From 6ed91ce102545bd90644906876e5e18affe82744 Mon Sep 17 00:00:00 2001 From: Zhenwen Dai Date: Thu, 20 Nov 2014 17:38:19 +0000 Subject: [PATCH] linear kernel speed up --- GPy/kern/_src/psi_comp/linear_psi_comp.py | 34 +++++++++++++---------- 1 file changed, 20 insertions(+), 14 deletions(-) diff --git a/GPy/kern/_src/psi_comp/linear_psi_comp.py b/GPy/kern/_src/psi_comp/linear_psi_comp.py index 93297e7e..50090428 100644 --- a/GPy/kern/_src/psi_comp/linear_psi_comp.py +++ b/GPy/kern/_src/psi_comp/linear_psi_comp.py @@ -6,6 +6,7 @@ The package for the Psi statistics computation of the linear kernel for Bayesian """ import numpy as np +from ....util.linalg import tdot def psicomputations(variance, Z, variational_posterior): """ @@ -19,9 +20,9 @@ def psicomputations(variance, Z, variational_posterior): mu = variational_posterior.mean S = variational_posterior.variance - psi0 = np.einsum('q,nq->n',variance,np.square(mu)+S) - psi1 = np.einsum('q,mq,nq->nm',variance,Z,mu) - psi2 = np.einsum('q,mq,oq,nq->mo',np.square(variance),Z,Z,S) + np.einsum('nm,no->mo',psi1,psi1) + psi0 = (variance*(np.square(mu)+S)).sum(axis=1) + psi1 = np.dot(mu,(variance*Z).T) + psi2 = np.dot(S.sum(axis=0)*np.square(variance)*Z,Z.T)+ tdot(psi1.T) return psi0, psi1, psi2 @@ -33,10 +34,12 @@ def psiDerivativecomputations(dL_dpsi0, dL_dpsi1, dL_dpsi2, variance, Z, variati # Compute for psi0 and psi1 mu2S = np.square(mu)+S - dL_dvar += np.einsum('n,nq->q',dL_dpsi0,mu2S) + np.einsum('nm,mq,nq->q',dL_dpsi1,Z,mu) - dL_dmu += np.einsum('n,q,nq->nq',dL_dpsi0,2.*variance,mu) + np.einsum('nm,q,mq->nq',dL_dpsi1,variance,Z) - dL_dS += np.einsum('n,q->nq',dL_dpsi0,variance) - dL_dZ += np.einsum('nm,q,nq->mq',dL_dpsi1, variance,mu) + dL_dpsi0_var = dL_dpsi0[:,None]*variance[None,:] + dL_dpsi1_mu = np.dot(dL_dpsi1.T,mu) + dL_dvar += (dL_dpsi0[:,None]*mu2S).sum(axis=0)+ (dL_dpsi1_mu*Z).sum(axis=0) + dL_dmu += 2.*dL_dpsi0_var*mu+np.dot(dL_dpsi1,Z)*variance + dL_dS += dL_dpsi0_var + dL_dZ += dL_dpsi1_mu*variance return dL_dvar, dL_dZ, dL_dmu, dL_dS @@ -55,17 +58,20 @@ def _psi2computations(dL_dpsi2, variance, Z, mu, S): # _psi2_dS NxQ variance2 = np.square(variance) - common_sum = np.einsum('q,mq,nq->nm',variance,Z,mu) # NxM - Z_expect = np.einsum('mo,mq,oq->q',dL_dpsi2,Z,Z) - common_expect = np.einsum('mo,mq,no->nq',dL_dpsi2+dL_dpsi2.T,Z,common_sum) + common_sum = np.dot(mu,(variance*Z).T) + Z_expect = (np.dot(dL_dpsi2,Z)*Z).sum(axis=0) + dL_dpsi2T = dL_dpsi2+dL_dpsi2.T + common_expect = np.dot(common_sum,np.dot(dL_dpsi2T,Z)) + Z2_expect = np.inner(common_sum,dL_dpsi2T) + Z1_expect = np.dot(dL_dpsi2T,Z) - dL_dvar = np.einsum('q,nq,q->q',Z_expect,2.*S,variance)+ np.einsum('nq,nq->q',common_expect,mu) + dL_dvar = 2.*S.sum(axis=0)*variance*Z_expect+(common_expect*mu).sum(axis=0) - dL_dmu = np.einsum('nq,q->nq',common_expect,variance) + dL_dmu = common_expect*variance dL_dS = np.empty(S.shape) - dL_dS[:] = np.einsum('q,q->q',Z_expect,variance2) + dL_dS[:] = Z_expect*variance2 - dL_dZ = 2.*(np.einsum('om,q,mq,nq->oq',dL_dpsi2,variance2,Z,S)+np.einsum('om,q,nq,nm->oq',dL_dpsi2,variance,mu,common_sum)) + dL_dZ = variance2*S.sum(axis=0)*Z1_expect+np.dot(Z2_expect.T,variance*mu) return dL_dvar, dL_dmu, dL_dS, dL_dZ