pkg/tests/testthat/test-optimParams.R

   1 context("OptimParams")
   2
   3 naive_f = function(link, M1,M2,M3, p,β,b)
   4 {
   5   d = length(M1)
   6   K = length(p)
   7   λ <- sqrt(colSums(β^2))
   8
   9   # Compute β x2,3 (self) tensorial products
  10   β2 = array(0, dim=c(d,d,K))
  11   β3 = array(0, dim=c(d,d,d,K))
  12   for (k in 1:K)
  13   {
  14     for (i in 1:d)
  15     {
  16       for (j in 1:d)
  17       {
  18         β2[i,j,k] = β[i,k]*β[j,k]
  19         for (l in 1:d)
  20           β3[i,j,l,k] = β[i,k]*β[j,k]*β[l,k]
  21       }
  22     }
  23   }
  24
  25   res = 0
  26   for (i in 1:d)
  27   {
  28     term = 0
  29     for (k in 1:K)
  30       term = term + p[k]*.G(link,1,λ[k],b[k])*β[i,k]
  31     res = res + (term - M1[i])^2
  32     for (j in 1:d)
  33     {
  34       term = 0
  35       for (k in 1:K)
  36         term = term + p[k]*.G(link,2,λ[k],b[k])*β2[i,j,k]
  37       res = res + (term - M2[i,j])^2
  38       for (l in 1:d)
  39       {
  40         term = 0
  41         for (k in 1:K)
  42           term = term + p[k]*.G(link,3,λ[k],b[k])*β3[i,j,l,k]
  43         res = res + (term - M3[i,j,l])^2
  44       }
  45     }
  46   }
  47   res
  48 }
  49
  50 test_that("naive computation provides the same result as vectorized computations",
  51 {
  52   h <- 1e-7 #for finite-difference tests
  53   tol <- 1e-3 #large tolerance, necessary in some cases... (generally 1e-6 is OK)
  54   for (dK in list( c(2,2), c(5,3)))
  55   {
  56     d = dK[1]
  57     K = dK[2]
  58
  59     M1 = runif(d, -1, 1)
  60     M2 = matrix(runif(d*d,-1,1), ncol=d)
  61     M3 = array(runif(d*d*d,-1,1), dim=c(d,d,d))
  62
  63     for (link in c("logit","probit"))
  64     {
  65       op = new("OptimParams", "li"=link, "M1"=as.double(M1),
  66         "M2"=as.double(M2), "M3"=as.double(M3), "K"=as.integer(K))
  67
  68       for (var in seq_len((2+d)*K-1))
  69       {
  70         p = runif(K, 0, 1)
  71         p = p / sum(p)
  72         β <- matrix(runif(d*K,-5,5),ncol=K)
  73         b = runif(K, -5, 5)
  74         x <- c(p[1:(K-1)],as.double(β),b)
  75
  76         # Test functions values
  77         expect_equal( op$f(x), naive_f(link,M1,M2,M3, p,β,b) )
  78
  79         # Test finite differences ~= gradient values
  80         dir_h <- rep(0, (2+d)*K-1)
  81         dir_h[var] = h
  82
  83         expect_equal( op$grad_f(x)[var], ( op$f(x+dir_h) - op$f(x) ) / h, tol )
  84       }
  85     }
  86   }
  87 })
  88
  89 test_that("W computed in C and in R are the same",
  90 {
  91   # TODO: provide data X,Y + parameters theta
  92   dd <- d + d^2 + d^3
  93   p <- θ$p
  94   β <- θ$β
  95   λ <- sqrt(colSums(β^2))
  96   b <- θ$b
  97   β2 <- apply(β, 2, function(col) col %o% col)
  98   β3 <- apply(β, 2, function(col) col %o% col %o% col)
  99   M <- c(
 100     β  %*% (p * .G(li,1,λ,b)),
 101     β2 %*% (p * .G(li,2,λ,b)),
 102     β3 %*% (p * .G(li,3,λ,b)))
 103   Id <- as.double(diag(d))
 104   E <- diag(d)
 105   v1 <- Y * X
 106   v2 <- Y * t( apply(X, 1, function(Xi) Xi %o% Xi - Id) )
 107   v3 <- Y * t( apply(X, 1, function(Xi) { return (Xi %o% Xi %o% Xi
 108     - Reduce('+', lapply(1:d, function(j) as.double(Xi %o% E[j,] %o% E[j,])), rep(0, d*d*d))
 109     - Reduce('+', lapply(1:d, function(j) as.double(E[j,] %o% Xi %o% E[j,])), rep(0, d*d*d))
 110     - Reduce('+', lapply(1:d, function(j) as.double(E[j,] %o% E[j,] %o% Xi)), rep(0, d*d*d))) } ) )
 111   Omega1 <- matrix(0, nrow=dd, ncol=dd)
 112   for (i in 1:n)
 113   {
 114     gi <- t(as.matrix(c(v1[i,], v2[i,], v3[i,]) - M))
 115     Omega1 <- Omega1 + t(gi) %*% gi / n
 116   }
 117   Omega2 <- matrix( .C("Compute_Omega",
 118     X=as.double(X), Y=as.double(Y), M=as.double(M),
 119     pn=as.integer(n), pd=as.integer(d),
 120     W=as.double(W), PACKAGE="morpheus")$W, nrow=dd, ncol=dd )
 121   rg <- range(Omega1 - Omega2)
 122   expect_that(rg[2] - rg[1] <= 1e8)
 123 })