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GPy/GPy/inference/latent_function_inference/var_dtc_gpu.py
Zhenwen Dai ca1edecce4 rbf gpu usable
2014-06-20 18:02:35 +01:00

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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
# Licensed under the BSD 3-clause license (see LICENSE.txt)
from posterior import Posterior
from ...util.linalg import jitchol, backsub_both_sides, tdot, dtrtrs
from ...util import diag
from ...core.parameterization.variational import VariationalPosterior
import numpy as np
from ...util.misc import param_to_array
from . import LatentFunctionInference
log_2_pi = np.log(2*np.pi)
from ...util import gpu_init
try:
import scikits.cuda.linalg as culinalg
import pycuda.gpuarray as gpuarray
from scikits.cuda import cublas
from ...util.linalg_gpu import logDiagSum, strideSum, mul_bcast, sum_axis, outer_prod, mul_bcast_first, join_prod, traceDot
except:
pass
class VarDTC_GPU(LatentFunctionInference):
"""
An object for inference when the likelihood is Gaussian, but we want to do sparse inference.
The function self.inference returns a Posterior object, which summarizes
the posterior.
For efficiency, we sometimes work with the cholesky of Y*Y.T. To save repeatedly recomputing this, we cache it.
"""
const_jitter = np.float64(1e-6)
def __init__(self, batchsize=None, gpu_memory=4., limit=1):
self.batchsize = batchsize
self.gpu_memory = gpu_memory
self.midRes = {}
self.batch_pos = 0 # the starting position of the current mini-batch
self.cublas_handle = gpu_init.cublas_handle
# Initialize GPU caches
self.gpuCache = None
def _initGPUCache(self, kern, num_inducing, input_dim, output_dim, Y):
ndata = Y.shape[0]
if self.batchsize==None:
self.batchsize = self._estimateBatchSize(kern, ndata, num_inducing, input_dim, output_dim)
if self.gpuCache == None:
self.gpuCache = {# inference_likelihood
'Kmm_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'Lm_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'ones_gpu' :gpuarray.empty(num_inducing, np.float64,order='F'),
'LL_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'b_gpu' :gpuarray.empty((num_inducing,output_dim),np.float64,order='F'),
'v_gpu' :gpuarray.empty((num_inducing,output_dim),np.float64,order='F'),
'vvt_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'KmmInvPsi2LLInvT_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'KmmInvPsi2P_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'dL_dpsi2R_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'dL_dKmm_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'psi1Y_gpu' :gpuarray.empty((num_inducing,output_dim),np.float64,order='F'),
'psi2_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'beta_gpu' :gpuarray.empty((ndata,),np.float64,order='F'),
'YT_gpu' :gpuarray.to_gpu(np.asfortranarray(Y.T)), # DxN
'betaYT_gpu' :gpuarray.empty(Y.T.shape,np.float64,order='F'), # DxN
# inference_minibatch
'dL_dpsi0_gpu' :gpuarray.empty((self.batchsize,),np.float64,order='F'),
'dL_dpsi1_gpu' :gpuarray.empty((self.batchsize,num_inducing),np.float64,order='F'),
'dL_dpsi2_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
'psi0p_gpu' :gpuarray.empty((self.batchsize,),np.float64,order='F'),
'psi1p_gpu' :gpuarray.empty((self.batchsize,num_inducing),np.float64,order='F'),
'psi2p_gpu' :gpuarray.empty((num_inducing,num_inducing),np.float64,order='F'),
}
self.gpuCache['ones_gpu'].fill(1.0)
YT_gpu = self.gpuCache['YT_gpu']
self._trYYT = cublas.cublasDdot(self.cublas_handle, YT_gpu.size, YT_gpu.gpudata, 1, YT_gpu.gpudata, 1)
def _estimateMemoryOccupation(self, N, M, D):
"""
Estimate the best batch size.
N - the number of total datapoints
M - the number of inducing points
D - the number of observed (output) dimensions
return: the constant memory size, the memory occupation of batchsize=1
unit: GB
"""
return (M+9.*M*M+3*M*D+N+2.*N*D)*8./1024./1024./1024., (4.+3.*M+D+3.*M*M)*8./1024./1024./1024.
def _estimateBatchSize(self, kern, N, M, Q, D):
"""
Estimate the best batch size.
