可重复的例子

Question

我是每个人，

我有一个优化的功能，受线性约束。我实际上正在使用maxLik R-package，但这是各种方法的包装器，因此我实际上在constrOptim中运行。

问题如下：我有一个约束矩阵，n ^ 2 x n，但是n是~10 ^ 3，所以矩阵很大，例程就会因内存问题而停止。

Cholmod error 'problem too large' at file ../Core/cholmod_dense.c, line 105

使用Matrix包转换到稀疏矩阵（实际上我的矩阵非常稀疏）似乎很自然，但我总是得到以下错误

Error: Matrices must have same dimensions in ineqA * gi.old

即使是小n。这是否意味着constrOptim不支持sparseMatrix？你知道出路吗？

可重复的例子

你可以在这里找到我用来优化的数据集： http://konect.uni-koblenz.de/downloads/extraction/opsahl.tar.bz2

在这里你有代码

#read edgelist
edgelist <- read.table('out.opsahl-usairport',skip=2)
colnames(edgelist) = c('V1','V2','weight')
require(igraph)
g = graph_from_data_frame(edgelist)
s_in = strength(g,v=V(g), mode= 'in')
s_out = strength(g,v=V(g),mode='out')
n = length(s_in)


# optimization function

objective_fun = function(x){
    theta_out = x[1:(length(x)/2)]; theta_in = x[(length(x)/2+1):length(x)];

    llikelihood(s_out,s_in,theta_out,theta_in)
  }

llikelihood = function(s_out,s_in,theta_out, theta_in){
  theta_sum_mat = outer(theta_out,rep(1,length(theta_out))) + outer(rep(1,length(theta_in)),theta_in)
  theta_sum_mat = log(1-exp(-theta_sum_mat))
  diag(theta_sum_mat) = 0 # avoid self loops
  f = -sum(s_out*theta_out+s_in*theta_in) + sum(theta_sum_mat)
  f
}    

#choose appropriate starting point
starting_point = function(s_out,s_in){
  s_tot = sum(s_in) # =sum(s_out)
  s_mean = mean(mean(s_in),mean(s_out))
  z = log((s_tot + s_mean^2)/(s_mean^2))
  list(theta_out = rep(1,length(s_out)), theta_in=rep(z-1,length(s_in))) # starting parameters
}

#gradient

grad = function(x){
  theta_out = x[1:(length(x)/2)]; theta_in = x[(length(x)/2+1):length(x)];
  ret = grad_fun(s_out,s_in,theta_out,theta_in)
  ret
}

grad_fun = function(s_out,s_in, theta_out, theta_in){
  theta_sum_mat = outer(theta_out,rep(1,length(theta_out))) + outer(rep(1,length(theta_in)),theta_in)
  theta_sum_mat = exp(-theta_sum_mat)/(1-exp(-theta_sum_mat))
  diag(theta_sum_mat) = 0 # avoid self loops
  c(-s_out + rowSums(theta_sum_mat), -s_in + colSums(theta_sum_mat))
}


#constraints
  constraints = function(n){
    a1 = Diagonal(n); a2 = sparseMatrix(c(1:n),rep(1,n), x=1, dims=c(n,n)) # Diagonal is a sparse diagonal matrix
    a12 = cBind(a1,a2)
    a12[1,] = 0 # avoid self loops
    dd = function(j){
      sparseMatrix(c(1:n),rep(j,n), x=rep(1,n), dims=c(n,n))
    }
    b1 = sparseMatrix(i=1, j=1, x=1, dims=c(n^2,1)) # 1,0,0,...  n^2 vector
    for(j in c(2:n)) {
      a = cBind(Diagonal(n),dd(j))
      a[j,]=0 # avoid self loops
      a12 = rBind(a12, a)
      b1[(j-1)*n+j] = 1 # add 1 to ''self loops'' rows, in order to have the inequality satisfied
    }
    return(list(A=a12, B=b1))
  }

  # starting point
  theta_0 = starting_point(s_out,s_in)
  x_0 =  c(theta_0$theta_out, theta_0$theta_in)

  #constraints
  constr = list(ineqA=constraints(n)$A, ineqB=constraints(n)$B)

  # optimization 
  co = maxControl(printLevel = 1, iterlim=500, tol=1e-4)  #tol=1e-8 (def)  iterlim=150 (def)  
  res = maxLik(objective_fun, grad=grad, start=x_0, constraints=constr, control=co)

稀疏矩阵约束constrOptim

可重复的例子

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