get_inner=function(theta_gamma, K, W_aW) {
## inner=<W_j, f(x_i)>, k*1 vector for each observation
## n*k matrix for each lambda, column bind for all lambdas
K=K+1
theta_gamma=as.matrix(theta_gamma)
m=ncol(theta_gamma)
inner=lapply(1:m, function(j) -K%*%(theta_gamma[, j]*W_aW))
do.call('cbind', inner)
}
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