N - the number of total datapoints
M - the number of inducing points
D - the number of observed (output) dimensions
return: the constant memory size, the memory occupation of batchsize=1
unit: GB
"""
if kern.useGPU:
x0,x1 = kern.psicomp.estimateMemoryOccupation(N,M,Q)
else:
x0, x1 = 0.,0.
y0, y1 = self._estimateMemoryOccupation(N, M, D)
opt_batchsize = min(int((self.gpu_memory-y0-x0)/(x1+y1)), N)
return opt_batchsize
def _get_YYTfactor(self, Y):
"""
find a matrix L which satisfies LLT = YYT.
Note that L may have fewer columns than Y.
"""
N, D = Y.shape
if (N>=D):
return param_to_array(Y)
else:
return jitchol(tdot(Y))
def gatherPsiStat(self, kern, X, Z, Y, beta, uncertain_inputs, het_noise):
num_inducing, input_dim = Z.shape[0], Z.shape[1]
num_data, output_dim = Y.shape
trYYT = self._trYYT
psi1Y_gpu = self.gpuCache['psi1Y_gpu']
psi2_gpu = self.gpuCache['psi2_gpu']
beta_gpu = self.gpuCache['beta_gpu']
YT_gpu = self.gpuCache['YT_gpu']
betaYT_gpu = self.gpuCache['betaYT_gpu']
beta_gpu.fill(beta)
betaYT_gpu.fill(0.)
cublas.cublasDaxpy(self.cublas_handle, betaYT_gpu.size, beta, YT_gpu.gpudata, 1, betaYT_gpu.gpudata, 1)
YRY_full = trYYT*beta
if kern.useGPU:
psi1Y_gpu.fill(0.)
psi2_gpu.fill(0.)
psi0_full = 0
for n_start in xrange(0,num_data,self.batchsize):
n_end = min(self.batchsize+n_start, num_data)
ndata = n_end - n_start
X_slice = X[n_start:n_end]
betaYT_gpu_slice = betaYT_gpu[:,n_start:n_end]
if uncertain_inputs:
psi0 = kern.psi0(Z, X_slice)
psi1p_gpu = kern.psi1(Z, X_slice)
psi2p_gpu = kern.psi2(Z, X_slice)
else:
psi0 = kern.Kdiag(X_slice)
psi1p_gpu = kern.K(X_slice, Z)
cublas.cublasDgemm(self.cublas_handle, 'T', 'T', num_inducing, output_dim, ndata, 1.0, psi1p_gpu.gpudata, ndata, betaYT_gpu_slice.gpudata, output_dim, 1.0, psi1Y_gpu.gpudata, num_inducing)
psi0_full += psi0.sum()
if uncertain_inputs:
sum_axis(psi2_gpu,psi2p_gpu,1,1)
else:
cublas.cublasDgemm(self.cublas_handle, 'T', 'N', num_inducing, num_inducing, ndata, beta, psi1p_gpu.gpudata, ndata, psi1p_gpu.gpudata, ndata, 1.0, psi2_gpu.gpudata, num_inducing)
psi0_full *= beta
if uncertain_inputs:
cublas.cublasDscal(self.cublas_handle, psi2_gpu.size, beta, psi2_gpu.gpudata, 1)
else:
psi2_full = np.zeros((num_inducing,num_inducing))
psi1Y_full = np.zeros((output_dim,num_inducing)) # DxM
psi0_full = 0.
YRY_full = 0.
