale) # M,M,Q322        _psi2_Z_sq_sum = (np.square(Z[:,None,:])+np.square(Z[None,:,:]))/lengthscale2 # MxMxQ323        # psi2324        _psi2_denom = 2.*S / lengthscale2 + 1. # NxQ325        _psi2_denom_sqrt = np.sqrt(_psi2_denom)326        _psi2_mudist = mu[:,None,None,:]-_psi2_Zhat #N,M,M,Q327        _psi2_mudist_sq = np.square(_psi2_mudist)/(lengthscale2*_psi2_denom[:,None,None,:])328        _psi2_common = gamma/(lengthscale2 * _psi2_denom * _psi2_denom_sqrt) # NxQ329        _psi2_exponent1 = -_psi2_Zdist_sq -_psi2_mudist_sq -0.5*np.log(_psi2_denom[:,None,None,:])+np.log(gamma[:,None,None,:]) #N,M,M,Q330        _psi2_exponent2 = np.log(1.-gamma[:,None,None,:]) - 0.5*(_psi2_Z_sq_sum) # NxMxMxQ331        _psi2_exponent_max = np.maximum(_psi2_exponent1, _psi2_exponent2)332        _psi2_exponent = _psi2_exponent_max+np.log(np.exp(_psi2_exponent1-_psi2_exponent_max) + np.exp(_psi2_exponent2-_psi2_exponent_max))333        _psi2_exp_sum = _psi2_exponent.sum(axis=-1) #NxM334        _psi2_q = variance*variance * np.exp(_psi2_exp_sum[:,:,:,None]-_psi2_exponent) # NxMxMxQ335        _psi2_exp_dist_sq = np.exp(-_psi2_Zdist_sq -_psi2_mudist_sq) # NxMxMxQ336        _psi2_exp_Z = np.exp(-0.5*_psi2_Z_sq_sum) # MxMxQ337        _psi2 = variance*variance * (np.exp(_psi2_exp_sum).sum(axis=0)) # MxM338        _dL_dvariance = np.einsum('mo,mo->',dL_dpsi2,_psi2)*2./variance339        _dL_dgamma = np.einsum('mo,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,(_psi2_exp_dist_sq/_psi2_denom_sqrt[:,None,None,:] - _psi2_exp_Z))340        _dL_dmu = -2.*np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q,_psi2_common,_psi2_mudist,_psi2_exp_dist_sq)341        _dL_dS = np.einsum('mo,nmoq,nq,nmoq,nmoq->nq',dL_dpsi2,_psi2_q, _psi2_common, (2.*_psi2_mudist_sq-1.), _psi2_exp_dist_sq)342        _dL_dZ = 2.*np.einsum('mo,nmoq,nmoq->mq',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(-_psi2_Zdist*_psi2_denom[:,None,None,:]+_psi2_mudist)*_psi2_exp_dist_sq - (1-gamma[:,None,None,:])*Z[:,None,:]/lengthscale2*_psi2_exp_Z))343        _dL_dlengthscale = 2.*lengthscale* np.einsum('mo,nmoq,nmoq->q',dL_dpsi2,_psi2_q,(_psi2_common[:,None,None,:]*(S[:,None,None,:]/lengthscale2+_psi2_Zdist_sq*_psi2_denom[:,None,None,:]+_psi2_mudist_sq)*_psi2_exp_dist_sq+(1-gamma[:,None,None,:])*_psi2_Z_sq_sum*0.5/lengthscale2*_psi2_exp_Z))...
Automation Testing Tutorials

Learn to execute automation testing from scratch with LambdaTest Learning Hub. Right from setting up the prerequisites to run your first automation test, to following best practices and diving deeper into advanced test scenarios. LambdaTest Learning Hubs compile a list of step-by-step guides to help you be proficient with different test automation frameworks i.e. Selenium, Cypress, TestNG etc.