for n_start in xrange(0,num_data,self.batchsize):
n_end = min(self.batchsize+n_start, num_data)
Y_slice = Y[n_start:n_end]
X_slice = X[n_start:n_end]
if het_noise:
b = beta[n_start]
YRY_full += np.inner(Y_slice, Y_slice)*b
else:
b = beta
if uncertain_inputs:
psi0 = kern.psi0(Z, X_slice)
psi1 = kern.psi1(Z, X_slice)
psi2_full += kern.psi2(Z, X_slice)*b
else:
psi0 = kern.Kdiag(X_slice)
psi1 = kern.K(X_slice, Z)
psi2_full += np.dot(psi1.T,psi1)*b
psi0_full += psi0.sum()*b
psi1Y_full += np.dot(Y_slice.T,psi1)*b # DxM
if not het_noise:
YRY_full = trYYT*beta
psi1Y_gpu.set(psi1Y_full)
psi2_gpu.set(psi2_full)
return psi0_full, YRY_full
def inference_likelihood(self, kern, X, Z, likelihood, Y):
"""
The first phase of inference:
Compute: log-likelihood, dL_dKmm
Cached intermediate results: Kmm, KmmInv,
"""
num_inducing, input_dim = Z.shape[0], Z.shape[1]
num_data, output_dim = Y.shape
#see whether we've got a different noise variance for each datum
beta = 1./np.fmax(likelihood.variance, 1e-6)
het_noise = beta.size > 1
if het_noise:
self.batchsize=0
self._initGPUCache(kern, num_inducing, input_dim, output_dim, Y)
if isinstance(X, VariationalPosterior):
uncertain_inputs = True
else:
uncertain_inputs = False
psi1Y_gpu = self.gpuCache['psi1Y_gpu']
psi2_gpu = self.gpuCache['psi2_gpu']
psi0_full, YRY_full = self.gatherPsiStat(kern, X, Z, Y, beta, uncertain_inputs, het_noise)
#======================================================================
# Compute Common Components
#======================================================================
Kmm = kern.K(Z).copy()
Kmm_gpu = self.gpuCache['Kmm_gpu']
Kmm_gpu.set(np.asfortranarray(Kmm))
diag.add(Kmm, self.const_jitter)
ones_gpu = self.gpuCache['ones_gpu']
cublas.cublasDaxpy(self.cublas_handle, num_inducing, self.const_jitter, ones_gpu.gpudata, 1, Kmm_gpu.gpudata, num_inducing+1)
# assert np.allclose(Kmm, Kmm_gpu.get())
# Lm = jitchol(Kmm)
#
Lm_gpu = self.gpuCache['Lm_gpu']
cublas.cublasDcopy(self.cublas_handle, Kmm_gpu.size, Kmm_gpu.gpudata, 1, Lm_gpu.gpudata, 1)
culinalg.cho_factor(Lm_gpu,'L')
# print np.abs(np.tril(Lm)-np.tril(Lm_gpu.get())).max()
# Lambda = Kmm+psi2_full
# LL = jitchol(Lambda)
#
Lambda_gpu = self.gpuCache['LL_gpu']
cublas.cublasDcopy(self.cublas_handle, Kmm_gpu.size, Kmm_gpu.gpudata, 1, Lambda_gpu.gpudata, 1)
cublas.cublasDaxpy(self.cublas_handle, psi2_gpu.size, np.float64(1.0), psi2_gpu.gpudata, 1, Lambda_gpu.gpudata, 1)
LL_gpu = Lambda_gpu
culinalg.cho_factor(LL_gpu,'L')
# print np.abs(np.tril(LL)-np.tril(LL_gpu.get())).max()
# b,_ = dtrtrs(LL, psi1Y_full)
# bbt_cpu = np.square(b).sum()
#
b_gpu = self.gpuCache['b_gpu']
cublas.cublasDcopy(self.cublas_handle, b_gpu.size, psi1Y_gpu.gpudata, 1, b_gpu.gpudata, 1)
cublas.cublasDtrsm(self.cublas_handle , 'L', 'L', 'N', 'N', num_inducing, output_dim, np.float64(1.0), LL_gpu.gpudata, num_inducing, b_gpu.gpudata, num_inducing)
bbt = cublas.cublasDdot(self.cublas_handle, b_gpu.size, b_gpu.gpudata, 1, b_gpu.gpudata, 1)
# print np.abs(bbt-bbt_cpu)
# v,_ = dtrtrs(LL.T,b,lower=False)
# vvt = np.einsum('md,od->mo',v,v)
# LmInvPsi2LmInvT = backsub_both_sides(Lm,psi2_full,transpose='right')
#
v_gpu = self.gpuCache['v_gpu']
cublas.cublasDcopy(self.cublas_handle, v_gpu.size, b_gpu.gpudata, 1, v_gpu.gpudata, 1)
cublas.cublasDtrsm(self.cublas_handle , 'L', 'L', 'T', 'N', num_inducing, output_dim, np.float64(1.0), LL_gpu.gpudata, num_inducing, v_gpu.gpudata, num_inducing)
vvt_gpu = self.gpuCache['vvt_gpu']
cublas.cublasDgemm(self.cublas_handle, 'N', 'T', num_inducing, num_inducing, output_dim, np.float64(1.0), v_gpu.gpudata, num_inducing, v_gpu.gpudata, num_inducing, np.float64(0.), vvt_gpu.gpudata, num_inducing)
LmInvPsi2LmInvT_gpu = self.gpuCache['KmmInvPsi2LLInvT_gpu']
cublas.cublasDcopy(self.cublas_handle, psi2_gpu.size, psi2_gpu.gpudata, 1, LmInvPsi2LmInvT_gpu.gpudata, 1)
cublas.cublasDtrsm(self.cublas_handle , 'L', 'L', 'N', 'N', num_inducing, num_inducing, np.float64(1.0), Lm_gpu.gpudata, num_inducing, LmInvPsi2LmInvT_gpu.gpudata, num_inducing)
cublas.cublasDtrsm(self.cublas_handle , 'r', 'L', 'T', 'N', num_inducing, num_inducing, np.float64(1.0), Lm_gpu.gpudata, num_inducing, LmInvPsi2LmInvT_gpu.gpudata, num_inducing)
#tr_LmInvPsi2LmInvT = cublas.cublasDasum(self.cublas_handle, num_inducing, LmInvPsi2LmInvT_gpu.gpudata, num_inducing+1)
tr_LmInvPsi2LmInvT = float(strideSum(LmInvPsi2LmInvT_gpu, num_inducing+1).get())
# print np.abs(vvt-vvt_gpu.get()).max()
# print np.abs(np.trace(LmInvPsi2LmInvT)-tr_LmInvPsi2LmInvT)
# Psi2LLInvT = dtrtrs(LL,psi2_full)[0].T
# LmInvPsi2LLInvT= dtrtrs(Lm,Psi2LLInvT)[0]
# KmmInvPsi2LLInvT = dtrtrs(Lm,LmInvPsi2LLInvT,trans=True)[0]
# KmmInvPsi2P = dtrtrs(LL,KmmInvPsi2LLInvT.T, trans=True)[0].T
#
KmmInvPsi2LLInvT_gpu = LmInvPsi2LmInvT_gpu # Reuse GPU memory (size:MxM)
cublas.cublasDcopy(self.cublas_handle, psi2_gpu.size, psi2_gpu.gpudata, 1, KmmInvPsi2LLInvT_gpu.gpudata, 1)
cublas.cublasDtrsm(self.cublas_handle , 'L', 'L', 'N', 'N', num_inducing, num_inducing, np.float64(1.0), Lm_gpu.gpudata, num_inducing, KmmInvPsi2LLInvT_gpu.gpudata, num_inducing)
cublas.cublasDtrsm(self.cublas_handle , 'r', 'L', 'T', 'N', num_inducing, num_inducing, np.float64(1.0), LL_gpu.gpudata, num_inducing, KmmInvPsi2LLInvT_gpu.gpudata, num_inducing)
cublas.cublasDtrsm(self.cublas_handle , 'L', 'L', 'T', 'N', num_inducing, num_inducing, np.float64(1.0), Lm_gpu.gpudata, num_inducing, KmmInvPsi2LLInvT_gpu.gpudata, num_inducing)
KmmInvPsi2P_gpu = self.gpuCache['KmmInvPsi2P_gpu']
cublas.cublasDcopy(self.cublas_handle, KmmInvPsi2LLInvT_gpu.size, KmmInvPsi2LLInvT_gpu.gpudata, 1, KmmInvPsi2P_gpu.gpudata, 1)
cublas.cublasDtrsm(self.cublas_handle , 'r', 'L', 'N', 'N', num_inducing, num_inducing, np.float64(1.0), LL_gpu.gpudata, num_inducing, KmmInvPsi2P_gpu.gpudata, num_inducing)
# print np.abs(KmmInvPsi2P-KmmInvPsi2P_gpu.get()).max()
# dL_dpsi2R = (output_dim*KmmInvPsi2P - vvt)/2. # dL_dpsi2 with R inside psi2
#
dL_dpsi2R_gpu = self.gpuCache['dL_dpsi2R_gpu']
cublas.cublasDcopy(self.cublas_handle, vvt_gpu.size, vvt_gpu.gpudata, 1, dL_dpsi2R_gpu.gpudata, 1)
cublas.cublasDaxpy(self.cublas_handle, KmmInvPsi2P_gpu.size, np.float64(-output_dim), KmmInvPsi2P_gpu.gpudata, 1, dL_dpsi2R_gpu.gpudata, 1)
cublas.cublasDscal(self.cublas_handle, dL_dpsi2R_gpu.size, np.float64(-0.5), dL_dpsi2R_gpu.gpudata, 1)
# print np.abs(dL_dpsi2R_gpu.get()-dL_dpsi2R).max()
#======================================================================
# Compute log-likelihood
#======================================================================
if het_noise:
logL_R = -np.log(beta).sum()
else:
logL_R = -num_data*np.log(beta)
# logL_old = -(output_dim*(num_data*log_2_pi+logL_R+psi0_full-np.trace(LmInvPsi2LmInvT))+YRY_full-bbt)/2.-output_dim*(-np.log(np.diag(Lm)).sum()+np.log(np.diag(LL)).sum())
logdetKmm = float(logDiagSum(Lm_gpu,num_inducing+1).get())
logdetLambda = float(logDiagSum(LL_gpu,num_inducing+1).get())
logL = -(output_dim*(num_data*log_2_pi+logL_R+psi0_full-tr_LmInvPsi2LmInvT)+YRY_full-bbt)/2.+output_dim*(logdetKmm-logdetLambda)
# print np.abs(logL_old - logL)
#======================================================================
# Compute dL_dKmm
#======================================================================
# dL_dKmm = -(output_dim*np.einsum('md,od->mo',KmmInvPsi2LLInvT,KmmInvPsi2LLInvT) + vvt)/2.
#
dL_dKmm_gpu = self.gpuCache['dL_dKmm_gpu']
cublas.cublasDgemm(self.cublas_handle, 'N', 'T', num_inducing, num_inducing, num_inducing, np.float64(1.0), KmmInvPsi2LLInvT_gpu.gpudata, num_inducing, KmmInvPsi2LLInvT_gpu.gpudata, num_inducing, np.float64(0.), dL_dKmm_gpu.gpudata, num_inducing)
cublas.cublasDaxpy(self.cublas_handle, dL_dKmm_gpu.size, np.float64(1./output_dim), vvt_gpu.gpudata, 1, dL_dKmm_gpu.gpudata, 1)
cublas.cublasDscal(self.cublas_handle, dL_dKmm_gpu.size, np.float64(-output_dim/2.), dL_dKmm_gpu.gpudata, 1)
# print np.abs(dL_dKmm - dL_dKmm_gpu.get()).max()
#======================================================================
# Compute the Posterior distribution of inducing points p(u|Y)
#======================================================================
post = Posterior(woodbury_inv=KmmInvPsi2P_gpu.get(), woodbury_vector=v_gpu.get(), K=Kmm_gpu.get(), mean=None, cov=None, K_chol=Lm_gpu.get())
#======================================================================
# Compute dL_dthetaL for uncertian input and non-heter noise
#======================================================================
if not het_noise:
dL_dthetaL = (YRY_full + output_dim*psi0_full - num_data*output_dim)/-2.
dL_dthetaL += cublas.cublasDdot(self.cublas_handle,dL_dpsi2R_gpu.size, dL_dpsi2R_gpu.gpudata,1,psi2_gpu.gpudata,1)
dL_dthetaL += cublas.cublasDdot(self.cublas_handle,v_gpu.size, v_gpu.gpudata,1,psi1Y_gpu.gpudata,1)
self.midRes['dL_dthetaL'] = -beta*dL_dthetaL
return logL, dL_dKmm_gpu.get(), post
def inference_minibatch(self, kern, X, Z, likelihood, Y):
"""
The second phase of inference: Computing the derivatives over a minibatch of Y
Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
return a flag showing whether it reached the end of Y (isEnd)
"""
num_data, output_dim = Y.shape
num_inducing = Z.shape[0]
if isinstance(X, VariationalPosterior):
uncertain_inputs = True
else:
uncertain_inputs = False
beta = 1./np.fmax(likelihood.variance, 1e-6)
het_noise = beta.size > 1
n_start = self.batch_pos
n_end = min(self.batchsize+n_start, num_data)
if n_end==num_data:
isEnd = True
self.batch_pos = 0
else:
isEnd = False
self.batch_pos = n_end
nSlice = n_end-n_start
X_slice = X[n_start:n_end]
if het_noise:
beta = beta[n_start] # nSlice==1
if kern.useGPU:
if not uncertain_inputs:
psi0p_gpu = kern.Kdiag(X_slice)
psi1p_gpu = kern.K(X_slice, Z)
psi2p_gpu = self.gpuCache['psi2p_gpu']
elif het_noise:
psi0p_gpu = kern.psi0(Z, X_slice)
psi1p_gpu = kern.psi1(Z, X_slice)
psi2p_gpu = kern.psi2(Z, X_slice)
elif not uncertain_inputs or het_noise:
if not uncertain_inputs:
psi0 = kern.Kdiag(X_slice)
psi1 = kern.K(X_slice, Z)
elif het_noise:
psi0 = kern.psi0(Z, X_slice)
psi1 = kern.psi1(Z, X_slice)
psi2 = kern.psi2(Z, X_slice)
psi0p_gpu = self.gpuCache['psi0p_gpu']
psi1p_gpu = self.gpuCache['psi1p_gpu']
psi2p_gpu = self.gpuCache['psi2p_gpu']
if psi0p_gpu.shape[0] > nSlice:
psi0p_gpu = psi0p_gpu[:nSlice]
psi1p_gpu = psi1p_gpu.ravel()[:nSlice*num_inducing].reshape(nSlice,num_inducing)
psi0p_gpu.set(np.asfortranarray(psi0))
psi1p_gpu.set(np.asfortranarray(psi1))
if uncertain_inputs:
psi2p_gpu.set(np.asfortranarray(psi2))
#======================================================================
# Compute dL_dpsi
#======================================================================
dL_dpsi2R_gpu = self.gpuCache['dL_dpsi2R_gpu']
v_gpu = self.gpuCache['v_gpu']
dL_dpsi0_gpu = self.gpuCache['dL_dpsi0_gpu']
dL_dpsi1_gpu = self.gpuCache['dL_dpsi1_gpu']
dL_dpsi2_gpu = self.gpuCache['dL_dpsi2_gpu']
betaYT_gpu = self.gpuCache['betaYT_gpu']
betaYT_gpu_slice = betaYT_gpu[:,n_start:n_end]
# Adjust to the batch size
if dL_dpsi0_gpu.shape[0] > nSlice:
dL_dpsi0_gpu = dL_dpsi0_gpu.ravel()[:nSlice]
dL_dpsi1_gpu = dL_dpsi1_gpu.ravel()[:nSlice*num_inducing].reshape(nSlice,num_inducing)
dL_dpsi0_gpu.fill(-output_dim *beta/2.)
cublas.cublasDgemm(self.cublas_handle, 'T', 'T', nSlice, num_inducing, output_dim, 1.0, betaYT_gpu_slice.gpudata, output_dim, v_gpu.gpudata, num_inducing, 0., dL_dpsi1_gpu.gpudata, nSlice)
if uncertain_inputs:
cublas.cublasDcopy(self.cublas_handle, dL_dpsi2R_gpu.size, dL_dpsi2R_gpu.gpudata, 1, dL_dpsi2_gpu.gpudata, 1)
cublas.cublasDscal(self.cublas_handle, dL_dpsi2_gpu.size, beta, dL_dpsi2_gpu.gpudata, 1)
else:
cublas.cublasDgemm(self.cublas_handle, 'N', 'N', nSlice, num_inducing, output_dim, beta, psi1p_gpu.gpudata, nSlice, dL_dpsi2R_gpu.gpudata, num_inducing, 1.0, dL_dpsi1_gpu.gpudata, nSlice)
#======================================================================
# Compute dL_dthetaL
#======================================================================
if het_noise:
betaY = betaYT_gpu_slice.get()
dL_dthetaL = ((np.square(betaY)).sum(axis=-1) + np.square(beta)*(output_dim*psi0p_gpu.get())-output_dim*beta)/2.
dL_dthetaL += -beta*beta*cublas.cublasDdot(self.cublas_handle,dL_dpsi2R_gpu.size, dL_dpsi2R_gpu.gpudata,1,psi2p_gpu.gpudata,1)
dL_dthetaL += -beta*(betaY*np.dot(psi1p_gpu.get(),v_gpu.get())).sum(axis=-1)
if kern.useGPU:
dL_dpsi0 = dL_dpsi0_gpu
dL_dpsi1 = dL_dpsi1_gpu
else:
dL_dpsi0 = dL_dpsi0_gpu.get()
dL_dpsi1 = dL_dpsi1_gpu.get()
if uncertain_inputs:
if kern.useGPU:
dL_dpsi2 = dL_dpsi2_gpu
else:
dL_dpsi2 = dL_dpsi2_gpu.get()
if not het_noise:
if isEnd:
dL_dthetaL = self.midRes['dL_dthetaL']
else:
dL_dthetaL = 0.
if uncertain_inputs:
grad_dict = {'dL_dpsi0':dL_dpsi0,
'dL_dpsi1':dL_dpsi1,
'dL_dpsi2':dL_dpsi2,
'dL_dthetaL':dL_dthetaL}
else:
grad_dict = {'dL_dKdiag':dL_dpsi0,
'dL_dKnm':dL_dpsi1,
'dL_dthetaL':dL_dthetaL}
return isEnd, (n_start,n_end), grad_dict
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